CN103499354A - Neyman-Pearson criterion-based zero speed detection method - Google Patents

Abstract

The invention discloses a zero-speed detection method based on the Neiman-Pearson criterion. The method includes: receiving the measurement information output by the sensor when the footsteps are moving in the individual soldier navigation system in real time with a hand-held palm computer; according to the system sampling frequency and data transmission Determine the window function N of the speed; use the double hypothesis test theory to transform the zero-speed detection problem into a modeled mathematical problem, and obtain the zero-speed detection inequality under the Neiman-Pearson criterion; determine the output signal of the miniature inertial measurement unit sensor and the handheld computer The mathematical model of the received signal; obtain the joint probability density function of the output signal of the miniature inertial measurement unit sensor; use the maximum likelihood estimation value of the unknown signal element to replace the unknown element in the zero-speed detection inequality to obtain the extensive probability likelihood ratio inequality; the miniature The inertial measurement unit output data is substituted into the extensive probability-likelihood ratio inequality to detect the zero-velocity condition. The invention makes the problem of the detection method mathematized and modeled, and improves the detection accuracy.

Description

A Zero Speed Detection Method Based on Neyman-Pearson Criterion

technical field

The invention belongs to the technical field of zero-speed detection of an individual soldier's autonomous navigation system, and in particular relates to a zero-speed detection method based on the Neyman-Pearson criterion.

Background technique

When the individual navigation autonomous positioning device based on the inertial calculation of the Micro Inertial Measurement Unit is working, the error of the inertial device of the Micro-Electro-Mechanical System (Micro-Electro-Mechanical System) diverges seriously. The results of dead reckoning have verified that in the navigation stage, if the error of the MEMS inertial device cannot be effectively compensated, the position error will diverge with the trend of the cube of time, and the system will eventually lose its navigation function. Therefore, the inertial calculation algorithm of the MEMS is applied to The biggest difficulty of the individual navigation system is to design an effective error correction algorithm. Zero-speed correction is an effective error compensation algorithm. When a normal person walks, each foot has both gait static and gait motion (two kinds of motion) The duration is about 0.5 seconds) Two movement modes, the individual navigation system based on the micro inertial measurement unit is fixedly connected to the walker's shoes, which are called "navigation shoes". When the foot touches the ground, the inertial solution is obtained The theoretical value of the velocity should be zero, but the velocity component can be obtained through the inertial solution. This velocity component is the velocity error caused by the accumulation of the error of the micromechanical inertial measurement device over time. This velocity component is input to the zero-speed correction error compensator Correction of inertial device measurements and navigation output;

However, most of the existing individual navigation systems that use zero-speed correction as an inertial solution error correction algorithm have the problem of inaccurate zero-speed detection. Zero-speed detection is the prerequisite for triggering zero-speed correction. The previous zero-speed detection schemes mainly If the output of the three-axis accelerometer or three-axis gyroscope is less than a certain threshold within the set time, it is judged to be in the zero-speed interval, and the selection of the threshold lacks theoretical research. In actual measurement, the previous detection methods can only detect the zero-speed interval during normal walking, and the detection of the zero-speed interval during running is relatively difficult, and the existing zero-speed detection methods are all in a specific way, not suitable for all For the individual soldier's movement state, for example, the motion acceleration variance detection scheme is not suitable for uniformly accelerated linear motion, and the acceleration amplitude detection scheme cannot be used to detect the rotation of a single foot around a certain axis.

Generally speaking, the existing zero-speed detection method has poor stability, resulting in low navigation accuracy after zero-speed correction, which is difficult to meet the requirements of accurate and reliable individual navigation.

Contents of the invention

The purpose of the embodiments of the present invention is to provide a zero-speed detection method based on the Neiman-Pearson criterion, aiming to solve the problem of poor stability and low accuracy in the existing zero-speed detection method, which leads to poor navigation accuracy after zero-speed correction. Low, it is difficult to meet the requirements of accurate and reliable individual navigation.

The embodiment of the present invention is achieved in this way, a zero-speed detection method based on the Neiman-Pearson criterion, the zero-speed detection method based on the Neiman-Pearson criterion includes the following steps:

Step 1, the handheld handheld computer receives and stores the measurement information output by the step miniature inertial measurement unit in the individual soldier's autonomous navigation system in real time;

Step 2: According to the sampling frequency of each sensor in the individual soldier's autonomous navigation system, the static time length of the miniature inertial measurement unit before the system is used, and the data transmission rate between the miniature inertial measurement unit and the handheld computer during the measurement process of step 1, obtain the current zero speed The specific value of the window function N during the detection process, where N is an integer;

则H₁为真，即单兵自主导航系统零速检测结果为脚步微型惯性测量单元静止；函数L(z_n)与概率比有关，对于z_n的每个值，表示了H₁假设概率值对H₀假设概率值的比值；Step 3: Using the output data of the miniature inertial measurement unit collected in step 1 and the window function N determined in step 2, the zero-speed detection problem is transformed into a modeled double hypothesis testing problem, and the detection result is the hypothetical miniature inertial measurement unit motion H ₀ , One of the static miniature inertial measurement units H ₁ , using the Neiman-Pearson theorem to obtain the mathematical model of zero-speed detection and judgment: when the false alarm probability P _FA = α is known, if the zero-speed judgment inequality is satisfied:

Then H ₁ is true, that is, the zero-speed detection result of the individual soldier's autonomous navigation system is that the miniature inertial measurement unit is stationary; the function L(z _n ) is related to the probability ratio, and for each value of z _n , it represents the hypothetical probability value of H ₁ the ratio of hypothesized probability values to H ₀ ;

定义；p(z_n;H₀)、p(z_n;H₁)分别表示两种假设下观测数据的概率密度函数；Among them, the false alarm probability P _FA ={H ₁ ∣H ₀ } indicates the probability that the miniature inertial measurement unit is judged to be in a static state when it is in motion; z _n ={y _k }n+N-1k=n is the miniature inertial measurement unit within a period of time The measured value of the inertial measurement unit; the value of γ is given by the formula

Definition; p(z _n ;H ₀ ) and p(z _n ;H ₁ ) respectively represent the probability density functions of the observed data under two assumptions;

Step 4: Utilize the characteristics of the output signal of the miniature inertial measurement unit sensor, the nature of the signal received by the handheld computer and the error disturbance signal, and the formula to obtain the mathematical model of the output signal of the miniature inertial measurement unit inertial sensor;

Step 5: Using the data output by the miniature inertial measurement unit collected in step 1 during the movement of the individual autonomous navigation system, the mathematical model and formula of the output signal of the miniature inertial measurement unit inertial sensor determined in step 4, to obtain the sensor quantity measurement Joint probability density function p(z _n ;θ _i ,H _i );

Step 6: Using the joint probability density function p(z _n ;θ _i ,H _i ) of the observation signals obtained in step 5, according to the formula, obtain a broad probability likelihood ratio test for zero-speed detection of the individual autonomous navigation system with unknown elements L _g (z _n );

Step 7: Use formula:

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

Obtain maximum likelihood estimates of unknown signal elements under two assumptions

是在假设H₁条件未知元素的极大似然估计；

是在假设H₀条件下未知元素的极大似然估计；p(z_n;θ₁,H₁)表示在假设H₁条件下，未知信号元素集合为θ₁时微型惯性测量单元输出信息的联合概率密度函数；p(z_n;θ₀,H₀)表示在假设H₀条件下，未知信号元素集合为θ₀时微型惯性测量单元输出信息的联合概率密度函数；argmax(·)表示使括号内取最大值时未知元素集合的值；In the formula,

is the maximum likelihood estimate of the unknown element under the assumption of H ₁ condition;

is the maximum likelihood estimation of unknown elements under the assumption of H ₀ ; p(z _n ;θ ₁ ,H ₁ ) represents the output information of the miniature inertial measurement unit when the set of unknown signal elements is θ ₁ under the assumption of H ₁ Joint probability density function; p(z _n ;θ ₀ ,H ₀ ) represents the joint probability density function of the output information of the micro IMU when the set of unknown signal elements is θ ₀ under the assumption of H ₀ ; argmax(·) represents the The value of the unknown element set when taking the maximum value in the brackets;

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

Step 8: Use Step 7 to obtain the maximum likelihood estimation of the unknown signal elements Replacing the unknown signal element set in step six L _g (z _n ) to obtain a broad probability likelihood ratio L _G (z _n ) that does not contain unknown elements;

Step 9: Use L _G (z _n ) and the inequality obtained in Step 8 to determine the zero-speed detection result of the individual autonomous navigation system.

