技术领域technical field
本发明属于雷达目标跟踪技术领域，特别涉及一种基于分布式PHD的多站雷达站址定位和联合跟踪方法。The invention belongs to the technical field of radar target tracking, in particular to a multi-station radar site location and joint tracking method based on distributed PHD.
背景技术Background technique
在现代战争中，利用广泛分布在作战区域内的多站雷达联合对目标进行跟踪已然是目前雷达跟踪领域的一个研究热点。相比于单部雷达，利用多站雷达能够获得关于目标的更多维度，更广范围的信息，从而提高对目标的探测性能和系统的鲁棒性。在利用多站雷达对目标进行联合跟踪时，需要已知多站雷达的精确位置，以便在信息融合时进行空间对准等操作。然而在实际场景中，由于存在定位误差等原因，系统无法提供雷达的准确位置，这就导致多站雷达系统对目标进行联合跟踪时性能恶化。因此，高效的多站雷达站址定位和联合跟踪方法具有重要的理论价值和实际意义。In modern warfare, using multi-station radars widely distributed in the combat area to jointly track targets is already a research hotspot in the field of radar tracking. Compared with a single radar, the use of multi-station radar can obtain more dimensions and wider range of information about the target, thereby improving the detection performance of the target and the robustness of the system. When multi-station radars are used to jointly track targets, the precise positions of the multi-station radars need to be known in order to perform operations such as spatial alignment during information fusion. However, in actual scenarios, due to positioning errors and other reasons, the system cannot provide the accurate position of the radar, which leads to performance degradation when the multi-station radar system jointly tracks the target. Therefore, an efficient multi-station radar site location and joint tracking method has important theoretical value and practical significance.
针对多站雷达站址定位和联合跟踪问题，部分学者已经进行了研究并取得了相应的研究成果，目前的大多数成果都是基于最大似然和期望-最大方法，在这类方法中，雷达的位置信息包含在利用多个雷达量测形成的联合似然函数中，这些雷达的位置信息能够通过最大化该似然函数得到。在专利“敬忠良，李旻哲，潘汉，联合多传感器配准和多目标跟踪，中国，108519595A，2018-03-20”中，便采用了这样的方法，并且利用GLMB滤波器进行多目标跟踪。然而这种方法需要收集来自于所有雷达的所有量测信息，因此在高密度杂波环境下，构建联合似然函数会造成巨大的通信负担，并且这种方法采用了集中式的融合架构，导致整个系统鲁棒性较差。在文献“M.Uney,B.Mulgrew,and D.E.Clark,”A Cooperativeapproach to sensor localisation in distributed fusion networks,”IEEETrans.Signal Process.,vol.64,no.5,pp.1187-1199,Oct.2016.”中提出了一种基于后验信息的雷达联合跟踪和自定位方法，但是这种方法利用的是高维粒子来表征本地的后验，这样多部雷达之间就需要传输大量的粒子来进行对后验信息的估计，造成极大的通信负担，并且在传感器之间传输的信息采用的是置信传播技术，并不适用于环形的多传感器网络结构。Aiming at the problem of multi-station radar site location and joint tracking, some scholars have conducted research and achieved corresponding research results. Most of the current results are based on maximum likelihood and expectation-maximum methods. In this type of method, radar The position information of is included in the joint likelihood function formed by using multiple radar measurements, and the position information of these radars can be obtained by maximizing the likelihood function. In the patent "Jing Zhongliang, Li Minzhe, Pan Han, Joint multi-sensor registration and multi-target tracking, China, 108519595A, 2018-03-20", such a method is adopted, and the GLMB filter is used for multi-target tracking. However, this method needs to collect all measurement information from all radars, so in a high-density clutter environment, building a joint likelihood function will cause a huge communication burden, and this method uses a centralized fusion architecture, resulting in The whole system is less robust. In the literature "M.Uney, B.Mulgrew, and D.E.Clark," A Cooperative approach to sensor localization in distributed fusion networks," IEEETrans.Signal Process., vol.64, no.5, pp.1187-1199, Oct.2016 A radar joint tracking and self-localization method based on posterior information was proposed in ". However, this method uses high-dimensional particles to represent the local posterior, so a large number of particles need to be transmitted between multiple radars to Estimating the posteriori information causes a huge communication burden, and the information transmitted between sensors uses the belief propagation technology, which is not suitable for the ring multi-sensor network structure.
