WO2017124299A1

WO2017124299A1 - Multi-target tracking method and tracking system based on sequential bayesian filtering

Info

Publication number: WO2017124299A1
Application number: PCT/CN2016/071347
Authority: WO
Inventors: 刘宗香; 邹燕妮; 吴德辉; 李良群
Original assignee: 深圳大学
Priority date: 2016-01-19
Filing date: 2016-01-19
Publication date: 2017-07-27

Abstract

A multi-target tracking method and tracking system based on sequential Bayesian filtering, belonging to the technical field of multi-sensor information fusion. The method comprises: predicting edge distributions of various targets in different models and existence probabilities thereof at the current moment; according to the predicted edge distributions and the existence probabilities thereof, using a Bayesian rule for processing so as to obtain updated edge distributions and existence probabilities thereof; fusing the updated edge distributions and the existence probabilities thereof so as to form an updated edge distribution and an existence probability thereof at the current moment; combining an edge distribution and an existence probability thereof of a new target with the updated edge distribution and the existence probability thereof respectively so as to generate an edge distribution and an existence probability thereof at the current moment; and cutting an edge distribution with an existence probability less than a first threshold value, and extracting and outputting an edge distribution with an existence probability greater than a second threshold value. The multi-target tracking method guarantees the real-time performance of data processing and also effectively solves a tracking problem for a multi-maneuvering object with moving modes being switched between different models.

Description

基于序贯贝叶斯滤波的多目标跟踪方法及跟踪***Multi-target tracking method and tracking system based on sequential Bayesian filtering

技术领域Technical field

本发明属于多传感器信息融合技术领域，尤其涉及基于序贯贝叶斯滤波的多目标跟踪方法及跟踪***。The invention belongs to the field of multi-sensor information fusion technology, and in particular relates to a multi-target tracking method and a tracking system based on sequential Bayesian filtering.

背景技术Background technique

贝叶斯滤波技术能够提供一种强大的统计方法工具，用于协助解决测量数据具有不确定性情况下的多传感器信息的融合与处理。为了解决多目标贝叶斯滤波方法对新收到的测量数据不能被及时处理而产生的信息延迟问题以及未知目标初始位置情况下的多目标跟踪问题，我们已提出了解决办法，具体请参考申请号为CN201510284138.3、一种传递边缘分布的测量驱动目标跟踪方法与跟踪***的专利申请。然而，该方法不能对运动模式在不同模型间转换的机动目标进行有效跟踪，如何对运动模式在不同模型间转换的机动目标跟踪是多目标贝叶斯滤波方法中需要探索和解决的一个关键技术问题。Bayesian filtering technology provides a powerful statistical method tool to assist in the fusion and processing of multi-sensor information with uncertainties in measurement data. In order to solve the multi-target Bayesian filtering method, the information delay problem caused by the newly received measurement data can not be processed in time and the multi-target tracking problem in the case of the unknown target initial position, we have proposed a solution. Please refer to the application for details. No. CN201510284138.3, a patent application for measuring the driving target tracking method and tracking system for transmitting edge distribution. However, this method can not effectively track the maneuvering target whose motion mode is switched between different models. How to track the maneuvering target that converts the motion mode between different models is a key technology that needs to be explored and solved in the multi-objective Bayesian filtering method. problem.

发明内容Summary of the invention

本发明所要解决的技术问题在于提供一种基于序贯贝叶斯滤波的多目标跟踪方法及跟踪***，旨在解决运动模式在不同模型间转换的多机动目标的跟踪问题。The technical problem to be solved by the present invention is to provide a multi-target tracking method and a tracking system based on sequential Bayesian filtering, aiming at solving the problem of tracking multiple maneuvering targets whose motion modes are switched between different models.

本发明是这样实现的，一种基于序贯贝叶斯滤波的多目标跟踪方法，包括以下步骤：The present invention is implemented in this way, a multi-target tracking method based on sequential Bayesian filtering, comprising the following steps:

步骤A、当接收到新的测量数据后，计算出接收到所述新的测量数据的时刻与接收到前一个测量数据的时刻的时间差，以接收到所述新的测量数据的时刻为当前时刻，接收到前一个测量数据的时刻为前一时刻；根据所述时间差、各个模型间的转移概率以及前一时刻各个目标的边缘分布及其存在概率，预测出当前时刻各个目标在不同模型下的边缘分布及其存在概率；Step A: After receiving the new measurement data, calculate a time difference between a time when the new measurement data is received and a time when the previous measurement data is received, to receive the new measurement data. Inscribed as the current time, the time when the previous measurement data is received is the previous time; according to the time difference, the transition probability between each model, and the edge distribution of each target at the previous moment and its existence probability, it is predicted that each target at the current time is Edge distribution under different models and their existence probability;

步骤B、根据所述预测的当前时刻各个目标在不同模型下的边缘分布及其存在概率，利用贝叶斯规则序贯处理当前时刻的每一个测量数据得到各个目标在不同模型下的更新边缘分布及其存在概率；Step B: According to the predicted edge current distribution and the existence probability of each target under different models, the Bayes rule is used to sequentially process each measurement data of the current time to obtain the updated edge distribution of each target under different models. And its probability of existence;

步骤C、将所述当前时刻各个目标在不同模型下的更新边缘分布及其存在概率进行融合，形成当前时刻各个目标的更新边缘分布及存在概率；Step C: merging the updated edge distributions and the existence probabilities of the respective targets in the different models at the current moment to form an updated edge distribution and an existence probability of each target at the current moment;

步骤D、利用当前时刻的每一个测量数据产生新目标的边缘分布，为其指定存在概率和模型标签；同时，将当前时刻新目标的边缘分布及其存在概率分别与所述当前时刻各个目标的更新边缘分布及其存在概率进行合并，生成当前时刻的各个目标的边缘分布及其存在概率；Step D: using each measurement data of the current moment to generate an edge distribution of the new target, assigning an existence probability and a model label thereto; and simultaneously, respectively, an edge distribution of the new target at the current moment and its existence probability are respectively associated with each target of the current moment Update the edge distribution and its existence probability to merge, and generate the edge distribution of each target at the current moment and its existence probability;

步骤E、从合并后所生成的当前时刻各个目标的边缘分布中将存在概率小于第一阈值的边缘分布裁减掉，并且将裁减后的边缘分布及其存在概率作为下一时刻递归滤波的输入，同时，从裁减后的边缘分布中提取存在概率大于第二阈值的边缘分布作为当前时刻的输出，并且将各个输出边缘分布的均值与方差分别作为当前时刻目标的状态估计与误差估计。Step E: The edge distribution with the probability of being less than the first threshold is cut off from the edge distribution of each target at the current moment generated after the merge, and the reduced edge distribution and its existence probability are used as input of recursive filtering at the next moment. At the same time, the edge distribution with the existence probability greater than the second threshold is extracted from the reduced edge distribution as the output of the current time, and the mean and the variance of the respective output edge distributions are respectively used as the state estimation and the error estimation of the current time target.

本发明还提供了一种基于序贯贝叶斯滤波的多目标跟踪***，该***同样能解决运动模式在不同模型间转换的多机动目标的跟踪问题，且可以确保数据处理的实时性。The invention also provides a multi-target tracking system based on sequential Bayesian filtering, which can also solve the tracking problem of multiple maneuvering targets converted between different models of motion modes, and can ensure the real-time performance of data processing.

该多目标跟踪***，包括：The multi-target tracking system includes:

预测模块，当接收到新的测量数据后，计算出接收到所述新的测量数据的时刻与接收到前一个测量数据的时刻的时间差，以接收到所述新的测量数据的时刻为当前时刻，接收到前一个测量数据的时刻为前一时刻；根据所述时间差、各个模型间的转移概率以及前一时刻各个目标的边缘分布及其存在概率，预测出当前时刻各个目标在不同模型下的边缘分布及其存在概率； And a prediction module, after receiving the new measurement data, calculating a time difference between a time when the new measurement data is received and a time when the previous measurement data is received, to receive the new measurement data as a current time The time at which the previous measurement data is received is the previous time; according to the time difference, the transition probability between each model, and the edge distribution of each target at the previous moment and its existence probability, it is predicted that each target at the current time is under a different model. Edge distribution and its existence probability;

更新模块，根据所述预测模块中预测的当前时刻各个目标在不同模型下的边缘分布及其存在概率，利用贝叶斯规则序贯处理当前时刻的每一个测量数据得到各个目标在不同模型下的更新边缘分布及其存在概率；An update module, according to the edge distribution of each target in the prediction module at the current moment and the existence probability of each target under different models, using Bayes rule to sequentially process each measurement data of the current moment to obtain each target under different models Update the edge distribution and its existence probability;

模型融合模块，将所述更新模块中当前时刻各个目标在不同模型下的更新边缘分布及其存在概率进行融合，形成当前时刻各个目标的更新边缘分布及存在概率；The model fusion module integrates the updated edge distribution and the existence probability of each target in the update module under different models at the current moment to form an updated edge distribution and existence probability of each target at the current moment;

边缘分布生成模块，利用当前时刻的每一个测量数据产生新目标的边缘分布，为其指定存在概率和模型标签；同时，将当前时刻新目标的边缘分布及其存在概率分别与所述模型融合模块中当前时刻各个目标的更新边缘分布及其存在概率进行合并，生成当前时刻的各个目标的边缘分布及其存在概率；The edge distribution generation module generates an edge distribution of the new target by using each measurement data at the current moment, and specifies the existence probability and the model label for the current target; meanwhile, the edge distribution of the new target at the current moment and the existence probability thereof are respectively combined with the model fusion module The updated edge distribution of each target in the current moment and its existence probability are combined to generate the edge distribution of each target at the current moment and its existence probability;

边缘分布提取模块，从所述边缘分布生成模块中将合并后所生成的当前时刻各个目标的边缘分布中将存在概率小于第一阈值的边缘分布裁减掉，并且将裁减后的边缘分布及其存在概率作为下一时刻递归滤波的输入，同时，从裁减后的边缘分布中提取存在概率大于第二阈值的边缘分布作为当前时刻的输出，并且将各个输出边缘分布的均值与方差分别作为当前时刻目标的状态估计与误差估计。The edge distribution extraction module removes, from the edge distribution generation module, the edge distribution of each target at the current moment generated by the merge, the edge distribution whose existence probability is less than the first threshold, and the edge distribution after the reduction and the existence thereof Probability is used as the input of recursive filtering at the next moment. At the same time, the edge distribution with the existence probability greater than the second threshold is extracted from the reduced edge distribution as the output of the current time, and the mean and variance of each output edge distribution are respectively used as the current time target. State estimation and error estimation.

