WO2018010099A1 - 一种用于跟踪转弯机动目标的方法及其系统 - Google Patents

一种用于跟踪转弯机动目标的方法及其系统 Download PDF

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WO2018010099A1
WO2018010099A1 PCT/CN2016/089824 CN2016089824W WO2018010099A1 WO 2018010099 A1 WO2018010099 A1 WO 2018010099A1 CN 2016089824 W CN2016089824 W CN 2016089824W WO 2018010099 A1 WO2018010099 A1 WO 2018010099A1
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target
time
edge distribution
existence probability
current
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PCT/CN2016/089824
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French (fr)
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刘宗香
吴德辉
邹燕妮
李良群
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深圳大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis

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  • the present invention relates to the field of multi-sensor information fusion technologies, and in particular, to a method and system for tracking a turning maneuver target.
  • 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.
  • the information delay caused by the newly received measurement data can not be processed in time and the multi-target tracking problem under the initial position of the unknown target, the solution has been proposed.
  • No. CN201510284138.3 is a patent application for transmitting edge-measured measurement-driven target tracking method and tracking system.
  • this method can not effectively track the maneuvering target with the change of turning rate. How to track the maneuvering target with changing the turning rate is a key technical problem that needs to be explored and solved in the multi-objective Bayesian filtering method.
  • an object of the present invention is to provide a method and system for tracking a turning maneuvering target, which aims to solve the problem that the maneuvering target that cannot change the turning rate can be effectively tracked in the prior art.
  • the invention provides a method for tracking a turning maneuvering target, characterized in that the method comprises:
  • Step 1 According to the edge distribution, the existence probability and the turning rate of each target at the previous moment, and the time difference between the current moment and the previous moment, predict the edge distribution and the existence probability of each target at the current moment;
  • N k-1 , x i, k-1 is the state vector of the target i at time k-1, m i, k-1 and P i, k-1 respectively represent the state mean and the state of the target i at time k-1 Variance, N k-1 is the total number of targets at the previous moment;
  • the edge distribution N(x i,k-1 ;m i,k-1 ,P i,k-1 ), the existence probability ⁇ i,k-1 and the turning rate ⁇ i,k- of the target i from time k-1 1 Predicting the edge distribution and existence probability of the target i at the current time are N(x i,k ;m i,k
  • k-1 F i,k
  • k-1 Q i,k-1 +F i,k
  • k-1 p S,k (t k -t k-1 ) ⁇ i,k-1
  • Q i,k-1 is the process noise covariance matrix of target i at time k-1
  • p S,k (t k - t k-1 ) is the surviving probability of the target
  • T is the sampling period
  • Step 2 According to the edge distribution and the existence probability of each target at the previous moment, the time difference between the current time and the previous time, and the measurement set of the current time estimate each target of the current time corresponds to each measured turning rate;
  • Step 3 According to the estimated respective targets, the cornering rate corresponding to each measurement, the edge distribution of each target at the previous moment, the predicted existence probability of each target at the current moment, the time difference between the current moment and the previous moment, and the measurement set of the current moment. , determining an updated edge distribution, an existence probability, and a turning rate of each existing target at the current time;
  • Step 4 generating an edge distribution of the new target by using each measurement of the current time, and assigning the existence probability and the turning rate to the current time; meanwhile, the edge distribution, the existence probability, and the turning rate of the new target at the current moment respectively exist with the current moment
  • the updated edge distribution, the existence probability and the turning rate of the target are combined to generate the edge distribution, the existence probability and the turning rate of each target at the current time;
  • Step 5 The target having the probability of being less than the first threshold is cut out from the merged targets, and the edge distribution, the existence probability and the turning rate of the remaining target after the reduction are used as the input of the next time recursive filtering, and Extracting an edge distribution having an existence probability greater than a second threshold as an output of the current time from the edge distribution of the remaining target after the clipping, and And the mean and variance of each output edge distribution are respectively used as the state estimation and error estimation of the current time target.
  • the step 2 specifically includes:
  • Sub-step A set among them with Representing the x and y components of the target i position, respectively. with Representing the x and y components of their velocity, respectively. with Representing the x and y components of the measurement y j,k , respectively, the superscript T represents the transpose of the matrix or vector; using m i,k-1 and y j,k to obtain the vector by transformation among them
  • Sub-step B using the transformed vector Get turn rate among them, t k-1 and t k are times of k-1 time and k time, respectively;
  • the step 3 specifically includes:
  • Sub-step D the edge distribution N(x i,k-1 ;m i,k-1 ,P i,k-1 ) of the target i from time k-1 , and the turning rate
  • Sub-step E using Bayesian rules to measure y j,k , to obtain the existence probability that the target i corresponds to the measurement y j,k Filter gain Mean vector Covariance matrix
  • H k is the observation matrix
  • R k is the observed noise variance matrix
  • p D,k is the detection probability of the target
  • ⁇ c,k is the clutter density
  • I represents the identity matrix
  • the present invention also provides a system for tracking a turning maneuvering target, the system comprising:
  • a prediction module configured to predict an edge distribution and an existence probability of each target at a current moment according to an edge distribution, an existence probability, and a turning rate of each target at a previous moment, and a time difference between the current moment and a previous moment;
  • N k-1 , x i, k-1 is the state vector of the target i at time k-1, m i, k-1 and P i, k-1 respectively represent the state mean and the state of the target i at time k-1 Variance, N k-1 is the total number of targets at the previous moment;
  • the edge distribution N(x i,k-1 ;m i,k-1 ,P i,k-1 ), the existence probability ⁇ i,k-1 and the turning rate ⁇ i,k- of the target i from time k-1 1 Predicting the edge distribution and existence probability of the target i at the current time are N(x i,k ;m i,k
  • k-1 F i,k
  • k-1 Q i,k-1 +F i,k
  • k-1 p S,k (t k -t k-1 ) ⁇ i,k-1
  • Q i,k-1 is the process noise covariance matrix of target i at time k-1
  • p S,k (t k - t k-1 ) is the surviving probability of the target
  • T is the sampling period
  • a turn rate estimation module configured to estimate, according to an edge distribution and an existence probability of each target at a previous moment, a time difference between the current time and the previous time, and a measurement set of the current time, each of the targets at the current time corresponds to each measured turning rate;
  • An update module configured to correspond to each measured turn rate according to the estimated each target, an edge distribution of each target at a previous moment, a predicted existence probability of each target at the current moment, a time difference between the current moment and the previous moment, and a current time Measure the set to obtain the updated edge distribution, existence probability and turning rate of each existing target at the current time;
  • a new target generation module configured to generate an edge distribution of a new target by using each measurement of the current moment, assigning an existence probability and a turning rate thereto; and simultaneously, respectively, an edge distribution, an existence probability, and a turning rate of the new target at the current moment are respectively
  • the updated edge distribution, the existence probability and the turning rate of the existing target at the current moment are combined to generate the edge distribution, the existence probability and the turning rate of each target at the current time;
  • a target state extraction module configured to cut off a target whose probability of existence is less than a first threshold from the merged targets, and recursively filter the edge distribution, the existence probability, and the turn rate of the remaining target after the reduction
  • the input at the same time, extracts the edge distribution whose existence probability is greater than the second threshold from the edge distribution of the remaining target as the current moment output, and uses the mean and variance of each output edge distribution as the state estimation and error of the current time target respectively. estimate.
  • the technical solution provided by the present invention can combine the turn rate estimation with the sequential Bayesian filter by predicting, turning rate estimation, updating, new target generation and target state extraction, while ensuring the real-time performance of data processing. It effectively solves the tracking problem of multiple maneuvering targets with varying turning rates, and has strong practicability.
  • FIG. 1 is a flow chart of a method for tracking a turning maneuvering target according to an embodiment of the present invention
  • FIG. 2 is a schematic diagram showing the internal structure of a system 10 for tracking a turning maneuvering target according to an embodiment of the present invention
  • FIG. 3 is a measurement data diagram of a sensor provided by an embodiment of the present invention in 70 scanning cycles according to an embodiment of the present invention
  • FIG. 4 is a diagram showing the result of processing the method for tracking a turning maneuvering target according to the present invention in an embodiment of the present invention
  • FIG. 5 is a diagram of a result obtained by processing a Gaussian mixture probability hypothesis density filtering method according to a hopping Markov system model according to an embodiment of the present invention
  • FIG. 6 is a schematic diagram of an average SPAC distance obtained by 100 experiments using the method for tracking a turning maneuvering target and the hopping Markov system model of the present invention according to an embodiment of the present invention.
  • the invention provides a method for tracking a turning maneuvering target by combining the steps of prediction, turning rate estimation, updating, new target generation and target state extraction to combine the turning rate estimation with the sequential Bayesian filter.
  • the tracking problem of multiple maneuvering targets with changing turning rate is effectively solved, and it has strong practicability.
  • FIG. 1 is a flowchart of a method for tracking a turning maneuvering target according to an embodiment of the present invention.
