Maneuvering target tracking method based on model adaptation

Abstract

The invention discloses a maneuvering target tracking method based on model adaptation, which combines Bayesian online change point detection and a model selection method, and is characterized in that the Bayesian online change point detection detects change points of generated parameters in sequence data in an online mode, so that the change of a target motion state can be perceived in real time; according to the model selection method, the motion model matched with the target motion state can be selected in the model set according to the change of the target motion state; specifically, the change of the motion state of a target is detected in real time through a Bayesian online change point detection technology, when a change point is detected, a model selection mechanism is triggered, a proper motion model is selected according to the current motion state of the target, and parameters of a tracking filter are updated, so that accurate tracking of the maneuvering target is realized. The method not only can adapt to the change of the motion state of the target, but also can make full use of information in historical data, and improves the robustness and accuracy of a tracking algorithm.

Description

Technical Field

[0001] The invention belongs to the single-sensor single-maneuvering target tracking subsystem technology in the field of target tracking, and relates to a maneuvering target tracking method based on model adaptation, which is suitable for a dynamic system with unknown target maneuvering mode. Background Art

[0002] The use of radar, sonar and other sensors to track the position of maneuvering targets in a timely, accurate and continuous manner has been widely used in the fields of intelligent security and unmanned driving. Target maneuvering refers to the sudden changes in speed, direction, acceleration and other parameters that a target may experience during its movement. In the process of tracking maneuvering targets, the target's motion state is often uncertain and may change at any time, which requires the tracking algorithm to be able to perceive and adapt to these changes in real time. Traditional target tracking methods are usually based on fixed motion models, such as the uniform velocity model (CV model) or the uniform acceleration model (CA model). These methods can achieve good tracking results when the target's motion state is stable, but when the target is maneuvering, the mismatch between the model and the actual motion state often leads to a sharp drop in tracking performance.

[0003] To solve this problem, researchers have proposed a variety of adaptive maneuvering target tracking methods, which adapt to changes in the target's motion state by adjusting the parameters of the tracking filter in real time or switching different motion models. However, these methods still have certain limitations in practical applications. For example, although the variable-dimensional filter can adaptively switch different motion models, it relies on an accurate maneuvering detector, and the performance of the maneuvering detector is often affected by noise and interference; although the Singer model algorithm can handle the maneuvering noise of the target, it assumes that the structure of the target motion state transfer model is fixed, and may not be able to effectively deal with complex maneuvering situations. Summary of the invention

[0004] In order to solve the problems of low filtering accuracy and untimely maneuvering response in existing maneuvering target tracking methods, the present invention proposes a maneuvering target tracking method based on model adaptation, which detects target maneuverability in real time, effectively handles state estimation problems, and improves maneuvering target tracking performance.

[0005] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0006] A maneuvering target tracking method based on model adaptation comprises the following steps:

[0007] Step 1: The subject constructs a target motion state transfer model set and a target measurement model to represent the possible motion modes of the maneuvering target and the measurement data obtained by the sensor, respectively, and constructs a change point model to represent the time when the target motion mode changes, and determines the transition probability of the change point model and the target motion state transfer model and the parameters to be estimated at the current moment;

[0008] Step 2, starting from the current moment, the subject obtains the measurement data of the target through the sensor, and calculates the posterior prediction probability density of the measurement data for all motion state transition models and run lengths at each moment according to the target motion state transition model and the target measurement model; the posterior prediction density is conditioned on the target motion state transition model, the run length and the measurement data at the previous moment;

[0009] Step 3, the subject calculates the joint distribution of the measurement data, the running length and the target motion state transition model from the initial moment to the current moment according to the change point model;

[0010] Step 4, the subject determines the run length of the parameter to be estimated at the current moment and the recursive calculation formula of the target motion state transfer model according to the joint distribution of the run length and the target motion state transfer model;

[0011] Step 5, the subject uses the recursive calculation formula to calculate the state estimated mean and the corresponding estimated covariance of the target motion state transfer model, thereby obtaining the posterior distribution of the target state of the parameter to be estimated, and the posterior distribution contains the estimated mean and estimated covariance of the target at the current moment, wherein the estimated mean of the target contains an estimate of the destination position, thereby achieving tracking of the target.

[0012] Furthermore, the subject described in step 1 constructs a target motion state transition model set and a target measurement model to respectively represent the possible motion modes of the maneuvering target and the measurement data obtained by the sensor, and constructs a change point model to represent the time when the target motion mode changes, including:

[0013] Step 1.1, introduce a non-negative discrete integer variable r k ∈[1, k] is used as a change point model to represent the number of moments from the last change point of the measured data sequence to time k, that is, the running length at time k; r k =1 indicates that a change point occurs at time k; and r k =r k-1 +1 means there is no change point at time k, and the measurement data sequence continues to grow. k and k-1 represent the current time and the previous time, respectively;

[0014] Step 1.2, target motion state transfer model set It is composed of the target's motion state transfer model; m krepresents the target motion state transition model used at time k;