本发明与现有技术相比，有益效果在于：所述的基于序贯贝叶斯滤波的多目标跟踪方法通过预测、更新、融合、边缘分布生成及边缘分布提取的步骤能将序贯贝叶斯滤波器与不同的模型结合起来，既保证了数据处理的实时性，同时又有效地解决了运动模式在不同模块之间的多机动目标的跟踪问题，且具有广泛的实用性。Compared with the prior art, the present invention has the beneficial effects that the multi-target tracking method based on sequential Bayesian filtering can sequentially sequence Bayesian by the steps of prediction, update, fusion, edge distribution generation and edge distribution extraction. The combination of different filters and different models not only ensures the real-time performance of data processing, but also effectively solves the problem of multi-maneuvering target tracking between different modules, and has wide practicality.

附图说明DRAWINGS

图1是本发明序贯贝叶斯滤波的多目标跟踪方法的流程图；1 is a flow chart of a multi-target tracking method for sequential Bayesian filtering of the present invention;

图2是本发明序贯贝叶斯滤波的多目标跟踪***的结构示意图；2 is a schematic structural diagram of a multi-target tracking system of sequential Bayesian filtering according to the present invention;

图3是本发明实施例提供的传感器在50个扫描周期的测量数据； 3 is a measurement data of a sensor in 50 scan cycles according to an embodiment of the present invention;

图4是根据本发明的多目标跟踪方法与基于跳跃马尔科夫***模型的GM-PHD目标跟踪方法处理得到的结果；4 is a result of processing a multi-target tracking method according to the present invention and a GM-PHD target tracking method based on a hop Markov system model;

图5是根据本发明的多目标跟踪方法与基于跳跃马尔科夫***模型的GM-PHD滤波方法处理得到的结果；5 is a result of processing by a multi-target tracking method according to the present invention and a GM-PHD filtering method based on a hop Markov system model;

图6是根据本发明的多目标跟踪方法与基于跳跃马尔科夫***模型的GM-PHD-JMS滤波方法在经过100次实验得到的平均OSPA距离示意图。6 is a schematic diagram of the average OFPA distance obtained after 100 experiments by the multi-target tracking method according to the present invention and the GM-PHD-JMS filtering method based on the hop Markov system model.

具体实施方式Detailed ways

为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It is understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

本发明的基于序贯贝叶斯滤波的多目标跟踪方法通过对各个目标的边缘分布及其存在概率进行预测、更新、融合、生成以及提取，从而解决了在不同模型间进行转换的机动目标跟踪问题并且能够及时处理当前时刻接收到的测量数据。The multi-target tracking method based on sequential Bayesian filtering of the present invention solves the maneuvering target tracking for converting between different models by predicting, updating, merging, generating and extracting the edge distribution of each target and its existence probability. The problem and the timely processing of the measurement data received at the current time.

如图1所示，基于序贯贝叶斯滤波的多目标跟踪方法，包括以下步骤：As shown in FIG. 1, the multi-target tracking method based on sequential Bayesian filtering includes the following steps:

步骤A、当接收到新的测量数据后，计算出接收到所述新的测量数据的时刻与接收到前一个测量数据的时刻的时间差，以接收到所述新的测量数据的时刻为当前时刻，接收到前一个测量数据的时刻为前一时刻；根据所述时间差、各个模型间的转移概率以及前一时刻各个目标的边缘分布及其存在概率，预测出当前时刻各个目标在不同模型下的边缘分布及其存在概率。Step A: After receiving new measurement data, calculate a time difference between a time when the new measurement data is received and a time when the previous measurement data is received, so that the time when the new measurement data is received is the current time The time at which the previous measurement data is received is the previous time; according to the time difference, the transition probability between each model, and the edge distribution of each target at the previous moment and its existence probability, it is predicted that each target at the current time is under a different model. Edge distribution and its probability of existence.

模型为目标的运动提供场所，设模型表示为r_i,k。目标是需要测试、跟踪的对象。根据模型间的转移概率可以将不同模型转化为同一个模型，以方便运动模式在不同模型间的测量、跟踪。The model provides a place for the target's motion, and the model is represented as r _i,k . The target is the object that needs to be tested and tracked. According to the transition probability between models, different models can be transformed into the same model to facilitate the measurement and tracking of motion patterns between different models.

以k-1表示前一时刻，k表示当前时刻，t_k-1表示前一时刻的时间，t_k表示当前时刻的时间，r_i,k-1表示前一时刻第i个边缘分布的模型标签，r_i,k表示当前时刻第i个边缘分布的模型标签，1≤r_i,k≤M_r，M_r表示模型的总数目。The previous moment is represented by k-1, k represents the current time, t _k-1 represents the time of the previous moment, t _k represents the time of the current moment, and r _i,k-1 represents the model of the i-th edge distribution of the previous moment. _tag, r _{i, k} denotes the i-th model edge label distributions current _{_{time, 1≤r i, k ≤M r,}} M r represents the total number of models.

已知前一时刻第i个边缘分布为N(x_i,k-1；m_i,k-1(r_i,k-1),P_i,k-1(r_i,k-1))，i＝1,2,...,N_k-1，前一时刻第i个边缘分布的存在概率为ρ_i,k-1(r_i,k-1)，i＝1,…,N_k-1；其中，N表示高斯分布，x_i,k-1表示为前一时刻第i个边缘分布的状态向量，m_i,k-1(r_i,k-1)和P_i,k-1(r_i,k-1)分别表示前一时刻第i个边缘分布的均值和方差，N_k-1为前一时刻目标的总数，i为索引号，1≤i≤N_k-1。It is known that the i-th edge distribution at the previous moment is N(x _i,k-1 ;m _i,k-1 (r _i,k-1 ), P _i,k-1 (r _i,k-1 )) , i = 1, 2, ..., N _k-1 , the existence probability of the i-th edge distribution at the previous moment is ρ _i,k-1 (r _i,k-1 ), i=1,...,N _K-1 ; where N denotes a Gaussian distribution, x _i,k-1 denotes a state vector of the i-th edge distribution at the previous moment, m _i,k-1 (r _i,k-1 ) and P _{i,k -1} (r _i,k-1 ) respectively represent the mean and variance of the i-th edge distribution at the previous moment, N _k-1 is the total number of targets at the previous moment, i is the index number, _{1 ≤} i ≤ N _k-1 .

根据前一时刻的边缘分布及其存在概率、当前时刻与前一时刻的时间差以及模型间的转移概率得出当前时刻各目标在不同模型下预测的边缘分布为N(x_i,k；m_i,k|k-1(r_i,k),P_i,k|k-1(r_i,k))，i＝1,2,...,N_k-1，1≤r_i,k≤M_r；当前时刻各预测边缘分布的存在概率为ρ_i,k|k-1(r_i,k)＝p_S,k(t_k-t_k-1)t_k|k-1(r_i,k|r_i,k-1)ρ_i,k-1(r_i,k-1)，i＝1,2,...,N_k-1，1≤r_i,k≤M_r；其中，m_i,k|k-1(r_i,k)＝F_k-1(r_i,k)m_i,k-1(r_i,k-1)为当前时刻目标i在模型r_i,k下的预测边缘分布的均值，

为目标i在模型r_i,k下的预测边缘分布的方差，t_k|k-1(r_i,k|r_i,k-1)为模型转移概率，

为目标的幸存概率，△t＝t_k-t_k-1为当前时刻与前一时刻的时间差，T为采样周期，δ为给定的常数，F_k-1(r_i,k)为前一时刻第i个边缘分布的状态转移矩阵，Q_k-1(r_i,k)为前一时刻第i个边缘分布的过程噪声方差矩阵，r_i,k-1为前一时刻第i个边缘分布的模型标签，上标T表示为矩阵或向量的转置。According to the edge distribution of the previous moment and its existence probability, the time difference between the current moment and the previous moment, and the transition probability between the models, the edge distribution predicted by each target under different models at the current moment is N(x _i,k ;m _{i ,k|k-1} (r _i,k ),P _i,k|k-1 (r _i,k )),i=1,2,...,N _k-1 ,1≤r _i,k ≤M _r ; the existence probability of each predicted edge distribution at the current time is ρ _i,k|k-1 (r _i,k )=p _S,k (t _k -t _k-1 )t _k|k-1 (r _i,k |r _i,k-1 )ρ _i,k-1 (r _i,k-1 ),i=1,2,...,N _k-1 ,1≤r _i,k ≤M _r Where m _i,k|k-1 (r _i,k )=F _k-1 (r _i,k )m _i,k-1 (r _i,k-1 ) is the current time target i in the model r The mean of the predicted edge distribution under _i,k ,

For the variance of the predicted edge distribution of the target i under the model r _i,k , t _k|k-1 (r _i,k |r _i,k-1 ) is the model transition probability,

For the surviving probability of the target, Δt=t _k -t _k-1 is the time difference between the current time and the previous time, T is the sampling period, δ is the given constant, and F _k-1 (r _i,k ) is the former The state transition matrix of the i-th edge distribution at a moment, Q _k-1 (r _i,k ) is the process noise variance matrix of the i-th edge distribution at the previous moment, r _i,k-1 is the ith of the previous moment The model label of the edge distribution, the superscript T is represented as a transpose of a matrix or a vector.

步骤B、根据所述预测的当前时刻各个目标在不同模型下的边缘分布及其存在概率，利用贝叶斯规则序贯处理当前时刻的每一个测量数据得到各个目标在不同模型下的更新边缘分布及其存在概率。Step B: According to the predicted edge current distribution and the existence probability of each target under different models, the Bayes rule is used to sequentially process each measurement data of the current time to obtain the updated edge distribution of each target under different models. And its probability of existence.