Further, in step 1, the total output information of the miniature inertial measurement unit received at any time k: is:

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>{\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}& {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}\end{array}\right]}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; ;</span>$

Among them, T represents the transpose operation, ${\mathrm{the\; y}}_k^{\mathrm{\&omega;}}={\left[\begin{array}{ccc}{\mathrm{the\; y}}_k^{\mathrm{\&omega;x}}& {\mathrm{the\; y}}_k^{\mathrm{\&omega;y}}& {\mathrm{the\; y}}_k^{\mathrm{\&omega;z}}\end{array}\right]}^T$ Angular rate information output by the three-axis gyroscope of the micro-mechanical system; ${\mathrm{the\; y}}_k^a={\left[\begin{array}{ccc}{\mathrm{the\; y}}_k^{\mathrm{ax}}& {\mathrm{the\; y}}_k^{\mathrm{ay}}& {\mathrm{the\; y}}_k^{\mathrm{az}}\end{array}\right]}^T$ It is the specific force information output by the MEMS triaxial accelerometer.

Further, in step 4, through the formula:

y _k = s _k (θ) + v _k

Obtain the mathematical model of the output signal of the inertial sensor of the miniature inertial measurement unit;

和

分别表示与加速度计和陀螺仪相关的噪声集合，T表示转置操作；假设噪声是独立、零均值高斯分布的，协方差矩阵为 $C=E\left\{\begin{array}{cc}{v}_k& {v_k}^T\end{array}\right\}=\mathrm{diag}{\left[\begin{array}{cc}{{\mathrm{\&sigma;}}_a}^2{I}_3& {{\mathrm{\&sigma;}}_{\mathrm{\&omega;}}}^2{I}_3\end{array}\right]}^T,$ 其中I₃(0₃)表示3×3的单位(零)阵；diag[·]表示对角阵；E{·}表示求期望，和

分别表示微机械加速度计和陀螺仪的噪声方差。In the formula, ${\mathrm{the\; s}}_k\left(\mathrm{\&theta;}\right)={\left[\begin{array}{cc}{\mathrm{the\; s}}_k^a\left(\mathrm{\&theta;}\right)& {\mathrm{the\; s}}_k^{\mathrm{\&omega;}}\left(\mathrm{\&theta;}\right)\end{array}\right]}^T,$ $v_k={\left[\begin{array}{cc}{v}_k^a& v_k^{\mathrm{\&omega;}}\end{array}\right]}^T,$ ${\mathrm{the\; s}}_k^a\left(\mathrm{\&theta;}\right)\&Element;{\mathrm{\&Omega;}}^3$ , ${\mathrm{the\; s}}_k^{\mathrm{\&omega;}}\left(\mathrm{\&theta;}\right)\&Element;{\mathrm{\&Omega;}}^3$ respectively represent the specific force and angular rate information measured by the micro inertial measurement unit at time k, and θ represents the set of unknown elements that need to be described in the signal;

and

Represents the noise collection associated with the accelerometer and gyroscope, respectively, and T represents the transpose operation; assuming that the noise is independent and zero-mean Gaussian distribution, the covariance matrix is $C=\mathrm{E.}\left\{\begin{array}{cc}{v}_k& {v_k}^T\end{array}\right\}=\mathrm{diag}{\left[\begin{array}{cc}{{\mathrm{\&sigma;}}_a}^2{I}_3& {{\mathrm{\&sigma;}}_{\mathrm{\&omega;}}}^2{I}_3\end{array}\right]}^T,$ Among them, I ₃ (0 ₃ ) represents a 3×3 unit (zero) matrix; diag[ ] represents a diagonal matrix; E{ } represents expectation, and

denote the noise variance of the micromachined accelerometer and gyroscope, respectively.

Further, in step five, through the formula:

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>$

Obtain the joint probability density function p(z _n ;θ _i ,H _i ) of the sensor quantity measurement;

i=0，1；θ_i表示在假设H_i条件下未知信号元素集合，Π表示连乘；p(z_n;θ_i,H_i)表示在假设H_i条件下未知信号元素集合为θ_i时单兵自主导航系统输出信号的联合概率密度函数；

表示k时刻，在假设H_i条件下未知信号元素集合为θ_i时微机械加速度计输出概率密度函数；

表示k时刻，在假设H_i条件下未知信号元素集合为θ_i时微机械陀螺仪输出的概率密度函数；in,

i=0, 1; θ _i represents the set of unknown signal elements under the assumption of H _i , and Π represents the multiplication; p(z _n ;θ _i ,H _i ) represents the set of unknown signal elements under the assumption of H _i as θ _i The joint probability density function of the output signal of the individual autonomous navigation system;

Represents the probability density function of the output probability density function of the micromachined accelerometer when the set of unknown signal elements is θ _i under the assumption of H _i at time k;

Indicates the probability density function of the output of the micromechanical gyroscope when the set of unknown signal elements is θ _i at time k under the assumption that H _i is assumed;

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \}</span>$

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \}</span>$

Among them, exp{.} represents the exponential function of e; ||.|| represents the norm; σ2a and σ2ω represent the noise variance of the accelerometer and gyroscope, respectively.

Further, in step six, according to the formula:

${\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}$

Obtain an extensive probability likelihood ratio test L _g (z _n ) for zero-speed detection of an individual soldier autonomous navigation system containing unknown elements;

Among them, assuming that the H ₁ conditional signal s _k (θ) is completely unknown, the set of unknown elements is:

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&equiv;</span><span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{<span\; class="notranslate">\; \}</span>}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ;</span>$

Under the condition of assuming H ₀ only the direction of the force vector is unknown, the set of unknown elements is:

θ ₁ ≡ gu _n ,

where u _n ∈Ω _u , Ω _u ={u∈R ³ :‖u‖=1}; g is the local gravity vector;

表示k时刻在假设H₁条件下，未知信号元素集合为θ₁时微机械加速度计输出信号的概率密度函数；

表示k时刻在假设H₀条件下，未知信号元素集合为θ₀时微机械加速度计输出信号的概率密度函数；

表示k时刻在假设H₁条件下，未知信号元素集合为θ₁时微机械陀螺仪输出信号的概率密度函数；

表示k时刻在假设H₀条件下，未知信号元素集合为θ₀时微机械陀螺仪输出信号的概率密度函数。

Represents the probability density function of the output signal of the micromachined accelerometer when the set of unknown signal elements is θ ₁ under the assumption of H ₁ at time k;

Represents the probability density function of the output signal of the micromachined accelerometer when the set of unknown signal elements is θ ₀ under the assumption of H ₀ at time k;

Represents the probability density function of the output signal of the micromechanical gyroscope when the set of unknown signal elements is θ ₁ under the assumption of H ₁ at time k;

Represents the probability density function of the output signal of the micromechanical gyroscope when the set of unknown signal elements is θ ₀ under the assumption of H ₀ at time k.

