CN114624688B - Tracking and positioning method based on multi-sensor combination - Google Patents

Abstract

The invention belongs to the technical field of tracking and positioning, and particularly relates to a tracking and positioning method based on multi-sensor combination. According to the method, smooth filtering is carried out on the measured data, and then the joint positioning of multi-sensor confidence fusion is carried out, so that the generation of a required target is effectively avoided. The whole system is based on a Bayesian framework, and the information transmission is based on a probability description form, so that the proposed scheme has good performance, environmental adaptability and robustness and can meet the design requirements in engineering.

Description

A tracking and positioning method based on multi-sensor combination

Technical Field

The invention belongs to the technical field of tracking and positioning, and specifically relates to a tracking and positioning method based on multi-sensor combination.

Background Art

Traditional radiation source tracking mainly involves sorting and identifying targets in the reconnaissance area, then performing frequency association, and then positioning and tracking. This process often involves data association and hard judgment in the initial sorting and identification process. The results obtained in this way are often irreparable in the next stage, and as the dimensions of the target and the measurement dimension increase, the amount of calculation will increase exponentially, making it difficult to effectively track multiple targets in real time in complex scenarios. Therefore, this traditional method is to first process the target into a single target and then track it.

In recent years, tracking algorithms based on the framework of random finite set theory have received widespread attention. Without considering the correlation between measurement and target, it can quickly realize multi-target tracking with an unknown number of targets. Among them, the probability hypothesis density (PHD) filter is widely used in multi-target tracking applications because of its low computational complexity and easy implementation. And the tracking algorithm is mainly used for smoothing its measurement information (direction of arrival (DOA)) to reduce the impact of its clutter on it. Based on the above smoothed results, the target position is estimated by joint positioning of multiple sensors. Tracking by this smoothing-then-positioning method avoids hard decisions, and can improve the adaptability and robustness of the algorithm to complex scenes, and improve the tracking performance of multiple targets.

Summary of the invention

In view of the above problems, the present invention proposes a multi-sensor joint tracking and positioning algorithm to realize the multi-radiation source tracking problem of an unknown number of radiation sources when the initial position of the target is unknown. The algorithm has good performance, adaptability to the environment and robustness, and can meet the design requirements in the project.

The technical solution adopted by the present invention is:

The present invention adopts the method of smoothing and filtering the measured data first, and then performing joint positioning of multi-sensor confidence fusion, which effectively avoids the generation of the required target. The whole system is based on the Bayesian framework, and its information transmission is based on the probabilistic description form, so the proposed scheme has strong robustness and scalability.

已知k时刻，由观测站i接收信号提取出的有关目标j的状态向量为

其中，1≤k≤K，

和

分别为目标j相对观测站i的到达角度及到达角度加速度，

为观测站i测得的目标j的信号频率，对应的置信度为

设k时刻目标j的坐标为

观测站i的坐标为(x_i,y_i)，定义：Assume the total observation sampling time K, the total number of observation stations M, the actual number of targets N _k , and the total number of targets detected by the i-th observation station is

It is known that at time k, the state vector of target j extracted from the signal received by observation station i is

Among them, 1≤k≤K,

and

are the arrival angle and arrival angle acceleration of target j relative to observation station i,

is the signal frequency of target j measured by observation station i, and the corresponding confidence level is

Assume the coordinates of target j at time k are

The coordinates of observation station i are (x _i ,y _i ), and the definition is:

的高斯分布，1≤i≤M其特征在于，跟踪定位方法包括以下步骤：Where n _i is the angle measurement error of the i-th observation station, which has zero mean and variance is

Gaussian distribution, 1≤i≤M, characterized in that the tracking and positioning method comprises the following steps:

S1. Use PHD filtering algorithm to smooth the measured data, including:

S11. Define that the target and the observation station are both located on the XY plane. It is known that the observation quantity obtained by observation station i at time k about target j is

S12, using a mixed Gaussian probability hypothesis density filter to smooth the measured data, the steps are as follows:

则观测站i的目标后验强度

为高斯混合形式：S121. Define the total number of targets at observation station i at time k-1 as

Then the target posterior intensity of observation station i is

In the form of a Gaussian mixture:

定义了均值为m，方差为P的高斯函数。

分别表示了相应目标j的置信度，状态向量和协方差矩阵。in

A Gaussian function with mean m and variance P is defined.

They represent the confidence, state vector and covariance matrix of the corresponding target j respectively.