贝叶斯规则(Bayes theorem)为一个数学公式，用数学语言表达为：支持某项属性的事件发生得愈多，则该属性成立的可能性就愈大。通俗地讲就是当不能准确知悉一个事物的本质时，可以依靠与事物特定本质相关的事件出现的多少去判断其本质属性的概率。贝叶斯规则是关于随机事件A和B的条件概率和边缘概率的。相应术语解释：Pr(A)是A的先验概率或边缘概率，之所以称为先验是因为它不考虑任何B方面的因素；Pr(A|B)是已知B发生后A的条件概率，也由于得知B的取值而被称作A的后验概率；Pr(B|A)是已知A发生后B的条件概率，也由于得知A的取值而被称作B的后验概率；Pr(B)是B的先验概率或边缘概率，也作标准化常量(normalized constant)。根据这些术语，Bayes法则可表述为：后验概率＝(相似度×先验概率)/标准化常量，也就是说，后验概率与先验概率和相似度的乘积成正比。The Bayesian rule (Bayes theorem) is a mathematical formula expressed in a mathematical language: the more events that support an attribute occur, the greater the likelihood that the attribute will be established. In layman's terms, when the nature of a thing cannot be accurately known, the probability of its essential attribute can be judged by the number of events associated with the specific nature of the thing. Bayesian rules are conditional probabilities for random events A and B And the probability of the edge. Corresponding term explanation: Pr(A) is the prior probability or edge probability of A, which is called a priori because it does not consider any B factor; Pr(A|B) is the condition of A after B is known to occur. The probability is also called the posterior probability of A because it knows the value of B; Pr(B|A) is the conditional probability of B after the known A occurs, and is also called B because it knows the value of A. The posterior probability; Pr(B) is the prior probability or edge probability of B, and is also a normalized constant. According to these terms, Bayes' rule can be expressed as: posterior probability = (similarity × prior probability) / normalized constant, that is, the posterior probability is proportional to the product of prior probability and similarity.

设当前时刻接收到的观测集为y_k＝(y_1,k,…,y_M,k)，其中，M为当前时刻接收到的测量数据总数。利用贝叶斯规则对当前时刻接收到的测量数据进行序贯处理的步骤包括：Let the observation set received at the current time be y _k =(y _1,k ,...,y _M,k ), where M is the total number of measurement data received at the current time. The steps of sequentially processing the measurement data received at the current time by using the Bayes rule include:

步骤01、取边缘分布

取存在概率

其中，i＝1,2,...,N_k-1，r_i,k＝1,…,M_r。Step 01, take the edge distribution

Presence probability

Wherein, i = 1,2, ..., N k-1, r i, k = 1, ..., M r.

步骤02、利用贝叶斯规则将第1个至M个测量数据依次进行处理：设

为第j个测量数据处理前目标i在模型r_i,k下的边缘分布，

为第j个测量数据处理前目标i在模型r_i,k下的边缘分布的存在概率，其中，1≤j≤M；由

和

求得第j个测量数据更新时的存在概率为

均值向量

协方差矩阵

滤波器增益

其中，H_k(r_i,k)为模型r_i,k的观测矩阵，R_k(r_i,k)为模型r_i,k的观测噪声方差矩阵，p_D,k为目标的检测概率，λ_c,k为杂波密度，I表示单位矩阵，y_j,k为当前时刻接收到的第j测量数据，上标T表示为矩阵或向量的转置，r_i,k＝1,…,M_r。 Step 02: sequentially process the first to M measurement data by using a Bayes rule:

The edge distribution of the target i under the model r _i,k before processing the jth measurement data,

The existence probability of the edge distribution of the target i under the model r _i,k for the jth measurement data, where 1 ≤ j ≤ M;

with

The probability of existence when the jth measurement data is updated is

Mean vector

Covariance matrix

Filter gain

Where H _k (r _i,k ) is the observation matrix of the model r _i,k , R _k (r _i,k ) is the observed noise variance matrix of the model r _i,k , p _D,k is the detection probability of the target, λ _c,k is the clutter density, I represents the unit matrix, y _j,k is the jth measurement data received at the current time, and the superscript T is represented as the transpose of the matrix or vector, r _i,k =1,..., M _r .

由

和

计算得到

和

by

with

Calculated

with

如果

则第j个测量数据处理后的目标i在模型r_i,k下的边缘分布为

其存在概率为

其中，

r_i,k＝1,…,M_r。in case

Then the edge of the target i processed by the jth measurement data is distributed under the model r _i,k

Its probability of existence is

among them,

r _i,k =1,...,M _r .

如果

则第j个测量数据处理后的目标i在模型r_i,k下的边缘分布为

其存在概率为

其中，

r_i,k＝1,…,M_r。in case

Its probability of existence is

among them,

r _i,k =1,...,M _r .

步骤03、第M个测量数据被处理后目标i在模型r_i,k下的边缘分布为

其存在概率为

其中，i＝1,…,N_k-1，r_i,k＝1,…,M_r。Step 03: After the Mth measurement data is processed, the edge distribution of the target i under the model r _i,k is

Its probability of existence is

Where i=1,...,N _k-1 ,r _i,k =1,...,M _r .

由此得到当前时刻目标i在模型r_i,k下的更新边缘分布为

更新边缘分布的存在概率为

其中，

i＝1,…,N_k-1，r_i,k＝1,…,M_r。Thus, the updated edge distribution of the current time target i under the model r _i,k is obtained as

The existence probability of updating the edge distribution is

among them,

i=1,...,N _k-1 ,r _i,k =1,...,M _r .

步骤C、将当前时刻各个目标在不同模型下的更新边缘分布及其存在概率进行融合，形成当前时刻各个目标的更新边缘分布及存在概率。Step C: merging the updated edge distribution and the existence probability of each target in different models at the current moment to form an updated edge distribution and existence probability of each target at the current moment.

当前时刻目标i的更新边缘分布为

r_i,k＝1,…,M_r，其存在概率为

r_i,k＝1,…,M_r。将当前时刻目标i的M_r个更新边缘分布及其存在概率融合成一个边缘分布N(x_q,k；m_q,k(r_q,k),P_q,k(r_q,k))和一个存在概率ρ_q,k(r_q,k)，其中

表示M_r个模型中存在概率最大模型的标签，均值向量

q＝1,…,N_k-1，协方差矩阵

q＝1,…,N_k-1。The update edge distribution of the current time target i is

r _i,k =1,...,M _r , whose probability of existence is

r _i,k =1,...,M _r . The M _r of the current time i a target edge updated existence probability distribution and integration into one edge profile _{N (x q, k; m} q, k (r q, k), P q, k (r q, k)) And an existence probability ρ _q,k (r _q,k ), where

Represents the label with the largest probability model in the _rm models, the mean vector

q=1,...,N _k-1 ,covariance matrix

q=1,...,N _k-1 .

步骤D、利用当前时刻的每一个测量数据产生新目标的边缘分布，为其指定存在概率和模型标签；同时，将当前时刻新目标的边缘分布及其存在概率分别与所述当前时刻各个目标的更新边缘分布及其存在概率进行合并，生成当前时刻的各个目标的边缘分布及其存在概率。Step D: using each measurement data of the current moment to generate an edge distribution of the new target, which is referred to The existence probability and the model label are determined; at the same time, the edge distribution of the new target at the current moment and the existence probability thereof are respectively combined with the updated edge distribution of each target at the current moment and the existence probability thereof, and the edge distribution of each target at the current moment is generated and Its probability of existence.

具体包括以下步骤：Specifically, the following steps are included:

利用当前时刻M个测量数据生成当前时刻新生目标的边缘分布

j＝1,…,M，为当前时刻各新生目标的边缘分布指定存在概率

j＝1,…,M，其中，ρ_γ为指定的存在概率，指定模型1为当前时刻的模型标签，即r_j,k＝1；其中，

为第j个新生边缘分布的协方差，

为第j个新生的边缘分布的均值，

由当前时刻的第j个测量数据y_j,k＝[x_j,k y_j,k]^T产生，并且

Using the current measurement data to generate the edge distribution of the new target at the current time

j=1,...,M, specify the existence probability of the edge distribution of each new target at the current time

j=1,...,M, where ρ _γ is the specified existence probability, and model 1 is specified as the model label of the current time, that is, r _j,k =1; wherein

The covariance of the distribution of the jth new edge,

The mean of the distribution of the edges of the jth newborn,

Generated from the jth measurement data y _j,k =[x _j,k y _j,k ] ^T at the current time, and

将融合后的边缘分布与当前时刻新生的边缘分布进行合并，形成当前时刻的边缘分布为

将当前时刻融合后边缘分布的存在概率与当前时刻新生目标边缘分布的存在概率合并，生成当前时刻边缘分布的存在概率为

其中N_k＝N_k-1+M。Combining the merged edge distribution with the newly created edge distribution at the current moment to form the edge distribution of the current moment is

The existence probability of the edge distribution after the current time is merged with the existence probability of the new target edge distribution at the current time, and the existence probability of the edge distribution at the current time is generated as

Where N _k = N _k-1 + M.

步骤E、从合并后所生成的当前时刻各个目标的边缘分布中将存在概率小于第一阈值的边缘分布裁减掉，并且将裁减后的边缘分布及其存在概率作为下一时刻递归滤波的输入。同时，从裁减后的边缘分布中提取存在概率大于第二阈值的边缘分布作为当前时刻的输出，并且将各个输出边缘分布的均值与方差分别作为当前时刻目标的状态估计与误差估计。Step E: The edge distribution with the probability of being less than the first threshold is cut off from the edge distribution of each target at the current moment generated after the merge, and the reduced edge distribution and its existence probability are used as inputs of the next time recursive filtering. At the same time, the edge distribution with the existence probability greater than the second threshold is extracted from the reduced edge distribution as the output of the current time, and the mean and the variance of the respective output edge distributions are respectively used as the state estimation and the error estimation of the current time target.