[0015] The time between adjacent change points in the measurement data sequence is a run length; in each run length, for the target motion state transfer model set The motion state transfer model it contains It can be uniformly expressed as in, and Represents model m k and model m k-1 In the run length r k 、r k-1 The target state vector at time , including the position and velocity in the x direction and the position and velocity in the y direction; f m (·) is the model m k The state transition function, is the model m k The process noise is zero-mean Gaussian distribution noise. is the model m k The corresponding process noise covariance matrix;

[0016] Step 1.3: During the tracking of a maneuvering target, the raw data acquired by the sensor for the maneuvering target can be preprocessed by coordinate transformation and registration to obtain the target's measurement data, which can be expressed as follows according to the sensor's measurement characteristics: Among them, y k is the measurement data of the target state, h(·) is the measurement function constructed according to the measurement characteristics of the sensor; is the measurement noise of the sensor, which is zero-mean Gaussian distribution noise, R k is the measurement noise covariance matrix.

[0017] Furthermore, the determination of the transition probabilities of the change point model and the target motion state transition model and the parameters to be estimated at the current moment in step 1 includes:

[0018] Step 1.4, the transition probability of the change point model is set to: run length r k-1 to r k The transition probability is p(r k |r k-1 ), when r k =1, p(r k |r k-1 )=H(r k-1 +1); otherwise r k =r k-1 +1, p(r k |r k-1 )=1-H(r k-1+1); H(·) represents the risk function of the change point model;

[0019] The transition probability of the target motion state transition model is: based on the measurement data y at the previous k-1 moments 1：(k-1) , with a run length of r k When the model is conditional k-1 To model m k The transition probability is q(m k |y 1：(k-1) , m k-1 , r k ), when r k =1, q(m k |y 1：(k-1) , m k-1 , r k )=q(m k ), q(m k ) represents the model m at time k k The prior probability of k =r k-1 +1, q(m k |y 1：(k-1) , m k-1 , r k )=q(m k-1 |y 1：(k-1) , r k-1 ), q(m k-1 |y 1：(k-1) , r k-1 ) represents the measurement data y based on the previous k-1 moments 1：(k-1) , given a run length r k-1 Time Model k-1 The posterior probability of; when the target motion mode changes, let r k =1, at this time, the measured data sequence produces a change point; when the target motion mode does not change, r k =r k-1 +1, the measurement data sequence continues to grow;

[0020] Step 1.5, select (x k , r k , m k ) as the parameter to be estimated at time k, x k is the target state vector to be estimated at the current k moment, representing the target's position and velocity in the x direction, as well as the position and velocity in the y direction.

[0021] Furthermore, the step 2 specifically includes:

[0022] Step 2.1, calculate the running length r from the motion state transition model in step 1.2 k Time Modelk The state prediction mean and the corresponding predicted covariance

[0023]

[0024] in, Represents model m k-1 In the run length r k-1 The target state vector at time , is the sign for partial derivative; Indicates that the running length from time k-1 to time k is r k Time Model k The state prediction vector, represents the k-1 moment The state estimation vector of and The running length of each k-1 moment is r k-1 Time k-1 The state estimated mean and the corresponding estimated covariance of ; the superscript T indicates transposition; if r k =1, then It should be reinitialized, which consists of the measurement data at time k-1 and the estimated speed at time k-1; It should also be reinitialized, and its diagonal elements consist of the variance of the measurement noise and the variance of the estimated velocity at time k-1;

[0025] Step 2.2, calculate the run length r from the target measurement model in step 1.3 k Time Model k The measured predicted mean and the corresponding predicted covariance

[0026]

[0027] in, Indicates that the running length from time k-1 to time k is r k Time Model k The measurement prediction vector of is the sign for partial derivative; and They are respectively the model m when the running length is r at time k in step 2.1 k The state prediction mean and corresponding prediction covariance of ;

[0028] Step 2.3: For all target motion state transfer models m k and run length r k Calculate the measurement data y kThe posterior prediction probability density p(y k |y 1：(k-1) , m k , r k ):

[0029]

[0030] in, and are the predicted covariances corresponding to the measured predicted means in step 3.2 respectively.

[0031] Furthermore, the step 3 specifically includes:

[0032] Step 3.1, joint distribution p(y 1：k , r k , m k ) can be expressed recursively as:

[0033]

[0034] Among them, p(y k |y 1：(k-1) , m k , r k ) is the measured posterior prediction probability density in step 2; q(m k |y 1：(k-1) , m k-1 , r k ) is the run length r in step 1.4 k When the model is conditional k-1 The transition probability p(r k |r k-1 ) is the run length r in step 1.4 k-1 The transition probability p(y 1：(k-1) , r k-1 , m k-1 ) is the joint distribution of the k-1 time measurement data, run length and model;

[0035] Step 3.2: Transform the model transfer probability q(m k |y 1：(k-1) , m k-1 , r k ) and the run length transition probability p(r k |r k-1 ) into the joint distribution p(y 1：k , r k , m k ) expression, and then give the joint probability p(y 1：k , r k =1,m k) and the joint probability p(y 1：k , r k =r k-1 +1, m k ) is calculated as follows:

[0036]

[0037] Furthermore, the step 4 specifically includes:

[0038] Step 4.1, based on the joint distribution p(y 1：k , r k , m k ), calculate the marginal likelihood p(y 1：k ):

[0039]

[0040] Step 4.2, based on the marginal likelihood of the above measurement and the measurement data y from the initial moment to the k moment 1：k , according to Bayes' theorem, the model m is calculated k and run length r k The joint distribution of:

[0041] p(r k , m k |y 1：k )=p(y 1：k ,rk,m k ) / p(y 1：k )

[0042] Step 4.3, based on the above joint distribution and the measured data y from the initial moment to the k moment 1：k , the model m is calculated by the total probability theorem k Posterior:

[0043]

[0044] Step 4.4, based on the above model posterior and the measured data y from the initial moment to the k moment 1：k , calculated by Bayesian theorem with model m k The run length probability conditional on:

[0045] p(r k |m k ,y 1：k )=p(r k , m k |y 1：k ) / p(m k |y 1：k )

[0046] Step 4.5, based on the above run length probability and the measured data y from the initial time to time k 1：k , calculate the global run length probability by the total probability theorem:

[0047]

[0048] Step 4.6, based on the above model and the joint distribution of run lengths and the global run length distribution, determine the joint probability formula p(y) when the run length increases in step 3.2 1：k , r k =r k-1 +1, m k ) in the model transition probability q(m k-1 |y 1：(k-1) , r k-1 ) is as follows:

[0049]

[0050] Among them, p(r k-1 , m k-1 |y 1：(k-1) ) is the model m calculated according to step 5.2 k-1 and run length r k-1 The joint distribution of k-1 |y 1：(k-1) ) is the global run length probability at time k-1 calculated according to step 5.4.

[0051] Furthermore, the step 5 specifically includes:

[0052] Step 5.1, through the measurement data y at the current k moment k , calculate the run length r k Time Model k The state estimate mean and the corresponding estimated covariance

[0053]

[0054] in, is the gain matrix, and and are the state prediction mean, state prediction covariance, measurement prediction mean and measurement prediction covariance in steps 2.1 and 2.2 respectively, As given in step 2.2, I represents the identity matrix;

[0055] Step 5.2, pruning: Given a threshold τ, prune the model m in step 4.4 kThe probability of all run lengths p(r k |m k ,y 1：k ) Sort from large to small, retaining the first τ run length probabilities;

[0056] Step 5.3: Through weighted fusion, we can get the k-time model m k The state estimate mean and the corresponding estimated covariance

[0057]

[0058] in, For time k in a run of length r k Time Model k The corresponding weight expression is as follows:

[0059]

[0060] p(r k |m k ,y 1：k ) is the run length probability after pruning in step 5.2; and After pruning in step 5.2, the kth time is in the running length r k Time Model k The corresponding state estimated mean and estimated covariance;

[0061] Step 5.4, select the model m in step 4.3 k The posterior p(m k |y 1：k ) model when the maximum The Model The state estimate mean determined in step 5.3 and the corresponding estimated covariance That is, as the target state vector x k The estimated mean μ(x k|k ), estimated covariance∑(x k|k ), where μ(x k|k ) contains the required position estimation of the maneuvering target in the x-direction and the y-direction, thereby achieving tracking of the maneuvering target;

[0062] Determine whether the measurement data at time k is the measurement data of the sensor at the last moment; if so, end the tracking; otherwise, jump to step 2.

[0063] A terminal device comprises a processor, a memory and a computer program stored in the memory; when the processor is executed by a computer, the model-adaptive maneuvering target tracking method is implemented.

[0064] A computer-readable storage medium stores a computer program; when the computer program is executed by a processor, the model-adaptive maneuvering target tracking method is implemented.

[0065] Compared with the prior art, the present invention has the following technical features:

[0066] The maneuvering target tracking method provided by the present invention is based on model adaptation and uses Bayesian online change point detection and multi-model estimator to realize simultaneous state estimation and change point detection. The method divides the time series data into non-overlapping observation sets based on the run length, that is, the change point position is modeled using the run length, and the moment when the change point is generated is the moment when the target maneuvers, and the non-stationary process in the maneuvering target tracking scenario is converted into a partitioned stationary process. For each partitioned stationary process, the most likely model in the model set is selected to model the partitioned time series stationary process, thereby improving the maneuvering target tracking performance. Through the simulation scenes of six groups of Benchmark aerial targets in Matlab, it is shown that the method of the present invention has the advantages of high tracking accuracy and robust tracking effect compared with the existing method based on interactive multiple models. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is a schematic diagram of the process of the present invention;

[0068] Figure 2-7 They are target motion trajectory diagrams of scenarios S1-S6 of the embodiments of the present invention respectively;

[0069] Figure 8-13 They are RMSE curves of the target position under different model sets in the scenarios S1-S6 of the embodiments of the present invention, and the process noise sets of the model sets from left to right in each group of figures are η=[16, 14, 60] / 10, η=[16, 40, 60], and η=[16, 40, 60]×10, respectively. DETAILED DESCRIPTION

[0070] Considering the combination of Bayesian online change point detection technology and model selection method, the present invention proposes a maneuvering target tracking method based on model adaptation; Bayesian online change point detection technology detects the mutation point of the generated parameters in the sequence data in an online manner, that is, the change point, so that the change of the target motion state can be perceived in real time. The model selection method can select a matching motion model in the model set according to the change of the target motion state. Specifically, the change of the target motion state is detected in real time by Bayesian online change point detection technology. When the change point is detected, the model selection mechanism is triggered, and the appropriate motion model is selected according to the current target motion state, and the parameters of the tracking filter are updated, so as to achieve accurate tracking of the maneuvering target. This method can not only adapt to the change of the target motion state, but also make full use of the information in the historical data to improve the robustness and accuracy of the tracking algorithm. The maneuvering target in the present invention includes moving objects such as ships, vehicles, and aircraft that can be detected by sensors (such as radar).