  • step 1 according to the edge distribution, the existence probability and the turning rate of each target at the previous moment, and the time difference between the current time and the previous time, the edge distribution and the existence probability of each target at the current time are predicted;
  • N k-1 , x i, k-1 is the state vector of the target i at time k-1, m i, k-1 and P i, k-1 respectively represent the state mean and the state of the target i at time k-1 Variance, N k-1 is the total number of targets at the previous moment;
  • the edge distribution N(x i,k-1 ;m i,k-1 ,P i,k-1 ), the existence probability ⁇ i,k-1 and the turning rate ⁇ i,k- of the target i from time k-1 1 Predicting the edge distribution and existence probability of the target i at the current time are N(x i,k ;m i,k
  • k-1 F i,k
  • k-1 Q i,k-1 +F i,k
  • k-1 p S,k (t k -t k-1 ) ⁇ i,k-1
  • Q i,k-1 is the process noise covariance matrix of target i at time k-1
  • p S,k (t k - t k-1 ) is the surviving probability of the target
  • T is the sampling period
  • the state of the target is composed of position and velocity, expressed as Where x and y represent positional components, respectively.
  • the superscript T represents the transpose of the vector
  • k-1 represents the previous time
  • k represents the current time
  • t k-1 represents the time of the previous time
  • t k represents the time of the current time
  • the edge distribution of the target i at time k-1 exists.
  • the probability and turning rate are expressed as N(x i,k-1 ;m i,k-1 ,P i,k-1 ), ⁇ i,k-1 and ⁇ i,k-1 , respectively, where N represents a Gaussian distribution.
  • i 1, 2, ...
  • N k-1 , x i, k-1 is the state vector of the target i at time k-1, m i, k-1 and P i, k-1 respectively represent the target at k-1
  • the state mean and covariance of i, N k-1 is the total number of targets at the previous moment;
  • the edge distribution N(x i,k-1 ;m i,k-1 ,P i,k-1 ), the existence probability ⁇ i,k-1 and the turning rate ⁇ i,k- of the target i from time k-1 1 Predicting the edge distribution and existence probability of the target i at the current time are N(x i,k ;m i,k
  • k-1 F i,k
  • k-1 Q i,k-1 +F i,k
  • k-1 p S,k (t k -t k-1 ) ⁇ i,k-1
  • Q i,k-1 is the process noise covariance matrix of target i at time k-1
  • p S,k (t k - t k-1 ) is the surviving probability of the target
  • T is the sampling period
  • step 2 according to the edge distribution and the existence probability of each target at the previous moment, the time difference between the current time and the previous time, and the measurement set of the current time estimate the current time each target corresponds to each measured turning rate.
  • step 2 according to the edge distribution N(x i,k-1 ;m i,k-1 ,P i,k-1 ) of the target i at the k-1 time, k
  • the estimated k time target i corresponds to the measurement Y j,k turning rate
  • Sub-step A set among them with Representing the x and y components of the target i position, respectively. with Representing the x and y components of their velocity, respectively. with Representing the x and y components of the measurement y j,k , respectively, the superscript T represents the transpose of the matrix or vector; using m i,k-1 and y j,k to obtain the vector by transformation among them
  • Sub-step B using the transformed vector Obtaining a turning rate ⁇ i a ,j , where t k-1 and t k are times of k-1 time and k time, respectively;
  • step 3 according to the estimated respective targets corresponding to each measured turning rate, the edge distribution of each target at the previous moment, the predicted existence probability of each target at the current moment, the time difference between the current moment and the previous moment, and the current time
  • the measurement set determines the updated edge distribution, existence probability, and turn rate of each existing target at the current time.
  • step 3 according to the edge distribution N(x i,k-1 ;m i,k-1 ,P i,k-1 ) of the target i at the k-1 time, k
  • k-1 of the time target i, and the target i corresponds to the turning rate of the measured y j,k
  • the steps of obtaining the updated edge distribution, the existence probability and the turning rate of each existing target at the current time are as follows:
  • Sub-step D the edge distribution N(x i,k-1 ;m i,k-1 ,P i,k-1 ) of the target i from time k-1 , and the turning rate
  • Sub-step E using Bayesian rules to measure y j,k , to obtain the existence probability that the target i corresponds to the measurement y j,k Filter gain Mean vector Covariance matrix
  • H k is the observation matrix
  • R k is the observed noise variance matrix
  • p D,k is the detection probability of the target
  • ⁇ c,k is the clutter density
  • I represents the identity matrix
  • step 4 the edge distribution of the new target is generated by using the respective measurements at the current time, and the existence probability and the turning rate are specified for the same time; meanwhile, the edge distribution, the existence probability and the turning rate of the new target at the current time are respectively associated with the current moment.
  • the updated edge distribution, the existence probability, and the turning rate of the existing target are combined to generate the edge distribution, the existence probability, and the turning rate of each target at the current time;
  • step 5 the target whose probability of existence is less than the first threshold is cut out from the merged targets, and the edge distribution, the existence probability and the turning rate of the remaining target after the reduction are used as the input of the next time recursive filtering.
  • the edge distribution with the existence probability greater than the second threshold is extracted from the edge distribution of the remaining target 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.
  • the invention provides a method for tracking a turning maneuvering target, which can combine the turning rate estimation with the sequential Bayesian filter through the steps of prediction, turning rate estimation, updating, new target generation and target state extraction. While ensuring the real-time performance of data processing, it effectively solves the tracking problem of multiple maneuvering targets with varying turning rates, and has strong practicability.
  • a specific embodiment of the present invention also provides a system 10 for tracking a turning maneuvering target, which mainly includes:
  • the prediction module 11 is configured to predict an edge distribution and an existence probability of each target at a current moment according to an edge distribution, an existence probability, and a turning rate of each target at a previous moment, and a time difference between the current moment and a previous moment;
  • the turn rate estimation module 12 is configured to estimate, according to an edge distribution and an existence probability of each target at a previous moment, a time difference between the current time and the previous time, and a measurement set of the current time, each of the targets at the current time corresponds to each measured turning rate;
  • the updating module 13 is configured to: according to the estimated respective targets, the turn rate corresponding to each measurement, the edge distribution of each target at the previous moment, the predicted existence probability of each target at the current moment, the time difference between the current moment and the previous moment, and the current moment The measurement set, the updated edge distribution, the existence probability and the turning rate of each existing target at the current time;
  • the new target generating module 14 generates the edge distribution of the new target by using the respective measurements at the current time, and specifies the existence probability and the turning rate for the new target; meanwhile, the edge distribution, the existence probability, and the turning rate of the new target at the current time are respectively associated with the current current.
  • the updated edge distribution, the existence probability and the turning rate of the existing existing target are combined to generate the edge distribution, the existence probability and the turning rate of each target at the current time;
  • the target state extraction module 15 is configured to cut off the target whose existence probability is less than the first threshold from the merged targets, and recursively divide the edge distribution, the existence probability, and the turning rate of the remaining target after the reduction Filtering the input, at the same time, extracting the edge distribution whose existence probability is greater than the second threshold from the edge distribution of the remaining target as the output of the current time, and using the mean and the variance of each output edge distribution as the state estimation of the current time target respectively Error estimate.
  • the system 10 for tracking a turning maneuvering target provided by the present invention can estimate the turning rate by the prediction module 11, the turning rate estimating module 12, the updating module 13, the new target generating module 14, and the target state extracting module 15.
  • the sequential Bayesian filter combines to ensure the tracking of multiple maneuvering targets with varying turning rates while ensuring the real-time performance of data processing, and it has strong practicability.
  • FIG. 2 a schematic structural diagram of a system 10 for tracking a turning maneuvering target according to an embodiment of the present invention is shown.
  • the system 10 for tracking a turning maneuver target mainly includes a prediction module 11, a turning rate estimating module 12, an updating module 13, a new target generating module 14, and a target state extracting module 15.
  • the prediction module 11 is configured to predict an edge distribution and an existence probability of each target at a current moment according to an edge distribution, an existence probability, and a turning rate of each target at a previous moment, and a time difference between the current moment and a previous moment;
  • N k-1 , x i, k-1 is the state vector of the target i at time k-1, m i, k-1 and P i, k-1 respectively represent the state mean and the state of the target i at time k-1 Variance, N k-1 is the total number of targets at the previous moment;
  • the edge distribution N(x i,k-1 ;m i,k-1 ,P i,k-1 ), the existence probability ⁇ i,k-1 and the turning rate ⁇ i,k- of the target i from time k-1 1 Predicting the edge distribution and existence probability of the target i at the current time are N(x i,k ;m i,k
  • k-1 F i,k
  • k-1 Q i,k-1 +F i,k
  • k-1 p S,k (t k -t k-1 ) ⁇ i,k-1
  • Q i,k-1 is the process noise covariance matrix of target i at time k-1
  • p S,k (t k - t k-1 ) is the surviving probability of the target
  • T is the sampling period
  • the turn rate estimation module 12 is configured to estimate, according to the edge distribution and the existence probability of each target at a previous moment, the time difference between the current time and the previous time, and the measurement set of the current time, each of the targets at the current time corresponds to each measured turning rate.
  • the estimated k time target i corresponds to the measurement y j , k turning rate
  • Step A set among them with Representing the x and y components of the target i position, respectively. with Representing the x and y components of their velocity, respectively. with Representing the x and y components of the measurement y j,k , respectively, the superscript T represents the transpose of the matrix or vector; using m i,k-1 and y j,k to obtain the vector by transformation among them
  • Step B using the converted vector Get turn rate among them, t k-1 and t k are times of k-1 time and k time, respectively;
  • Step C by the The maximum turning rate ⁇ max and the minimum turning rate ⁇ min result in a turning ratio of the target i corresponding to the measurement y j,k among them ⁇ max and ⁇ min are two known parameters.