当前时刻合并后的边缘分布为N(x_i,k；m_i,k(r_i,k),P_i,k(r_i,k))，i＝1,…,N_k，当前时刻合并后各边缘分布的存在概率为ρ_i,k(r_i,k)，i＝1,…,N_k。从合并后所生成当前时刻的边缘分布中将存在概率小于第一阈值的边缘分布裁减掉，裁减后的边缘分布及其存在概率作为下一时刻滤波器的递归输入，同时，选择存在概率大于第二阈值的边缘分布作为当前时刻的输出。第一阈值也称为裁减阈值，其取值范围为：大于0而小于所指定的新生目标存在概率；第二阈值也称为裁减阈值，其取值范围为：大于0而小于1。The merged edge distribution at the current time is N(x _i,k ;m _i,k (r _i,k ), P _i,k (r _i,k )), i=1,...,N _k , the current time merge The existence probabilities of the subsequent edge distributions are ρ _i,k (r _i,k ), i=1,...,N _k . The edge distribution with the probability less than the first threshold is cut off from the edge distribution of the current time generated after the combination, and the edge distribution after clipping and its existence probability are used as the recursive input of the filter at the next moment, and the probability of existence is greater than The edge distribution of the two thresholds is taken as the output of the current time. The first threshold is also referred to as a reduction threshold, and the value ranges from greater than 0 to less than the specified new target existence probability; the second threshold is also referred to as a reduction threshold, and the value ranges from greater than 0 to less than 1.

如图2所示，一种基于序贯贝叶斯滤波的多目标跟踪***，包括：预测模块201、更新模块202、模型融合模块203、边缘分布生成模块204以及边缘分布提取模块205。As shown in FIG. 2, a multi-target tracking system based on sequential Bayesian filtering includes: a prediction module 201, an update module 202, a model fusion module 203, an edge distribution generation module 204, and an edge distribution extraction module 205.

预测模块201接收到新的测量数据后，计算出接收到新的测量数据的时刻与接收到前一个测量数据的时刻的时间差，以接收到所述新的测量数据的时刻为当前时刻，接收到前一个测量数据的时刻为前一时刻；根据所述时间差、模型间的转移概率以及前一时刻各个目标的边缘分布及其存在概率，预测出当前时刻各个目标在不同模型下的边缘分布及其存在概率。After receiving the new measurement data, the prediction module 201 calculates the time difference between the time when the new measurement data is received and the time when the previous measurement data is received, so that the time when the new measurement data is received is the current time, and the received time is received. The time of the previous measurement data is the previous time; according to the time difference, the transition probability between the models, and the edge distribution of each target at the previous moment and the existence probability thereof, the edge distribution of each target under different models at the current time is predicted and Probability of existence.

更新模块202根据预测模块201中预测的当前时刻各个目标在不同模型下的边缘分布及其存在概率，利用贝叶斯规则序贯处理当前时刻的每一个测量数据得到各个目标在不同模型下的更新边缘分布及其存在概率。The update module 202 sequentially processes each measurement data of the current time according to the edge distribution of each target under different models predicted by the prediction module 201 at the current time, and obtains the update of each target under different models by using the Bayes rule. Edge distribution and its probability of existence.

模型融合模块203用于将更新模块202中当前时刻各个目标在不同模型下的更新边缘分布及其存在概率进行融合，形成当前时刻各个目标的更新边缘分布及存在概率。The model fusion module 203 is configured to combine the updated edge distributions and the existence probabilities of the respective targets in the update module 202 at different moments in the different models to form an updated edge distribution and an existence probability of each target at the current moment.

边缘分布生成模块204利用当前时刻的每一个测量数据产生新目标的边缘分布，为其指定存在概率和模型标签；同时，将当前时刻新目标的边缘分布及其存在概率分别与所述模型融合模块中当前时刻各个目标的更新边缘分布及其存在概率进行合并，生成当前时刻的各个目标的边缘分布及其存在概率。The edge distribution generation module 204 generates an edge distribution of the new target by using each measurement data of the current time, and specifies the existence probability and the model label for the current target; meanwhile, the edge distribution of the new target at the current moment and the existence probability thereof are respectively combined with the model fusion module. The updated edge distribution of each target in the current moment and its existence probability are combined to generate the edge distribution of each target at the current moment and its existence probability.

边缘分布提取模块205从所述边缘分布生成模块中将合并后所生成的当前时刻各个目标的边缘分布中将存在概率小于第一阈值的边缘分布裁减掉，并且将裁减后的边缘分布及其存在概率作为下一时刻递归滤波的输入，同时，从裁减后的边缘分布中提取存在概率大于第二阈值的边缘分布作为当前时刻的输出，并且将各个输出边缘分布的均值与方差分别作为当前时刻目标的状态估计与误差估计。The edge distribution extraction module 205 cuts off the edge distribution of the edge distribution of each target at the current moment generated by the merged edge generated by the merged edge, and reduces the edge distribution and the existence of the edge distribution Probability is used as the input of recursive filtering at the next moment. At the same time, the edge distribution with the existence probability greater than the second threshold is extracted from the reduced edge distribution as the output of the current time, and the mean and variance of each output edge distribution are respectively used as the current time target. State estimate With error estimates.

预测模块201中，以k-1表示前一时刻，k表示当前时刻，t_k-1表示前一时刻的时间，t_k表示当前时刻的时间，r_i,k-1表示前一时刻第i个边缘分布的模型标签，r_i,k表示当前时刻第i个边缘分布的模型标签，1≤r_i,k≤M_r，M_r表示模型的总数目。In the prediction module 201, the previous time is represented by k-1, k represents the current time, t _k-1 represents the time of the previous time, t _k represents the time of the current time, and r _i,k-1 represents the i-th time of the previous time. label edges distribution _model, r _{i, k} represents the current moment of the i-th label edge distribution _{_{model, 1≤r i, k ≤M r,}} M r represents the total number of models.

更新模块202中，设当前时刻接收到的观测集为y_k＝(y_1,k,…,y_M,k)，其中，M为当前时刻接收到的测量数据总数；利用贝叶斯规则对当前时刻接收到的测量数据进行序贯处理具体包括：In the update module 202, it is assumed that the observation set received at the current time is y _k = (y _{1, k} , ..., y _{M, k} ), where M is the total number of measurement data received at the current time; using Bayesian rule The sequential processing of the measurement data received at the current time specifically includes:

提取单元，用于提取边缘分布

取存在概率

其中，i＝1,2,...,N_k-1，r_i,k＝1,…,M_r；Extraction unit for extracting edge distribution

Presence probability

Where i=1,2,...,N _k-1 ,r _i,k =1,...,M _r ;

处理单元，利用贝叶斯规则将第1个至M个测量数据依次进行处理：设

为第j个测量数据处理前目标i在模型r_i,k下的边缘分布，

和

求得第j个测量数据更新时的存在概率为

均值向量

协方差矩阵

滤波器增益

其中，H_k(r_i,k)为模型r_i,k的观测矩阵，R_k(r_i,k)为模型r_i,k的观测噪声方差矩阵，p_D,k为目标的检测概率，λ_c,k为杂波密度，I表示单位矩阵，y_j,k为当前时刻接收到的第j测量数据，上标T表示为矩阵或向量的转置，r_i,k＝1,…,M_r。The processing unit sequentially processes the first to M measurement data by using a Bayes rule:

with

The probability of existence when the jth measurement data is updated is

Mean vector

Covariance matrix

Filter gain

计算单元，根据

和

计算得到

和

Computing unit, according to

with

Calculated

with

如果

则第j个测量数据处理后的目标i在模型r_i,k下的边缘分布为

其存在概率为

其中，

r_i,k＝1,…,M_r。in case

Its probability of existence is

among them,

r _i,k =1,...,M _r .

如果

则第j个测量数据处理后的目标i在模型r_i,k下的边缘分布为

其存在概率为

其中，

r_i,k＝1,…,M_r。in case

Its probability of existence is

among them,

r _i,k =1,...,M _r .

更新单元，第M个测量数据被处理后目标i在模型r_i,k下的边缘分布为

其存在概率为

其中，i＝1,…,N_k-1，r_i,k＝1,…,M_r。 Update unit, after the Mth measurement data is processed, the edge distribution of the target i under the model r _i,k is

Its probability of existence is

Where i=1,...,N _k-1 ,r _i,k =1,...,M _r .

由此得到当前时刻目标i在模型r_i,k下的更新边缘分布为

更新边缘分布的存在概率为

其中，

The existence probability of updating the edge distribution is

among them,

i=1,...,N _k-1 ,r _i,k =1,...,M _r .

模型融合模块203中，当前时刻目标i的更新边缘分布为

r_i,k＝1,…,M_r，其存在概率为

r_i,k＝1,…,M_r；将当前时刻目标i的M_r个更新边缘分布及其存在概率融合成一个边缘分布N(x_q,k；m_q,k(r_q,k),P_q,k(r_q,k))和一个存在概率ρ_q,k(r_q,k)，其中，

表示M_r个模型中存在概率最大模型的标签，均值向量

q＝1,…,N_k-1，协方差矩阵

q＝1,…,N_k-1。In the model fusion module 203, the updated edge distribution of the current time target i is

r _i,k =1,...,M _r , whose probability of existence is

_{r i, k = 1, ...} , M r; the M _r of the current time i a target edge updated existence probability distribution and integration into one edge profile _{N (x q, k; m} q, k (r q, k) , P _q,k (r _q,k )) and an existence probability ρ _q,k (r _q,k ), where

q=1,...,N _k-1 ,covariance matrix

q=1,...,N _k-1 .

边缘分布生成模块204中，利用当前时刻M个测量数据生成当前时刻新生目标的边缘分布

j＝1,…,M，为当前时刻各新生目标的边缘分布指定存在概率

为第j个新生边缘分布的协方差，

为第j个新生的边缘分布的均值，

由当前时刻的第j个测量数据y_j,k＝[x_j,k y_j,k]^T产生，并且

In the edge distribution generation module 204, the edge distribution of the new target at the current time is generated by using the M measurement data at the current time.

The covariance of the distribution of the jth new edge,

The mean of the distribution of the edges of the jth newborn,

其中N_k＝N_k-1+M。 Combining the merged edge distribution with the newly created edge distribution at the current moment to form the edge distribution of the current moment is

Where N _k = N _k-1 + M.