S122. The predicted multi-target intensity function of observation station i at time k also conforms to the Gaussian mixture form:

The expression is divided into two parts, namely the posterior strength of the survival target

其中p_S,k为目标存活概率，F_k|k-1为状态转移矩阵，Q_k-1为过程噪声协方差矩阵；and the posterior strength of the new target

Where p _S,k is the target survival probability, F _k|k-1 is the state transition matrix, and Q _k-1 is the process noise covariance matrix;

可得观测站i在k时刻的更新后验强度，同样是高斯混合的：S123, based on the predicted PHD function, combined with the measured value obtained at the current moment

The updated posterior intensity of observation station i at time k is also a Gaussian mixture:

Where H _k is the observation matrix, R _k is the observation noise covariance matrix, p _D,k is the target detection probability, and κ _k (z) is the clutter probability density;

S13, after one iteration, the output target state parameter is

S2. Target positioning based on ML algorithm and frequency association, including:

S21. Define that the target and the observation station are located on the XY plane. The position coordinates of the observation station are known (x _i , y _i ), 1≤i≤M. The observation azimuths of all observation stations with measurement errors are

S22. Divide the target plane into a grid of Q×R range, each grid point represents a position coordinate (p _q ,pr ) in the target plane, where q＝1,2,...,Q _, r＝1,2,...,R, traverse each grid point in the grid plane, and calculate the azimuth of the point (p _q , _pr ) relative to each observation station:

之间的误差e_k ^i,(q,r)：S23, calculate the azimuth _αki ^,(q,r) of each search point ( _pq , _pr ) relative to the observation station and all azimuths observed by the observation station

The error between _ek ^i,(q,r) :

in:

Assign weights to the azimuths of the search points relative to each observation station:

取得最小值的j，p_D,k是目标检测概率。Among them, j _min is such that

The j,p _D,k that achieves the minimum value is the target detection probability.

S24. Calculate the cost matrix T(q,r) consisting of the total error obtained from each search:

Where: q＝1,2,...,Q, r＝1,2,...,R,;

Calculate the weight matrix C composed of the total weights obtained from each search, and the matrix elements are:

where c _k ^i,(q,r) is the weight of the search grid point (p _q , _pr ) at time k relative to the i-th observation station

表示第k时刻估计出的目标总数；S25, traverse each grid point in the grid plane, and obtain T(q,r), q＝1,2,...,Q,r＝1,2,...,R, that is, obtain the pseudo spectrum of the target position, combine the weight matrix T, and obtain multiple target estimated positions through the peak value of the pseudo spectrum of the target position

represents the total number of targets estimated at the kth moment;

S3. Based on the estimated target coordinates, the frequency association algorithm is used to eliminate the false points in the multi-target positioning, so as to screen out the real target coordinates, including:

相对各个观测站的方位角，得出对应的频率：S31. Estimated coordinates based on target

Relative to the azimuth of each observation station, the corresponding frequency is obtained:

取得最小值的j；Among them, j _min is such that

Get the minimum value of j;

满足：任意两个f_k ^i,j'之间的差值均小于设定值，则判

为目标真实坐标；否则，为虚假坐标。S32, if the target coordinates are estimated

If the difference between any two f _k ^i,j' is less than the set value, then

is the real coordinate of the target; otherwise, it is a false coordinate.

The beneficial effect of the present invention is that the present invention can solve the joint tracking and positioning of multiple radiation sources under unknown radiation sources, and the method has strong robustness and good effect.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 shows the original sensor position and the target's actual trajectory;

Figure 2 is a confidence map of the grid.

Figure 3 is a diagram of target position estimation.

Figure 4 is a diagram of target number estimation.

Figure 5 shows the target OSPA error.

DETAILED DESCRIPTION

The present invention is described in detail below in conjunction with embodiments:

Example

This example uses Matlab to verify the above multi-sensor joint tracking and positioning algorithm. For simplicity, the following assumptions are made for the algorithm model:

The effectiveness of the present invention is explained below with reference to the accompanying drawings and simulation examples.

Simulation conditions and parameters

每个目标由位置(p_x,k,p_y,k)、速度

及频率f_k确定。而量测是目标的频率和角度DOA。二维平面内单个目标的状态方程和量测方程分别为x_k+1＝F_kx_k+Gw_k，y_k+1＝h(x_k+1)+v_k+1，其中w_k和v_k分别为过程噪声和量测噪声。他们是零均值,协方差分别为Q_k和R_k的高斯噪声向量。Simulation environment: For the sake of illustration, consider a representative two-dimensional scenario. In the cluttered area of the surveillance area [-1000, 1000] × [-1000, 1000] (m), three reconnaissance sensors located at [-3000, -7000], [5000, -7000], and [9000, -7000] are used to perceive an unknown number of targets that change over time. The target state vector is

Each target consists of a position (p _x,k , p _y,k ), a velocity

and frequency f _k . The measurement is the frequency and angle DOA of the target. The state equation and measurement equation of a single target in a two-dimensional plane are x _k+1 = F _k x _k + Gw _k , y _k+1 = h(x _k+1 )+v _k+1 , where w _k and v _k are process noise and measurement noise, respectively. They are Gaussian noise vectors with zero mean and covariances of Q _k and R _k , respectively.

The survival probability of each target p _S,k = 0.99, and the state transfer matrix and state noise matrix of its linear Gaussian motion state equation are as follows:

△ = 1s is the sampling period, the detection probability of each target p _D,k = 0.98, R _k = [(π/180)(rad)] ² is the measurement noise variance. The measurement equation is:

The four targets are born at 1s, 1s, 10s, and 20s respectively. The targets appear from four fixed points. The strength of the target birth model Poisson RFS Γ _k is as follows:

in,

P _γ = diag[1,2,1] ²

和

附近的自然新生。For simulation

and

Natural rebirth nearby.