Further, in step eight, the extensive probability likelihood ratio L _G (z _n ) is expressed as;

${\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ;</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ;</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}$

表示在假设H₁条件下，未知信号元素集合为

时微型惯性测量单元输出信息的联合概率密度函数；

表示在假设H₀条件下，未知信号元素集合为时微型惯性测量单元输出信息的联合概率密度函数。In the formula,

Indicates that under the assumption of H ₁ , the set of unknown signal elements is

The joint probability density function of the output information of the miniature inertial measurement unit;

Indicates that under the assumption of H ₀ , the set of unknown signal elements is The joint probability density function of the output information of the miniature inertial measurement unit.

Further, in step nine, the inequality is expressed as:

$\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; g</span>}\frac{{\stackrel{<span\; class="notranslate">\; -</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\stackrel{<span\; class="notranslate">\; -</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}$

If the inequality is established, the zero-speed detection result of the individual soldier autonomous navigation system is static—H ₁ is true, otherwise, the zero-speed detection result is motion—H ₀ is true;

in, ${\stackrel{-}{\mathrm{the\; y}}}_{\mathrm{no}}^a=\frac{1}{N}\underset{k\&Element;{\mathrm{\&Omega;}}_{\mathrm{no}}}{\mathrm{\&Sigma;}}{\mathrm{the\; y}}_k^a,$ $T\left(z_{\mathrm{no}}\right)=-\frac{2}{N}\ln L_G\left(z_{\mathrm{no}}\right),$ γ'=-(2/N)ln(γ), ln(.) means to seek the logarithm taking e as the base.

The zero-speed detection method based on the Neiman-Pearson criterion provided by the present invention uses the Neiman-Pearson criterion to mathematicize and model the detection method problem by means of double hypothesis testing and maximum likelihood estimation. The theoretical analysis and detection scheme using statistical detection overcomes the shortcomings of poor theory and low stability in the traditional threshold detection scheme, and improves the detection accuracy without increasing the system cost; the present invention adopts statistical detection theory analysis such as hypothesis testing The detection results make the zero-speed detection method based on the Neiman-Pearson criterion suitable for zero-speed detection in various sports situations, and overcome the shortcomings of the traditional zero-speed detection method in low accuracy in sudden maneuvers. The method of the invention is simple, high in stability and reliability, improves a convenient zero-speed detection method, and effectively improves the accuracy of the zero-speed correction technology.

Description of drawings

Fig. 1 is the flowchart of the zero-speed detection method based on Neyman-Pearson criterion provided by the embodiment of the present invention;

Fig. 2 is a schematic diagram of the output value of the Y-axis gyro when pedestrians walk (30-35s) and run (35-38s) according to the embodiment of the present invention;

Fig. 3 is a schematic diagram of the comparison of detection results in the zero-speed interval of different methods when walking and running provided by an embodiment of the present invention;

a: the real zero-speed interval when walking and running; b: the zero-speed interval detected by the variance threshold method when walking and running; c: the zero-speed interval detected by the zero-speed detection method based on the N-P criterion of the present invention when walking and running;

Fig. 4 is a schematic diagram of the output value of the Y-axis gyro when pedestrians are jogging (5-11s) and running fast (11-14s) according to the embodiment of the present invention;

Fig. 5 is a schematic diagram of the comparison of the zero-speed interval detection results of different methods when jogging and fast running provided by the embodiment of the present invention;

a: the real zero-speed interval when jogging and fast running; b: the zero-speed interval detected by the variance threshold method during jogging and fast running; c: the zero-speed detection method based on the N-P criterion of the present invention when jogging and fast running interval.

Detailed ways

In order to make the object, technical solution and advantages of the present invention more clear, the present invention will be further described in detail below in conjunction with the examples. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

Fig. 1 shows the flow of the zero-speed detection method based on the Neiman-Pearson criterion provided by the present invention. For ease of illustration, only the parts relevant to the present invention are shown.

The zero-speed detection method based on the Neiman-Pearson criterion of the embodiment of the present invention, the zero-speed detection method based on the Neiman-Pearson criterion comprises the following steps:

Step 1, the handheld handheld computer receives and stores the measurement information output by the step miniature inertial measurement unit in the individual soldier's autonomous navigation system in real time;

Step 2: According to the sampling frequency of each sensor in the individual soldier's autonomous navigation system, the static time length of the miniature inertial measurement unit before the system is used, and the data transmission rate between the miniature inertial measurement unit and the handheld computer during the measurement process of step 1, obtain the current zero speed The specific value of the window function N during the detection process, where N is an integer;

则H₁为真，即单兵自主导航系统零速检测结果为脚步微型惯性测量单元静止；函数L(z_n)与概率比有关，对于z_n的每个值，表示了H₁假设概率值对H₀假设概率值的比值；Step 3: Using the output data of the miniature inertial measurement unit collected in step 1 and the window function N determined in step 2, the zero-speed detection problem is transformed into a modeled double hypothesis testing problem, and the detection result is the hypothetical miniature inertial measurement unit motion H ₀ , One of the static miniature inertial measurement units H ₁ , using the Neiman-Pearson theorem to obtain the mathematical model of zero-speed detection and judgment: when the false alarm probability P _FA = α is known, if the zero-speed judgment inequality is satisfied:

Then H ₁ is true, that is, the zero-speed detection result of the individual soldier's autonomous navigation system is that the miniature inertial measurement unit is stationary; the function L(z _n ) is related to the probability ratio, and for each value of z _n , it represents the hypothetical probability value of H ₁ the ratio of hypothesized probability values to H ₀ ;

定义；p(z_n;H₀)、p(z_n;H₁)分别表示两种假设下观测数据的概率密度函数；Among them, the false alarm probability P _FA ={H ₁ ∣H ₀ } indicates the probability that the miniature inertial measurement unit is judged to be in a static state when it is in motion; z _n ={y _k }n+N-1k=n is the miniature inertial measurement unit within a period of time The measured value of the inertial measurement unit; the value of γ is given by the formula

Definition; p(z _n ;H ₀ ) and p(z _n ;H ₁ ) respectively represent the probability density functions of the observed data under two assumptions;

Step 4: Utilize the characteristics of the output signal of the miniature inertial measurement unit sensor, the nature of the signal received by the handheld computer and the error disturbance signal, and the formula to obtain the mathematical model of the output signal of the miniature inertial measurement unit inertial sensor;

Step 5: Using the data output by the miniature inertial measurement unit collected in step 1 during the movement of the individual autonomous navigation system, the mathematical model and formula of the output signal of the miniature inertial measurement unit inertial sensor determined in step 4, to obtain the sensor quantity measurement Joint probability density function p(z _n ;θ _i ,H _i );

Step 6: Use the joint probability density function of the observed signals obtained in step 5

p(z _n ;θ _i ,H _i ), according to

Formula, to obtain a broad probability likelihood ratio test L _g (z _n ) of the zero-speed detection of the individual autonomous navigation system containing unknown elements;

Step 7: Use formula:

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

Obtain maximum likelihood estimates of unknown signal elements under two assumptions

是在假设H₀条件下未知元素的极大似然估计；p(z_n;θ₁,H₁)表示在假设H₁条件下，未知信号元素集合为θ₁时微型惯性测量单元输出信息的联合概率密度函数；p(z_n;θ₀,H₀)表示在假设H₀条件下，未知信号元素集合为θ₀时微型惯性测量单元输出信息的联合概率密度函数；argmax(·)表示使括号内取最大值时未知元素集合的值；In the formula, is the maximum likelihood estimate of the unknown element under the assumption of H ₁ condition;

is the maximum likelihood estimation of unknown elements under the assumption of H ₀ ; p(z _n ;θ ₁ ,H ₁ ) represents the output information of the miniature inertial measurement unit when the set of unknown signal elements is θ ₁ under the assumption of H ₁ Joint probability density function; p(z _n ;θ ₀ ,H ₀ ) represents the joint probability density function of the output information of the micro IMU when the set of unknown signal elements is θ ₀ under the assumption of H ₀ ; argmax(·) represents the The value of the unknown element set when taking the maximum value in the brackets;

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

Step 8: Use Step 7 to obtain the maximum likelihood estimation of the unknown signal elements Replacing the unknown signal element set in step six L _g (z _n ) to obtain a broad probability likelihood ratio L _G (z _n ) that does not contain unknown elements;

Step 9: Use L _G (z _n ) and the inequality obtained in Step 8 to determine the zero-speed detection result of the individual autonomous navigation system.