当前时刻合并后的边缘分布为N(x_i,k；m_i,k(r_i,k),P_i,k(r_i,k))，i＝1,…,N_k，当前时刻合并后各边缘分布的存在概率为ρ_i,k(r_i,k)，i＝1,…,N_k。边缘分布提取模块205从合并后所生成当前时刻的边缘分布中将存在概率小于第一阈值的边缘分布裁减掉，裁减后的边缘分布及其存在概率作为下一时刻滤波器的递归输入，同时，选择存在概率大于第二阈值的边缘分布作为当前时刻的输出。The merged edge distribution at the current time is N(x _i,k ;m _i,k (r _i,k ), P _i,k (r _i,k )), i=1,...,N _k , the current time merge The existence probabilities of the subsequent edge distributions are ρ _i,k (r _i,k ), i=1,...,N _k . The edge distribution extraction module 205 cuts the edge distribution whose existence probability is less than the first threshold from the edge distribution of the current time generated after the combination, and reduces the edge distribution and the existence probability as the recursive input of the next time filter, and The edge distribution whose existence probability is greater than the second threshold is selected as the output of the current time.

作为本发明的一个实例，考虑二维空间[-400m，400m]×[-400m，400m]中运动的目标，目标的状态由位置和速度构成，表示为

其中x和y分别表示位置分量，

和

分别表示速度分量，上标T表示向量的转置，状态转移矩阵为

过程噪声方差矩阵为

其中，△t_k＝t_k-t_k-1为当前时刻与前一时刻的时间差，σ_v为过程噪声标准差；模型r_i,k＝1，r_i,k＝2，r_i,k＝3为三个不同的目标运动模型，模型r_i,k＝1的状态转移矩阵为F_k-1(r_i,k＝1)＝F(ω＝0°s^-1)，过程噪声方差矩阵为Q_k-1(r_i,k＝1)＝Q(σ_v＝1ms^-2)，模型r_i,k＝2的状态转移矩阵为F_k-1(r_i,k＝2)＝F(ω＝5°s^-1)，过程噪声方差矩阵为Q_k-1(r_i,k＝2)＝Q(σ_v＝3ms^-2)，模型r_i,k＝3的状态转移矩阵为F_k-1(r_i,k＝3)＝F(ω＝-5°s^-1)，过程噪声方差矩阵为Q_k-1(r_i,k＝3)＝Q(σ_v＝3ms^-2)。不同运动模型之间的马尔科夫转移概率矩阵为

观测矩阵

观测噪声方差矩阵

σ_w为观测噪声的标准差。As an example of the present invention, considering the target of motion in a two-dimensional space [-400m, 400m] × [-400m, 400m], the state of the target is composed of position and velocity, expressed as

Where x and y represent positional components, respectively.

with

Respectively represent the velocity component, the superscript T represents the transpose of the vector, and the state transition matrix is

The process noise variance matrix is

Where Δt _k =t _k -t _k-1 is the time difference between the current time and the previous time, σ _v is the standard deviation of the process noise; the model r _i,k =1, r _i,k =2, r _i,k =3 is three different target motion models. The state transition matrix of the model r _i,k =1 is F _k-1 (r _i,k =1)=F(ω=0°s ^-1 ), the process noise variance The matrix is Q _k-1 (r _i,k =1)=Q(σ _v =1ms ^-2 ), and the state transition matrix of the model r _i,k =2 is F _k-1 (r _i,k =2)= F(ω=5°s ^-1 ), the process noise variance matrix is Q _k-1 (r _i,k =2)=Q(σ _v =3ms ^-2 ), and the state transition matrix of the model r _i,k =3 For F _k-1 (r _i,k =3)=F(ω=-5°s ^-1 ), the process noise variance matrix is Q _k-1 (r _i,k =3)=Q(σ _v =3ms ^-2 ). The Markov transition probability matrix between different motion models is

Observation matrix

Observed noise variance matrix

σ _w is the standard deviation of the observed noise.

为了产生仿真数据，取幸存概率p_S,k＝1.0、检测概率p_D,k＝0.9、杂波密度λ_c,k＝1.6×10^-10m^-2、过程噪声的标准差σ_v＝1ms^-2和观测噪声的标准差σ_w＝1m。一次实验中传感器在50个扫描周期的仿真观测数据如图3所示。为了处理仿真数据，将本发明与基于马尔科夫***模型的高斯混合概率假设密度滤波器(Gaussian Mixture probability hypothesis density filter for jump Markov system models,GM-PHD-JMS滤波器)的相关参数设置为p_S,k＝1.0、p_D,k＝0.9、λ_c,k＝1.6×10^-10m^-2、σ_w＝2m、σ_v＝1ms^-2、第一阈值为10^-3、第二阈值为0.5、GM-PHD-JMS新生成目标的权重w_γ＝0.1，本发明新产生目标的存在概率p_γ＝0.1，新产生目标的协方差为

如图4和图5所示，为对比滤波器与本发明产生的结果。将本发明的多目标跟踪方法与现有的GM-PHD-JMS滤波器对图3的仿真数据进行处理，100次Monte Carlo实验得到平均OSPA(Optimal Subpattern Assignment，最优亚模式分配)距离如图6所示。将现有的基于跳跃马尔科夫模型的GM-PHD滤波与本发明相比，本发明的多目标跟踪方法在关联不确定、检测不确定和杂波的情况下对机动目标的跟踪获得更为精确和可靠的目标状态估计、其OSPA距离比现有的这种方法得到的OSPA距离要小。In order to generate simulation data, the surviving probability p _{S, k} = 1.0, the detection probability p _{D, k} = 0.9, the clutter density λ _{c, k} = 1.6 × 10 ^-10 m ^-2 , and the standard deviation of the process noise σ _v =1 ms ^-2 and the standard deviation of observed noise σ _w =1m. The simulated observation data of the sensor in 50 scan cycles in one experiment is shown in Fig. 3. In order to process the simulation data, the relevant parameters of the present invention and the Gaussian Mixture probability hypothesis density filter for jump Markov system models (GM-PHD-JMS filter) are set to p. _{S, k} = 1.0, p _{D, k} = 0.9, λ _{c, k} = 1.6 × 10 ^-10 m ^-2 , σ _w = 2m, σ _v =1ms ^-2 , the first threshold is 10 ^-3 , the second threshold For 0.5, the weight of the newly generated target of GM-PHD-JMS is w _γ = 0.1, the existence probability of the newly generated target of the present invention is p _γ = 0.1, and the covariance of the newly generated target is

As shown in Figures 4 and 5, this is the result of the comparison filter and the present invention. The multi-target tracking method of the present invention is processed with the existing GM-PHD-JMS filter for the simulation data of FIG. 3, and the average OFAP (Optimal Subpattern Assignment) distance is obtained by 100 Monte Carlo experiments. 6 is shown. Compared with the present invention, the existing GM-PHD filtering based on the hopping Markov model is more accurate in tracking the maneuvering target in the case of correlation uncertainty, detection uncertainty and clutter. Accurate and reliable target state estimation, its OFAC distance is smaller than the existing OSPA distance obtained by this method.

本发明的基于序贯贝叶斯滤波的多目标跟踪方法及多目标跟踪***将不同模型与序贯贝叶斯滤波器相结合，利用马尔科夫链控制模型间的转换，通过对当前时刻的测量数据序贯处理以获得当前时刻各目标在不同模型下更新的边缘分布及其存在概率，通过对目标在不同模型下的边缘分布的融合将多个边缘分布合成为一个边缘分布，这使得多目标跟踪方法既能对当前时刻接收到的测量数据进行及时的处理，从而避免了信息处理的延迟、确保了数据处理的实时性，同时又能对运动模式在不同模型间跳变的机动目标进行有效跟踪，进而扩大了实用性。The multi-target tracking method based on sequential Bayesian filtering and the multi-target tracking system of the present invention combine different models with sequential Bayesian filters, and use Markov chain to control the conversion between models, through the current moment Sequential processing of measurement data to obtain the edge distribution and its existence probability of each target updated under different models at the current time, and synthesize multiple edge distributions into one edge distribution by merging the edge distribution of the target under different models, which makes The target tracking method can not only timely process the measurement data received at the current time, thereby avoiding the delay of information processing, ensuring the real-time performance of the data processing, and at the same time, maneuvering the target with the motion pattern jumping between different models. Effective tracking, which has expanded Practicality.

以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。 The above is only the preferred embodiment of the present invention, and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection of the present invention. Within the scope.

Claims

基于序贯贝叶斯滤波的多目标跟踪方法，其特征在于，包括以下步骤：A multi-target tracking method based on sequential Bayesian filtering, comprising the following steps:

步骤A、当接收到新的测量数据后，计算出接收到所述新的测量数据的时刻与接收到前一个测量数据的时刻的时间差，以接收到所述新的测量数据的时刻为当前时刻，接收到前一个测量数据的时刻为前一时刻；根据所述时间差、各个模型间的转移概率以及前一时刻各个目标的边缘分布及其存在概率，预测出当前时刻各个目标在不同模型下的边缘分布及其存在概率；Step A: After receiving new measurement data, calculate a time difference between a time when the new measurement data is received and a time when the previous measurement data is received, so that the time when the new measurement data is received is the current time The time at which the previous measurement data is received is the previous time; according to the time difference, the transition probability between each model, and the edge distribution of each target at the previous moment and its existence probability, it is predicted that each target at the current time is under a different model. Edge distribution and its existence probability;

步骤B、根据所述预测的当前时刻各个目标在不同模型下的边缘分布及其存在概率，利用贝叶斯规则序贯处理当前时刻的每一个测量数据得到各个目标在不同模型下的更新边缘分布及其存在概率；Step B: According to the predicted edge current distribution and the existence probability of each target under different models, the Bayes rule is used to sequentially process each measurement data of the current time to obtain the updated edge distribution of each target under different models. And its probability of existence;

步骤C、将所述当前时刻各个目标在不同模型下的更新边缘分布及其存在概率进行融合，形成当前时刻各个目标的更新边缘分布及存在概率；Step C: merging the updated edge distributions and the existence probabilities of the respective targets in the different models at the current moment to form an updated edge distribution and an existence probability of each target at the current moment;

步骤D、利用当前时刻的每一个测量数据产生新目标的边缘分布，为其指定存在概率和模型标签；同时，将当前时刻新目标的边缘分布及其存在概率分别与所述当前时刻各个目标的更新边缘分布及其存在概率进行合并，生成当前时刻的各个目标的边缘分布及其存在概率；Step D: using each measurement data of the current moment to generate an edge distribution of the new target, assigning an existence probability and a model label thereto; and simultaneously, respectively, an edge distribution of the new target at the current moment and its existence probability are respectively associated with each target of the current moment Update the edge distribution and its existence probability to merge, and generate the edge distribution of each target at the current moment and its existence probability;