  • the updating module 13 is configured to: according to the estimated respective targets, the turn rate corresponding to each measurement, the edge distribution of each target at the previous moment, the predicted existence probability of each target at the current moment, the time difference between the current moment and the previous moment, and the current moment
  • the measurement set obtains the updated edge distribution, existence probability and turning rate of each existing target at the current time.
  • the k-time target i Predicting the existence probability ⁇ i,k
  • the steps of obtaining the updated edge distribution, the existence probability and the turning rate of each existing target at the current time are as follows:
  • Step D the edge distribution N (x i, k-1 ; m i, k-1 , P i, k-1 ) of the target i from time k-1 , and the turning rate
  • Step E Using the Bayesian rule to measure y j,k , the probability of existence of the target i corresponding to the measurement y j,k is obtained.
  • Filter gain Mean vector Covariance matrix Where H k is the observation matrix, R k is the observed noise variance matrix, p D,k is the detection probability of the target, ⁇ c,k is the clutter density, and I represents the identity matrix;
  • the new target generating module 14 is configured to generate an edge distribution of the new target by using each measurement of the current time, and specify the existence probability and the turning rate for the new target; and simultaneously, the edge distribution, the existence probability, and the turning rate of the new target at the current moment are respectively At the current moment, the updated edge distribution, the existence probability, and the turning rate of the existing target are combined, and the edge distribution, the existence probability, and the turning rate of each target at the current moment are generated.
  • the edge distribution of the new target at the current time is generated by using the M measurements at the current time.
  • the target state extraction module 15 is configured to cut off the target whose existence probability is less than the first threshold from the merged targets, and recursively divide the edge distribution, the existence probability, and the turning rate of the remaining target after the reduction Filtering the input, at the same time, extracting the edge distribution whose existence probability is greater than the second threshold from the edge distribution of the remaining target as the output of the current time, and using the mean and the variance of each output edge distribution as the state estimation of the current time target respectively Error estimate.
  • the simulated observation data of the sensor in 70 scan cycles in the experiment is shown in FIG.
  • the relevant parameters of the present invention and the hopping Markov system model Gaussian Mixture probability hypothesis density filter for jump Markov system models are set to p.
  • FIG. 6 is an average OSA (Optimal Subpattern Assignment) distance obtained by performing a Monte Carlo experiment with the existing hopping Markov model GM-PHD filter and the present invention, respectively.
  • OSA Optimal Subpattern Assignment
  • the comparison of the GM-PHD filter of the existing hopping Markov model with the experimental results of the present invention shows that the method of the present invention can obtain a more accurate and reliable target state estimation, and its OSPA distance is compared with the existing method. The resulting SPAC distance is small.
  • the system 10 for tracking a turning maneuvering target provided by the present invention can estimate the turning rate by the prediction module 11, the turning rate estimating module 12, the updating module 13, the new target generating module 14, and the target state extracting module 15.
  • the sequential Bayesian filter combines to ensure the tracking of multiple maneuvering targets with varying turning rates while ensuring the real-time performance of data processing, and it has strong practicability.
  • each unit included is only divided according to functional logic, but is not limited to the above division, as long as the corresponding function can be implemented; in addition, the specific name of each functional unit is also They are only used to facilitate mutual differentiation and are not intended to limit the scope of the present invention.
  • the program can be executed by instructing related hardware, and the corresponding program can be stored in a computer readable storage medium such as a ROM/RAM, a magnetic disk or an optical disk.

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Abstract

一种用于跟踪转弯机动目标的方法，其中，所述方法包括：预测步骤、估计步骤、更新步骤、生成步骤以及输出步骤。还提供一种用于跟踪转弯机动目标的系统。本方法在保证数据处理实时性的同时，有效地解决了转弯机动目标的跟踪问题。

Description

一种用于跟踪转弯机动目标的方法及其系统 技术领域
本发明涉及多传感器信息融合技术领域，尤其涉及一种用于跟踪转弯机动目标的方法及其系统。
背景技术
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，目前已提出了解决办法，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系统的专利申请。然而，该方法不能对转弯率变化的机动目标进行有效跟踪，如何对转弯率变化的机动目标进行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。