As an optimization scheme of the embodiment of the present invention, in step 1, the total output information of the miniature inertial measurement unit received at any time k is: ${\mathrm{the\; y}}_k={\left[\begin{array}{cc}{\mathrm{the\; y}}_k^a& {\mathrm{the\; y}}_k^{\mathrm{\&omega;}}\end{array}\right]}^T;$

Among them, T represents the transpose operation, ${\mathrm{the\; y}}_k^{\mathrm{\&omega;}}={\left[\begin{array}{ccc}{\mathrm{the\; y}}_k^{\mathrm{\&omega;x}}& {\mathrm{the\; y}}_k^{\mathrm{\&omega;y}}& {\mathrm{the\; y}}_k^{\mathrm{\&omega;z}}\end{array}\right]}^T$ Angular rate information output by the three-axis gyroscope of the micro-mechanical system; ${\mathrm{the\; y}}_k^a={\left[\begin{array}{ccc}{\mathrm{the\; y}}_k^{\mathrm{ax}}& {\mathrm{the\; y}}_k^{\mathrm{ay}}& {\mathrm{the\; y}}_k^{\mathrm{az}}\end{array}\right]}^T$ It is the specific force information output by the MEMS triaxial accelerometer.

As an optimization scheme of the embodiment of the present invention, in step 4, through the formula:

y _k = s _k (θ) + v _k

Obtain the mathematical model of the output signal of the inertial sensor of the miniature inertial measurement unit;

分别表示与加速度计和陀螺仪相关的噪声集合，T表示转置操作；假设噪声是独立、零均值高斯分布的，协方差矩阵为 $C=E\left\{\begin{array}{cc}{v}_k& {v_k}^T\end{array}\right\}=\mathrm{diag}{\left[\begin{array}{cc}{{\mathrm{\&sigma;}}_a}^2{I}_3& {{\mathrm{\&sigma;}}_{\mathrm{\&omega;}}}^2{I}_3\end{array}\right]}^T,$ 其中I₃(0₃)表示3×3的单位(零)阵；diag[·]表示对角阵；E{·}表示求期望，

和

分别表示微机械加速度计和陀螺仪的噪声方差。In the formula, ${\mathrm{the\; s}}_k\left(\mathrm{\&theta;}\right)={\left[\begin{array}{cc}{\mathrm{the\; s}}_k^a\left(\mathrm{\&theta;}\right)& {\mathrm{the\; s}}_k^{\mathrm{\&omega;}}\left(\mathrm{\&theta;}\right)\end{array}\right]}^T,$ $v_k={\left[\begin{array}{cc}{v}_k^a& v_k^{\mathrm{\&omega;}}\end{array}\right]}^T,$ ${\mathrm{the\; s}}_k^a\left(\mathrm{\&theta;}\right)\&Element;{\mathrm{\&Omega;}}^3$ ${\mathrm{the\; s}}_k^{\mathrm{\&omega;}}\left(\mathrm{\&theta;}\right)\&Element;{\mathrm{\&Omega;}}^3$ respectively represent the specific force and angular velocity measured by the micro inertial measurement unit at time k, and θ represents the set of unknown elements that need to be described in the signal; and

Represents the noise collection associated with the accelerometer and gyroscope, respectively, and T represents the transpose operation; assuming that the noise is independent and zero-mean Gaussian distribution, the covariance matrix is $C=\mathrm{E.}\left\{\begin{array}{cc}{v}_k& {v_k}^T\end{array}\right\}=\mathrm{diag}{\left[\begin{array}{cc}{{\mathrm{\&sigma;}}_a}^2{I}_3& {{\mathrm{\&sigma;}}_{\mathrm{\&omega;}}}^2{I}_3\end{array}\right]}^T,$ Among them, I ₃ (0 ₃ ) represents a 3×3 unit (zero) matrix; diag[ ] represents a diagonal matrix; E{ } represents expectation,

and

denote the noise variance of the micromachined accelerometer and gyroscope, respectively.

As an optimization scheme of the embodiment of the present invention, in step 5, through the formula:

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>$

Obtain the joint probability density function p(z _n ;θ _i ,H _i ) of the sensor quantity measurement;

表示k时刻，在假设H_i条件下未知信号元素集合为θ_i时微机械加速度计输出信息的概率密度函数；

表示k时刻，在假设H_i条件下未知信号元素集合为θ_i时微机械陀螺仪输出信息的概率密度函数；in, i=0, 1; θ _i represents the set of unknown signal elements under the assumption of H _i , and Π represents the multiplication; p(z _n ;θ _i ,H _i ) represents the set of unknown signal elements under the assumption of H _i as θ _i The joint probability density function of the output signal of the individual autonomous navigation system;

Indicates the probability density function of the output information of the micromachined accelerometer when the set of unknown signal elements is _θi under the assumption of H _i at time k;

Indicates the probability density function of the output information of the micromechanical gyroscope when the set of unknown signal elements is θ _i under the assumption of H _i at time k;

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \}</span>$

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \}</span>$

Among them, exp{.} represents the exponential function of e; ||.|| represents the norm; σ2a and σ2ω represent the noise variance of the accelerometer and gyroscope, respectively.

As an optimization scheme of the embodiment of the present invention, in step 6, according to the formula:

${\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}$

Obtain an extensive probability likelihood ratio test L _g (z _n ) for zero-speed detection of an individual soldier autonomous navigation system containing unknown elements;

Among them, assuming that the H ₁ conditional signal s _k (θ) is completely unknown, the set of unknown elements is:

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&equiv;</span><span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{<span\; class="notranslate">\; \}</span>}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ;</span>$

Under the condition of assuming H ₀ only the direction of the force vector is unknown, the set of unknown elements is:

θ ₁ ≡ gu _n ,

where u _n ∈Ω _u , Ω _u ={u∈R ³ :‖u‖=1}; g is the local gravity vector;

表示k时刻在假设H₁条件下，未知信号元素集合为θ₁时微机械加速度计输出概率密度函数；表示k时刻在假设H₀条件下，未知信号元素集合为θ₀时微机械加速度计输出概率密度函数；

表示k时刻在假设H₁条件下，未知信号元素集合为θ₁时微机械陀螺仪输出的概率密度函数；

表示k时刻在假设H₀条件下，未知信号元素集合为θ₀时微机械陀螺仪输出的概率密度函数。

Represents the output probability density function of the micromechanical accelerometer when the set of unknown signal elements is θ ₁ under the assumption of H ₁ at time k; Represents the output probability density function of the micromechanical accelerometer when the set of unknown signal elements is θ ₀ under the assumption of H ₀ at time k;

Represents the probability density function of the micromechanical gyroscope output when the set of unknown signal elements is θ ₁ under the assumption of H ₁ at time k;

Represents the probability density function of the micromachined gyroscope output when the set of unknown signal elements is θ ₀ under the assumption of H ₀ at time k.

As an optimization scheme of the embodiment of the present invention, in step 8, the broad probability likelihood ratio L _G (z _n ) is expressed as;

${\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ;</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ;</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}$

表示在假设H₁条件下，未知信号元素集合为时微型惯性测量单元输出信息的联合概率密度函数；

表示在假设H₀条件下，未知信号元素集合为

时微型惯性测量单元输出信息的联合概率密度函数。In the formula,

Indicates that under the assumption of H ₁ , the set of unknown signal elements is The joint probability density function of the output information of the miniature inertial measurement unit;

Indicates that under the assumption of H ₀ , the set of unknown signal elements is

The joint probability density function of the output information of the miniature inertial measurement unit.

