CN111487612A - A CPD-Based Robust Correlation Method for Radar/ESM Tracks in Different Locations - Google Patents
A CPD-Based Robust Correlation Method for Radar/ESM Tracks in Different Locations Download PDFInfo
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Abstract
Description
技术领域technical field
本发明属于目标跟踪领域中的航迹关联技术,针对异地配置的雷达和ESM传感器在存在系统偏差条件下的航迹关联问题,提供了一种基于相干点漂移(Coherent PointDrift,CPD)的航迹抗差关联方法。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.
背景技术Background technique
ESM是常用的无源传感器,能够提供目标属性信息和方位角量测,具有探测距离远、隐蔽性好、目标识别能力强等优点,对于远距离预警、侦察具有重要的意义。但对于多目标场景,单个ESM的量测难以保证所有目标的可观测性,通常需要联合有源传感器(如雷达)系统,优势互补,为战场指挥提供更加完整清晰的战场态势,因此研究雷达与EMS的航迹关联算法十分必要。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.
本发明旨在利用CPD算法实现异地配置下的雷达/ESM航迹抗差关联,适用于雷达与ESM之间距离较远的情况,对密集目标的关联效果较好。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.
发明内容SUMMARY OF THE INVENTION
本发明的目的在于针对异地配置的雷达/ESM在存在系统偏差条件下的航迹关联问题,提供一种基于相干点漂移的航迹抗差关联方法。考虑系统偏差对雷达和ESM参数航迹的影响,使用非线性变换函数描述雷达和ESM的同源航迹点之间的映射关系,将其建模为非刚性配准问题。对雷达和ESM在修正极坐标(Modified Polar Coordinate,MPC)下的目标点集进行批归一化处理,而后使用CPD算法估计非线性变换函数中的位移函数,得到配准后的点集。最后,使用全局优化和假设检验得到最终的雷达/ESM航迹抗差关联结果。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.
该发明适用于异地配置的雷达/ESM传感器航迹关联问题。该发明包括以下步骤: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问题描述1 Problem description
设某一时刻二维场景中有两个异地配置的平台,分别搭载雷达和ESM对目标进行观测。雷达和ESM分别位于pr=[xr yr]T和pe=[xe ye]T,速度分别为和第n个目标的位置和速度为ptn=[xtn ytn]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
其中,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Δθr分别表示雷达径向距离和方位角量测的系统误差,δρ和δθr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
其中,表示第n个目标到ESM的方位角量测,Δθe和δθe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.
雷达利用传统扩展卡尔曼滤波器(Extended Kalman Filter,EKF)估计目标状态,将对各个目标的滤波结果以及自身运动状态pr和vr发送至融合中心,其中{Xrn,P′rn}为雷达在其局部坐标系下对目标的滤波结果ESM对目标采用MPCEKF滤波算法,结果表示为{Yen,Pen},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系统偏差对航迹关联的影响2 Influence of System Deviation on Track Association
假设滤波结果已经完成时间对准,以ESM作为融合中心建立坐标系,雷达和ESM相距L编队移动,某时刻的场景示意图如图1所示。将{Xrn,P′rn}转换到ESM的局部MPC下得到{Yrn,Prn},由于MPC下前三个变量与第四个变量解耦,且第四个变量在某些时刻不可观,因此仅考虑前三个变量,其中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
其中,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.
忽略滤波后估计误差的影响,则存在系统误差条件下滤波结果Xrn为Ignoring the influence of the estimated error after filtering, the filtering result X rn under the condition of systematic error is:
将式(7)带入到式(4)可得Substituting equation (7) into equation (4), we can get
考虑MPC参数空间中的点集Yr={Yrn,n=1,2,…,N}和Ye={Yem,m=1,2,…,M},其中辐射源的数量M可能多与雷达目标数量N。观察式(8),可知Yr是关于Ye的非线性变换,且该变换参数依不同目标而不同。对同源数据点,变换关系Γ可建模为原点集与其位移函数的和。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.
Yr=Γ(Ye)=Ye+v(Ye) (9)Y r =Γ(Y e )=Y e +v(Y e ) (9)
3非刚性点集配准方法3 Non-rigid point set registration method
将Ye视作高斯混合模型(Gaussian Mixture Model,GMM)的中心,考虑Yr为该GMM生成的数据样本,则GMM的概率密度函数为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
其中,D为点集中数据点的维度,σ2为各向同性协方差,||·||表示欧几里得距离。方位角之差的范围为-π<<θr-θe>≤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
<θr-θe>=arccos(cosθrcosθe+sinθrsinθe) (12)<θ r -θ e >=arccos(cosθ r cosθ e +sinθ r sinθ e ) (12)
实际上,对于参数空间中的滤波结果,不同参数维度的尺度并不相同,比如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:
其中,Xnorm为归一化后的数据,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.