[0071] See attached Figure 1 The present invention provides a method for tracking a maneuvering target based on model adaptation. The subject of the method obtains the measurement data of the maneuvering target in real time through a sensor, and performs the following tracking process to obtain a more accurate estimated position of the target. The specific steps are as follows:

[0072] Step 1: The subject constructs a target motion state transition model set and a target measurement model to represent the possible motion modes of the maneuvering target and the measurement data obtained by the sensor, respectively, and constructs a change point model to represent the time when the target motion mode changes, and determines the transition probability of the change point model and the target motion state transition model; the details are as follows:

[0073] Step 1.1, introduce a non-negative discrete integer variable r k ∈[1, k] as the change point model to represent the number of moments from the last change point of the measured data sequence to time k, that is, the running length at time k; then, r k =1 indicates that a change point occurs at time k; and r k =r k-1 +1 means that there is no change point at time k, and the measurement data sequence continues to grow. k and k-1 represent the current time and the previous time, respectively.

[0074] Step 1.2, target motion state transfer model set It is composed of the target's motion state transfer model; the motion state transfer model usually includes a uniform speed model, a turning model, a uniform acceleration model, etc. k Represents the motion state transfer model used at time k;

[0075] The time between adjacent change points in the measurement data sequence is a run length; in each run length, for the target motion state transfer model set The motion state transfer model it contains It can be uniformly expressed as in, and Represents model m k and model m k-1 In the run length r k 、r k-1 The target state vector at time , including the position and velocity in the x direction and the position and velocity in the y direction; f m (·) is the model m k The state transfer function, such as uniform speed, uniform acceleration, turning, etc. is the model m k The process noise is zero-mean Gaussian distribution noise. is the model m k The corresponding process noise covariance matrix.

[0076] Step 1.3: During the tracking of a maneuvering target, the raw data acquired by the sensor for the maneuvering target can be preprocessed by coordinate transformation and registration to obtain the target's measurement data, which can be expressed as follows according to the sensor's measurement characteristics: Among them, y k is the measurement data of the target state, h(·) is the measurement function constructed according to the measurement characteristics of the sensor; is the measurement noise of the sensor, which is zero-mean Gaussian distribution noise, R k is the measurement noise covariance matrix.

[0077] Step 1.4, determine the run length transition probability p(r k |r k-1 ) and model transition probability q(m k |y 1：(k-1) , m k-1 , r k ).

[0078] The transition probability of the change point model is set to: run length r k-1 to r k The transition probability is p(r k |r k-1 ), when r k =1, p(r k |r k-1 )=H(r k-1 +1); otherwise r k =r k-1 +1, p(r k |rk-1 )=1-H(r k-1 +1); H(·) represents the hazard function of the change point model.

[0079] The transition probability of the target motion state transition model is: based on the measurement data y at the previous k-1 moments 1：(k-1) , with a run length of r k When the model is conditional k-1 To model m k The transition probability is q(m k |y 1：(k-1) , m k-1 , r k ), when r k =1, q(m k |y 1：(k-1) , m k-1 , r k )=q(m k ), q(m k ) represents the model m at time k k The prior probability of k =r k-1 +1, q(m k |y 1：(k-1) , m k-1 , r k )=q(m k-1 |y 1：(k-1) , r k-1 ), q(m k-1 |y 1：(k-1) , r k-1 ) represents the measurement data y based on the previous k-1 moments 1：(k-1) , given a run length r k-1 Time Model k-1 The posterior probability of; In this scheme, when the target motion mode changes, let r k =1, at this time, the measured data sequence produces a change point; when the target motion mode does not change, r k =r k-1 +1, the measurement data sequence continues to grow.

[0080] Step 1.5, select (x k , r k , m k ) as the parameter to be estimated at time k, x k is the target state vector to be estimated at the current k moment, indicating the position and velocity of the target in the x direction, as well as the position and velocity in the y direction; r k Indicates the running length at the current k moment, m k Represents the target motion state transition model used at the current k moment.