As an optimization scheme of the embodiment of the present invention, in step 9, the inequality is expressed as:

$\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; g</span>}\frac{{\stackrel{<span\; class="notranslate">\; -</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\stackrel{<span\; class="notranslate">\; -</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}$

If the inequality is established, the zero-speed detection result of the individual soldier autonomous navigation system is static—H ₁ is true, otherwise, the zero-speed detection result is motion—H ₀ is true;

in, ${\stackrel{-}{\mathrm{the\; y}}}_{\mathrm{no}}^a=\frac{1}{N}\underset{k\&Element;{\mathrm{\&Omega;}}_{\mathrm{no}}}{\mathrm{\&Sigma;}}{\mathrm{the\; y}}_k^a,$ $T\left(z_{\mathrm{no}}\right)=-\frac{2}{N}\ln L_G\left(z_{\mathrm{no}}\right),$ γ'=-(2/N)ln(γ), ln(.) means to seek the logarithm taking e as the base.

The application principle of the present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

As shown in Figure 1, the zero-speed detection method based on the Neyman-Pearson criterion of the embodiment of the present invention includes the following steps:

S101: The hand-held handheld computer receives and stores the measurement information output by the footstep miniature inertial measurement unit in the individual soldier's autonomous navigation system in real time;

S102: According to the sampling frequency of each sensor in the individual soldier's autonomous navigation system, the static time length of the miniature inertial measurement unit before the system is used, and the data transmission rate between the miniature inertial measurement unit and the handheld computer during the measurement process, obtain the zero-speed detection process. The specific value of the window function N;

S103: Using the collected output data of the micro inertial measurement unit and the window function N, transform the zero-speed detection problem into a modeled double hypothesis testing problem;

S104: Using the characteristics of the output signal of the miniature inertial measurement unit sensor, the nature of the signal received by the handheld computer and its error disturbance signal, and the formula, to obtain the mathematical model of the output signal of the miniature inertial measurement unit inertial sensor;

S105: Using the collected data output by the miniature inertial measurement unit during the movement of the individual soldier autonomous navigation system, the determined mathematical model and formula of the output signal of the miniature inertial measurement unit inertial sensor, to obtain a joint probability density function of sensor quantity measurement;

S106: Utilize the observed signal joint probability density function obtained, according to the formula, obtain a zero-velocity detection extensive probability likelihood ratio test of the individual soldier autonomous navigation system containing unknown elements;

S107: Using a formula to obtain maximum likelihood estimates of unknown signal elements under two assumptions;

S108: use: obtain the maximum likelihood estimate of the unknown signal element, replace the unknown signal element set in the extensive probability likelihood ratio test to obtain the extensive probability likelihood ratio without unknown elements;

S109: Using the obtained extensive probability likelihood ratio and inequality, determine the zero-speed detection result of the individual autonomous navigation system;

Concrete steps of the present invention are:

Step 1: The hand-held handheld computer receives and stores the measurement information output by the miniature inertial measurement unit in the individual soldier's autonomous navigation system in real time. The total output information of the miniature inertial measurement unit received by k at any time is ${\mathrm{the\; y}}_k={\left[\begin{array}{cc}{\mathrm{the\; y}}_k^a& {\mathrm{the\; y}}_k^{\mathrm{\&omega;}}\end{array}\right]}^T;$

Among them, T represents the transpose operation, ${\mathrm{the\; y}}_k^{\mathrm{\&omega;}}={\left[\begin{array}{ccc}{\mathrm{the\; y}}_k^{\mathrm{\&omega;x}}& {\mathrm{the\; y}}_k^{\mathrm{\&omega;y}}& {\mathrm{the\; y}}_k^{\mathrm{\&omega;z}}\end{array}\right]}^T$ The angular rate information output by the three-axis gyroscope of the Micro-Electro-Mechanical System; ${\mathrm{the\; y}}_k^a={\left[\begin{array}{ccc}{\mathrm{the\; y}}_k^{\mathrm{ax}}& {\mathrm{the\; y}}_k^{\mathrm{ay}}& {\mathrm{the\; y}}_k^{\mathrm{az}}\end{array}\right]}^T$ is the specific force information output by the three-axis accelerometer of the micro-mechanical system;

Step 2: According to the sampling frequency of each sensor in the individual soldier's autonomous navigation system, the static time length of the miniature inertial measurement unit before the system is used, and the data transmission rate between the miniature inertial measurement unit and the handheld computer during the measurement process of step 1, obtain the current zero speed The specific value of the window function N in the detection process (N is an integer);

则H₁为真，即单兵自主导航系统零速检测结果为脚步微型惯性测量单元静止；函数L(z_n)与概率比有关，对于z_n的每个值，它表示了H₁假设概率值对H₀假设概率值的比值；Step 3: Using the output data of the miniature inertial measurement unit collected in step 1 and the window function N determined in step 2, the zero-speed detection problem is transformed into a modeled double hypothesis testing problem, and the detection result is the hypothesis H ₀ (miniature inertial measurement unit Motion), one of H ₁ (miniature inertial measurement unit static), using the Neiman-Pearson theorem to obtain the mathematical model of zero-speed detection and judgment: when the false alarm probability P _FA = α is known, if the zero-speed judgment inequality is satisfied:

Then H ₁ is true, that is, the zero-speed detection result of the individual soldier's autonomous navigation system is that the miniature inertial measurement unit is stationary; the function L(z _n ) is related to the probability ratio, and for each value of z _n , it represents the hypothetical probability of H ₁ The ratio of the value to the hypothesized probability value of H ₀ ;

定义；p(z_n;H₀)、p(z_n;H₁)分别表示两种假设下观测数据的概率密度函数；Among them, the false alarm probability P _FA ={H ₁ ∣H ₀ } indicates the probability that the miniature inertial measurement unit is judged to be in a static state when it is in motion; z _n ={y _k }n+N-1k=n is a period of time The measured value of the inner miniature inertial measurement unit; the value of γ is given by the formula

Definition; p(z _n ;H ₀ ) and p(z _n ;H ₁ ) respectively represent the probability density functions of the observed data under two assumptions;

Step 4: Utilize the characteristics of the output signal of the miniature inertial measurement unit sensor, the nature of the signal received by the handheld computer and its error disturbance signal, and the formula:

y _k = s _k (θ) + v _k

Obtain the mathematical model of the output signal of the inertial sensor of the miniature inertial measurement unit;

和

分别表示与加速度计和陀螺仪相关的噪声集合，T表示转置操作；假设噪声是独立、零均值高斯分布的，其协方差矩阵为 $C=E\left\{\begin{array}{cc}{v}_k& {v_k}^T\end{array}\right\}=\mathrm{diag}{\left[\begin{array}{cc}{{\mathrm{\&sigma;}}_a}^2{I}_3& {{\mathrm{\&sigma;}}_{\mathrm{\&omega;}}}^2{I}_3\end{array}\right]}^T,$ 其中I₃(0₃)表示3×3的单位(零)阵；diag[·]表示对角阵；E{·}表示求期望，