步骤E、从合并后所生成的当前时刻各个目标的边缘分布中将存在概率小于第一阈值的边缘分布裁减掉，并且将裁减后的边缘分布及其存在概率作为下一时刻递归滤波的输入，同时，从裁减后的边缘分布中提取存在概率大于第二阈值的边缘分布作为当前时刻的输出，并且将各个输出边缘分布的均值与方差分别作为当前时刻目标的状态估计与误差估计。Step E: The edge distribution with the probability of being less than the first threshold is cut off from the edge distribution of each target at the current moment generated after the merge, and the reduced edge distribution and its existence probability are used as input of recursive filtering at the next moment. At the same time, the edge distribution with the existence probability greater than the second threshold is extracted from the reduced edge distribution as the output of the current time, and the mean and the variance of the respective output edge distributions are respectively used as the state estimation and the error estimation of the current time target.
根据权利要求1所述的多目标跟踪方法，其特征在于，所述步骤A中，以k-1表示前一时刻，k表示当前时刻，t_k-1表示前一时刻的时间，t_k表示当前时刻的时间，r_i,k-1表示前一时刻第i个边缘分布的模型标签，r_i,k表示当前时刻第i个边缘分布的模型标签，1≤r_i,k≤M_r，M_r表示模型的总数目； The multi-target tracking method according to claim 1, wherein, in the step A to k-1 represents a previous time, k represents the current time, the time T _k-1 represents a previous time, t _k represents At the current time, r _i,k-1 represents the model label of the i-th edge distribution at the previous moment, and r _i,k represents the model label of the i-th edge distribution at the current moment, 1≤r _i,k ≤M _r , M _r represents the total number of models;

已知前一时刻第i个边缘分布为N(x_i,k-1；m_i,k-1(r_i,k-1),P_i,k-1(r_i,k-1))，i＝1,2,...,N_k-1，前一时刻第i个边缘分布的存在概率为ρ_i,k-1(r_i,k-1)，i＝1,…,N_k-1；其中，N表示高斯分布，x_i,k-1表示为前一时刻第i个边缘分布的状态向量，m_i,k-1(r_i,k-1)和P_i,k-1(r_i,k-1)分别表示前一时刻第i个边缘分布的均值和方差，N_k-1为前一时刻目标的总数，i为索引号，1≤i≤N_k-1；It is known that the i-th edge distribution at the previous moment is N(x _i,k-1 ;m _i,k-1 (r _i,k-1 ), P _i,k-1 (r _i,k-1 )) , i = 1, 2, ..., N _k-1 , the existence probability of the i-th edge distribution at the previous moment is ρ _i,k-1 (r _i,k-1 ), i=1,...,N _K-1 ; where N denotes a Gaussian distribution, x _i,k-1 denotes a state vector of the i-th edge distribution at the previous moment, m _i,k-1 (r _i,k-1 ) and P _{i,k -1} (r _i,k-1 ) respectively represent the mean and variance of the i-th edge distribution at the previous moment, N _k-1 is the total number of targets at the previous moment, i is the index number, _{1 ≤} i ≤ N _k-1 ;

根据前一时刻的边缘分布及其存在概率、当前时刻与前一时刻的时间差以及模型间的转移概率得出当前时刻各目标在不同模型下预测的边缘分布为N(x_i,k；m_i,k|k-1(r_i,k),P_i,k|k-1(r_i,k))，i＝1,2,...,N_k-1，1≤r_i,k≤M_r；当前时刻各预测边缘分布的存在概率为ρ_i,k|k-1(r_i,k)＝p_S,k(t_k-t_k-1)t_k|k-1(r_i,k|r_i,k-1)ρ_i,k-1(r_i,k-1)，i＝1,2,...,N_k-1，1≤r_i,k≤M_r；其中，m_i,k|k-1(r_i,k)＝F_k-1(r_i,k)m_i,k-1(r_i,k-1)为当前时刻目标i在模型r_i,k下的预测边缘分布的均值，
为目标i在模型r_i,k下的预测边缘分布的方差，t_k|k-1(r_i,k|r_i,k-1)为模型间的转移概率，
为目标的幸存概率，△t＝t_k-t_k-1为当前时刻与前一时刻的时间差，T为采样周期，δ为给定的常数，F_k-1(r_i,k)为前一时刻第i个边缘分布的状态转移矩阵，Q_k-1(r_i,k)为前一时刻第i个边缘分布的过程噪声方差矩阵，r_i,k-1为前一时刻第i个边缘分布的模型标签，上标T表示为矩阵或向量的转置。According to the edge distribution of the previous moment and its existence probability, the time difference between the current moment and the previous moment, and the transition probability between the models, the edge distribution predicted by each target under different models at the current moment is N(x _i,k ;m _{i ,k|k-1} (r _i,k ),P _i,k|k-1 (r _i,k )),i=1,2,...,N _k-1 ,1≤r _i,k ≤M _r ; the existence probability of each predicted edge distribution at the current time is ρ _i,k|k-1 (r _i,k )=p _S,k (t _k -t _k-1 )t _k|k-1 (r _i,k |r _i,k-1 )ρ _i,k-1 (r _i,k-1 ),i=1,2,...,N _k-1 ,1≤r _i,k ≤M _r Where m _i,k|k-1 (r _i,k )=F _k-1 (r _i,k )m _i,k-1 (r _i,k-1 ) is the current time target i in the model r The mean of the predicted edge distribution under _i,k ,
For the variance of the predicted edge distribution of the target i under the model r _i,k , t _k|k-1 (r _i,k |r _i,k-1 ) is the transition probability between the models,
For the surviving probability of the target, Δt=t _k -t _k-1 is the time difference between the current time and the previous time, T is the sampling period, δ is the given constant, and F _k-1 (r _i,k ) is the former The state transition matrix of the i-th edge distribution at a moment, Q _k-1 (r _i,k ) is the process noise variance matrix of the i-th edge distribution at the previous moment, r _i,k-1 is the ith of the previous moment The model label of the edge distribution, the superscript T is represented as a transpose of a matrix or a vector.
根据权利要求2所述的多目标跟踪方法，其特征在于，所述步骤B中，设当前时刻接收到的观测集为y_k＝(y_1,k,…,y_M,k)，其中，M为当前时刻接收到的测量数据总数；利用贝叶斯规则对当前时刻接收到的测量数据进行序贯处理的步骤包括：The multi-target tracking method according to claim 2, wherein in the step B, the observation set received at the current time is y _k = (y _{1, k} , ..., y _{M, k} ), wherein M is the total number of measurement data received at the current time; the steps of sequentially processing the measurement data received at the current time by using the Bayes rule include:

步骤01、取边缘分布

取存在概率
其中，i＝1,2,...,N_k-1，r_i,k＝1,…,M_r；Step 01, take the edge distribution

Presence probability
Where i=1,2,...,N _k-1 ,r _i,k =1,...,M _r ;

步骤02、利用贝叶斯规则将第1个至M个测量数据依次进行处理：设
为第j个测量数据处理前目标i在模型r_i,k下的边缘分布，
为第j个测量数据处理前目标i在模型r_i,k下的边缘分布的存在概率，其中，1≤j≤M；由
和
求得第j个测量数据更新时的存在概率为
均值向量
协方差矩阵
滤波器增益
其中，H_k(r_i,k)为模型r_i,k的观测矩阵，R_k(r_i,k)为模型r_i,k的观测噪声方差矩阵，p_D,k为目标的检测概率，λ_c,k为杂波密度，I表示单位矩阵，y_j,k为当前时刻接收到的第j测量数据，上标T表示为矩阵或向量的转置，r_i,k＝1,…,M_r；Step 02: sequentially process the first to M measurement data by using a Bayes rule:
The edge distribution of the target i under the model r _i,k before processing the jth measurement data,
The existence probability of the edge distribution of the target i under the model r _i,k for the jth measurement data, where 1 ≤ j ≤ M;
with
The probability of existence when the jth measurement data is updated is
Mean vector
Covariance matrix
Filter gain
Where H _k (r _i,k ) is the observation matrix of the model r _i,k , R _k (r _i,k ) is the observed noise variance matrix of the model r _i,k , p _D,k is the detection probability of the target, λ _c,k is the clutter density, I represents the unit matrix, y _j,k is the jth measurement data received at the current time, and the superscript T is represented as the transpose of the matrix or vector, r _i,k =1,..., M _r ;

由
和
计算得到
和
by
with
Calculated
with

如果
则第j个测量数据处理后的目标i在模型r_i,k下的边缘分布为
其存在概率为
其中，
r_i,k＝1,…,M_r；in case
Then the edge of the target i processed by the jth measurement data is distributed under the model r _i,k
Its probability of existence is
among them,
r _i,k =1,...,M _r ;

如果
则第j个测量数据处理后的目标i在模型r_i,k下的边缘分布为
其存在概率为
其中，
r_i,k＝1,…,M_r；in case
Then the edge of the target i processed by the jth measurement data is distributed under the model r _i,k
Its probability of existence is
among them,
r _i,k =1,...,M _r ;

步骤03、第M个测量数据被处理后目标i在模型r_i,k下的边缘分布为
其存在概率为
其中，i＝1,…,N_k-1，r_i,k＝1,…,M_r；Step 03: After the Mth measurement data is processed, the edge distribution of the target i under the model r _i,k is
Its probability of existence is
Where i=1,...,N _k-1 ,r _i,k =1,...,M _r ;