[0081] Step 2: Starting from the current time k, the subject obtains the measurement data of the target through the sensor. The subject performs a calculation on all motion state transfer models m at each time according to the target motion state transfer model and target measurement model defined in step 1. k and run length r k Calculate the measurement data y k The posterior prediction probability density p(y k |y 1：(k-1) , m k , r k ), the posterior prediction density is based on the target motion state transfer model m k , run length rk and previous k-1 The measurement data y at a certain moment 1：(k-1) The conditions are as follows:

[0082] Step 2.1, calculate the running length r from the motion state transition model in step 1.2 k Time Model k The state prediction mean and the corresponding predicted covariance

[0083]

[0084] in, Represents model m k-1 In the run length r k-1 The target state vector at time , is the sign for partial derivative; Indicates that the running length from time k-1 to time k is r k Time Model k The state prediction vector, represents the k-1 moment The state estimation vector of and The running length of each k-1 moment is r k-1 Time k-1 The state estimated mean and the corresponding estimated covariance of ; the superscript T indicates transposition. k =1, then It should be reinitialized, which consists of the measurement data at time k-1 and the estimated speed at time k-1; It should also be reinitialized, and its diagonal elements consist of the variance of the measurement noise and the variance of the estimated velocity at time k-1.

[0085] Step 2.2, calculate the run length r from the target measurement model in step 1.3 k Time Model k The measured predicted mean and the corresponding predicted covariance

[0086]

[0087] in, Indicates that the running length from time k-1 to time k is r k Time Model k The measurement prediction vector of is the sign for partial derivative; and They are respectively the model m when the running length is r at time k in step 2.1 k The state prediction means and corresponding prediction covariances of .

[0088] Step 2.3: For all target motion state transfer models m k and run length r k Calculate the measurement data y k The posterior prediction probability density p(y k |y 1：(k-1) , m k , r k ):

[0089]

[0090] in, and are the predicted covariances corresponding to the measured predicted means in step 3.2 respectively.

[0091] Step 3: The subject calculates the measurement data y from the initial moment to the k moment according to the change point model in step 1 1：k , run length r k and target motion state transfer model m k The joint distribution p(y 2：k , r k , m k ), as follows:

[0092] Step 3.1, joint distribution p(y 1：k , r k , m k ) can be expressed recursively as:

[0093]

[0094] Among them, p(y k |y 1：(k-1) , m k , r k ) is the measured posterior prediction probability density in step 2; q(m k |y 1：(k-1) , mk-1 , r k ) is the run length r in step 1.4 k When the model is conditional k-1 The transition probability p(r k |r k-1 ) is the run length r in step 1.4 k-1 The transition probability p(y 1：(k-1) , r k-1 , m k-1 ) is the joint distribution of the k-1 time measurement data, run length and model.

[0095] Step 3.2: Transform the model transfer probability q(m k |y 1：(k-1) , m k-1 , r k ) and the run length transition probability p(r k |r k-1 ) into the joint distribution p(u 1：k , r k , m k ) expression, and then give the joint probability p(y 1：k , r k =1,m k ) and the joint probability p(y 1：k , r k =r k-1 +1, m k ) is calculated as follows:

[0096]

[0097] Step 4: The subject uses the joint distribution p(y 1：k , r k , m k ), calculate the running length r of the parameter to be estimated at time k k and target motion state transfer model m k The recursive calculation formula is as follows:

[0098] Step 4.1, based on the joint distribution p(y 1：k , r k , m k ), calculate the marginal likelihood p(y 1：k ):

[0099]

[0100] Step 4.2, based on the marginal likelihood of the above measurement and the measurement data y from the initial moment to the k moment1：k , according to Bayes' theorem, the model m is calculated k and run length r k The joint distribution of:

[0101] p(r k , m k |y 1：k )=p(y 1：k , r k , m k ) / p(y 1：k )

[0102] Step 4.3, based on the above joint distribution and the measured data y from the initial moment to the k moment 1：k , the model m is calculated by the total probability theorem k Posterior:

[0103]

[0104] Step 4.4, based on the above model posterior and the measured data y from the initial moment to the k moment 1：k , calculated by Bayesian theorem with model m k The run length probability conditional on:

[0105] p(r k |m k ,y 1：k )=p(r k , m k |y 1：k ) / p(m k |y 1：k )

[0106] Step 4.5, based on the above run length probability and the measured data y from the initial time to time k 1：k , calculate the global run length probability by the total probability theorem:

[0107]

[0108] Step 4.6, based on the above model and the joint distribution of run lengths and the global run length distribution, determine the joint probability formula p(y) when the run length increases in step 3.2 1：k , r k =r k-1 +1, m k ) in the model transition probability q(m k-1 |y 1：(k-1) , r k-1 ) is as follows:

[0109]

[0110] Among them, p(rk-1 , m k-1 |y 1：(k-1) ) is the model m calculated according to step 5.2 k-1 and run length r k-1 The joint distribution of k-1 |y 1：k-1) ) is the global run length probability at time k-1 calculated according to step 5.4.

[0111] Step 5: The subject uses the recursive calculation formula in step 4 to calculate the model m k The state estimated mean and the corresponding estimated covariance of the target state x are obtained. k The posterior distribution of where μ(x k|k ) and ∑(x k|k ) are the estimated mean and estimated covariance of the target at time k, as follows:

[0112] Step 5.1, through the measurement data y at the current k moment k , calculate the run length r k Time Model k The state estimate mean and the corresponding estimated covariance

[0113]

[0114] in, is the gain matrix, and and are the state prediction mean, state prediction covariance, measurement prediction mean and measurement prediction covariance in steps 2.1 and 2.2 respectively, As given in step 2.2, I represents the identity matrix.

