CN114037017B - Data fusion method based on error distribution fitting - Google Patents

Abstract

The invention discloses a data fusion method based on error distribution fitting, which mainly solves the problem of low accuracy of fusion of multiple groups of data in the prior art under the condition of inconsistent error distributions of different measurement data. The scheme includes: acquiring the measured ground test sequence and the flight test sequence of the radar receiver receiving the target, and calculating the difference between these two groups of test sequences to obtain error data; performing distribution fitting on the error data, and statistical distribution of the fitted error data, calculate its skewness and kurtosis to obtain the error data of the normal distribution; solve the unknown parameters of the normal distribution, and superimpose the normal distribution error data conforming to the unknown parameters after fitting to the ground test sequence to obtain the fused flight Test sequence; Kalman filtering is performed on the fused flight test sequence to improve the accuracy. The invention can judge the error distribution characteristics among multiple sets of measurement data, improve the accuracy of the fusion measurement data, and can be used for processing multi-sensor measurement data in communication.

Description

Data fusion method based on error distribution fitting

technical field

The invention belongs to the technical field of signal processing, and further relates to a data fusion method, which can be used for processing multi-sensor measurement data in communication.

Background technique

With the development of sensor measurement technology, multi-sensor data fusion technology has been widely used in both military and civil fields. The experimental data measured by a single sensor is difficult to reflect the complete information of the object to be measured, and in the experiment, due to the need to obtain accurate observation data of the object to be measured, many data fusion methods based on multi-sensors have appeared. There is also a corresponding data fusion method in the state of error distribution based on measurement data.

With the development and wide application of data distribution fitting technology, there is a certain error distribution in the data measured by multi-sensors, which will further generate unpredictable errors in the data fusion process and increase the error of fusion results. There are many ways to deal with measurement data errors. There are also corresponding error reduction methods for the reduction of errors in the process of data fusion.

Wei Lisheng et al. in "Using Data Fusion to Reduce Errors in Gyro Test Data Processing [J]. Tactical Guidance Technology, 2004, (2): 47-49. DOI: 10.3969/j.issn.1009-1300-B.2004.02 .012", a data fusion method based on adaptive weighting is proposed to minimize the variance of the measurement data, and this method is compared with the method based on multiple measurement de-averaging. Finally, it has better results in test data processing. However, since this method does not require any prior knowledge of the measurement data and needs to set the corresponding weights through the measurement data, the result has higher requirements for the weight setting.

Geng Feng, Zhu Xiaoping and others in "Target Tracking System Based on Fuzzy Multi-sensor Data Fusion [J]. Firepower and Command and Control, 2008, 33(3): 93-96.doi:10.3969/j.issn.1002-0640.2008 .03.026.", in order to overcome the limitations of a single sensor, a multi-sensor data fusion algorithm MSDF is introduced, which can not only reduce the noise of sensor measurements, but also eliminate invalid measurements in the estimation process. However, this method lacks target motion and sensor pre-statistical information included in the estimation process.

When the radar measurement target signal contains corresponding errors and the ground infield measurement target information also has certain errors, the above two methods will not only reduce the errors in the measurement process, but also increase the data fusion. Data error after data fusion.

SUMMARY OF THE INVENTION

The purpose of the present invention is to propose a data fusion method based on error distribution fitting in view of the above-mentioned shortcomings of the prior art, which is used to perform data fusion on sensor measurement data under different measurement conditions, reduce errors in the measurement process, and improve fusion. The accuracy of the data after.

To achieve the above purpose, the technical scheme of the present invention includes:

(1) Obtain the sequence σ(θ) that the radar receiver receives the target scattering as a function of the angle, where σ represents the scattering cross-sectional area of the target, and θ represents the illumination angle between the radar and the target;

(2) Measure the flight test data sequence σ ₁ (θ) and the ground test data sequence σ ₂ (θ) during the movement of the target, and calculate the difference Error _i (θ), i∈{1,…,i ,...,n} represents the ith scattering point on the target, and n represents the number of scattering points on the target;

(3) Calculate the skewness Skew(X) and the kurtosis Kurt(X) of the error data, use the skewness to measure the direction and degree of the error data distribution, and use the kurtosis to judge the distribution characteristics of the error data;

(4) Use the probability class method to estimate the parameters of the normally distributed error data obtained in (3):