发明内容Contents of the invention
本发明的目的在于克服现有技术的不足，提供一种可以在未知多站雷达精确位置的情况下，利用多个雷达对目标的量测信息，同时进行多站雷达的站址定位和多目标的跟踪以及信息融合，具有计算量小，收敛速度快等特点的基于分布式PHD的多站雷达站址定位和联合跟踪方法。The purpose of the present invention is to overcome the deficiencies of the prior art, to provide a method that can use the measurement information of multiple radars to target when the precise position of the multi-station radar is unknown, and simultaneously perform site positioning and multi-target detection of the multi-station radar. The distributed PHD-based multi-station radar site positioning and joint tracking method has the characteristics of small amount of calculation and fast convergence speed.
本发明的目的是通过以下技术方案来实现的：一种基于分布式PHD的多站雷达站址定位和联合跟踪方法，包括以下步骤：The purpose of the present invention is achieved through the following technical solutions: a multi-station radar site location and joint tracking method based on distributed PHD, comprising the following steps:
S1、接收回波信号，并采用概率假设密度滤波器进行本地跟踪滤波处理；S1. Receiving the echo signal, and performing local tracking and filtering processing by using a probability hypothesis density filter;
S2、将利用混合高斯形似表征的后验密度函数传送到其他雷达站点，在每两部雷达的后验之间计算切尔诺夫信息散度公式；S2. Transmit the posterior density function represented by the mixed Gaussian shape to other radar sites, and calculate the Chernoff information divergence formula between the posteriors of every two radars;
S3、利用在步骤S2中建立的有关两雷达位置的切尔诺夫信息散度构建优化问题模型；S3, using the Chernoff information divergence of the two radar positions established in step S2 to construct an optimization problem model;
S4、利用粒子群算法对优化模型进行求解，进而得到雷达j相对于雷达i的位置参数；并在所有两两雷达都进行相同操作，得到所有雷达相对于其他雷达站点的位置参数；S4. Use particle swarm optimization algorithm to solve the optimization model, and then obtain the position parameters of radar j relative to radar i; and perform the same operation on all pairs of radars, and obtain the position parameters of all radars relative to other radar sites;
S5、选定多传感器信息融合准则；S5. Selecting multi-sensor information fusion criteria;
S6、根据所有雷达相对于其他雷达站点的位置参数，联合后验分布变为边缘密度函数，根据多传感器信息融合准则，得到融合后的后验密度函数；S6. According to the position parameters of all radars relative to other radar sites, the joint posterior distribution becomes a marginal density function, and according to the multi-sensor information fusion criterion, the fused posterior density function is obtained;
S7、将融合后的后验密度函数以混合高斯的形式传送回各本地雷达。S7. Send the fused posterior density function back to each local radar in the form of Gaussian mixture.
进一步地，所述步骤S1具体实现方法为：Further, the specific implementation method of the step S1 is:
各个本地雷达得到的后验密度分布均为概率假设密度分布，利用混合高斯形式表征为：The posterior density distribution obtained by each local radar is a probability hypothesis density distribution, which is represented by the mixed Gaussian form as follows:
其中，vi,k(x)表示在第k个时刻来自于第i个雷达的后验密度函数，x表示目标状态变量，代表高斯概率密度函数，Ki表示该后验密度函数中高斯分量的个数，表示该高斯分量的权值，表示该高斯分量的均值，表示该高斯分量的协方差矩阵；Among them, vi,k (x) represents the posterior density function from the i-th radar at the k-th moment, x represents the target state variable, Represents the Gaussian probability density function, Ki represents the number of Gaussian components in the posterior density function, Indicates the weight of the Gaussian component, represents the mean of the Gaussian component, Represents the covariance matrix of the Gaussian component;
由于在向其他雷达站点传送后验信息时，雷达的位置信息包含在后验密度函数中，所以传输到其他雷达站点j的密度函数其实是关于目标状态变量和雷达位置的联合分布密度函数：Since the radar position information is included in the posterior density function when the posterior information is transmitted to other radar sites, the density function transmitted to other radar site j is actually the joint distribution density function of the target state variable and radar position:
其中in
θi,j表示在以雷达i为坐标原点时，雷达j相对于雷达i的位置。θi,j represents the position of radar j relative to radar i when radar i is taken as the coordinate origin.