[0115] Step 5.2, pruning: Given a threshold τ, prune the model m in step 4.4 k The probability of all run lengths p(r k |m k ,y 1：k ) Sort from large to small, retaining the first τ run length probabilities to reduce the computational complexity;

[0116] Step 5.3: Through weighted fusion, we can get the k-time model m k The state estimate mean and the corresponding estimated covariance

[0117]

[0118] in, For time k in a run of length r k Time Model k The corresponding weight expression is as follows:

[0119]

[0120] p(r k |m k ,y 1：k ) is the run length probability after pruning in step 5.2; similarly, and After pruning in step 5.2, the kth time is in the running length r k Time Model k The corresponding state estimated mean and estimated covariance.

[0121] Step 5.4, select the model m in step 4.3 k The posterior p(m k |y 1：k ) model when the maximum The Model The state estimate mean determined in step 5.3 and the corresponding estimated covariance That is, as the target state vector x k The estimated mean μ(x k|k ), estimated covariance∑(x k|k ), where μ(x k|k ) contains the required position estimates of the maneuvering target in the x and y directions, thereby achieving tracking of the maneuvering target.

[0122] Determine whether the measurement data at time k is the measurement data of the sensor at the last moment; if so, end the tracking; otherwise, jump to step 2.

[0123] Example:

[0124] In this specific example, six different scenarios are given to simulate the present invention, as follows:

[0125] 1. Scene Design

[0126] Scenario 1 (S1): The first target trajectory represents a large aircraft, such as a military cargo aircraft. The target initially flies at a constant speed of 290 m / s in the k∈[1,60) time period; at time k∈[60,80) and k∈[110,130), the target makes turns with accelerations of 2g and 3g (g is the acceleration of gravity) respectively; the target continues to fly at a constant speed in the other time periods.

[0127] Scenario 2 (S2): The second target trajectory represents a small and flexible aircraft, such as a jet or other similar high-performance commercial aircraft. The target initially flies at a constant speed of 305 m / s for a time period k∈[1,30); at time k∈[30,50), the target makes a 90° turn with an acceleration of 2.5 g (g is the acceleration of gravity); at time k∈[100,115), the target makes a turn with an acceleration of 4 g (g is the acceleration of gravity); the target continues to fly at a constant speed for the rest of the time period.

[0128] Scenario 3 (S3): The third target represents a medium-sized bomber flying at high speed with good maneuverability. When time k∈[1, 30), the target maintains a straight and horizontal flight at an initial constant speed of 457m / s; when time k∈[30, 40), the target makes a 45° turn with an acceleration of 4g (g is the acceleration of gravity); when time k∈[70, 110), the target makes a 90° turn with an acceleration of 4g (g is the acceleration of gravity), the heading changes to a horizontal straight line direction, and the speed drops to 274m / s; in other time periods, the target continues to fly at a constant speed on the new heading.

[0129] Scenario 4 (S4): The fourth target also represents a medium-sized bomber flying at high speed with good maneuverability. The target flies at an initial constant speed of 251 m / s within the time k∈[1,30); when time k∈[30,40), the target makes a 45° turn with an acceleration of 4g (g is the acceleration of gravity); when time k∈[70,80), the target makes a turn with an acceleration of 6g (g is the acceleration of gravity); in other time periods, the target maintains horizontal straight-line motion at a constant speed.

[0130] Scenario 5 (S5): The fifth target represents a fighter jet. The target flies at a constant speed at the beginning; then at time k∈[30, 40), k∈[60, 70), k∈[115, 170), the target makes turns with accelerations of 5g, 7g, and 6g (g is the acceleration of gravity) respectively; in other time periods, the target flies at a constant speed.

[0131] Scenario 6 (S6): The sixth target also represents a fighter jet. The target maintains a constant speed of 426 m / s for 30 seconds. Then, at time k∈[30, 40), k∈[70, 85), k∈[115, 125), k∈[125, 155], the target makes turns with accelerations of 7g, 6g, 6g, and 7g (g is the acceleration of gravity). In other time periods, the target maintains a constant speed and heading.

[0132] 2. Method-related configuration

[0133] The uniform motion model is used as the target motion state transfer model, and the target maneuver is captured by the difference in model process noise; then the motion state transfer model it contains It can be uniformly expressed as:

[0134]

[0135] Among them, k and k-1 represent the current moment and the previous moment respectively; and They represent the model m in the run length r k 、r k-1 The target state vector at time , including the position and velocity in the x direction and the position and velocity in the y direction; F k is the state transfer matrix of the model. Since the models in the model set all use uniform motion models, the F k are the same; is the process noise of model m, that is, zero-mean Gaussian distribution noise, is the process noise covariance matrix corresponding to model m. The state transfer matrix F k and the process noise covariance matrix as follows:

[0136]

[0137] Among them I 2 represents the 2×2 identity matrix, represents the process noise coefficient of model m, T represents the sensor sampling period, is the Kronecker product operator. Considering that these models cover different motion modes from near constant velocity (NCV) to high maneuverability, the three models selected in the model set are: η=[η 1 , η 2 , η 3 ]=[16,40,60], and reduce η by 10 times and enlarge it by 10 times respectively, considering three model sets in total.

