CN111487612A - A CPD-Based Robust Correlation Method for Radar/ESM Tracks in Different Locations - Google Patents

Abstract

The invention belongs to a track correlation technology in the field of target tracking, and provides a track robust correlation method based on Coherent Point Drift (CPD) aiming at the problem of track correlation of a radar and an ESM (automatic position sensing) sensor which are configured in different places under the condition of system deviation. And considering the influence of system deviation on the radar and ESM parameter tracks, describing the mapping relation between homologous track points of the radar and the ESM by using a nonlinear transformation function, and modeling the mapping relation as a non-rigid registration problem. And carrying out batch normalization processing on the target point sets of the radar and the ESM under the modified polar coordinates, and then estimating a displacement function in the nonlinear transformation function by using a CPD (compact peripheral component interconnect) method to obtain a point set after registration. And finally, obtaining a radar/ESM track robust correlation result by using global optimization and hypothesis testing, wherein the radar/ESM track robust correlation result is suitable for the condition that the distance between a radar and an ESM is long, and the correlation effect on a dense target is good.

Description

A CPD-Based Robust Correlation Method for Radar/ESM Tracks in Different Locations

technical field

The invention belongs to the track correlation technology in the field of target tracking, and provides a track correlation problem based on coherent point drift (Coherent Point Drift, CPD) for the problem of track correlation between radars and ESM sensors configured in different places under the condition of system deviation. Robust correlation method.

Background technique

ESM is a commonly used passive sensor, which can provide target attribute information and azimuth angle measurement. It has the advantages of long detection range, good concealment, and strong target recognition ability. However, for multi-target scenarios, the measurement of a single ESM is difficult to ensure the observability of all targets. It is usually necessary to combine active sensors (such as radar) systems to complement each other's advantages and provide a more complete and clear battlefield situation for battlefield command. The track correlation algorithm of EMS is very necessary.

The invention aims to realize the radar/ESM track robust correlation under the remote configuration by using the CPD algorithm, which is suitable for the situation where the distance between the radar and the ESM is relatively long, and the correlation effect on dense targets is better.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a method of track robustness correlation based on coherent point drift for the track association problem of radar/ESM configured in different places under the condition of system deviation. Considering the influence of the system deviation on the radar and ESM parameter tracks, a nonlinear transformation function is used to describe the mapping relationship between the homologous track points of the radar and the ESM, and it is modeled as a non-rigid registration problem. Batch normalize the target point set of radar and ESM under Modified Polar Coordinate (MPC), and then use the CPD algorithm to estimate the displacement function in the nonlinear transformation function to obtain the registered point set. Finally, the final radar/ESM track robust correlation results are obtained using global optimization and hypothesis testing.

The invention is applicable to the problem of track correlation of radar/ESM sensors configured in different places. The invention includes the following steps:

1 Problem description

和

第n个目标的位置和速度为p_tn＝[x_tn y_tn]^T和

考虑系统误差和随机误差，雷达量测可建模为Assume that there are two platforms configured in different places in a two-dimensional scene at a certain moment, respectively equipped with radar and ESM to observe the target. The radar and ESM are located at p _r = [x _r y _r ] ^T and p _e = [x _e y _e ] ^T , respectively, with velocities of

and

The position and velocity of the n-th target are p _tn = [x _tn y _tn ] ^T and

Considering systematic and random errors, radar measurements can be modeled as

表示第n个目标到雷达的径向距离，

表示第n个目标真实方位角量测，Δρ和Δθ_r分别表示雷达径向距离和方位角量测的系统误差，δρ和δθ_r表示量测的随机误差。相似地，ESM量测可以建模为in,

represents the radial distance from the nth target to the radar,

Represents the true azimuth measurement of the nth target, Δρ and Δθ _r represent the systematic error of the radar radial distance and azimuth measurement, respectively, and δρ and δθ _r represent the random error of the measurement. Similarly, ESM measurements can be modeled as

表示第n个目标到ESM的方位角量测，Δθ_e和δθ_e分别表示方位角量测的系统偏差和随机误差。in,

represents the azimuth measurement from the nth target to the ESM, and Δθ _e and δθ _e represent the systematic deviation and random error of the azimuth measurement, respectively.