Simulation content and result analysis

It can be seen from the grid confidence map in Figure 2 that in the process of cross-pointing, the fusion confidence can accurately locate the correct radiation source, as shown in the target position map in Figure 3. Relatively speaking, the algorithm can eventually obtain the trajectory of radiation source estimation through time accumulation. Figures 4 and 5 show that both its detection performance and OSPA performance meet the requirements. According to the above description, the proposed algorithm has strong robustness and adaptability to complex environments.

Claims (1)

1. A tracking and positioning method based on multi-sensor combination sets total observation sampling time K, total number of observation stations M and actual target number N _k The total number of the targets detected by the ith observation station is

Knowing the time k, the status vector associated with the target j extracted by the signal received by the observation station i is->

Wherein K is more than or equal to 1 and less than or equal to K>

And &>

Based on the angle of arrival and the acceleration of the angle of arrival of the target j relative to the observation station i>

For the signal frequency of the target j measured at the observation station i, the corresponding confidence is >>

Let the coordinate of the target j at time k be->

The coordinate of observation station i is (x) _i ,y _i ) Defining:

wherein n is _i For the angle measurement error of the ith observation station, the mean value is obeyed, and the variance is

I is more than or equal to 1 and less than or equal to M; the method is characterized by comprising the following steps:

s1, smoothing measured data by adopting a PHD filtering algorithm, which specifically comprises the following steps:

s11, defining that the target and the observation station are positioned on an XY plane, and knowing that the observation station i at the moment k acquires the observed quantity of the target j

S12, smoothing the measured data by using a Gaussian mixture probability hypothesis density filter, and the steps are as follows:

s121, defining the total number of targets of observation station i at the moment k-1 as

The posterior intensity of the target of observation station i

In the form of a mixture of gaussians:

wherein

Defines a Gaussian function with mean m and variance P>

Respectively representing the confidence coefficient, the state vector and the covariance matrix of the corresponding target j;

s122, defining a multi-target intensity function of the observation station i at the k moment to be in a Gaussian mixture form:

the expression is divided into two parts, namely the posterior intensity of the survival target

And posterior intensity of newborn target

Wherein p is _S,k To target survival probability, F _k|k-1 Being a state transition matrix, Q _k-1 Is a process noise covariance matrix;

s123, according to the predicted PHD function, combining the measurement value obtained at the current moment

The updated posterior strength of observation station i at time k can be obtained,also gaussian mixed: />

In the formula H _k To observe the matrix, R _k To observe the noise covariance matrix, p _D,k Is the target detection probability, κ _k (z) is the clutter probability density;

s13, outputting the target state parameter after one iteration to be

S2, positioning the target according to the ML algorithm and the frequency correlation, and specifically comprising the following steps:

s21, defining that the target and the observation station are positioned on an XY plane, and knowing the position coordinate (x) of the observation station _i ,y _i ) I is more than or equal to 1 and less than or equal to M, and all observation azimuth angles containing measurement errors of all observation stations are

S22, dividing the target plane into grids of a Q multiplied by R range, wherein each grid point represents one position coordinate (p) in the target plane _q ,p _r ) Where Q =1,2,., Q, R =1,2,.., R, traverses each grid point in the grid plane, calculates a point (p) _q ,p _r ) Azimuth angle with respect to each observation station:

s23, calculating each search point (p) _q ,p _r ) Azimuth angle alpha relative to observation station _k ^i,(q,r) All azimuth angles observed by the observation station

Error e between _k ^i,(q,r) ：

Wherein: j =1,2, \ 8230;,

and weighting the azimuth angles of the search points relative to each observation station:

wherein j is _min Is that make

Taking the minimum value of j, p _D,k Is the target detection probability;

s24, calculating a cost matrix T (q, r) consisting of total errors obtained by each search:

wherein: q =1,2,. Wherein Q, R =1,2,. Wherein R;

calculating a weight matrix C consisting of the total weights obtained by each search, wherein the matrix elements are as follows:

wherein c is _k ^i,(q,r) Searching for a grid point (p) for time k _q ,p _r ) A weight relative to an ith observation station;

s25, traversing each grid point in the grid plane to obtain T (Q, R), wherein Q =1,2, is, Q, R =1,2, R, namely, obtaining a pseudo spectrum of the position of the target, and obtaining a plurality of target estimated positions through the peak value of the pseudo spectrum of the target position by combining the weight matrix T

Representing the estimated target total number at the kth moment;

s3, based on the target estimated coordinates, eliminating false points in multi-target positioning by adopting a frequency correlation algorithm, thereby screening out real target coordinates, and specifically comprising the following steps:

s31, estimating coordinates based on target

And obtaining corresponding frequency according to the azimuth angle of each observation station:

wherein j is _min Is that make

Obtaining j of the minimum value;

s32, if the target is estimated to be the coordinate

Satisfies the following conditions: any two f _k ^i,j' If the difference values are less than the set value, then the judgment is made>

The target real coordinate is taken as the target real coordinate; otherwise, it is a false coordinate. />

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