进一步地，所述步骤S2具体实现方法为：在每两部雷达的后验之间计算切尔诺夫信息散度：Further, the specific implementation method of the step S2 is: calculating the Chernoff information divergence between the posteriors of each two radars:
其中，Γ(·)表示切尔诺夫信息散度；ωi表示分配给来自于雷达i的参数，满足0≤ωi≤1，ωi+ωj＝1；Π＝{(vi(x),ωi),(vj(x),ωj)}是包含多目标状态和相应权值的集合；N表示目标的个数；Among them, Γ( ) represents the Chernoff information divergence; ωi represents the parameters assigned to radar i, satisfying 0≤ωi ≤1, ωi +ωj =1; Π={(vi ( x),ωi ),(vj (x),ωj )} is a set containing multiple target states and corresponding weights; N represents the number of targets;
将由概率假设密度滤波器得到的混合高斯形式表示的后验密度分布代入切尔诺夫信息散度，得到：Substituting the posterior density distribution represented by the mixed Gaussian form obtained by the probability hypothesis density filter into the Chernoff information divergence, we get:
Γ(θi,j)表示由雷达i,j之间的位置θi,j导致的切尔诺夫信息散度，表示来自于雷达i，j的量测集合；Γ(θi,j ) represents the Chernoff information divergence caused by the position θi, j between radars i,j, Indicates the measurement set from radar i, j;
将由混合高斯形式表征的本地后验密度信息代入切尔诺夫散度公式，得到：Substituting the local posterior density information represented by the mixed Gaussian form into the Chernoff divergence formula, we get:
其中in
进一步地，所述步骤S3中构建的优化模型为：Further, the optimization model constructed in the step S3 is:
进一步地，所述步骤S5中，选定多传感器信息融合准则为：Further, in the step S5, the selected multi-sensor information fusion criterion is:
其中vf,k(x|Zi,k,Zj,k)表示融合后的后验密度函数，vi,k(x|Zi,k)和vj,k(x|Zj,k)分别代表雷达i和j的后验概率假设密度函数，ωi和ωj表示后验密度函数在融合时所占的权重。where vf,k (x|Zi,k ,Zj,k ) represents the fused posterior density function, vi,k (x|Zi,k ) and vj,k (x|Zj, k ) represent the posterior probability hypothesis density function of radar i and j respectively, and ωi and ωj represent the weight of the posterior density function in fusion.
进一步地，所述步骤S6具体实现方法为：Further, the specific implementation method of the step S6 is:
已知雷达位置参数θi,j后，联合后验分布vi,k(x,θi,j)变为边缘密度函数vi,k(x|θi,j)，根据多传感器信息融合准则，得到融合后的后验密度函数为：After the radar position parameters θi,j are known, the joint posterior distribution vi,k (x,θi,j ) becomes the marginal density function vi,k (x|θi,j ), according to the multi-sensor information fusion Criterion, the posterior density function obtained after fusion is:
将融合后的后验密度函数用混合高斯的形式表示：Express the fused posterior density function in the form of a mixture of Gaussians:
其中in
设雷达的个数为N，则多雷达融合后的后验密度函数通过序贯的进行上述用融合操作N-1次。Assuming that the number of radars is N, the posterior density function after multi-radar fusion is sequentially performed N-1 times by the above-mentioned fusion operation.