ESM对目标采用MPCEKF滤波算法，结果表示为{Y_en,P_en}，其中，

θ为方位角，

为距离变化率和距离之比(Inverse-Time-To-Go,ITTG)，

为方位角变化率，

为径向距离的逆。The radar uses the traditional Extended Kalman Filter (EKF) to estimate the target state, and sends the filtering results of each target and its own motion states _{pr and v r to} the fusion center, where {X _rn , P' _rn } is The result of the radar's filtering on the target in its local coordinate system

ESM uses the MPCEKF filtering algorithm for the target, and the result is expressed as {Y _en ,P _en }, where,

θ is the azimuth angle,

is the ratio of distance change rate and distance (Inverse-Time-To-Go, ITTG),

is the rate of change of the azimuth angle,

is the inverse of the radial distance.

2 Influence of System Deviation on Track Association

Assuming that the time alignment of the filtering results has been completed, the coordinate system is established with the ESM as the fusion center, and the radar and the ESM move in formation at a distance of L. The schematic diagram of the scene at a certain moment is shown in Figure 1. Convert {X _rn , P′ _rn } to the local MPC of ESM to get {Y _rn , P _rn }, because the first three variables under MPC are decoupled from the fourth variable, and the fourth variable is not considerable, so only the first three variables are considered, where

表示状态向量

的第i个元素，n＝1,2,…,N。in,

Represents a state vector

The ith element of , n=1,2,...,N.

Ignoring the influence of the estimated error after filtering, the filtering result X _rn under the condition of systematic error is:

Substituting equation (7) into equation (4), we can get

Consider the point sets Y _r ={Y _rn , _n =1,2,...,N} and Ye ={Y _em ,m=1,2,...,M} in the MPC parameter space, where the number of radiation sources M Possibly more than the number N of radar targets. Looking at Equation (8), it can be known that Y _r is a nonlinear transformation of Y _e , and the transformation parameters vary according to different targets. For homologous data points, the transformation relation Γ can be modeled as the sum of the origin set and its displacement function.

Y _r =Γ(Y _e )=Y _e +v(Y _e ) (9)

3 Non-rigid point set registration method

Taking Y _e as the center of the Gaussian Mixture Model (GMM), and considering Y _r as the data sample generated by the GMM, the probability density function of the GMM is

||·||表示欧几里得距离。方位角之差的范围为-π＜<θ_r-θ_e>≤π，使用余弦值计算角度之差where D is the dimension of the data points in the point set, σ ² is the isotropic covariance,

||·|| represents the Euclidean distance. The range of the azimuth difference is -π<<θ _r -θ _e >≤π, and the cosine value is used to calculate the angle difference

<θ _r -θ _e >=arccos(cosθ _r cosθ _e +sinθ _r sinθ _e ) (12)

和

中由于存在微分项，其在参数空间上的尺度远小于θ。因此，直接使用欧氏距离度量容易使尺度小的维度淹没在欧氏距离中，无法有效表征数据点在该维度上的差异。关联算法中通常使用马氏距离代替欧氏距离，但由于存在系统偏差和异地配置问题，导致同源目标的滤波结果在参数空间上存在较大偏差，使得其马氏距离较大，GMM的概率密度极小，无法计算，因此用批归一化(Batch Normalization，BN)对参数空间中数据点的每个维度进行预处理：In fact, for the filtering results in the parameter space, the scales of different parameter dimensions are not the same, such as

and

Due to the existence of a differential term in , its scale in the parameter space is much smaller than θ. Therefore, directly using the Euclidean distance metric can easily drown the dimension with small scale in the Euclidean distance, and cannot effectively characterize the difference of data points in this dimension. The Mahalanobis distance is usually used instead of the Euclidean distance in the association algorithm. However, due to the existence of systematic deviations and different configuration problems, the filtering results of the homologous targets have a large deviation in the parameter space, which makes the Mahalanobis distance larger and the probability of GMM. The density is too small to be calculated, so batch normalization (BN) is used to preprocess each dimension of the data points in the parameter space:

和

分别为不同维度上的均值和标准差。通过归一化，一方面可以提高使用欧氏距离时测量数据点相关性的能力，一方面可以改进收敛速度和配准精度。Among them, X _norm is the normalized data,

and

are the mean and standard deviation in different dimensions, respectively. Through normalization, on the one hand, the ability to measure the correlation of data points when using Euclidean distance can be improved, and on the other hand, the convergence speed and registration accuracy can be improved.

Assuming that the state estimates of the targets are independent and identically distributed, the unknown parameters v and σ ² can be estimated by minimizing the negative logarithm of the likelihood function

where φ(v) is the regularization term, and λ represents the trade-off factor between the likelihood function fit and the regularization term. The CPD method gives the optimal displacement function, and uses the maximum expectation method to solve the unknown variables to achieve non-rigid registration. Then, using the registered point set Z _e ={Z _en =Γ(Y _en )} to calculate the posterior probability, which is used to characterize the relationship between the point sets. However, directly selecting the correlation point pair with the largest posterior probability as the correlation result ignores the constraints in the track correlation problem, that is, a single radar target may carry multiple radiator targets, while a single ESM target corresponds to only one radar target. In addition, the posterior probability only uses the positional relationship of the data points, and does not consider each data point as the estimated value of the filter in the parameter space, and there is a certain estimation error. To sum up, we can use the registered point set Z _e and the radar point set Y _r in the parameter space to construct the statistic μ _nm

Among them, P _em and P _rn are the normalized estimated covariance matrices

表示归一化后矩阵中的元素，注意到由于非刚性转换定义为在原数据点上的平移，因此，点集Z_e中的数据点的协方差矩阵与Y_e相同。Among them, P ^(i,j) represents the (i,j)th element in the covariance matrix,

represents the elements in the normalized matrix, noting that since the non-rigid transformation is defined as a translation on the original data point, the _covariance matrix of the data points in the point set _Ze is the same as Ye.

The hypothesis testing problem is constructed as follows:

H ₀ : The track of the radar and ESM comes from the same target;

H ₁ : The radar and ESM tracks are from different targets.

α为显著性水平，令α＝0.9。It is easy to know that μ _nm obeys the chi-square distribution with the degree of freedom d, and γ is an appropriate threshold.

α is the significance level, let α=0.9.

Finally, based on the global optimal correlation decision method, the preliminary correlation results of the radar/ESM track are solved, and the global optimization objective function is constructed as

Among them, s _nm is a binary variable, and s _nm =1 indicates that the nth track of the radar and the mth track of the ESM are from the same target, otherwise s _nm =0. Use hypothesis testing to process preliminary association results to obtain final association results.

Numerical simulation results show that the proposed method can effectively correlate the tracks of radar and ESM under the condition of systematic deviation.

Description of drawings

Figure 1: Typical robust track association scenarios;

Figure 2: Implementation flowchart.

Detailed ways

The present invention will be further described in detail with reference to the flowchart of the implementation of the present invention shown in FIG. 2 .

Aiming at the problem of track association between radars and ESM sensors configured in different places under the condition of systematic deviation, the present invention provides a track error association method based on coherent point drift (CPD). Firstly, in the modified polar coordinate system with the ESM as the coordinate origin, the influence of the system deviation on the radar and ESM parameter tracks is analyzed, and the nonlinear transformation function is used to describe the mapping relationship between the homologous track points of the radar and ESM, Model it as a non-rigid registration problem. Secondly, normalize the target point set of radar and ESM under the modified polar coordinates, and then use the CPD algorithm to estimate the displacement function in the nonlinear transformation function to obtain the registered point set. Finally, the final radar/ESM track robust correlation results are obtained using global optimization and hypothesis testing.