发明内容
有鉴于此，本发明的目的在于提供一种用于跟踪转弯机动目标的方法及其系统，旨在解决现有技术中不能对转弯率变化的机动目标进行有效跟踪的问题。
本发明提出一种用于跟踪转弯机动目标的方法，其特征在于，所述方法包括：
步骤1、根据前一时刻各个目标的边缘分布、存在概率和转弯率，以及当前时刻与前一时刻的时间差，预测当前时刻各个目标的边缘分布和存在概率；
以k-1表示前一时刻，k表示当前时刻，tk-1表示前一时刻的时间，tk表示当前时刻的时间，k-1时刻目标i的边缘分布、存在概率和转弯率分别表示为N(xi,k-1；mi,k-1,Pi,k-1)、ρi,k-1和ωi,k-1，其中N表示高斯分布，i＝1,2,…Nk-1，xi,k-1为k-1时刻目标i的状态向量，mi,k-1和Pi,k-1分别表示k-1时刻目标i的状态均值和协方差，Nk-1为前一时刻目标的总数；
由k-1时刻目标i的边缘分布N(xi,k-1；mi,k-1,Pi,k-1)、存在概率ρi,k-1和转弯率ωi,k-1预测当前时刻目标i的边缘分布和存在概率分别为N(xi,k；mi,k|k-1,Pi,k|k-1)和ρi,k|k-1，其中mi,k|k-1＝Fi,k|k-1mi,k-1，Pi,k|k-1＝Qi,k-1+Fi,k|k-1Pi,k-1(Fi,k|k-1)T，ρi,k|k-1＝pS,k(tk-tk-1)ρi,k-1，
Figure PCTCN2016089824-appb-000001
△tk＝tk-tk-1为k时刻与k-1时刻的时间差，Qi,k-1为k-1时刻目标i的过程噪声协方差矩阵，pS,k(tk-tk-1)为目标的幸存概率，且
Figure PCTCN2016089824-appb-000002
T为采样周期，δ为给定的常数，i＝1,2,…Nk-1；
步骤2、根据前一时刻各个目标的边缘分布和存在概率，当前时刻与前一时刻的时间差，以及当前时刻的测量集合估计当前时刻各目标对应于每一个测量的转弯率；
步骤3、根据估计的各个目标对应于每一个测量的转弯率，前一时刻各个目标的边缘分布，当前时刻各目标的预测存在概率，当前时刻与前一时刻的时间差，以及当前时刻的测量集合，确定当前时刻各个已存在目标的更新边缘分布、存在概率和转弯率；
步骤4、利用当前时刻的各个测量产生新目标的边缘分布，为其指定存在概率和转弯率；同时，将当前时刻新目标的边缘分布、存在概率和转弯率分别与所述的当前时刻已存在目标的更新边缘分布、存在概率和转弯率进行合并，生成当前时刻的各个目标的边缘分布、存在概率和转弯率；
利用当前时刻M个测量生成当前时刻新生目标的边缘分布
Figure PCTCN2016089824-appb-000003
为当前时刻各新生目标指定存在概率
Figure PCTCN2016089824-appb-000004
和转弯率为
Figure PCTCN2016089824-appb-000005
其中，j＝1,…,M，ργ为所指定的存在概率，
Figure PCTCN2016089824-appb-000006
为第j个新生边缘分布的协方差，
Figure PCTCN2016089824-appb-000007
为第j个新生目标的边缘分布的均值，
Figure PCTCN2016089824-appb-000008
由当前时刻的第j个测量数据
Figure PCTCN2016089824-appb-000009
产生，并且
Figure PCTCN2016089824-appb-000010
将已存在目标的边缘分布与当前时刻新生的边缘分布进行合并，形成当前时刻各目标的边缘分布为
Figure PCTCN2016089824-appb-000011
合并后各目标的存在概率和转弯率分别为
Figure PCTCN2016089824-appb-000012
和
Figure PCTCN2016089824-appb-000013
其中Nk＝Nk-1+M；
步骤5、从所述的合并后的各个目标中将存在概率小于第一阈值的目标裁减掉，并且将裁减后余下目标的边缘分布、存在概率和转弯率作为下一时刻递归滤波的输入，同时，从裁减后余下目标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。
优选的，所述步骤2具体包括：
子步骤A、设
Figure PCTCN2016089824-appb-000014
其中
Figure PCTCN2016089824-appb-000015
和
Figure PCTCN2016089824-appb-000016
分别表示目标i位置的x分量和y分量，
Figure PCTCN2016089824-appb-000017
和
Figure PCTCN2016089824-appb-000018
分别表示其速度的x分量和y分量，
Figure PCTCN2016089824-appb-000019
和
Figure PCTCN2016089824-appb-000020
分别表示测量yj,k的x分量和y分量，上标T表示矩阵或向量的转置；利用mi,k-1和yj,k通过变换得到向量
Figure PCTCN2016089824-appb-000021
其中
Figure PCTCN2016089824-appb-000022
子步骤B、利用转换后的向量
Figure PCTCN2016089824-appb-000023
得到转弯率
Figure PCTCN2016089824-appb-000024
其中，
Figure PCTCN2016089824-appb-000025
tk-1和tk分别为k-1时刻和k时刻的时间；
子步骤C、由所述的
Figure PCTCN2016089824-appb-000026
最大转弯率ωmax和最小转弯率ωmin得到目标i对应于测量yj,k的转弯率
Figure PCTCN2016089824-appb-000027
其中
Figure PCTCN2016089824-appb-000028
ωmax和ωmin是两个已知的参数。
优选的，所述步骤3具体包括：
子步骤D、由k-1时刻目标i的边缘分布N(xi,k-1；mi,k-1,Pi,k-1)，以及所述的转弯率
Figure PCTCN2016089824-appb-000029
得到k时刻目标i对应于测量yj,k的预测边缘分布为
Figure PCTCN2016089824-appb-000030
其中i＝1,…,Nk-1，j＝1,…,M，
Figure PCTCN2016089824-appb-000031
为状态向量的均值，且
Figure PCTCN2016089824-appb-000032
Figure PCTCN2016089824-appb-000033
为状态向量的方差，且
Figure PCTCN2016089824-appb-000034
其中，
Figure PCTCN2016089824-appb-000035
为状态转移矩阵，且
Figure PCTCN2016089824-appb-000036
子步骤E、利用贝叶斯规则对测量yj,k处理，得到目标i对应于测量yj,k的存在概率
Figure PCTCN2016089824-appb-000037
滤波增益
Figure PCTCN2016089824-appb-000038
均值向量
Figure PCTCN2016089824-appb-000039
协方差矩阵
Figure PCTCN2016089824-appb-000040
其中，Hk为 观测矩阵，Rk为观测噪声方差矩阵，pD,k为目标的检测概率，λc,k为杂波密度，I表示单位矩阵；
所有的M个测量处理后，各个目标对应于各测量的更新边缘分布和存在概率分别为
Figure PCTCN2016089824-appb-000041
和
Figure PCTCN2016089824-appb-000042
其中i＝1,…,Nk-1，j＝1,…,M；
子步骤F、设
Figure PCTCN2016089824-appb-000043
其中
Figure PCTCN2016089824-appb-000044
则k时刻目标i的更新边缘分布取为
Figure PCTCN2016089824-appb-000045
相应的存在概率和转弯率分别取为
Figure PCTCN2016089824-appb-000046
和
Figure PCTCN2016089824-appb-000047
其中i＝1,…,Nk-1，当q＝M+1时有
Figure PCTCN2016089824-appb-000048
另一方面，本发明还提供一种用于跟踪转弯机动目标的系统，所述系统包括：
预测模块，用于根据前一时刻各个目标的边缘分布、存在概率和转弯率，以及当前时刻与前一时刻的时间差，预测当前时刻各个目标的边缘分布和存在概率；
以k-1表示前一时刻，k表示当前时刻，tk-1表示前一时刻的时间，tk表示当前时刻的时间，k-1时刻目标i的边缘分布、存在概率和转弯率分别表示为N(xi,k-1；mi,k-1,Pi,k-1)、ρi,k-1和ωi,k-1，其中N表示高斯分布，i＝1,2,…Nk-1，xi,k-1为k-1时刻目标i的状态向量，mi,k-1和Pi,k-1分别表示k-1时刻目标i的状态均值和协方差，Nk-1为前一时刻目标的总数；
由k-1时刻目标i的边缘分布N(xi,k-1；mi,k-1,Pi,k-1)、存在概率ρi,k-1和转弯率ωi,k-1预测当前时刻目标i的边缘分布和存在概率分别为N(xi,k；mi,k|k-1,Pi,k|k-1)和ρi,k|k-1，其中mi,k|k-1＝Fi,k|k-1mi,k-1，Pi,k|k-1＝Qi,k-1+Fi,k|k-1Pi,k-1(Fi,k|k-1)T，ρi,k|k-1＝pS,k(tk-tk-1)ρi,k-1，
Figure PCTCN2016089824-appb-000049
△tk＝tk-tk-1为k时刻与k-1时刻的时间差，Qi,k-1为k-1时刻目标i的过程噪声协方差矩阵，pS,k(tk-tk-1)为目标的幸存概率，且
Figure PCTCN2016089824-appb-000050
T为采样周期，δ为给定的常数，i＝1,2,…Nk-1；
转弯率估计模块，用于根据前一时刻各个目标的边缘分布和存在概率，当前时刻与前一时刻的时间差，以及当前时刻的测量集合估计当前时刻各目标对应于每一个测量的转弯率；
更新模块，用于根据估计的各个目标对应于每一个测量的转弯率，前一时刻各个目标的边缘分布，当前时刻各目标的预测存在概率，当前时刻与前一时刻的时间差，以及当前时刻的测量集合，得到当前时刻各个已存在目标的更新边缘分布、存在概率和转弯率；
新目标生成模块，用于利用当前时刻的各个测量产生新目标的边缘分布，为其指定存在概率和转弯率；同时，将当前时刻新目标的边缘分布、存在概率和转弯率分别与所述的当前时刻已存在目标的更新边缘分布、存在概率和转弯率进行合并，生成当前时刻的各个目标的边缘分布、存在概率和转弯率；
利用当前时刻M个测量生成当前时刻新生目标的边缘分布
Figure PCTCN2016089824-appb-000051
为当前时刻各新生目标指定存在概率
Figure PCTCN2016089824-appb-000052
和转弯率
Figure PCTCN2016089824-appb-000053
其中，j＝1,…,M，ργ为所指定的存在概率，
Figure PCTCN2016089824-appb-000054
为第j个新生边缘分布的协方差，
Figure PCTCN2016089824-appb-000055
为第j个新生的边缘分布的均值，
Figure PCTCN2016089824-appb-000056
由当前时刻的第j个测量数据
Figure PCTCN2016089824-appb-000057