本发明的有益效果是：本发明可以在未知多站雷达精确位置的情况下，利用多个雷达对目标的量测信息，同时进行多站雷达的站址定位和多目标的跟踪以及信息融合，并且具有计算量小，收敛速度快等特点。The beneficial effects of the present invention are: the present invention can use the measurement information of multiple radars to target under the condition that the precise position of the multi-station radar is not known, and simultaneously perform site positioning of the multi-station radar, tracking of multiple targets and information fusion, And it has the characteristics of small calculation amount and fast convergence speed.
附图说明Description of drawings
图1为本发明的基于分布式PHD的多站雷达站址定位和联合跟踪方法的流程图；Fig. 1 is the flowchart of the multi-station radar site location and joint tracking method based on distributed PHD of the present invention;
图2为本发明在以雷达i的位置为坐标原点时，雷达j和雷达n的位置参数表示方法；Fig. 2 is the position parameter representation method of radar j and radar n when the position of radar i is taken as the origin of coordinates in the present invention;
图3为在未知各个雷达的位置情况下未利用站址定位和利用本方法对多目标进行联合跟踪的仿真效果图。Fig. 3 is a simulation effect diagram of joint tracking of multiple targets without using site location and using this method when the position of each radar is unknown.
具体实施方式Detailed ways
本发明的解决方案是在多站雷达站址定位阶段，各雷达分别利用PHD滤波器进行本地滤波并得到由混合高斯形式表征的后验信息，然后利用这些后验信息计算每两部雷达之间的切尔诺夫信息散度，利用粒子群算法进行优化使得切尔诺夫信息散度最小化从而得到每两部雷达之间的相对位置。在联合跟踪阶段，根据得到的雷达相对位置，在分布式的框架下，利用广义协方差交叉准则对后验信息进行融合，得到联合跟踪结果。下面结合附图进一步说明本发明的技术方案。The solution of the present invention is that in the stage of multi-station radar site positioning, each radar uses PHD filter to perform local filtering and obtain the posterior information represented by the mixed Gaussian form, and then use these posterior information to calculate the distance between each two radars. The Chernoff information divergence of the particle swarm algorithm is used to optimize the Chernoff information divergence to obtain the relative position between each two radars. In the joint tracking stage, according to the obtained relative position of the radar, under the distributed framework, the posterior information is fused by using the generalized covariance intersection criterion, and the joint tracking result is obtained. The technical solution of the present invention will be further described below in conjunction with the accompanying drawings.
如图1所示，一种基于分布式PHD的多站雷达站址定位和联合跟踪方法，包括以下步骤：As shown in Figure 1, a multi-station radar site location and joint tracking method based on distributed PHD includes the following steps:
S1、接收回波信号，并采用概率假设密度滤波器进行本地跟踪滤波处理；具体实现方法为：S1. Receive the echo signal, and use the probability hypothesis density filter to perform local tracking and filtering processing; the specific implementation method is:
各个本地雷达得到的后验密度分布均为概率假设密度分布，利用混合高斯形式表征为：The posterior density distribution obtained by each local radar is a probability hypothesis density distribution, which is represented by the mixed Gaussian form as follows:
其中，vi,k(x)表示在第k个时刻来自于第i个雷达的后验密度函数，x表示目标状态变量，代表高斯概率密度函数，Ki表示该后验密度函数中高斯分量的个数，表示该高斯分量的权值，表示该高斯分量的均值，表示该高斯分量的协方差矩阵；Among them, vi,k (x) represents the posterior density function from the i-th radar at the k-th moment, x represents the target state variable, Represents the Gaussian probability density function, Ki represents the number of Gaussian components in the posterior density function, Indicates the weight of the Gaussian component, represents the mean of the Gaussian component, Represents the covariance matrix of the Gaussian component;
由于在向其他雷达站点传送后验信息时，雷达的位置信息包含在后验密度函数中，所以传输到其他雷达站点j的密度函数其实是关于目标状态变量和雷达位置的联合分布密度函数：Since the radar position information is included in the posterior density function when the posterior information is transmitted to other radar sites, the density function transmitted to other radar site j is actually the joint distribution density function of the target state variable and radar position:
其中in
θi,j表示在以雷达i为坐标原点时，雷达j相对于雷达i的位置，如图2所示。θi,j represents the position of radar j relative to radar i when radar i is taken as the coordinate origin, as shown in Figure 2.