The algorithm flow is as follows:

Step 1: The radar and ESM sensors use EKF and MPCEKF to filter and track the target, respectively, and obtain the target state estimation results as {X _rn ,P′ _rn }(n=1,2,...,N) and {Y _em ,P _em }(m=1,2,...,M), convert the radar estimation result to the modified polar coordinate system with ESM as the origin as {Y _rn ,P _rn }, where N and M are the radar and ESM observations, respectively target number;

Step 2.1: For the point set Y _r ={{Y _rn ,P _rn },n=1,2,...,N} and the point set Y _e ={{Y _em ,P _em },m=1,2,... ,M} are batch normalized separately for different dimensions:

表示归一化后矩阵中的第(i,j)个元素，

和

分别为点集在第i维度上的均值和标准差；Among them, X and X _norm represent the data before and after normalization, respectively, the superscript (i) represents the i-th dimension, and P ^{(i, j)} is the (i, j)-th element in the original covariance matrix,

represents the (i,j)th element in the normalized matrix,

and

are the mean and standard deviation of the point set in the i-th dimension, respectively;

Step 2.2: Take the point set _{Ye as the center of the Gaussian mixture model, regard the point set Y r as} the data sample generated by the Gaussian mixture model, use the CPD method to achieve non-rigid registration, and obtain the registered point set _Ze ={{Z _em ,P _em },m=1,2,...,M}, where Z _em =Γ(Y _em ), and Γ is the nonlinear transformation from the point set _{Ye to the point set Y r .}

Step 3: Calculate statistics from {Z _em ,P _em } and {Y _rn ,P _rn }

μ _nm =( _Yrn - _Zem ) ^T ( _Prn + _Pem ) ^-1 ( _Yrn - _Zem ), (25)

And use the method based on the global optimal association decision and hypothesis testing method to obtain the final association result.

Claims (2)

1. CPD-based off-site configuration radar/ESM track robust association method, is characterized in that, comprises the following steps: Step 1: The radar uses the EKF to track the target and filter the state, and obtain the target state estimate and its covariance matrix as {X _rn ,P' _rn }(n=1,2,...,N). The ESM sensor uses MPCEKF to measure the radiation. The source target is tracked and state filtered, and the target state estimate and its covariance matrix are obtained as {Y _em ,P _em }(m=1,2,...,M), and the radar estimation result is converted to the correction pole with ESM as the origin In the coordinate system, it is {Y _rn , P _rn }, where N and M are the number of targets observed by radar and ESM, respectively; Step 2: For the point set Y _r ={{Y _rn ,P _rn },n=1,2,...,N} and the point set Y _e ={{Y _em ,P _em },m=1,2,... ,M}, perform non-rigid registration, and obtain the non-rigid transformation result Z _e ={{Z _em ,P _em },m=1,2,...,M}; Step 3: Calculate statistics from {Z _em ,P _em } and {Y _rn ,P _rn } μ _nm =( _Yrn - _Zem ) ^T ( _Prn + _Pem ) ^-1 ( _Yrn - _Zem ), And use the method based on the global optimal association decision and hypothesis testing method to obtain the final association result. 2. The track robustness association method of claim 1, wherein the non-rigid registration in step 2 is specifically: Step 2.1, preprocess each state vector and its covariance matrix in point set Y _r and point set Y _e using batch normalization

Among them, X and X _norm represent the data before and after normalization, respectively, the superscript (i) represents the i-th dimension, and P ^{(i, j)} is the (i, j)-th element in the original covariance matrix,

represents the (i,j)th element in the normalized matrix,

and

are the mean and standard deviation of the point set in the i-th dimension, respectively; Step 2.2, regard the point set _{Ye as the center of the Gaussian mixture model, regard the point set Y r as} the data sample generated by the Gaussian mixture model, use the CPD method to achieve non-rigid registration, and obtain the registered point set _Ze ={{Z _em ,P _em },m=1,2,...,M}, where Z _em =Γ(Y _em ), and Γ is the nonlinear transformation from the point set _{Ye to the point set Y r .}

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