产生，并且
Figure PCTCN2016089824-appb-000058
将已存在目标的边缘分布与当前时刻新生的边缘分布进行合并，形成当前时刻各目标的边缘分布为
Figure PCTCN2016089824-appb-000059
合并后各目标的存在概率和转弯率分别为
Figure PCTCN2016089824-appb-000060
其中Nk＝Nk-1+M；
目标状态提取模块，用于从所述的合并后的各个目标中将存在概率小于第一阈值的目标裁减掉，并且将裁减后余下目标的边缘分布、存在概率和转弯率作为下一时刻递归滤波的输入，同时，从裁减后余下目标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。
本发明提供的技术方案通过预测、转弯率估计、更新、新目标生成及目标状态提取这些步骤能将转弯率估计与序贯贝叶斯滤波器相结合，在保证数据处理的实时性的同时，有效地解决了转弯率变化的多机动目标的跟踪问题，且具有很强的实用性。
附图说明
图1为本发明一实施方式中用于跟踪转弯机动目标的方法流程图；
图2为本发明一实施方式中用于跟踪转弯机动目标的系统10的内部结构示意图；
图3为本发明一实施方式中利用本发明实施例提供的传感器在70个扫描周期的测量数据图；
图4为本发明一实施方式中利用本发明用于跟踪转弯机动目标方法处理得到的结果图；
图5为本发明一实施方式中根据跳变马尔科夫系统模型高斯混合概率假设密度滤波方法处理得到的结果图；
图6为本发明一实施方式中利用本发明用于跟踪转弯机动目标方法与跳变马尔科夫系统模型高斯混合概率假设密度滤波方法在经过100次实验得到的平均OSPA距离示意图。
具体实施方式
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。
本发明提供的一种用于跟踪转弯机动目标的方法通过预测、转弯率估计、更新、新目标生成及目标状态提取这些步骤能将转弯率估计与序贯贝叶斯滤波器相结合，在保证数据处理的实时性的同时，有效地解决了转弯率变化的多机动目标的跟踪问题，且具有很强的实用性。
以下将对本发明所提供的一种用于跟踪转弯机动目标的方法进行详细说明。
请参阅图1，为本发明一实施方式中用于跟踪转弯机动目标的方法流程图。
在步骤1中，根据前一时刻各个目标的边缘分布、存在概率和转弯率，以及当前时刻与前一时刻的时间差，预测当前时刻各个目标的边缘分布和存在概率；
以k-1表示前一时刻，k表示当前时刻，tk-1表示前一时刻的时间，tk表示当前时刻的时间，k-1时刻目标i的边缘分布、存在概率和转弯率分别表示为N(xi,k-1；mi,k-1,Pi,k-1)、ρi,k-1和ωi,k-1，其中N表示高斯分布，i＝1,2,…Nk-1，xi,k-1为k-1时刻目标i的状态向量，mi,k-1和Pi,k-1分别表示k-1时刻目标i的状态均值和协方差，Nk-1为前一时刻目标的总数；
由k-1时刻目标i的边缘分布N(xi,k-1；mi,k-1,Pi,k-1)、存在概率ρi,k-1和转弯率ωi,k-1预测当前时刻目标i的边缘分布和存在概率分别为N(xi,k；mi,k|k-1,Pi,k|k-1)和ρi,k|k-1，其中mi,k|k-1＝Fi,k|k-1mi,k-1，Pi,k|k-1＝Qi,k-1+Fi,k|k-1Pi,k-1(Fi,k|k-1)T，ρi,k|k-1＝pS,k(tk-tk-1)ρi,k-1，
Figure PCTCN2016089824-appb-000061
△tk＝tk-tk-1为k时刻与k-1时刻的时 间差，Qi,k-1为k-1时刻目标i的过程噪声协方差矩阵，pS,k(tk-tk-1)为目标的幸存概率，且
Figure PCTCN2016089824-appb-000062
T为采样周期，δ为给定的常数，i＝1,2,…Nk-1。
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
Figure PCTCN2016089824-appb-000063
其中x和y分别表示位置分量，
Figure PCTCN2016089824-appb-000064
和
Figure PCTCN2016089824-appb-000065
分别表示速度分量，上标T表示向量的转置；过程噪声方差矩阵为
Figure PCTCN2016089824-appb-000066
其中，△tk＝tk-tk-1为当前时刻与前一时刻的时间差，σv为过程噪声标准差；观测噪声方差矩阵
Figure PCTCN2016089824-appb-000067
σw为观测噪声的标准差；参数δ取为δ＝2.5，最大转弯率和最小转弯率分别取为ωmax＝6度/秒和ωmin＝-6度/秒。
为了产生仿真数据，取幸存概率pS,k＝1.0、检测概率pD,k＝0.9、杂波密度λc,k＝1.6×10-10m-2、过程噪声的标准差σv＝1ms-2、观测噪声的标准差σw＝1m和传感器的扫描周期T＝1s。
在本实施方式中，以k-1表示前一时刻，k表示当前时刻，tk-1表示前一时刻的时间，tk表示当前时刻的时间，k-1时刻目标i的边缘分布、存在概率和转弯率分别表示为N(xi,k-1；mi,k-1,Pi,k-1)、ρi,k-1和ωi,k-1，其中N表示高斯分布，i＝1,2,…Nk-1，xi,k-1为k-1时刻目标i的状态向量，mi,k-1和Pi,k-1分别表示k-1时刻目标i的状态均值和协方差，Nk-1为前一时刻目标的总数；
由k-1时刻目标i的边缘分布N(xi,k-1；mi,k-1,Pi,k-1)、存在概率ρi,k-1和转弯率ωi,k-1预测当前时刻目标i的边缘分布和存在概率分别为N(xi,k；mi,k|k-1,Pi,k|k-1)和ρi,k|k-1，其中mi,k|k-1＝Fi,k|k-1mi,k-1，Pi,k|k-1＝Qi,k-1+Fi,k|k-1Pi,k-1(Fi,k|k-1)T，ρi,k|k-1＝pS,k(tk-tk-1)ρi,k-1， △tk＝tk-tk-1为k时刻与k-1时刻的时间差，Qi,k-1为k-1时刻目标i的过程噪声协方差矩阵，pS,k(tk-tk-1)为目标的幸存概率，且
Figure PCTCN2016089824-appb-000069
T为采样周期，δ为给定的常数，i＝1,2,…Nk-1。
在步骤2中，根据前一时刻各个目标的边缘分布和存在概率，当前时刻与前一时刻的时间差，以及当前时刻的测量集合估计当前时刻各目标对应于每一个测量的转弯率。
在本实施方式中，所述步骤2中，根据所述的k-1时刻目标i的边缘分布N(xi,k-1；mi,k-1,Pi,k-1)，k时刻与k-1时刻的时间差，以及k时刻的测量集合yk＝(y1,k,…,yM,k)中的第j个测量yj,k，估计k时刻目标i对应于测量yj,k的转弯率
Figure PCTCN2016089824-appb-000070
其中i＝1,2,…Nk-1，j＝1,2,…M，M为测量的总数；
Figure PCTCN2016089824-appb-000071
的估计步骤如下：
子步骤A、设
Figure PCTCN2016089824-appb-000072
其中
Figure PCTCN2016089824-appb-000073
和
Figure PCTCN2016089824-appb-000074
分别表示目标i位置的x分量和y分量，
Figure PCTCN2016089824-appb-000075
和
Figure PCTCN2016089824-appb-000076
分别表示其速度的x分量和y分量，
Figure PCTCN2016089824-appb-000077
和
Figure PCTCN2016089824-appb-000078
分别表示测量yj,k的x分量和y分量，上标T表示矩阵或向量的转置；利用mi,k-1和yj,k通过变换得到向量
Figure PCTCN2016089824-appb-000079
其中
Figure PCTCN2016089824-appb-000080
子步骤B、利用转换后的向量
Figure PCTCN2016089824-appb-000081
得到转弯率ωi a ,j，其中，
Figure PCTCN2016089824-appb-000082
tk-1和tk分别为k-1时刻和k时刻的时间；
子步骤C、由所述的
Figure PCTCN2016089824-appb-000083
最大转弯率ωmax和最小转弯率ωmin得到目标i对应于测量yj,k的转弯率
Figure PCTCN2016089824-appb-000084
其中
Figure PCTCN2016089824-appb-000085
ωmax和ωmin是两个已知的参数。
在步骤3中，根据估计的各个目标对应于每一个测量的转弯率，前一时刻各个目标的边缘分布，当前时刻各目标的预测存在概率，当前时刻与前一时刻的时间差，以及当前时刻的测量集合，确定当前时刻各个已存在目标的更新边缘分布、存在概率和转弯率。
在本实施方式中，所述步骤3中，根据所述的k-1时刻目标i的边缘分布N(xi,k-1；mi,k-1,Pi,k-1)，k时刻目标i的预测存在概率ρi,k|k-1，目标i对应于测量yj,k的转弯率
Figure PCTCN2016089824-appb-000086
以及当前时刻的测量集合yk，求取当前时刻各个已存在目标的更新边缘分布、存在概率和转弯率的步骤如下：
子步骤D、由k-1时刻目标i的边缘分布N(xi,k-1；mi,k-1,Pi,k-1)，以及所述的转弯率
Figure PCTCN2016089824-appb-000087
得到k时刻目标i对应于测量yj,k的预测边缘分布为
Figure PCTCN2016089824-appb-000088
其中i＝1,…,Nk-1，j＝1,…,M，
Figure PCTCN2016089824-appb-000089
为状态向量的均值，且
Figure PCTCN2016089824-appb-000090
Figure PCTCN2016089824-appb-000091
为状态向量的方差，且
Figure PCTCN2016089824-appb-000092
其中，
Figure PCTCN2016089824-appb-000093
为状态转移矩阵，且
Figure PCTCN2016089824-appb-000094
子步骤E、利用贝叶斯规则对测量yj,k处理，得到目标i对应于测量yj,k的存在概率
Figure PCTCN2016089824-appb-000095
滤波增益
Figure PCTCN2016089824-appb-000096
均值向量
Figure PCTCN2016089824-appb-000097
协方差矩阵
Figure PCTCN2016089824-appb-000098
其中，Hk为观测矩阵，Rk为观测噪声方差矩阵，pD,k为目标的检测概率，λc,k为杂波密度，I表示单位矩阵；
所有的M个测量处理后，各个目标对应于各测量的更新边缘分布和存在概率分别为
Figure PCTCN2016089824-appb-000099
和
Figure PCTCN2016089824-appb-000100
其中i＝1,…,Nk-1，j＝1,…,M；
子步骤F、设
Figure PCTCN2016089824-appb-000101
其中
Figure PCTCN2016089824-appb-000102
则k时刻目标i的更新边缘分布取为
Figure PCTCN2016089824-appb-000103
相应的存在概率和转弯率分别取为和
Figure PCTCN2016089824-appb-000105
其中i＝1,…,Nk-1，当q＝M+1时有
Figure PCTCN2016089824-appb-000106