S2、将利用混合高斯形似表征的后验密度函数传送到其他雷达站点，在每两部雷达的后验之间计算切尔诺夫信息散度公式；具体实现方法为：在每两部雷达的后验之间计算切尔诺夫信息散度：S2. Transmit the posterior density function represented by the mixed Gaussian shape to other radar sites, and calculate the Chernoff information divergence formula between the posteriors of every two radars; the specific implementation method is: in every two radars Calculate Chernoff information divergence between posteriors:
其中，Γ(·)表示切尔诺夫信息散度；ωi表示分配给来自于雷达i的参数，满足0≤ωi≤1，ωi+ωj＝1，这个参数决定了后验密度函数在计算切尔诺夫信息散度时的权重；Among them, Γ(·) represents the Chernoff information divergence; ωi represents the parameter assigned to radar i, satisfying 0≤ωi ≤1, ωi +ωj =1, this parameter determines the posterior density The weight of the function when calculating the Chernoff information divergence;
Π＝{(vi(x),ωi),(vj(x),ωj)}是包含多目标状态和相应权值的集合；N表示目标的个数；Π={(vi (x),ωi ),(vj (x),ωj )} is a set containing multi-target states and corresponding weights; N represents the number of targets;
将由概率假设密度滤波器得到的混合高斯形式表示的后验密度分布代入切尔诺夫信息散度，得到：Substituting the posterior density distribution represented by the mixed Gaussian form obtained by the probability hypothesis density filter into the Chernoff information divergence, we get:
Γ(θi,j)表示由雷达i,j之间的位置θi,j导致的切尔诺夫信息散度，表示来自于雷达i,j的量测集合；Γ(θi,j ) represents the Chernoff information divergence caused by the position θi, j between radars i,j, Indicates the measurement set from radar i,j;
将由混合高斯形式表征的本地后验密度信息代入切尔诺夫散度公式，得到：Substituting the local posterior density information represented by the mixed Gaussian form into the Chernoff divergence formula, we get:
其中in
S3、利用在步骤S2中建立的有关两雷达位置的切尔诺夫信息散度构建优化问题模型：构建的优化模型为：S3. Utilize the Chernoff information divergence of the positions of the two radars established in step S2 to construct an optimization problem model: the constructed optimization model is:
S4、利用粒子群算法对优化模型进行求解，进而得到雷达j相对于雷达i的位置参数；并在所有两两雷达都进行相同操作，得到所有雷达相对于其他雷达站点的位置参数；S4. Use particle swarm optimization algorithm to solve the optimization model, and then obtain the position parameters of radar j relative to radar i; and perform the same operation on all pairs of radars, and obtain the position parameters of all radars relative to other radar sites;
S5、选定多传感器信息融合准则为：S5. The selected multi-sensor information fusion criterion is:
其中vf,k(x|Zi,k,Zj,k)表示融合后的后验密度函数，vi,k(x|Zi,k)和vj,k(x|Zj,k)分别代表雷达i和j的后验概率假设密度函数，ωi和ωj表示后验密度函数在融合时所占的权重。where vf,k (x|Zi,k ,Zj,k ) represents the fused posterior density function, vi,k (x|Zi,k ) and vj,k (x|Zj, k ) represent the posterior probability hypothesis density function of radar i and j respectively, and ωi and ωj represent the weight of the posterior density function in fusion.