由此得到当前时刻目标i在模型r_i,k下的更新边缘分布为
更新边缘分布的存在概率为
其中，
i＝1,…,N_k-1，r_i,k＝1,…,M_r。 Thus, the updated edge distribution of the current time target i under the model r _i,k is obtained as
The existence probability of updating the edge distribution is
among them,
i=1,...,N _k-1 ,r _i,k =1,...,M _r .
根据权利要求1所述的多目标跟踪方法，其特征在于，所述步骤C中，当前时刻目标i的更新边缘分布为
r_i,k＝1,…,M_r，其存在概率为
r_i,k＝1,…,M_r；将当前时刻目标i的M_r个更新边缘分布及其存在概率融合成一个边缘分布N(x_q,k；m_q,k(r_q,k),P_q,k(r_q,k))和一个存在概率ρ_q,k(r_q,k)，其中
表示M_r个模型中存在概率最大模型的标签，均值向量
q＝1,…,N_k-1，协方差矩阵
q＝1,…,N_k-1。The multi-target tracking method according to claim 1, wherein in the step C, the updated edge distribution of the target i at the current time is
r _i,k =1,...,M _r , whose probability of existence is
_{r i, k = 1, ...} , M r; the M _r of the current time i a target edge updated existence probability distribution and integration into one edge profile _{N (x q, k; m} q, k (r q, k) , P _q,k (r _q,k )) and an existence probability ρ _q,k (r _q,k ), where
Represents the label with the largest probability model in the _rm models, the mean vector
q=1,...,N _k-1 ,covariance matrix
q=1,...,N _k-1 .
根据权利要求4所述的多目标跟踪方法，其特征在于，所述步骤D具体包括以下步骤：The multi-target tracking method according to claim 4, wherein the step D specifically comprises the following steps:

利用当前时刻M个测量数据生成当前时刻新生目标的边缘分布
j＝1,…,M，为当前时刻各新生目标的边缘分布指定存在概率
j＝1,…,M，其中，ρ_γ为指定的存在概率，指定模型1为当前时刻的模型标签，即r_j,k＝1；其中，
为第j个新生边缘分布的协方差，
为第j个新生的边缘分布的均值，
由当前时刻的第j个测量数据y_j,k＝[x_j,k y_j,k]^T产生，并且
Using the current measurement data to generate the edge distribution of the new target at the current time
j=1,...,M, specify the existence probability of the edge distribution of each new target at the current time
j=1,...,M, where ρ _γ is the specified existence probability, and model 1 is specified as the model label of the current time, that is, r _j,k =1; wherein
The covariance of the distribution of the jth new edge,
The mean of the distribution of the edges of the jth newborn,
Generated from the jth measurement data y _j,k =[x _j,k y _j,k ] ^T at the current time, and

将融合后的边缘分布与当前时刻新生的边缘分布进行合并，形成当前时刻的边缘分布为
将当前时刻融合后边缘分布的存在概率与当前时刻新生目标边缘分布的存在概率合并，生成当前时刻边缘分布的存在概率为
其中N_k＝N_k-1+M。Combining the merged edge distribution with the newly created edge distribution at the current moment to form the edge distribution of the current moment is
The existence probability of the edge distribution after the current time is merged with the existence probability of the new target edge distribution at the current time, and the existence probability of the edge distribution at the current time is generated as
Where N _k = N _k-1 + M.
根据权利要求5所述的多目标跟踪方法，其特征在于，所述步骤E中，当前时刻合并后的边缘分布为N(x_i,k；m_i,k(r_i,k),P_i,k(r_i,k))，i＝1,…,N_k，当前时刻合并后各边缘分布的存在概率为ρ_i,k(r_i,k)，i＝1,…,N_k，所述步骤E具体为：The multi-target tracking method according to claim 5, wherein in the step E, the merged edge distribution at the current time is N(x _i,k ;m _i,k (r _i,k ), P _{i , k} (r _i,k )), i=1,...,N _k , the existence probability of each edge distribution after the current time is ρ _i,k (r _i,k ),i=1,...,N _k , The step E is specifically:

从合并后所生成当前时刻的边缘分布中将存在概率小于第一阈值的边缘分布裁减掉，裁减后的边缘分布及其存在概率作为下一时刻滤波器的递归输入，同时，选择存在概率大于第二阈值的边缘分布作为当前时刻的输出。The edge distribution with the probability less than the first threshold is cut off from the edge distribution of the current time generated after the combination, and the edge distribution after clipping and its existence probability are used as the recursive input of the filter at the next moment, and the probability of existence is greater than The edge distribution of the two thresholds is taken as the output of the current time.
基于序贯贝叶斯滤波的多目标跟踪***，其特征在于，包括：A multi-target tracking system based on sequential Bayesian filtering, comprising:

预测模块，当接收到新的测量数据后，计算出接收到所述新的测量数据的时刻与接收到前一个测量数据的时刻的时间差，以接收到所述新的测量数据的时刻为当前时刻，接收到前一个测量数据的时刻为前一时刻；根据所述时间差、各个模型间的转移概率以及前一时刻各个目标的边缘分布及其存在概率，预测出当前时刻各个目标在不同模型下的边缘分布及其存在概率；And a prediction module, after receiving the new measurement data, calculating a time difference between a time when the new measurement data is received and a time when the previous measurement data is received, to receive the new measurement data as a current time The time at which the previous measurement data is received is the previous time; according to the time difference, the transition probability between each model, and the edge distribution of each target at the previous moment and its existence probability, it is predicted that each target at the current time is under a different model. Edge distribution and its existence probability;

更新模块，根据所述预测模块中预测的当前时刻各个目标在不同模型下的边缘分布及其存在概率，利用贝叶斯规则序贯处理当前时刻的每一个测量数据得到各个目标在不同模型下的更新边缘分布及其存在概率；An update module, according to the edge distribution of each target in the prediction module at the current moment and the existence probability of each target under different models, using Bayes rule to sequentially process each measurement data of the current moment to obtain each target under different models Update the edge distribution and its existence probability;

模型融合模块，将所述更新模块中当前时刻各个目标在不同模型下的更新边缘分布及其存在概率进行融合，形成当前时刻各个目标的更新边缘分布及存在概率；The model fusion module integrates the updated edge distribution and the existence probability of each target in the update module under different models at the current moment to form an updated edge distribution and existence probability of each target at the current moment;

边缘分布生成模块，利用当前时刻的每一个测量数据产生新目标的边缘分布，为其指定存在概率和模型标签；同时，将当前时刻新目标的边缘分布及其存在概率分别与所述模型融合模块中当前时刻各个目标的更新边缘分布及其存在概率进行合并，生成当前时刻的各个目标的边缘分布及其存在概率；The edge distribution generation module generates an edge distribution of the new target by using each measurement data at the current moment, and specifies the existence probability and the model label for the current target; meanwhile, the edge distribution of the new target at the current moment and the existence probability thereof are respectively combined with the model fusion module The updated edge distribution of each target in the current moment and its existence probability are combined to generate the edge distribution of each target at the current moment and its existence probability;

边缘分布提取模块，从所述边缘分布生成模块中将合并后所生成的当前时刻各个目标的边缘分布中将存在概率小于第一阈值的边缘分布裁减掉，并且将裁减后的边缘分布及其存在概率作为下一时刻递归滤波的输入，同时，从裁减后的边缘分布中提取存在概率大于第二阈值的边缘分布作为当前时刻的输出，并且将各个输出边缘分布的均值与方差分别作为当前时刻目标的状态估计与误差估计。The edge distribution extraction module removes, from the edge distribution generation module, the edge distribution of each target at the current moment generated by the merge, the edge distribution whose existence probability is less than the first threshold, and the edge distribution after the reduction and the existence thereof Probability is used as the input of recursive filtering at the next moment. At the same time, the edge distribution with the existence probability greater than the second threshold is extracted from the reduced edge distribution as the output of the current time, and the mean and variance of each output edge distribution are respectively used as the current time target. State estimation and error Difference estimate.
根据权利要求7所述的多目标跟踪***，其特征在于，所述预测模块中，以k-1表示前一时刻，k表示当前时刻，t_k-1表示前一时刻的时间，t_k表示当前时刻的时间，r_i,k-1表示前一时刻第i个边缘分布的模型标签，r_i,k表示当前时刻第i个边缘分布的模型标签，1≤r_i,k≤M_r，M_r表示模型的总数目；Multi-target tracking system according to claim 7, wherein said prediction module to k-1 represents a previous time, k represents the current time, the time T _k-1 represents a previous time, t _k represents At the current time, r _i,k-1 represents the model label of the i-th edge distribution at the previous moment, and r _i,k represents the model label of the i-th edge distribution at the current moment, 1≤r _i,k ≤M _r , M _r represents the total number of models;

已知前一时刻第i个边缘分布为N(x_i,k-1；m_i,k-1(r_i,k-1),P_i,k-1(r_i,k-1))，i＝1,2,...,N_k-1，前一时刻第i个边缘分布的存在概率为ρ_i,k-1(r_i,k-1)，i＝1,…,N_k-1；其中，N表示高斯分布，x_i,k-1表示为前一时刻第i个边缘分布的状态向量，m_i,k-1(r_i,k-1)和P_i,k-1(r_i,k-1)分别表示前一时刻第i个边缘分布的均值和方差，N_k-1为前一时刻目标的总数，i为索引号，1≤i≤N_k-1；It is known that the i-th edge distribution at the previous moment is N(x _i,k-1 ;m _i,k-1 (r _i,k-1 ), P _i,k-1 (r _i,k-1 )) , i = 1, 2, ..., N _k-1 , the existence probability of the i-th edge distribution at the previous moment is ρ _i,k-1 (r _i,k-1 ), i=1,...,N _K-1 ; where N denotes a Gaussian distribution, x _i,k-1 denotes a state vector of the i-th edge distribution at the previous moment, m _i,k-1 (r _i,k-1 ) and P _{i,k -1} (r _i,k-1 ) respectively represent the mean and variance of the i-th edge distribution at the previous moment, N _k-1 is the total number of targets at the previous moment, i is the index number, _{1 ≤} i ≤ N _k-1 ;