在步骤4中，利用当前时刻的各个测量产生新目标的边缘分布，为其指定存在概率和转弯率；同时，将当前时刻新目标的边缘分布、存在概率和转弯率分别与所述的当前时刻已存在目标的更新边缘分布、存在概率和转弯率进行合并，生成当前时刻的各个目标的边缘分布、存在概率和转弯率；
利用当前时刻M个测量生成当前时刻新生目标的边缘分布
Figure PCTCN2016089824-appb-000107
为当前时刻各新生目标指定存在概率
Figure PCTCN2016089824-appb-000108
和转弯率为
Figure PCTCN2016089824-appb-000109
其中，j＝1,…,M，ργ为所指定的存在概率，
Figure PCTCN2016089824-appb-000110
为第j个新生边缘分布的协方差，
Figure PCTCN2016089824-appb-000111
为第j个新生目标的边缘分布的均值，
Figure PCTCN2016089824-appb-000112
由当前时刻的第j个测量数据
Figure PCTCN2016089824-appb-000113
产生，并且
Figure PCTCN2016089824-appb-000114
将已存在目标的边缘分布与当前时刻新生的边缘分布进行合并，形成当前时刻各目标的边缘分布为
Figure PCTCN2016089824-appb-000115
合并后各目标的存在概率和转弯率分别为
Figure PCTCN2016089824-appb-000116
和
Figure PCTCN2016089824-appb-000117
其中Nk＝Nk-1+M。
在步骤5中，从所述的合并后的各个目标中将存在概率小于第一阈值的目标裁减掉，并且将裁减后余下目标的边缘分布、存在概率和转弯率作为下一时刻递归滤波的输入，同时，从裁减后余下目标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。
本发明提供的一种用于跟踪转弯机动目标的方法，通过预测、转弯率估计、更新、新目标生成及目标状态提取这些步骤能将转弯率估计与序贯贝叶斯滤波器相结合，在保证数据处理的实时性的同时，有效地解决了转弯率变化的多机动目标的跟踪问题，且具有很强的实用性。
本发明具体实施方式还提供一种用于跟踪转弯机动目标的系统10，主要包括：
预测模块11，用于根据前一时刻各个目标的边缘分布、存在概率和转弯率，以及当前时刻与前一时刻的时间差，预测当前时刻各个目标的边缘分布和存在概率；
转弯率估计模块12，用于根据前一时刻各个目标的边缘分布和存在概率，当前时刻与前一时刻的时间差，以及当前时刻的测量集合估计当前时刻各目标对应于每一个测量的转弯率；
更新模块13，用于根据估计的各个目标对应于每一个测量的转弯率，前一时刻各个目标的边缘分布，当前时刻各目标的预测存在概率，当前时刻与前一时刻的时间差，以及当前时刻的测量集合，得到当前时刻各个已存在目标的更新边缘分布、存在概率和转弯率；
新目标生成模块14，利用当前时刻的各个测量产生新目标的边缘分布，为其指定存在概率和转弯率；同时，将当前时刻新目标的边缘分布、存在概率和转弯率分别与所述的当前时刻已存在目标的更新边缘分布、存在概率和转弯率进行合并，生成当前时刻的各个目标的边缘分布、存在概率和转弯率；
目标状态提取模块15，用于从所述的合并后的各个目标中将存在概率小于第一阈值的目标裁减掉，并且将裁减后余下目标的边缘分布、存在概率和转弯率作为下一时刻递归滤波的输入，同时，从裁减后余下目标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。
本发明提供的一种用于跟踪转弯机动目标的系统10，通过预测模块11、转弯率估计模块12、更新模块13、新目标生成模块14以及目标状态提取模块15这些模块能将转弯率估计与序贯贝叶斯滤波器相结合，在保证数据处理的实时性的同时，有效地解决了转弯率变化的多机动目标的跟踪问题，且具有很强的实用性。
请参阅图2，所示为本发明一实施方式中用于跟踪转弯机动目标的系统10的结构示意图。
在本实施方式中，用于跟踪转弯机动目标的系统10，主要包括预测模块11、转弯率估计模块12、更新模块13、新目标生成模块14以及目标状态提取模块15。
预测模块11，用于根据前一时刻各个目标的边缘分布、存在概率和转弯率，以及当前时刻与前一时刻的时间差，预测当前时刻各个目标的边缘分布和存在概率；
以k-1表示前一时刻，k表示当前时刻，tk-1表示前一时刻的时间，tk表示当前时刻的时间，k-1时刻目标i的边缘分布、存在概率和转弯率分别表示为N(xi,k-1；mi,k-1,Pi,k-1)、ρi,k-1和ωi,k-1，其中N表示高斯分布，i＝1,2,…Nk-1，xi,k-1为k-1时刻目标i的状态向量，mi,k-1和Pi,k-1分别表示k-1时刻目标i的状态均值和协方差，Nk-1为前一时刻目标的总数；
由k-1时刻目标i的边缘分布N(xi,k-1；mi,k-1,Pi,k-1)、存在概率ρi,k-1和转弯率ωi,k-1预测当前时刻目标i的边缘分布和存在概率分别为N(xi,k；mi,k|k-1,Pi,k|k-1)和ρi,k|k-1，其中mi,k|k-1＝Fi,k|k-1mi,k-1，Pi,k|k-1＝Qi,k-1+Fi,k|k-1Pi,k-1(Fi,k|k-1)T，ρi,k|k-1＝pS,k(tk-tk-1)ρi,k-1，
Figure PCTCN2016089824-appb-000118
△tk＝tk-tk-1为k时刻与k-1时刻的时间差，Qi,k-1为k-1时刻目标i的过程噪声协方差矩阵，pS,k(tk-tk-1)为目标的幸存概率，且
Figure PCTCN2016089824-appb-000119
T为采样周期，δ为给定的常数，i＝1,2,…Nk-1
转弯率估计模块12，用于根据前一时刻各个目标的边缘分布和存在概率，当前时刻与前一时刻的时间差，以及当前时刻的测量集合估计当前时刻各目标对应于每一个测量的转弯率。
在所述转弯率估计模块12中，根据所述的k-1时刻目标i的边缘分布N(xi,k-1；mi,k-1,Pi,k-1)，k时刻与k-1时刻的时间差，以及k时刻的测量集合yk＝(y1,k,…,yM,k)中的第j个测量yj,k，估计k时刻目标i对应于测量yj,k的转弯率
Figure PCTCN2016089824-appb-000120
其中i＝1,2,…Nk-1，j＝1,2,…M，M为测量的总数；
Figure PCTCN2016089824-appb-000121
的估计步骤如下：
步骤A、设
Figure PCTCN2016089824-appb-000122
其中
Figure PCTCN2016089824-appb-000123
和
Figure PCTCN2016089824-appb-000124
分别表示目标i位置的x分量和y分量，
Figure PCTCN2016089824-appb-000125
和
Figure PCTCN2016089824-appb-000126
分别表示其速度的x分量和y分量，
Figure PCTCN2016089824-appb-000127
和
Figure PCTCN2016089824-appb-000128
分别表示测量yj,k的x分量和y分量，上标T表示矩阵或向量的转置；利用mi,k-1和yj,k通过变换得到向量
Figure PCTCN2016089824-appb-000129
其中
Figure PCTCN2016089824-appb-000130
步骤B、利用转换后的向量
Figure PCTCN2016089824-appb-000131
得到转弯率
Figure PCTCN2016089824-appb-000132
其中，
Figure PCTCN2016089824-appb-000133
tk-1和tk分别为k-1时刻和k时刻的时间；
步骤C、由所述的
Figure PCTCN2016089824-appb-000134
最大转弯率ωmax和最小转弯率ωmin得到目标i对应于测量yj,k的转弯率
Figure PCTCN2016089824-appb-000135
其中
Figure PCTCN2016089824-appb-000136
ωmax和ωmin是两个已知的参数。
更新模块13，用于根据估计的各个目标对应于每一个测量的转弯率，前一时刻各个目标的边缘分布，当前时刻各目标的预测存在概率，当前时刻与前一时刻的时间差，以及当前时刻的测量集合，得到当前时刻各个已存在目标的更新边缘分布、存在概率和转弯率。
在所述更新模块13中，根据所述的k-1时刻目标i的边缘分布N(xi,k-1；mi,k-1,Pi,k-1)，k时刻目标i的预测存在概率ρi,k|k-1，目标i对应于测量yj,k的转弯率
Figure PCTCN2016089824-appb-000137
以及当前时刻的测量集合yk，求取当前时刻各个已存在目标的更新边缘分布、存在概率和转弯率的步骤如下：
步骤D、由k-1时刻目标i的边缘分布N(xi,k-1；mi,k-1,Pi,k-1)，以及所述的转弯率
Figure PCTCN2016089824-appb-000138
得到k时刻目标i对应于测量yj,k的预测边缘分布为
Figure PCTCN2016089824-appb-000139
其中i＝1,…,Nk-1，j＝1,…,M，
Figure PCTCN2016089824-appb-000140
为状态向量的均值，且
Figure PCTCN2016089824-appb-000141
Figure PCTCN2016089824-appb-000142
为状态向量的方差，且
Figure PCTCN2016089824-appb-000143
其中，
Figure PCTCN2016089824-appb-000144
为状态转移矩阵，且
Figure PCTCN2016089824-appb-000145
步骤E、利用贝叶斯规则对测量yj,k处理，得到目标i对应于测量yj,k的存在概率
Figure PCTCN2016089824-appb-000146
滤波增益
Figure PCTCN2016089824-appb-000147
均值向量
Figure PCTCN2016089824-appb-000148
协方差矩阵
Figure PCTCN2016089824-appb-000149
其中，Hk为观测矩阵，Rk为观测噪声方差矩阵，pD,k为目标的检测概率，λc,k为杂波密度，I表示单位矩阵；
所有的测量处理后，各个目标对应于各测量的更新边缘分布和存在概率分别为
Figure PCTCN2016089824-appb-000150
其中i＝1,…,Nk-1，j＝1,…,M；
步骤F、设
Figure PCTCN2016089824-appb-000151
其中
Figure PCTCN2016089824-appb-000152
则k时刻目标i的更新边缘分布取为
Figure PCTCN2016089824-appb-000153
相应的存在概率和转弯率分别取为
Figure PCTCN2016089824-appb-000154
和
Figure PCTCN2016089824-appb-000155
其中i＝1,…,Nk-1，当q＝M+1时有
Figure PCTCN2016089824-appb-000156
新目标生成模块14，用于利用当前时刻的各个测量产生新目标的边缘分布，为其指定存在概率和转弯率；同时，将当前时刻新目标的边缘分布、存在概率和转弯率分别与所述的当前时刻已存在目标的更新边缘分布、存在概率和转弯率进行合并，生成当前时刻的各个目标的边缘分布、存在概率和转弯率。
在本实施方式中，利用当前时刻M个测量生成当前时刻新生目标的边缘分布
Figure PCTCN2016089824-appb-000157
为当前时刻各新生目标指定存在概率