和

分别表示微机械加速度计和陀螺仪的噪声方差；In the formula, ${\mathrm{the\; s}}_k\left(\mathrm{\&theta;}\right)={\left[\begin{array}{cc}{\mathrm{the\; s}}_k^a\left(\mathrm{\&theta;}\right)& {\mathrm{the\; s}}_k^{\mathrm{\&omega;}}\left(\mathrm{\&theta;}\right)\end{array}\right]}^T,$ $v_k={\left[\begin{array}{cc}{v}_k^a& v_k^{\mathrm{\&omega;}}\end{array}\right]}^T,$ ${\mathrm{the\; s}}_k^a\left(\mathrm{\&theta;}\right)\&Element;{\mathrm{\&Omega;}}^3,$ ${\mathrm{the\; s}}_k^{\mathrm{\&omega;}}\left(\mathrm{\&theta;}\right)\&Element;{\mathrm{\&Omega;}}^3$ respectively represent the specific force and angular velocity measured by the micro inertial measurement unit at time k, and θ represents the set of unknown elements that need to be described in the signal;

and

Represents the noise collection associated with the accelerometer and gyroscope, respectively, and T represents the transpose operation; assuming that the noise is independent and zero-mean Gaussian distribution, its covariance matrix is $C=\mathrm{E.}\left\{\begin{array}{cc}{v}_k& {v_k}^T\end{array}\right\}=\mathrm{diag}{\left[\begin{array}{cc}{{\mathrm{\&sigma;}}_a}^2{I}_3& {{\mathrm{\&sigma;}}_{\mathrm{\&omega;}}}^2{I}_3\end{array}\right]}^T,$ Among them, I ₃ (0 ₃ ) represents a 3×3 unit (zero) matrix; diag[ ] represents a diagonal matrix; E{ } represents expectation,

and

denote the noise variance of the micromachined accelerometer and gyroscope, respectively;

Step 5: Use the data output by the miniature inertial measurement unit collected in step 1 during the movement of the individual soldier's autonomous navigation system, the mathematical model and formula of the output signal of the miniature inertial measurement unit inertial sensor determined in step 4:

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>$

Obtain the joint probability density function p(z _n ;θ _i ,H _i ) of the sensor quantity measurement;

i=0，1；θ_i表示在假设H_i条件下未知信号元素集合，Π表示连乘；p(z_n;θ_i,H_i)表示在假设H_i条件下未知信号元素集合为θ_i时单兵自主导航系统输出信号的联合概率密度函数；

表示k时刻，在假设H_i条件下未知信号元素集合为θ_i时微机械加速度计输出信号的概率密度函数；

表示k时刻，在假设H_i条件下未知信号元素集合为θ_i时微机械陀螺仪输出信号的概率密度函数；in,

i=0, 1; θ _i represents the set of unknown signal elements under the assumption of H _i , and Π represents the multiplication; p(z _n ;θ _i ,H _i ) represents the set of unknown signal elements under the assumption of H _i as θ _i The joint probability density function of the output signal of the individual autonomous navigation system;

Indicates the probability density function of the output signal of the micromechanical accelerometer when the set of unknown signal elements is θ _i at time k under the assumption of H _i ;

Indicates the probability density function of the output signal of the micromechanical gyroscope when the set of unknown signal elements is θ _i at time k, assuming H _i ;

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \}</span>$

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \}</span>$

Among them, exp{.} represents the exponential function of e; ||.|| represents the norm; σ2a and σ2ω represent the noise variance of the accelerometer and gyroscope respectively;

Step 6: Use the joint probability density function of the observed signals obtained in step 5

p(z _n ;θ _i ,H _i ), according to the formula: $L_g\left(z_{\mathrm{no}}\right)=\frac{\underset{k\&Element;{\mathrm{\&Omega;}}_{\mathrm{no}}}{\mathrm{\&Pi;}}p({\mathrm{the\; y}}_k^a;{\mathrm{\&theta;}}_1,h_1)p({\mathrm{the\; y}}_k^{\mathrm{\&omega;}};{\mathrm{\&theta;}}_1,h_1)}{\underset{k\&Element;{\mathrm{\&Omega;}}_{\mathrm{no}}}{\mathrm{\&Pi;}}p({\mathrm{the\; y}}_k^a;{\mathrm{\&theta;}}_0,h_0)p({\mathrm{the\; y}}_k^{\mathrm{\&omega;}};{\mathrm{\&theta;}}_0,h_0)}$

Obtain an extensive probability likelihood ratio test L _g (z _n ) for zero-speed detection of an individual soldier autonomous navigation system containing unknown elements;

Among them, assuming that the H ₁ conditional signal s _k (θ) is completely unknown, the set of unknown elements is:

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&equiv;</span><span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{<span\; class="notranslate">\; \}</span>}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ;</span>$

Under the condition of assuming H ₀ only the direction of the force vector is unknown, the set of unknown elements is:

θ ₁ ≡ gu _n ,

where u _n ∈Ω _u , Ω _u ={u∈R ³ :‖u‖=1}; g is the local gravity vector;

表示k时刻在假设H₀条件下，未知信号元素集合为θ₀时微机械加速度计输出信号的概率密度函数；

表示k时刻在假设H₁条件下，未知信号元素集合为θ₁时微机械陀螺仪输出信号的概率密度函数；

表示k时刻在假设H₀条件下，未知信号元素集合为θ₀时微机械陀螺仪输出信号的概率密度函数； Represents the probability density function of the output signal of the micromachined accelerometer when the set of unknown signal elements is θ ₁ under the assumption of H ₁ at time k;

Represents the probability density function of the output signal of the micromachined accelerometer when the set of unknown signal elements is θ ₀ under the assumption of H ₀ at time k;

Represents the probability density function of the output signal of the micromechanical gyroscope when the set of unknown signal elements is θ ₁ under the assumption of H ₁ at time k;

Represents the probability density function of the output signal of the micromechanical gyroscope when the set of unknown signal elements is θ ₀ under the assumption of H ₀ at time k;

Step 7: Use the formula:

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

Obtain maximum likelihood estimates of unknown signal elements under two assumptions

是在假设H₁条件未知元素的极大似然估计；

是在假设H₀条件下未知元素的极大似然估计；p(z_n;θ₁,H₁)表示在假设H₁条件下，未知信号元素集合为θ₁时微型惯性测量单元输出信息的联合概率密度函数；p(z_n;θ₀,H₀)表示在假设H₀条件下，未知信号元素集合为θ₀时微型惯性测量单元输出信息的联合概率密度函数；argmax(·)表示使括号内取最大值时未知元素集合的值；In the formula,

is the maximum likelihood estimate of the unknown element under the assumption of H ₁ condition;

is the maximum likelihood estimation of unknown elements under the assumption of H ₀ ; p(z _n ;θ ₁ ,H ₁ ) represents the output information of the miniature inertial measurement unit when the set of unknown signal elements is θ ₁ under the assumption of H ₁ Joint probability density function; p(z _n ;θ ₀ ,H ₀ ) represents the joint probability density function of the output information of the micro IMU when the set of unknown signal elements is θ ₀ under the assumption of H ₀ ; argmax(·) represents the The value of the unknown element set when taking the maximum value in the brackets;

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

取代步骤六L_g(z_n)中的未知信号元素集合得到不含未知元素的广泛概率似然比L_G(z_n)；Step 8: Use Step 7 to obtain the maximum likelihood estimation of the unknown signal elements

Replacing the unknown signal element set in step six L _g (z _n ) to obtain a broad probability likelihood ratio L _G (z _n ) that does not contain unknown elements;

${\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ;</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ;</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}$

表示在假设H₁条件下，未知信号元素集合为

时微型惯性测量单元输出信息的联合概率密度函数；

表示在假设H₀条件下，未知信号元素集合为

时微型惯性测量单元输出信息的联合概率密度函数；In the formula,

Indicates that under the assumption of H ₁ , the set of unknown signal elements is

The joint probability density function of the output information of the miniature inertial measurement unit;

Indicates that under the assumption of H ₀ , the set of unknown signal elements is

The joint probability density function of the output information of the miniature inertial measurement unit;

Step 9: Use L _G (z _n ) and inequality obtained in step 8:

$\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; g</span>}\frac{{\stackrel{<span\; class="notranslate">\; -</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\stackrel{<span\; class="notranslate">\; -</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}$

Determine the zero-speed detection result of the individual soldier's autonomous navigation system: if the inequality is established, the zero-speed detection result of the individual soldier's autonomous navigation system is static—H ₁ is true, otherwise, the zero-speed detection result is motion—H ₀ is true;

in, ${\stackrel{-}{\mathrm{the\; y}}}_{\mathrm{no}}^a=\frac{1}{N}\underset{k\&Element;{\mathrm{\&Omega;}}_{\mathrm{no}}}{\mathrm{\&Sigma;}}{\mathrm{the\; y}}_k^a,$ $T\left(z_{\mathrm{no}}\right)=-\frac{2}{N}\ln L_G\left(z_{\mathrm{no}}\right),$ γ '=-(2/N) ln (γ), ln (.) represents asking for the logarithm of base number with e;

The beneficial effect of the present invention is further described in conjunction with the following experiments:

A self-developed three-axis inertial measurement component (integrated with a micro-mechanical system three-axis magnetometer, accelerometer, and gyroscope) is used to build a real individual navigation system model. The reliability, practicability, and accuracy of the individual navigation zero-speed detection algorithm based on the inertial solution of dual micro-inertial measurement units in the real environment. The test scene was selected in the open outdoor military playground of Harbin Engineering University.