假设目标的状态估计之间独立同分布,可通过最小化似然函数的负对数来估计未知参数v和σ2 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
其中,φ(v)是正则项,λ表示似然函数拟合度和正则项之间的权衡因子。CPD方法给出了最优位移函数,并利用最大期望方法求解未知变量,从而实现非刚性配准。而后,使用配准后的点集Ze={Zen=Γ(Yen)}计算后验概率,用于表征点集间的关联关系。但是,直接选取后验概率最大的关联点对为关联结果忽略了航迹关联问题中的约束,即单个雷达目标可能搭载有多个辐射源目标,而单个ESM目标仅对应一个雷达目标。此外,后验概率仅利用数据点的位置关系,没有考虑每个数据点作为滤波器在参数空间的估计值,存在一定的估计误差。综上所述,可以利用配准后的点集Ze和雷达在参数空间中的点集Yr,构造统计量μnm 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
其中,Pem和Prn为归一化后的估计协方差矩阵Among them, P em and P rn are the normalized estimated covariance matrices
其中,P(i,j)表示协方差矩阵中第(i,j)个元素,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Ze中的数据点的协方差矩阵与Ye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.
假设检验问题构造如下:The hypothesis testing problem is constructed as follows:
H0:雷达和ESM的航迹来自同一个目标;H 0 : The track of the radar and ESM comes from the same target;
H1:雷达和ESM的航迹来自不同目标。H 1 : The radar and ESM tracks are from different targets.
易知μnm服从自由度为d的卡方分布,γ为合适的门限,可取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.
最后,基于全局最优关联判决方法,求解雷达/ESM航迹的初步关联结果,构建全局优化目标函数为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
其中,snm为二进制变量,snm=1表示雷达的第n个航迹和ESM的第m航迹来自同一目标则,否则snm=0。利用假设检验对初步的关联结果进行处理,得到最终的关联结果。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.
数值仿真结果表明所提方法能够有效在存在系统偏差条件下,对雷达和ESM的航迹进行关联,适用于异地配置的雷达和ESM传感器,在目标密集的情况下具有更好的效果。Numerical simulation results show that the proposed method can effectively correlate the tracks of radar and ESM under the condition of systematic deviation.
附图说明Description of drawings
图1:典型抗差航迹关联场景;Figure 1: Typical robust track association scenarios;
图2:实施流程图。Figure 2: Implementation flowchart.
具体实施方式Detailed ways
结合图2所述的本发明实施流程图,对本发明作进一步详细描述。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 .
本发明针对异地配置的雷达和ESM传感器在存在系统偏差的条件下的航迹关联问题,提供了一种基于相干点漂移(coherent point drift,CPD)的航迹抗差关联方法。首先,在以ESM为坐标原点的修正极坐标系下,分析了系统偏差对雷达和ESM参数航迹的影响,使用非线性变换函数描述雷达和ESM的同源航迹点之间的映射关系,将其建模为非刚性配准问题。其次,对雷达和ESM在修正极坐标下的目标点集进行归一化处理,而后使用CPD算法估计非线性变换函数中的位移函数,得到配准后的点集。最后,使用全局优化和假设检验得到最终的雷达/ESM航迹抗差关联结果。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.
算法流程如下:The algorithm flow is as follows:
步骤1:雷达和ESM传感器分别利用EKF和MPCEKF对目标进行滤波跟踪,得到目标状态估计结果分别为{Xrn,P′rn}(n=1,2,…,N)和{Yem,Pem}(m=1,2,…,M),将雷达估计结果转换到以ESM为原点的修正极坐标系下为{Yrn,Prn},其中N和M分别为雷达和ESM观测到的目标数量;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;
步骤2.1:对点集Yr={{Yrn,Prn},n=1,2,…,N}和点集Ye={{Yem,Pem},m=1,2,…,M}的不同维度分别进行批归一化: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:
其中,X和Xnorm分别表示归一化前后的数据,上标(i)表示第i维度,P(i,j)为原协方差矩阵中第(i,j)个元素,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;
步骤2.2:将点集Ye视作高斯混合模型的中心,将点集Yr视作该高斯混合模型生成的数据样本,使用CPD方法实现非刚性配准,得到配准后的点集Ze={{Zem,Pem},m=1,2,…,M},其中Zem=Γ(Yem),Γ为点集Ye到点集Yr的非线性变换。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 .
步骤3:根据{Zem,Pem}和{Yrn,Prn}计算统计量Step 3: Calculate statistics from {Z em ,P em } and {Y rn ,P rn }
μnm=(Yrn-Zem)T(Prn+Pem)-1(Yrn-Zem), (25)μ nm =( Yrn - Zem ) T ( Prn + Pem ) -1 ( Yrn - Zem ), (25)
并使用基于全局最优关联判决和假设检验方法的方法,得到的最终的关联结果。And use the method based on the global optimal association decision and hypothesis testing method to obtain the final association result.
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