Figure PCTCN2016089824-appb-000158
和转弯率
Figure PCTCN2016089824-appb-000159
其中，j＝1,…,M，ργ为所指定的存在概率，
Figure PCTCN2016089824-appb-000160
为第j个新生边缘分布的协方差，
Figure PCTCN2016089824-appb-000161
为第j个新生的边缘分布的均值，
Figure PCTCN2016089824-appb-000162
由当前时刻的第j个测量数据
Figure PCTCN2016089824-appb-000163
产生，并且
Figure PCTCN2016089824-appb-000164
将已存在目标的边缘分布与当前时刻新生的边缘分布进行合并，形成当前时刻各目标的边缘分布为
Figure PCTCN2016089824-appb-000165
合并后各目标的存在概率和转弯率分别为
Figure PCTCN2016089824-appb-000166
和
Figure PCTCN2016089824-appb-000167
其中Nk＝Nk-1+M。
目标状态提取模块15，用于从所述的合并后的各个目标中将存在概率小于第一阈值的目标裁减掉，并且将裁减后余下目标的边缘分布、存在概率和转弯率作为下一时刻递归滤波的输入，同时，从裁减后余下目标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。
在本实施方式中，在实验中传感器在70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，将本发明与跳变马尔科夫系统模型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pS,k＝1.0、pD,k＝0.9、λc,k＝1.6×10-10m-2、σw＝2m、σv＝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wγ＝0.1，本发明新产生目标的存在概率pγ＝0.1，新产生目标的协方差为图4和图5分别为用现有的跳变马尔科夫模型GM-PHD滤波器与本发明对图3中的数据处理得到的结果。图6为用现有的跳变马尔科夫模型GM-PHD滤波器与本发明分别进行100次Monte Carlo实验得到的平均OSPA(Optimal Subpattern Assignment，最优亚模式分配)距离。现有的跳变马尔科夫模型的GM-PHD滤波器与本发明的实验结果比较表明，本发明的方法可以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。
本发明提供的一种用于跟踪转弯机动目标的系统10，通过预测模块11、转弯率估计模块12、更新模块13、新目标生成模块14以及目标状态提取模块15这些模块能将转弯率估计与序贯贝叶斯滤波器相结合，在保证数据处理的实时性的同时，有效地解决了转弯率变化的多机动目标的跟踪问题，且具有很强的实用性。
值得注意的是，上述实施例中，所包括的各个单元只是按照功能逻辑进行划分的，但并不局限于上述的划分，只要能够实现相应的功能即可；另外，各功能单元的具体名称也只是为了便于相互区分，并不用于限制本发明的保护范围。
另外，本领域普通技术人员可以理解实现上述各实施例方法中的全部或部分步骤是可以 通过程序来指令相关的硬件来完成，相应的程序可以存储于一计算机可读取存储介质中，所述的存储介质，如ROM/RAM、磁盘或光盘等。
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。

Claims (6)

  1. 一种用于跟踪转弯机动目标的方法，其特征在于，所述方法包括：
    步骤1、根据前一时刻各个目标的边缘分布、存在概率和转弯率，以及当前时刻与前一时刻的时间差，预测当前时刻各个目标的边缘分布和存在概率；
    以k-1表示前一时刻，k表示当前时刻，tk-1表示前一时刻的时间，tk表示当前时刻的时间，k-1时刻目标i的边缘分布、存在概率和转弯率分别表示为N(xi,k-1；mi,k-1,Pi,k-1)、ρi,k-1和ωi,k-1，其中N表示高斯分布，i＝1,2,…Nk-1，xi,k-1为k-1时刻目标i的状态向量，mi,k-1和Pi,k-1分别表示k-1时刻目标i的状态均值和协方差，Nk-1为前一时刻目标的总数；
    由k-1时刻目标i的边缘分布N(xi,k-1；mi,k-1,Pi,k-1)、存在概率ρi,k-1和转弯率ωi,k-1预测当前时刻目标i的边缘分布和存在概率分别为N(xi,k；mi,k|k-1,Pi,k|k-1)和ρi,k|k-1，其中mi,k|k-1＝Fi,k|k-1mi,k-1，Pi,k|k-1＝Qi,k-1+Fi,k|k-1Pi,k-1(Fi,k|k-1)T，ρi,k|k-1＝pS,k(tk-tk-1)ρi,k-1，
    Figure PCTCN2016089824-appb-100001
    △tk＝tk-tk-1为k时刻与k-1时刻的时间差，Qi,k-1为k-1时刻目标i的过程噪声协方差矩阵，pS,k(tk-tk-1)为目标的幸存概率，且
    Figure PCTCN2016089824-appb-100002
    T为采样周期，δ为给定的常数，i＝1,2,…Nk-1；
    步骤2、根据前一时刻各个目标的边缘分布和存在概率，当前时刻与前一时刻的时间差，以及当前时刻的测量集合估计当前时刻各目标对应于每一个测量的转弯率；
    步骤3、根据估计的各个目标对应于每一个测量的转弯率，前一时刻各个目标的边缘分布，当前时刻各目标的预测存在概率，当前时刻与前一时刻的时间差，以及当前时刻的测量集合，确定当前时刻各个已存在目标的更新边缘分布、存在概率和转弯率；
    步骤4、利用当前时刻的各个测量产生新目标的边缘分布，为其指定存在概率和转弯率；同时，将当前时刻新目标的边缘分布、存在概率和转弯率分别与所述的当前时刻已存在目标的更新边缘分布、存在概率和转弯率进行合并，生成当前时刻的各个目标的边缘分布、存在概率和转弯率；
    利用当前时刻M个测量生成当前时刻新生目标的边缘分布
    Figure PCTCN2016089824-appb-100003
    为当前时刻 各新生目标指定存在概率
    Figure PCTCN2016089824-appb-100004
    和转弯率为
    Figure PCTCN2016089824-appb-100005
    其中，j＝1,…,M，ργ为所指定的存在概率，
    Figure PCTCN2016089824-appb-100006
    为第j个新生边缘分布的协方差，
    Figure PCTCN2016089824-appb-100007
    为第j个新生目标的边缘分布的均值，
    Figure PCTCN2016089824-appb-100008
    由当前时刻的第j个测量数据
    Figure PCTCN2016089824-appb-100009
    产生，并且
    Figure PCTCN2016089824-appb-100010
    将已存在目标的边缘分布与当前时刻新生的边缘分布进行合并，形成当前时刻各目标的边缘分布为
    Figure PCTCN2016089824-appb-100011
    合并后各目标的存在概率和转弯率分别为
    Figure PCTCN2016089824-appb-100012
    和
    Figure PCTCN2016089824-appb-100013
    其中Nk＝Nk-1+M；
    步骤5、从所述的合并后的各个目标中将存在概率小于第一阈值的目标裁减掉，并且将裁减后余下目标的边缘分布、存在概率和转弯率作为下一时刻递归滤波的输入，同时，从裁减后余下目标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。
  2. 如权利要求1所述的用于跟踪转弯机动目标的方法，其特征在于，所述步骤2具体包括：
    子步骤A、设
    Figure PCTCN2016089824-appb-100014
    其中
    Figure PCTCN2016089824-appb-100015
    和
    Figure PCTCN2016089824-appb-100016
    分别表示目标i位置的x分量和y分量，
    Figure PCTCN2016089824-appb-100017
    和
    Figure PCTCN2016089824-appb-100018
    分别表示其速度的x分量和y分量，
    Figure PCTCN2016089824-appb-100019
    和
    Figure PCTCN2016089824-appb-100020
    分别表示测量yj,k的x分量和y分量，上标T表示矩阵或向量的转置；利用mi,k-1和yj,k通过变换得到向量
    Figure PCTCN2016089824-appb-100021
    其中
    Figure PCTCN2016089824-appb-100022
    子步骤B、利用转换后的向量
    Figure PCTCN2016089824-appb-100023
    得到转弯率
    Figure PCTCN2016089824-appb-100024
    其中，
    Figure PCTCN2016089824-appb-100025
    tk-1和tk分别为k-1时刻和k时刻的时间；
    子步骤C、由所述的
    Figure PCTCN2016089824-appb-100026
    最大转弯率ωmax和最小转弯率ωmin得到目标i对应于测量yj,k的转弯率
    Figure PCTCN2016089824-appb-100027
    其中
    Figure PCTCN2016089824-appb-100028
    ωmax和ωmin是两个已知的参数。
  3. 如权利要求2所述的用于跟踪转弯机动目标的方法，其特征在于，所述步骤3具体包括：
    子步骤D、由k-1时刻目标i的边缘分布N(xi,k-1；mi,k-1,Pi,k-1)，以及所述的转弯率
    Figure PCTCN2016089824-appb-100029
    得到k时刻目标i对应于测量yj,k的预测边缘分布为
    Figure PCTCN2016089824-appb-100030
    其中i＝1,…,Nk-1，j＝1,…,M，
    Figure PCTCN2016089824-appb-100031
    为状态向量的均值，且
    Figure PCTCN2016089824-appb-100032
    Figure PCTCN2016089824-appb-100033
    为状态向量的方差，且
    Figure PCTCN2016089824-appb-100034
    其中，
    Figure PCTCN2016089824-appb-100035
    为状态转移矩阵，且
    Figure PCTCN2016089824-appb-100036
    子步骤E、利用贝叶斯规则对测量yj,k处理，得到目标i对应于测量yj,k的存在概率
    Figure PCTCN2016089824-appb-100037
    滤波增益
    Figure PCTCN2016089824-appb-100038
    均值向量
    Figure PCTCN2016089824-appb-100039
    协方差矩阵