S6、根据所有雷达相对于其他雷达站点的位置参数，联合后验分布变为边缘密度函数，根据多传感器信息融合准则，得到融合后的后验密度函数；具体实现方法为：S6. According to the position parameters of all radars relative to other radar sites, the joint posterior distribution becomes a marginal density function, and according to the multi-sensor information fusion criterion, the fused posterior density function is obtained; the specific implementation method is as follows:
已知雷达位置参数θi,j后，联合后验分布vi,k(x,θi,j)变为边缘密度函数vi,k(x|θi,j)，根据多传感器信息融合准则，得到融合后的后验密度函数为：After the radar position parameters θi,j are known, the joint posterior distribution vi,k (x,θi,j ) becomes the marginal density function vi,k (x|θi,j ), according to the multi-sensor information fusion Criterion, the posterior density function obtained after fusion is:
将融合后的后验密度函数用混合高斯的形式表示：Express the fused posterior density function in the form of a mixture of Gaussians:
其中in
设雷达的个数为N，则多雷达融合后的后验密度函数通过序贯的进行上述用融合操作N-1次。Assuming that the number of radars is N, the posterior density function after multi-radar fusion is sequentially performed N-1 times by the above-mentioned fusion operation.
S7、将融合后的后验密度函数以混合高斯的形式传送回各本地雷达。S7. Send the fused posterior density function back to each local radar in the form of Gaussian mixture.
图3为在未知各个雷达的位置情况下未利用站址定位和利用本方法对多目标进行联合跟踪的仿真效果图。从图中可以看出，在同样的场景下，相比于未进行雷达站址定位的结果，采用本发明的方法对多目标进行联合跟踪，能够获得更高的跟踪精度。Fig. 3 is a simulation effect diagram of joint tracking of multiple targets without using site location and using this method when the position of each radar is unknown. It can be seen from the figure that, in the same scene, compared with the results without radar site positioning, using the method of the present invention to jointly track multiple targets can obtain higher tracking accuracy.
本发明利用各个雷达的后验密度函数，而不是各个雷达的量测信息来进行多基地雷达位置的计算，这样极大地降低了雷达间的信息传输负载。并且在本发明中，通过计算每两部雷达后验间的切尔诺夫信息散度来获得雷达间的相对位置信息，这样就将高维信息计算问题进行了降维处理，大幅度地降低了系统的计算量。另外，由于用混合高斯的形式表示切尔诺夫信息散度时，所得到的关于雷达位置信息的优化函数模型是一个非凸优化问题，基于梯度的优化方法不再适用，本发明采用了粒子群算法解决了该问题。The present invention uses the posterior density function of each radar instead of the measurement information of each radar to calculate the position of multi-base radars, thus greatly reducing the information transmission load between radars. And in the present invention, the relative position information between the radars is obtained by calculating the Chernoff information divergence between the posteriori of every two radars, thus reducing the dimensionality of the high-dimensional information calculation problem, greatly reducing the the calculation amount of the system. In addition, when the Chernoff information divergence is expressed in the form of mixed Gaussian, the obtained optimization function model about the radar position information is a non-convex optimization problem, and the gradient-based optimization method is no longer applicable. The present invention adopts the particle Group algorithms solve this problem.
本领域的普通技术人员将会意识到，这里所述的实施例是为了帮助读者理解本发明的原理，应被理解为本发明的保护范围并不局限于这样的特别陈述和实施例。本领域的普通技术人员可以根据本发明公开的这些技术启示做出各种不脱离本发明实质的其它各种具体变形和组合，这些变形和组合仍然在本发明的保护范围内。Those skilled in the art will appreciate that the embodiments described here are to help readers understand the principles of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical revelations disclosed in the present invention without departing from the essence of the present invention, and these modifications and combinations are still within the protection scope of the present invention.
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| CN201910573146.8ACN110187336B (en) | 2019-06-28 | 2019-06-28 | Multi-station radar site positioning and joint tracking method based on distributed PHD |
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| CN201910573146.8ACN110187336B (en) | 2019-06-28 | 2019-06-28 | Multi-station radar site positioning and joint tracking method based on distributed PHD |
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