Table 1 The performance indicators of each sensor of the self-developed miniature inertial measurement unit inertial measurement component

During the experiment, the relevant parameters were set as follows:

Individual navigation autonomous positioning system sampling frequency: 100Hz

window function N: 5

MEMS gyro standard deviation: σ _a ＝0.01m/s ²

Micromachined accelerometer standard deviation: σ _g = 0.1*pi/180rad/s

Parameter γ = 0.3e ⁵

Before the start of the experiment, the tester performed a 15-minute static warm-up of the system in the experimental field to complete the initialization of the system;

Test 1:

The testers performed "walking (1.05m/s)", "jogging (2.14m/s)", "fast running (3.50m/s)" and other sports on the track of the rectangular playground, and the data were collected and saved in real time during the experiment The output data of the miniature inertial measurement unit is used as a reference, and the zero-speed interval obtained by observing the output value of the gyro is regarded as the real zero-speed interval, as shown in Figure 2, the output value of the Y-axis gyro when the pedestrian walks first and then jogs;

Experimental data is carried out off-line analysis, in order to compare and verify the experimental result of the present invention, provide the detection result of traditional variance threshold zero-speed detection method and the zero-speed detection method based on N-P criterion that the present invention proposes simultaneously, and compare with the original of gyroscope The data are compared, as shown in Figure 3, it is the detection result of first walking and then jogging with different detection methods;

As can be seen from Figure 3, the variance threshold footstep detection method is invalid when jogging, and the algorithm mentioned in the present invention can accurately detect the zero-speed interval;

Figure 4 shows the output value of the Y-axis gyro when the pedestrian is jogging and running fast. Result invalidation, in above-mentioned experiment, the algorithm mentioned in the present invention can accurately detect zero-speed interval;

Test 2:

In order to quantitatively compare the performance of various methods, we let walkers walk or run 30 steps at different speeds, each step has a zero-speed interval, and there are 30 zero-speed intervals in total. The number of zero-speed intervals detected by the zero-speed detection method based on the Neiman-Pearson (N-P) criterion proposed by the invention is shown in Table 2. When walking, both algorithms can accurately detect the zero-speed interval; when running, The variance threshold zero-speed detection method fails, and the algorithm of the present invention can accurately detect the number of zero-speed intervals no matter walking or running,

Table 2 Comparison of the number of zero-speed intervals detected by different methods (the actual number of zero-speed intervals is 30)

Table 3 shows the number of false detections in the zero-speed interval of various algorithms, that is, the number of false detections of non-zero-speed intervals as zero-speed intervals. It can be seen from Table 3 that the variance threshold zero-speed detection method sometimes incorrectly detects zero speed interval, and the N-P zero-speed detection algorithm mentioned in the present invention can accurately and reliably detect the zero-speed interval whether it is a walking state or a running state. This algorithm is all effective for the zero-speed detection during normal walking and running, and the reliability High, good stability;

Table 3 Comparison of the number of false detection zero-speed intervals by different methods

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention should be included in the protection of the present invention. within range.

Claims (7)

1. a zero-speed detection method based on Neiman-Pearson criterion, it is characterized in that, this zero-speed detection method based on Neiman-Pearson criterion comprises the following steps: Step 1, the handheld handheld computer receives and stores the measurement information output by the step miniature inertial measurement unit in the individual soldier's autonomous navigation system in real time; Step 2: According to the sampling frequency of each sensor in the individual soldier's autonomous navigation system, the static time length of the miniature inertial measurement unit before the system is used, and the data transmission rate between the miniature inertial measurement unit and the handheld computer during the measurement process of step 1, obtain the current zero speed The specific value of the window function N during the detection process, where N is an integer; Step 3: Using the output data of the miniature inertial measurement unit collected in step 1 and the window function N determined in step 2, the zero-speed detection problem is transformed into a modeled double hypothesis testing problem, assuming that the detection result is the miniature inertial measurement unit motion H ₀ , One of the static miniature inertial measurement units H ₁ , using the Neiman-Pearson theorem to obtain the mathematical model of zero-speed detection and judgment: when the false alarm probability P _FA = α is known, if the zero-speed judgment inequality is satisfied:

Then H ₁ is true, that is, the zero-speed detection result of the individual soldier autonomous navigation system is that the miniature inertial measurement unit is stationary; the function L(z _n ) is related to the probability ratio, and for each value of z _n , it represents the pair of hypothetical probability values of H ₁ H ₀ The ratio of hypothesized probability values; Among them, the false alarm probability P _FA ={H ₁ ∣H ₀ } indicates the probability that the zero-speed detection result is in a stationary state when the miniature inertial measurement unit is in motion; z _n ={y _k }n+N-1k=n is The measured value of the miniature inertial measurement unit within a period of time; the value of γ is given by the formula

Definition; p(z _n ;H ₀ ) and p(z _n ;H ₁ ) respectively represent the probability density functions of the observed data under two assumptions; Step 4: Utilize the characteristics of the output signal of the miniature inertial measurement unit sensor, the nature of the signal received by the handheld computer and the error disturbance signal, and the formula to obtain the mathematical model of the output signal of the miniature inertial measurement unit inertial sensor; Step 5: Using the data output by the miniature inertial measurement unit collected in step 1 during the movement of the individual autonomous navigation system, the mathematical model and formula of the output signal of the miniature inertial measurement unit inertial sensor determined in step 4, to obtain the sensor quantity measurement Joint probability density function p(z _n ;θ _i ,H _i ); Step 6: Using the joint probability density function p(z _n ;θ _i ,H _i ) of the observation signals obtained in step 5, according to the formula, obtain a broad probability likelihood ratio test for zero-speed detection of the individual autonomous navigation system with unknown elements L _g (z _n ); Step 7: Use formula: ${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$ ${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$ Obtain maximum likelihood estimates of unknown signal elements under two assumptions

In the formula,

is the maximum likelihood estimate of the unknown element under the assumption of H ₁ condition;

is the maximum likelihood estimation of unknown elements under the assumption of H ₀ ; p(z _n ;θ ₁ ,H ₁ ) represents the output information of the miniature inertial measurement unit when the set of unknown signal elements is θ ₁ under the assumption of H ₁ Joint probability density function; p(z _n ;θ ₀ ,H ₀ ) represents the joint probability density function of the output information of the micro IMU when the set of unknown signal elements is θ ₀ under the assumption of H ₀ ; argmax(·) represents the The value of the unknown element set when taking the maximum value in the brackets; $\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>$ $\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ Step 8: Use Step 7 to obtain the maximum likelihood estimation of the unknown signal elements