看作随机变量，在随机变量被给定的条件下，设飞行试验数据σ₁(θ)和地面试验数据σ₂(θ)的总体误差x的条件分布为

由先验信息得出的先验分布为

从总体误差x的条件分布中抽取样本容量为n的样本Z＝(x₁,x₂,…,x_i,…,x_n)得到样本Z和未知参数

的联合概率密度函数

(4a) put the unknown parameters

As a random variable, under the condition that the random variable is given, the conditional distribution of the overall error x of the flight test data σ ₁ (θ) and the ground test data σ ₂ (θ) is

The prior distribution derived from the prior information is

Draw a sample Z=(x ₁ ,x ₂ ,..., _xi ,...,x _n ) from the conditional distribution of the overall error x to obtain the sample Z and unknown parameters

The joint probability density function of

的联合分布为：(4b) Using the Bayesian formula to obtain the sample Z and unknown parameters

The joint distribution of is:

和后验分布

得到样本Z的边缘密度函数m(Z)为：(4c) According to the joint probability density function

and the posterior distribution

The edge density function m(Z) of the sample Z is obtained as:

和边缘密度函数m(Z)得到后验分布

(4d) According to the joint distribution

and the edge density function m(Z) to get the posterior distribution

为关于未知参数

的似然函数；in,

for the unknown parameter

the likelihood function of ;

求解，得未知参数

为：(4e) According to the principle of maximum likelihood estimation, the likelihood function

Solve, get unknown parameters

for:

将误差数据Error(θ)的拟合结果叠加到地面试验数据，得到到融合后的RCS飞行试验粗序列Lock_i(θ)：(5) According to the parameters

The fitting result of the error data Error(θ) is superimposed on the ground test data, and the fused RCS flight test rough sequence Lock _i (θ) is obtained:

Lock _i (θ)=σ ₂ (θ)+histfit[(Error(θ))]

Among them, histfit means fitting the distribution data of Error(θ);

(6) Perform Kalman filtering and smoothing on the above-mentioned coarse sequence Lock(θ) in turn to obtain the final fused RCS flight test sequence newLock _i (θ):

newLock _i (θ)=AnewLock _(i-1) (θ)+BLock _i (θ)

Among them, newLock _i (θ) represents the optimal estimated value of Kalman filter at time i, newLock(i-1) is the optimal estimated value of the previous moment, A is the set state transition matrix, and B is a unit with a value of 1 matrix, Lock _i (θ) represents the RCS flight test coarse sequence.

Compared with the prior art, the present invention has the following advantages:

First, for the measurement data under different measurement conditions, the present invention obtains that the error distribution between the flight test sequence and the ground test sequence is a normal distribution according to the skewness and kurtosis, and is positive according to the distribution between the two. The state distribution is used to process the flight test sequence and the ground test sequence, which reduces the error of the two during the fusion process and improves the accuracy of the flight test sequence after fusion.

Second, the present invention aims at the characteristic that the error distribution between the flight test sequence and the ground test sequence is a normal distribution, first perform data fusion on the flight test sequence and the ground test sequence to obtain the RCS flight test rough sequence, and then further carry out the Karl Mann filtering can obtain the RCS flight test sequence with high accuracy, which can not only reduce the measurement error in the flight test sequence and the ground test sequence, but also reduce the error generated in the fusion process.

和后验分布

的乘积得到后验分布

可以大幅度减少参数估计过程中的计算量。Third, when the present invention uses the probability class estimation method to estimate the parameters of the error distribution characteristics, the joint probability density function is used to estimate the parameters of the error distribution.

and the posterior distribution

The product of the posterior distribution is obtained

The amount of computation in the parameter estimation process can be greatly reduced.

Description of drawings

Fig. 1 is the realization flow chart of the present invention;

Fig. 2 is the RCS angle sequence of the scattering cross section of the flight test target obtained by radar measurement;

Fig. 3 is the RCS angle sequence of the scattering cross section of the ground test target measured in a specific inner field;

Fig. 4 is the error distribution histogram of flight test sequence and ground test sequence in the present invention;

Fig. 5 is the RCS error distribution histogram obtained by fitting in the present invention;

Fig. 6 is the flight test RCS angle sequence obtained after fusion in the present invention;

FIG. 7 is an RCS angle sequence obtained by Kalman filtering in the present invention.

Detailed ways

The examples and effects of the present invention will be described in further detail below in conjunction with the accompanying drawings.

The working scenario of this example includes a flying target and a radar, and the radar is equipped with a transmitting antenna and a receiver.

Referring to Figure 1, this example is based on the data fusion method of error distribution fitting, and the implementation steps are as follows:

Step 1, obtain the flight test sequence and ground test sequence of the target.