[0138] For the target measurement model, it is assumed that the original measurement data obtained by the sensor can obtain the target position measurement after preprocessing such as coordinate transformation and registration. The measurement data characteristics of the target after preprocessing can be expressed as:

[0139]

[0140] Among them, k represents the current time. Represents model m k In the run length r k The target state at time y k is the measured value; H kIt is a measurement matrix constructed based on the sensor measurement characteristics; is the measurement noise of the sensor, which is zero-mean Gaussian distribution noise, R k is the measurement noise covariance matrix. In this implementation case, it is assumed that the measurements obtained are the position in the x direction and the position in the y direction, and the measurement matrix and the measurement noise covariance matrix are specifically set as follows:

[0141]

[0142] In this example, the initial values ​​of the relevant parameters are set as follows:

[0143] Given an initial value r for the run length 1 =1; given the initial value q(m 1 ), since there are 3 models in the model set, we set q(m 1 )=1 / 3. Given the measurement data, run length and the initial joint distribution of the model p(y 1：1 , r 1 , m 1 )=1; given the risk function H, let H(·)=1 / 10.

[0144] 3. Assessment of mobile target tracking:

[0145] The following comparative evaluation is conducted on the maneuver filtering effect using the interactive multi-model filtering method (IMM).

[0146] In the method of the present invention, the filtering method based on Bayesian online change point detection and model selection is called BOCPDMS. The evaluation index includes the root mean square error RMSE of the target radial distance. The smaller the RMSE, the better the filtering effect.

[0147] The simulation results and analysis are as follows:

[0148] Referring to the six sets of Benchmark data in MATLAB, six single target tracking scenarios with variable acceleration maneuvers are considered. The total step length of each tracking scenario is k total =187s, the sensor sampling period is G=1s. Considering the case where the noise covariance is known, the model process noise coefficient in the model set is set to η=[η 1 , η 2 , η 3 ]=[16,40,60], and reduce η in the model set of the algorithm BOCPDMS of this scheme and enlarge η in the model set of the comparison algorithm IMM by 10 times and 10 times respectively, and consider three model sets in total.

[0149] Table 1 Average position RMSE statistics of each method in different scenarios and different model domains

[0150]

[0151] Figure 2-7 They are target motion trajectory diagrams for scenes S1-S6 respectively. Figure 8-13 The following are the target position RMSE curves of scenes S1-S6 under different model sets. The process noise sets of the model sets from left to right in each group of figures are η=[16,40,60] / 10, η=[16,40,60], and η=[16,40,60]×10. It can be seen from the target position RMSE curve that the RMSE values ​​of the algorithm of this scheme are all smaller than those of the comparison algorithm IMM, indicating that the tracking effect of the algorithm of this scheme is better. Moreover, when η in the model set is m When the model set is incomplete, the tracking error of the proposed algorithm is significantly smaller than that of the comparison algorithm. Table 1 shows the average position RMSE of different model sets for scenes S1-S6. From the numerical results in this table, it can be seen that when η in the model set is m When it increases, the value of RMSE will also increase, because η m When η increases, high maneuvering behavior can be captured, but the tracking uncertainty will also increase and the tracking accuracy will decrease. Therefore, the tracking accuracy of the algorithm of this scheme and the comparison algorithm has decreased, but the RMSE of the algorithm proposed in this scheme is still smaller than that of the comparison algorithm. m When the model set is incomplete, the RMSE value of the proposed algorithm is significantly smaller than that of the comparison algorithm. The tracking results of different model sets show that the proposed algorithm can also maintain effective tracking when the model set is incomplete, and its tracking performance is more robust than that of IMM.

[0152] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A maneuvering target tracking method based on model adaptation, characterized in that: The following steps are involved: Step 1: The subject constructs a target motion state transfer model set and a target measurement model to represent the possible motion modes of the maneuvering target and the measurement data obtained by the sensor, respectively, and constructs a change point model to represent the time when the target motion mode changes, and determines the transition probability of the change point model and the target motion state transfer model and the parameters to be estimated at the current moment; Step 2, starting from the current moment, the subject obtains the measurement data of the target through the sensor, and calculates the posterior prediction probability density of the measurement data for all motion state transition models and run lengths at each moment according to the target motion state transition model and the target measurement model; the posterior prediction density is conditioned on the target motion state transition model, the run length and the measurement data at the previous moment; Step 3, the subject calculates the joint distribution of the measurement data, the running length and the target motion state transition model from the initial moment to the current moment according to the change point model; Step 4, the subject determines the run length of the parameter to be estimated at the current moment and the recursive calculation formula of the target motion state transfer model according to the joint distribution of the run length and the target motion state transfer model; Step 5, the subject uses the recursive calculation formula to calculate the state estimated mean and the corresponding estimated covariance of the target motion state transfer model, thereby obtaining the posterior distribution of the target state of the parameter to be estimated, and the posterior distribution contains the estimated mean and estimated covariance of the target at the current moment, wherein the estimated mean of the target contains an estimate of the destination position, thereby achieving tracking of the target.