Replacing the unknown signal element set in step six L _g (z _n ) to obtain a broad probability likelihood ratio L _G (z _n ) that does not contain unknown elements; Step 9: Use L _G (z _n ) and the inequality obtained in Step 8 to determine the zero-speed detection result of the individual autonomous navigation system. 2. the zero-speed detection method based on Neiman-Pearson criterion as claimed in claim 1, is characterized in that, in step 1, the total output information of the miniature inertial measurement unit that arbitrary moment k receives is ${\mathrm{the\; y}}_k={\left[\begin{array}{cc}{\mathrm{the\; y}}_k^a& {\mathrm{the\; y}}_k^{\mathrm{\&omega;}}\end{array}\right]}^T;$ Among them, T represents the transpose operation, ${\mathrm{the\; y}}_k^{\mathrm{\&omega;}}={\left[\begin{array}{ccc}{\mathrm{the\; y}}_k^{\mathrm{\&omega;x}}& {\mathrm{the\; y}}_k^{\mathrm{\&omega;y}}& {\mathrm{the\; y}}_k^{\mathrm{\&omega;z}}\end{array}\right]}^T$ Angular rate information output by the three-axis gyroscope of the micro-mechanical system; ${\mathrm{the\; y}}_k^a={\left[\begin{array}{ccc}{\mathrm{the\; y}}_k^{\mathrm{ax}}& {\mathrm{the\; y}}_k^{\mathrm{ay}}& {\mathrm{the\; y}}_k^{\mathrm{az}}\end{array}\right]}^T$ It is the specific force information output by the MEMS triaxial accelerometer. 3. the zero-speed detection method based on Neiman-Pearson criterion as claimed in claim 1, is characterized in that, in step 4, by formula: y _k = s _k (θ) + v _k Obtain the mathematical model of the output signal of the inertial sensor of the miniature inertial measurement unit; In the formula, ${\mathrm{the\; s}}_k\left(\mathrm{\&theta;}\right)={\left[\begin{array}{cc}{\mathrm{the\; s}}_k^a\left(\mathrm{\&theta;}\right)& {\mathrm{the\; s}}_k^{\mathrm{\&omega;}}\left(\mathrm{\&theta;}\right)\end{array}\right]}^T,$ $v_k={\left[\begin{array}{cc}{v}_k^a& v_k^{\mathrm{\&omega;}}\end{array}\right]}^T,$ ${\mathrm{the\; s}}_k^a\left(\mathrm{\&theta;}\right)\&Element;{\mathrm{\&Omega;}}^3$ , ${\mathrm{the\; s}}_k^{\mathrm{\&omega;}}\left(\mathrm{\&theta;}\right)\&Element;{\mathrm{\&Omega;}}^3$ respectively represent the specific force and angular velocity measured by the micro inertial measurement unit at time k, and θ represents the set of unknown elements that need to be described in the signal;

and

Represents the noise collection associated with the accelerometer and gyroscope, respectively, and T represents the transpose operation; assuming that the noise is independent and zero-mean Gaussian distribution, the covariance matrix is $C=\mathrm{E.}\left\{\begin{array}{cc}{v}_k& {v_k}^T\end{array}\right\}=\mathrm{diag}{\left[\begin{array}{cc}{{\mathrm{\&sigma;}}_a}^2{I}_3& {{\mathrm{\&sigma;}}_{\mathrm{\&omega;}}}^2{I}_3\end{array}\right]}^T,$ Among them, I ₃ (0 ₃ ) represents a 3×3 unit (zero) matrix; diag[ ] represents a diagonal matrix; E{ } represents expectation,

and

denote the noise variance of the micromachined accelerometer and gyroscope, respectively. 4. the zero-speed detection method based on Neiman-Pearson criterion as claimed in claim 1, is characterized in that, in step 5, by formula: $\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>$ $<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>$ Obtain the joint probability density function p(z _n ;θ _i ,H _i ) of the sensor quantity measurement; in,

i=0, 1; θ _i represents the set of unknown signal elements under the assumption of H _i , and Π represents the multiplication; p(z _n ;θ _i ,H _i ) represents the set of unknown signal elements under the assumption of H _i as θ _i The joint probability density function of the output signal of the individual autonomous navigation system;

Indicates the probability density function of the output signal of the micromechanical accelerometer when the set of unknown signal elements is θ _i at time k under the assumption of H _i ;

Indicates the probability density function of the output signal of the micromechanical gyroscope when the set of unknown signal elements is θ _i at time k, assuming H _i ; $\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \}</span>$ $\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \}</span>$ Among them, exp{.} represents the exponential function of e; ||·|| represents the norm; σ2a and σ2ω represent the noise variance of the accelerometer and gyroscope, respectively. 5. the zero speed detection method based on Neyman-Pearson criterion as claimed in claim 1, is characterized in that, In step six, according to the formula: $L_g\left(z_{\mathrm{no}}\right)=\frac{\underset{k\&Element;{\mathrm{\&Omega;}}_{\mathrm{no}}}{\mathrm{\&Pi;}}p({\mathrm{the\; y}}_k^a;{\mathrm{\&theta;}}_1,h_1)p({\mathrm{the\; y}}_k^{\mathrm{\&omega;}};{\mathrm{\&theta;}}_1,h_1)}{\underset{k\&Element;{\mathrm{\&Omega;}}_{\mathrm{no}}}{\mathrm{\&Pi;}}p({\mathrm{the\; y}}_k^a;{\mathrm{\&theta;}}_0,h_0)p({\mathrm{the\; y}}_k^{\mathrm{\&omega;}};{\mathrm{\&theta;}}_0,h_0)}$ Obtain an extensive probability likelihood ratio test L _g (z _n ) for zero-speed detection of an individual soldier autonomous navigation system containing unknown elements; Among them, assuming that the H ₁ conditional signal s _k (θ) is completely unknown, the set of unknown elements is: ${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&equiv;</span><span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{<span\; class="notranslate">\; \}</span>}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ;</span>$ Under the condition of assuming H ₀ only the direction of the force vector is unknown, the set of unknown elements is: θ ₁ ≡ gu _n , where u _n ∈Ω _u , Ω _u ={u∈R ³ :‖u‖=1}; g is the local gravity vector;

Represents the probability density function of the output signal of the micromachined accelerometer when the set of unknown signal elements is θ ₁ under the assumption of H ₁ at time k;

Represents the probability density function of the output signal of the micromachined accelerometer when the set of unknown signal elements is θ ₀ under the assumption of H ₀ at time k;

Represents the probability density function of the output signal of the micromechanical gyroscope when the set of unknown signal elements is θ ₁ under the assumption of H ₁ at time k;

Represents the probability density function of the output signal of the micromechanical gyroscope when the set of unknown signal elements is θ ₀ under the assumption of H ₀ at time k. 6. the zero-speed detection method based on Neyman-Pearson criterion as claimed in claim 1, is characterized in that, in step 8, extensive probability likelihood ratio L _G (z _n ) is expressed as; ${\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ;</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ;</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}$ In the formula,

Indicates that under the assumption of H ₁ , the set of unknown signal elements is

The joint probability density function of the output information of the miniature inertial measurement unit;

Indicates that under the assumption of H ₀ , the set of unknown signal elements is The joint probability density function of the output information of the miniature inertial measurement unit. 7. the zero-speed detection method based on Neiman-Pearson criterion as claimed in claim 1, is characterized in that, in step 9, inequality is expressed as: $\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; g</span>}\frac{{\stackrel{<span\; class="notranslate">\; -</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\stackrel{<span\; class="notranslate">\; -</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}$ If the inequality is established, the zero-speed detection result of the individual soldier autonomous navigation system is static—H ₁ is true, otherwise, the zero-speed detection result is motion—H ₀ is true; in, ${\stackrel{-}{\mathrm{the\; y}}}_{\mathrm{no}}^a=\frac{1}{N}\underset{k\&Element;{\mathrm{\&Omega;}}_{\mathrm{no}}}{\mathrm{\&Sigma;}}{\mathrm{the\; y}}_k^a,$ $T\left(z_{\mathrm{no}}\right)=-\frac{2}{N}\ln L_G\left(z_{\mathrm{no}}\right),$ γ'=-(2/N)ln(γ), ln(.) means to seek the logarithm taking e as the base.

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