The radar antenna transmits signals to track the flying target in the air, and the radar receiver receives the flight test sequence during the flight of the target. The representation is as follows:

The target ground test sequence obtained by the test measurement in the ground field is expressed as follows:

Among them, σ _1i represents the scattering cross-sectional area of the ith scattering point of the target in the flight test sequence, L _1i represents the distance between the ith scattering point of the flight test sequence and the radar, and σ _2i represents the ith scattering point of the target in the ground test sequence. The scattering cross-sectional area of the point, L _2i is the distance between the ith scattering point of the ground test sequence target and the radar, θ is the illumination angle between the radar and the target, i∈{1,…,n} is the scattering on the target The number of points, n represents a total of n scattering points on the target.

Step 2: Calculate the difference between the flight test sequence and the ground test sequence to obtain the error sequence of the two.

Error(θ) is obtained by calculating the difference between the values corresponding to the n scattering points on the flight test sequence and the ground test sequence:

Error(θ)=(σ ₁₁ (θ)-σ ₂₁ (θ))+…+(σ _1i (θ)-σ _2i (θ))+…(σ _1n (θ)+σ _2n (θ))

Among them, σ _1i (θ) represents the ith scattering point on the flight test sequence, σ _2i (θ) represents the ith scattering point on the ground test sequence, i∈{1,…,n}.

Step 3, solve the skewness and kurtosis of the error series.

3.1) Statistically distribute the error sequence Error(θ) to obtain a sequence X with mean μ and variance σ:

X～N _Error(θ) (μ,σ ² );

3.2) To solve the mean and variance of the sequence X, the formula is as follows:

Among them, Xi represents the _i -th data after statistical distribution, and n represents a total of n data after statistical distribution;

3.3) Calculate the skewness Skew(X) and the kurtosis Kurt(X) of the sequence X according to the mean μ and variance σ of the sequence X and the sequence X:

Step 4: Use skewness to measure the direction and degree of error data distribution, and use kurtosis to judge the distribution characteristics of error data.

4.1) Set the measurement threshold to 0, and use skewness to measure the direction and degree of error data distribution:

If the skewness of X is 0, it means that the direction and degree of the error data are centered;

If the skewness of X is greater than 0, it means that the direction and degree of the error data is a right-skewed distribution;

If the skewness of X is less than 0, it means that the direction and degree of the error data are left skewed distribution.

4.2) Set the judgment threshold to 3, and use the kurtosis to judge the distribution characteristics of the error data:

If the kurtosis Kurt(X) of X is 3, it means that the distribution characteristics of the error data are normal distribution;

If the kurtosis Kurt(X) of X is greater than 3, it means that the peak value of the curve of the error data is greater than the normal distribution;

If the kurtosis Kurt(X) of X is less than 3, it means that the peak value of the curve of the error data is smaller than the normal distribution.

Step 5, use the probability method to estimate the unknown parameters that conform to the normal distribution.

看作随机变量，在随机变量被给定的条件下，设飞行试验数据σ₁(θ)和地面试验数据σ₂(θ)的总体误差x的条件分布为

由先验信息得出的先验分布为

5.1) Put unknown parameters

As a random variable, under the condition that the random variable is given, let the conditional distribution of the overall error x of the flight test data σ ₁ (θ) and the ground test data σ ₂ (θ) be

The prior distribution derived from the prior information is

的联合概率密度函数

5.2) From the conditional distribution of the overall error x, extract a sample Z=(x ₁ ,x ₂ ,..., _xi ,...,x _n ) with a sample size of n to obtain the sample Z and unknown parameters

The joint probability density function of

Among them, x _i represents the ith sample in sample Z;

和先验分布

利用贝叶斯理论公式得样本Z及未知参数

的联合分布为：5.3) According to the above joint probability density function

and the prior distribution

Using the Bayesian formula to obtain the sample Z and unknown parameters

The joint distribution of is:

和后验分布

得到样本Z的边缘密度函数m(Z)为：5.4) According to the joint probability density function

and the posterior distribution

The edge density function m(Z) of the sample Z is obtained as:

和边缘密度函数m(Z)得后验分布

5.5) by the above joint distribution

and the edge density function m(Z) to get the posterior distribution

为关于未知参数

的似然函数，根据极大似然估计原理对似然函数

求解，得未知参数

in,

for the unknown parameter

The likelihood function of , according to the principle of maximum likelihood estimation, the likelihood function

Solve, get unknown parameters

Step 6, superimpose the sequence data of error distribution characteristics on the ground test sequence to obtain the fused flight test sequence Lock(θ) with high accuracy:

Lock(θ)=σ ₂ (θ)+histfit[(Error(θ))]

Among them, histfit represents fitting Error(θ).