根据前一时刻的边缘分布及其存在概率、当前时刻与前一时刻的时间差以及模型间的转移概率得出当前时刻各目标在不同模型下预测的边缘分布为N(x_i,k；m_i,k|k-1(r_i,k),P_i,k|k-1(r_i,k))，i＝1,2,...,N_k-1，1≤r_i,k≤M_r；当前时刻各预测边缘分布的存在概率为ρ_i,k|k-1(r_i,k)＝p_S,k(t_k-t_k-1)t_k|k-1(r_i,k|r_i,k-1)ρ_i,k-1(r_i,k-1)，i＝1,2,...,N_k-1，1≤r_i,k≤M_r；其中，m_i,k|k-1(r_i,k)＝F_k-1(r_i,k)m_i,k-1(r_i,k-1)为当前时刻目标i在模型r_i,k下的预测边缘分布的均值，
为目标i在模型r_i,k下的预测边缘分布的方差，t_k|k-1(r_i,k|r_i,k-1)为模型间的转移概率，
为目标的幸存概率，△t＝t_k-t_k-1为当前时刻与前一时刻的时间差，T为采样周期，δ为给定的常数，F_k-1(r_i,k)为前一时刻第i个边缘分布的状态转移矩阵，Q_k-1(r_i,k)为前一时刻第i个边缘分布的过程噪声方差矩阵，r_i,k-1为前一时刻第i个边缘分布的模型标签，上标T表示为矩阵或向量的转置。According to the edge distribution of the previous moment and its existence probability, the time difference between the current moment and the previous moment, and the transition probability between the models, the edge distribution predicted by each target under different models at the current moment is N(x _i,k ;m _{i ,k|k-1} (r _i,k ),P _i,k|k-1 (r _i,k )),i=1,2,...,N _k-1 ,1≤r _i,k ≤M _r ; the existence probability of each predicted edge distribution at the current time is ρ _i,k|k-1 (r _i,k )=p _S,k (t _k -t _k-1 )t _k|k-1 (r _i,k |r _i,k-1 )ρ _i,k-1 (r _i,k-1 ),i=1,2,...,N _k-1 ,1≤r _i,k ≤M _r Where m _i,k|k-1 (r _i,k )=F _k-1 (r _i,k )m _i,k-1 (r _i,k-1 ) is the current time target i in the model r The mean of the predicted edge distribution under _i,k ,
For the variance of the predicted edge distribution of the target i under the model r _i,k , t _k|k-1 (r _i,k |r _i,k-1 ) is the transition probability between the models,
For the surviving probability of the target, Δt=t _k -t _k-1 is the time difference between the current time and the previous time, T is the sampling period, δ is the given constant, and F _k-1 (r _i,k ) is the former The state transition matrix of the i-th edge distribution at a moment, Q _k-1 (r _i,k ) is the process noise variance matrix of the i-th edge distribution at the previous moment, r _i,k-1 is the ith of the previous moment The model label of the edge distribution, the superscript T is represented as a transpose of a matrix or a vector.
根据权利要求8所述的多目标跟踪***，其特征在于，所述更新模块中，设当前时刻接收到的观测集为y_k＝(y_1,k,…,y_M,k)，其中，M为当前时刻接收到的测量数据总数；利用贝叶斯规则对当前时刻接收到的测量数据进行序贯处理具体包括：The multi-target tracking system according to claim 8, wherein in the updating module, the observation set received at the current time is y _k = (y _{1, k} , ..., y _{M, k} ), wherein M is the total number of measurement data received at the current time; the sequential processing of the measurement data received at the current time by using the Bayes rule includes:

提取单元，用于提取边缘分布

取存在概率
其中，i＝1,2,...,N_k-1，r_i,k＝1,…,M_r；Extraction unit for extracting edge distribution

Presence probability
Where i=1,2,...,N _k-1 ,r _i,k =1,...,M _r ;

处理单元，利用贝叶斯规则将第1个至M个测量数据依次进行处理：设
为第j个测量数据处理前目标i在模型r_i,k下的边缘分布，
为第j个测量数据处理前目标i在模型r_i,k下的边缘分布的存在概率，其中，1≤j≤M；由
和
求得第j个测量数据更新时的存在概率为
均值向量
协方差矩阵
滤波器增益
其中，H_k(r_i,k)为模型r_i,k的观测矩阵，R_k(r_i,k)为模型r_i,k的观测噪声方差矩阵，p_D,k为目标的检测概率，λ_c,k为杂波密度，I表示单位矩阵，y_j,k为当前时刻接收到的第j测量数据，上标T表示为矩阵或向量的转置，r_i,k＝1,…,M_r；The processing unit sequentially processes the first to M measurement data by using a Bayes rule:
The edge distribution of the target i under the model r _i,k before processing the jth measurement data,
The existence probability of the edge distribution of the target i under the model r _i,k for the jth measurement data, where 1 ≤ j ≤ M;
with
The probability of existence when the jth measurement data is updated is
Mean vector
Covariance matrix
Filter gain
Where H _k (r _i,k ) is the observation matrix of the model r _i,k , R _k (r _i,k ) is the observed noise variance matrix of the model r _i,k , p _D,k is the detection probability of the target, λ _c,k is the clutter density, I represents the unit matrix, y _j,k is the jth measurement data received at the current time, and the superscript T is represented as the transpose of the matrix or vector, r _i,k =1,..., M _r ;

计算单元，根据
和
计算得到
和
Computing unit, according to
with
Calculated
with

如果
则第j个测量数据处理后的目标i在模型r_i,k下的边缘分布为
其存在概率为
其中，
r_i,k＝1,…,M_r；in case
Then the edge of the target i processed by the jth measurement data is distributed under the model r _i,k
Its probability of existence is
among them,
r _i,k =1,...,M _r ;

如果
则第j个测量数据处理后的目标i在模型r_i,k下的边缘分布为
其存在概率为
其中，
r_i,k＝1,…,M_r； in case
Then the edge of the target i processed by the jth measurement data is distributed under the model r _i,k
Its probability of existence is
among them,
r _i,k =1,...,M _r ;

更新单元，第M个测量数据被处理后目标i在模型r_i,k下的边缘分布为
其存在概率为
其中，i＝1,…,N_k-1，r_i,k＝1,…,M_r；Update unit, after the Mth measurement data is processed, the edge distribution of the target i under the model r _i,k is
Its probability of existence is
Where i=1,...,N _k-1 ,r _i,k =1,...,M _r ;

由此得到当前时刻目标i在模型r_i,k下的更新边缘分布为
更新边缘分布的存在概率为
其中，
i＝1,…,N_k-1，r_i,k＝1,…,M_r。Thus, the updated edge distribution of the current time target i under the model r _i,k is obtained as
The existence probability of updating the edge distribution is
among them,
i=1,...,N _k-1 ,r _i,k =1,...,M _r .
根据权利要求7所述的多目标跟踪***，其特征在于，在所述模型融合模块中，当前时刻目标i的更新边缘分布为
r_i,k＝1,…,M_r，其存在概率为
r_i,k＝1,…,M_r；将当前时刻目标i的M_r个更新边缘分布及其存在概率融合成一个边缘分布N(x_q,k；m_q,k(r_q,k),P_q,k(r_q,k))和一个存在概率ρ_q,k(r_q,k)，其中，
表示M_r个模型中存在概率最大模型的标签，均值向量
q＝1,…,N_k-1，协方差矩阵
q＝1,…,N_k-1。The multi-target tracking system according to claim 7, wherein in the model fusion module, the updated edge distribution of the current time target i is
r _i,k =1,...,M _r , whose probability of existence is
_{r i, k = 1, ...} , M r; the M _r of the current time i a target edge updated existence probability distribution and integration into one edge profile _{N (x q, k; m} q, k (r q, k) , P _q,k (r _q,k )) and an existence probability ρ _q,k (r _q,k ), where
Represents the label with the largest probability model in the _rm models, the mean vector
q=1,...,N _k-1 ,covariance matrix
q=1,...,N _k-1 .
根据权利要求10所述的多目标跟踪***，其特征在于，所述边缘分布生成模块中：The multi-target tracking system according to claim 10, wherein in the edge distribution generating module:

利用当前时刻M个测量数据生成当前时刻新生目标的边缘分布
j＝1,…,M，为当前时刻各新生目标的边缘分布指定存在概率
j＝1,…,M，其中，ρ_γ为指定的存在概率，指定模型1为当前时刻的模型标签，即r_j,k＝1；其中，
为第j个新生边缘分布的协方差，
为第j个新生的边缘分布的均值，
由当前时刻的第j个测量数据y_j,k＝[x_j,k y_j,k]^T产生，并且
Using the current measurement data to generate the edge distribution of the new target at the current time
j=1,...,M, specify the existence probability of the edge distribution of each new target at the current time
j=1,...,M, where ρ _γ is the specified existence probability, and model 1 is specified as the model label of the current time, that is, r _j,k =1; wherein
The covariance of the distribution of the jth new edge,
The mean of the distribution of the edges of the jth newborn,
Generated from the jth measurement data y _j,k =[x _j,k y _j,k ] ^T at the current time, and

将融合后的边缘分布与当前时刻新生的边缘分布进行合并，形成当前时刻的边缘分布为
将当前时刻融合后边缘分布的存在概率与当前时刻新生目标边缘分布的存在概率合并，生成当前时刻边缘分布的存在概率为
其中N_k＝N_k-1+M。Combining the merged edge distribution with the newly created edge distribution at the current moment to form the edge distribution of the current moment is
The existence probability of the edge distribution after the current time is merged with the existence probability of the new target edge distribution at the current time, and the existence probability of the edge distribution at the current time is generated as
Where N _k = N _k-1 + M.
根据权利要求11所述的多目标跟踪***，其特征在于，当前时刻合并后的边缘分布为N(x_i,k；m_i,k(r_i,k),P_i,k(r_i,k))，i＝1,…,N_k，当前时刻合并后各边缘分布的存在概率为ρ_i,k(r_i,k)，i＝1,…,N_k，所述边缘分布提取模块中，The multi-target tracking system according to claim 11, wherein the merged edge distribution at the current time is N(x _i,k ;m _i,k (r _i,k ), P _i,k (r _{i, k} )), i=1,...,N _k , the existence probability of each edge distribution after the current time is ρ _i,k (r _i,k ), i=1,...,N _k , the edge distribution extraction module in,

从合并后所生成当前时刻的边缘分布中将存在概率小于第一阈值的边缘分布裁减掉，裁减后的边缘分布及其存在概率作为下一时刻滤波器的递归输入，同时，选择存在概率大于第二阈值的边缘分布作为当前时刻的输出。 The edge distribution with the probability less than the first threshold is cut off from the edge distribution of the current time generated after the combination, and the edge distribution after clipping and its existence probability are used as the recursive input of the filter at the next moment, and the probability of existence is greater than The edge distribution of the two thresholds is taken as the output of the current time.