    Figure PCTCN2016089824-appb-100040
    其中，Hk为观测矩阵，Rk为观测噪声方差矩阵，pD,k为目标的检测概率，λc,k为杂波密度，I表示单位矩阵；
    所有的M个测量处理后，各个目标对应于各测量的更新边缘分布和存在概率分别为
    Figure PCTCN2016089824-appb-100041
    和
    Figure PCTCN2016089824-appb-100042
    其中i＝1,…,Nk-1，j＝1,…,M；
    子步骤F、设
    Figure PCTCN2016089824-appb-100043
    其中
    Figure PCTCN2016089824-appb-100044
    则k时刻目标i的更新边缘分布取为
    Figure PCTCN2016089824-appb-100045
    相应的存在概率和转弯率分别取为
    Figure PCTCN2016089824-appb-100046
    和
    Figure PCTCN2016089824-appb-100047
    其中i＝1,…,Nk-1，当q＝M+1时有
    Figure PCTCN2016089824-appb-100048
  4. 一种用于跟踪转弯机动目标的系统，其特征在于，所述系统包括：
    预测模块，用于根据前一时刻各个目标的边缘分布、存在概率和转弯率，以及当前时刻与前一时刻的时间差，预测当前时刻各个目标的边缘分布和存在概率；
    以k-1表示前一时刻，k表示当前时刻，tk-1表示前一时刻的时间，tk表示当前时刻的时间，k-1时刻目标i的边缘分布、存在概率和转弯率分别表示为N(xi,k-1；mi,k-1,Pi,k-1)、ρi,k-1和ωi,k-1，其中N表示高斯分布，i＝1,2,…Nk-1，xi,k-1为k-1时刻目标i的状态向量，mi,k-1和Pi,k-1分别表示k-1时刻目标i的状态均值和协方差，Nk-1为前一时刻目标的总数；
    由k-1时刻目标i的边缘分布N(xi,k-1；mi,k-1,Pi,k-1)、存在概率ρi,k-1和转弯率ωi,k-1预测当前时刻目标i的边缘分布和存在概率分别为N(xi,k；mi,k|k-1,Pi,k|k-1)和ρi,k|k-1，其中mi,k|k-1＝Fi,k|k-1mi,k-1，Pi,k|k-1＝Qi,k-1+Fi,k|k-1Pi,k-1(Fi,k|k-1)T，ρi,k|k-1＝pS,k(tk-tk-1)ρi,k-1，
    Figure PCTCN2016089824-appb-100049
    △tk＝tk-tk-1为k时刻与k-1时刻的时间差，Qi,k-1为k-1时刻目标i的过程噪声协方差矩阵，pS,k(tk-tk-1)为目标的幸存概率，且
    Figure PCTCN2016089824-appb-100050
    T为采样周期，δ为给定的常数，i＝1,2,…Nk-1；
    转弯率估计模块，用于根据前一时刻各个目标的边缘分布和存在概率，当前时刻与前一时刻的时间差，以及当前时刻的测量集合估计当前时刻各目标对应于每一个测量的转弯率；
    更新模块，用于根据估计的各个目标对应于每一个测量的转弯率，前一时刻各个目标的边缘分布，当前时刻各目标的预测存在概率，当前时刻与前一时刻的时间差，以及当前时刻的测量集合，得到当前时刻各个已存在目标的更新边缘分布、存在概率和转弯率；
    新目标生成模块，用于利用当前时刻的各个测量产生新目标的边缘分布，为其指定存在概率和转弯率；同时，将当前时刻新目标的边缘分布、存在概率和转弯率分别与所述的当前时刻已存在目标的更新边缘分布、存在概率和转弯率进行合并，生成当前时刻的各个目标的边缘分布、存在概率和转弯率；
    利用当前时刻M个测量生成当前时刻新生目标的边缘分布
    Figure PCTCN2016089824-appb-100051
    为当前时刻各新生目标指定存在概率
    Figure PCTCN2016089824-appb-100052
    和转弯率
    Figure PCTCN2016089824-appb-100053
    其中，j＝1,…,M，ργ为所指定的存在概率，
    Figure PCTCN2016089824-appb-100054
    为第j个新生边缘分布的协方差，
    Figure PCTCN2016089824-appb-100055
    为第j个新生的边缘分布的均值，
    Figure PCTCN2016089824-appb-100056
    由当前时刻的第j个测量数据
    Figure PCTCN2016089824-appb-100057
    产生，并且
    Figure PCTCN2016089824-appb-100058
    将已存在目标的边缘分布与当前时刻新生的边缘分布进行合并，形成当前时刻各目标的边缘分布为
    Figure PCTCN2016089824-appb-100059
    合并后各目标的存在概率和转弯率分别为
    Figure PCTCN2016089824-appb-100060
    和
    Figure PCTCN2016089824-appb-100061
    其中 Nk＝Nk-1+M；
    目标状态提取模块，用于从所述的合并后的各个目标中将存在概率小于第一阈值的目标裁减掉，并且将裁减后余下目标的边缘分布、存在概率和转弯率作为下一时刻递归滤波的输入，同时，从裁减后余下目标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。
  5. 如权利要求4所述的用于跟踪转弯机动目标的系统，其特征在于，所述转弯率估计模块具体用于根据所述的k-1时刻目标i的边缘分布N(xi,k-1；mi,k-1,Pi,k-1)，k时刻与k-1时刻的时间差，以及k时刻的测量集合yk＝(y1,k,…,yM,k)中的第j个测量yj,k，估计k时刻目标i对应于测量yj,k的转弯率
    Figure PCTCN2016089824-appb-100062
    其中i＝1,2,…Nk-1，j＝1,2,…M，M为测量的总数；其中
    Figure PCTCN2016089824-appb-100063
    的估计步骤如下：
    步骤A、设
    Figure PCTCN2016089824-appb-100064
    其中
    Figure PCTCN2016089824-appb-100065
    和
    Figure PCTCN2016089824-appb-100066
    分别表示目标i位置的x分量和y分量，
    Figure PCTCN2016089824-appb-100067
    和
    Figure PCTCN2016089824-appb-100068
    分别表示其速度的x分量和y分量，
    Figure PCTCN2016089824-appb-100069
    和
    Figure PCTCN2016089824-appb-100070
    分别表示测量yj,k的x分量和y分量，上标T表示矩阵或向量的转置；利用mi,k-1和yj,k通过变换得到向量
    Figure PCTCN2016089824-appb-100071
    其中
    Figure PCTCN2016089824-appb-100072
    步骤B、利用转换后的向量
    Figure PCTCN2016089824-appb-100073
    得到转弯率
    Figure PCTCN2016089824-appb-100074
    其中，
    Figure PCTCN2016089824-appb-100075
    tk-1和tk分别为k-1时刻和k时刻的时间；
    步骤C、由所述的
    Figure PCTCN2016089824-appb-100076
    最大转弯率ωmax和最小转弯率ωmin得到目标i对应于测量yj,k的转弯率
    Figure PCTCN2016089824-appb-100077
    其中
    Figure PCTCN2016089824-appb-100078
    ωmax和ωmin是两个已知的参数。
  6. 如权利要求5所述的用于跟踪转弯机动目标的系统，其特征在于，所述更新模块具体用于根据所述的k-1时刻目标i的边缘分布N(xi,k-1；mi,k-1,Pi,k-1)，k时刻目标i的预测存在概率ρi,k|k-1，目标i对应于测量yj,k的转弯率
    Figure PCTCN2016089824-appb-100079
    以及当前时刻的测量集合yk，求取当前时刻各个已存在目标的更新边缘分布、存在概率和转弯率，其中求取的步骤如下：
    步骤D、由k-1时刻目标i的边缘分布N(xi,k-1；mi,k-1,Pi,k-1)，以及所述的转弯率
    Figure PCTCN2016089824-appb-100080
    得到k时刻目标i对应于测量yj,k的预测边缘分布为
    Figure PCTCN2016089824-appb-100081
    其中i＝1,…,Nk-1，j＝1,…,M，
    Figure PCTCN2016089824-appb-100082
    为状态向量的均值，且
    Figure PCTCN2016089824-appb-100083
    Figure PCTCN2016089824-appb-100084
    为状态向量的方差，且
    Figure PCTCN2016089824-appb-100085
    其中，
    Figure PCTCN2016089824-appb-100086
    为状态转移矩阵，且
    Figure PCTCN2016089824-appb-100087
    步骤E、利用贝叶斯规则对测量yj,k处理，得到目标i对应于测量yj,k的存在概率
    Figure PCTCN2016089824-appb-100088
    滤波增益
    Figure PCTCN2016089824-appb-100089
    均值向量
    Figure PCTCN2016089824-appb-100090
    协方差矩阵
    Figure PCTCN2016089824-appb-100091
    其中，Hk为观测矩阵，Rk为观测噪声方差矩阵，pD,k为目标的检测概率，λc,k为杂波密度，I表示单位矩阵；
    所有的测量处理后，各个目标对应于各测量的更新边缘分布和存在概率分别为
    Figure PCTCN2016089824-appb-100092
    其中i＝1,…,Nk-1，j＝1,…,M；
    步骤F、设
    Figure PCTCN2016089824-appb-100093
    其中
    Figure PCTCN2016089824-appb-100094
    则k时刻目标i的更新边缘分布取为
    Figure PCTCN2016089824-appb-100095
    相应的存在概率和转弯率分别取为
    Figure PCTCN2016089824-appb-100096
    和
    Figure PCTCN2016089824-appb-100097
    其中i＝1,…,Nk-1，当q＝M+1时有
    Figure PCTCN2016089824-appb-100098
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