Step 7: Kalman filtering is performed on the flight test RCS data obtained after fusion to reduce errors in the fusion process. The filtering process is expressed as follows:

newLock _(i|i-1) (θ)=AnewLock _(i-1|i-1) (θ)+BLock _i (θ)

Among them, newLock(i-1|i-1) represents the optimal estimated value of Kalman filtering at the previous moment, newLock(i|i-1) represents the optimal estimated value of filtering at the current moment, and A is the set state transition matrix , B is a matrix whose value is 1.

The effect of the present invention is further described below in conjunction with simulation experiments:

1. Simulation experiment environment

Experimental environment: MATLAB R2016b, 11th Gen Intel(R)Core(TM)i7-11800H@2.30GHz2.30GHz, Windows 10.

Simulation software MATLAB R2016b, operating system Windows 10, computer processor 11th Gen Intel(R)Core(TM)i7-11800H@2.30GHz,

The flight test sequence used in the simulation is shown in Figure 2, and the ground test sequence is shown in Figure 3.

2. Simulation experiment content:

In simulation experiment 1, in the above experimental environment, the difference between the flight test sequence and the ground test sequence is calculated, and the distribution histogram of the error sequence is drawn. The results are shown in Figure 4. It can be seen from Figure 4 that the histogram data distribution of the error series basically conforms to the distribution state of the normal distribution, and its distribution state is that more data are centered, and the data on the left and right sides decrease in turn.

In simulation experiment 2, the error sequences of the flight test sequence and the ground test sequence are fitted, and a normal distribution histogram that conforms to the error distribution characteristics is obtained. The results are shown in Figure 5. It can be seen from Figure 5 that the fitted curve conforms to the normal distribution characteristics, indicating that the error sequence distribution characteristics of the flight test sequence and the ground test sequence are normal distribution characteristics.

In simulation experiment 3, the fitted normal distribution histogram is fused with the ground test sequence to obtain the fused flight test sequence, as shown in Figure 6. It can be seen from Figure 6 that the fused flight test sequence is compared with that before fusion. The accuracy of the flight test sequence and ground test sequence has been significantly improved.

In simulation experiment 4, Kalman filtering is performed on the fused flight test sequence to obtain a flight test sequence with high accuracy, as shown in Figure 7. It can be seen from Figure 7 that the accuracy of the flight test sequence after Kalman filtering has been further improved compared to the fused flight test sequence.

The above experimental results show that:

First, the data fusion method based on error distribution fitting proposed by the present invention has good fitting error distribution characteristics and fusion performance. In practice, statistical knowledge can be used to obtain the set of RCS sequences to the ground with higher accuracy obtained by infield measurements, and the multiple sets of RCS sequences obtained by multiple radar measurements to obtain the target, and further perform error distribution fitting and Data fusion to obtain a flight test sequence with high accuracy.

Second, the present invention not only performs mid-fit for error sequences conforming to normal distribution, but also fits error sequences conforming to other distribution characteristics.

The above simulation analyses and proves the correctness and effectiveness of the method proposed in the present invention.

The parts of the present invention that are not described in detail belong to the common knowledge of those skilled in the art.

The above are only preferred embodiments of the present invention, and are not intended to limit the present invention. Obviously, for those skilled in the art, after understanding the content and principles of the present invention, they may not deviate from the principles of the present invention, In the case of the structure, various corrections and changes in form and details are made, but these corrections and changes based on the idea of the present invention are still within the scope of protection of the claims of the present invention.

Claims (7)

1. a data fusion method based on error distribution fitting, is characterized in that, comprises: (1) Obtain the sequence σ(θ) that the radar receiver receives the target scattering as a function of the angle, where σ represents the scattering cross-sectional area of the target, and θ represents the illumination angle between the radar and the target; (2) Measure the flight test data sequence σ ₁ (θ) and the ground test data sequence σ ₂ (θ) during the movement of the target, and calculate the difference Error _i (θ), i∈{1,…,i ,...,n} represents the ith scattering point on the target, and n represents the number of scattering points on the target; (3) Calculate the skewness Skew(X) and the kurtosis Kurt(X) of the error data, use the skewness to measure the direction and degree of the error data distribution, and use the kurtosis to judge the distribution characteristics of the error data; (4) Use the probability class method to estimate the parameters of the normally distributed error data obtained in (3): (4a) put the unknown parameters

As a random variable, under the condition that the random variable is given, the conditional distribution of the overall error x of the flight test data σ ₁ (θ) and the ground test data σ ₂ (θ) is

The prior distribution derived from the prior information is

Draw a sample Z=(x ₁ ,x ₂ ,..., _xi ,...,x _n ) from the conditional distribution of the overall error x to obtain the sample Z and unknown parameters

The joint probability density function of

(4b) Using the Bayesian formula to obtain the sample Z and unknown parameters

The joint distribution of is:

(4c) According to the joint probability density function

and the prior distribution

The edge density function m(Z) of the sample Z is obtained as:

(4d) According to the joint distribution

and the edge density function m(Z) to get the posterior distribution

in,

for the unknown parameter

the likelihood function of ; (4e) According to the principle of maximum likelihood estimation, the likelihood function

Solve, get unknown parameters

for:

(5) According to the parameters

The fitting result of the error data Error(θ) is superimposed on the ground test data, and the fused flight test rough sequence Lock _i (θ) is obtained: Lock _i (θ)=σ ₂ (θ)+histfit[(Error(θ))] Among them, histfit means fitting the distribution data of Error(θ); (6) Perform Kalman filtering and smoothing on the above-mentioned coarse sequence Lock(θ) in turn to obtain the final fusion flight test sequence newLock _i (θ): newLock _i (θ)=AnewLock _(i-1) (θ)+BLock _i (θ) Among them, newLock _i (θ) represents the optimal estimated value of Kalman filter at time i, newLock(i-1) is the optimal estimated value of the previous moment, A is the set state transition matrix, and B is a unit with a value of 1 matrix, Lock _i (θ) represents the flight test coarse sequence. 2. method according to claim 1, is characterized in that: (2) in flight test data sequence σ ₁ (θ) and ground test data sequence σ ₂ (θ), respectively represent as follows:

Among them, a _l represents the coefficient of the l-th item of the flight test data sequence σ ₁ (θ), b _l represents the coefficient of the l-th item of the ground test data sequence σ ₂ (θ), and l∈{0,1,…,n} , σ _1i (θ) represents the ith scattering point on the flight test, σ _2i (θ) represents the ith scattering point on the ground test, i∈{1,…,n}. 3. method according to claim 1 is characterized in that: (2) the difference Error (θ) of flight test data sequence σ ₁ (θ) and ground test data sequence σ ₂ (θ) is expressed as follows: Error(θ)=(σ ₁₁ (θ)-σ ₂₁ (θ))+…+(σ _1i (θ)-σ _2i (θ))+…(σ _1n (θ)+σ _2n (θ)) Among them, σ _1i (θ) represents the ith scattering point on the flight test sequence, σ _2i (θ) represents the ith scattering point on the ground test sequence, i∈{1,…,i,…,n}. 4. method according to claim 1 is characterized in that: in (3), the skewness Skew (X) and kurtosis Kurt (X) of calculating error data, formula is as follows:

Among them, X represents the error data Error(θ) after statistical distribution, and μ and σ represent the mean and variance of Error(θ), respectively. 5. method according to claim 1 is characterized in that: in described (3), utilize kurtosis to judge the distribution characteristic of error data, is to set judgment threshold value as 3, by combining the kurtosis of X Kurt (X) with The threshold comparison results in the judgment result: If the kurtosis Kurt(X) of X is 3, it means that the distribution characteristics of the error data are normal distribution; If the kurtosis Kurt(X) of X is greater than 3, it means that the peak value of the curve of the error data is greater than the normal distribution; If the kurtosis Kurt(X) of X is less than 3, it means that the peak value of the curve of the error data is smaller than the normal distribution. 6. method according to claim 1 is characterized in that: sample Z and unknown parameter obtained in (4a)

The joint probability density function of

It is expressed as follows:

Among them, Π is the symbol of multiplication, x _i represents the i-th individual in the sample Z,

Indicates an unknown parameter

Likelihood function of . 7. The method according to claim 1, wherein: histfit[(Error(θ))] in (5) is expressed as follows: histfit[(Error(θ))]=c ₀ +c ₁ histfit[(Error ₁ (θ))]+…+c _l (histfit[(Error _i (θ))]) ⁱ +…+c _n (histfit [(Error _n (θ))]) ⁿ Among them, c _l represents the coefficient of the lth item in the fitted error data histfit[(Error(θ))], l∈{0,1,…,n}, histfit[(Error _i (θ))] represents The i-th fitted error data i∈{1,…,n}.

Images