2. The method for tracking a maneuvering target based on model adaptation according to claim 1, characterized in that: The subject described in step 1 constructs a target motion state transfer model set and a target measurement model to respectively represent the possible motion modes of the maneuvering target and the measurement data obtained by the sensor, and constructs a change point model to represent the time when the target motion mode changes, including: Step 1.1, introduce a non-negative discrete integer variable r k ∈[1, k] is used as a change point model to represent the number of moments from the last change point of the measured data sequence to time k, that is, the running length at time k; r k =1 indicates that a change point occurs at time k; and r k =r k-1 +1 means there is no change point at time k, and the measurement data sequence continues to grow. k and k-1 represent the current time and the previous time, respectively; Step 1.2, target motion state transfer model set It is composed of the target's motion state transfer model; m k represents the target motion state transition model used at time k; The time between adjacent change points in the measurement data sequence is a run length; in each run length, for the target motion state transfer model set The motion state transfer model it contains It can be uniformly expressed as in, and Represents model m k and model m k-1 In the run length r k 、r k-1 The target state vector at time , including the position and velocity in the x direction and the position and velocity in the y direction; f m (·) is the model m k The state transition function, is the model m k The process noise is zero-mean Gaussian distribution noise. is the model m k The corresponding process noise covariance matrix; Step 1.3: During the tracking of a maneuvering target, the raw data acquired by the sensor for the maneuvering target can be preprocessed by coordinate transformation and registration to obtain the target's measurement data, which can be expressed as follows according to the sensor's measurement characteristics: Among them, y k is the measurement data of the target state, h(·) is the measurement function constructed according to the measurement characteristics of the sensor; is the measurement noise of the sensor, which is zero-mean Gaussian distribution noise, R k is the measurement noise covariance matrix.

3. The method for tracking a maneuvering target based on model adaptation according to claim 2, characterized in that: The determination of the transition probabilities of the change point model and the target motion state transition model and the parameters to be estimated at the current moment in step 1 includes: Step 1.4, the transition probability of the change point model is set to: run length r k-1 to r k The transition probability is p(r k |r k-1 ), when r k =1, p(r k |r k-1 )=H(r k-1 +1); otherwise r k =r k-1 +1, p(r k |r k-1 )=1-H(r k-1 +1); H(·) represents the risk function of the change point model; The transition probability of the target motion state transition model is: based on the measurement data y at the previous k-1 moments 1：(k-1) , with a run length of r k When the model is conditional k-1 To model m k The transition probability is q(m k |y 1：(k-1) , m k-1 , r k ), when r k =1, q(m k |y 1：(k-1) , m k-1 , r k )=q(m k ), q(m k ) represents the model m at time k k The prior probability of k =r k-1 +1, q(m k |y 1：(k-1) , m k-1 , r k )q(m k-1 |y 1：(k-1) , r k-1 ), q(m k-1 |y 1：(k-1) , r k-1 ) represents the measurement data y based on the previous k-1 moments 1：(k-1) , given a run length r k-1 Time Model k-1 The posterior probability of; when the target motion mode changes, let r k =1, at this time, the measured data sequence produces a change point; when the target motion mode does not change, r k =r k-1 +1, the measurement data sequence continues to grow; Step 1.5, select (x k , r k , m k ) as the parameter to be estimated at time k, x k is the target state vector to be estimated at the current k moment, representing the target's position and velocity in the x direction, as well as the position and velocity in the y direction.

4. The method for tracking a maneuvering target based on model adaptation according to claim 3, characterized in that: The step 2 specifically includes: Step 2.1, calculate the running length r from the motion state transition model in step 1.2 k Time Model k The state prediction mean and the corresponding predicted covariance in, Represents model m k-1 In the run length r k-1 The target state vector at time , is the sign for partial derivative; Indicates that the running length from time k-1 to time k is r k Time Model k The state prediction vector, represents the k-1 moment The state estimation vector of and The running length of each k-1 moment is r k-1 Time k-1 The state estimated mean and the corresponding estimated covariance of ; the superscript T indicates transposition; if r k =1, then It should be reinitialized, which consists of the measurement data at time k-1 and the estimated speed at time k-1; It should also be reinitialized, and its diagonal elements consist of the variance of the measurement noise and the variance of the estimated velocity at time k-1; Step 2.2, calculate the run length r from the target measurement model in step 1.3 k Time Model k The measured predicted mean and the corresponding predicted covariance in, Indicates that the running length from time k-1 to time k is r k Time Model k The measurement prediction vector of is the sign for partial derivative; and They are respectively the model m when the running length is r at time k in step 2.1 k The state prediction means and corresponding prediction covariances of ; Step 2.3: For all target motion state transfer models m k and run length r k Calculate the measurement data y k The posterior prediction probability density p(y k |y 1：(k-1) , m k , r k ): in, and are the predicted covariances corresponding to the measured predicted means in step 3.2 respectively.

5. The method for tracking a maneuvering target based on model adaptation according to claim 4, characterized in that: The step 3 specifically includes: Step 3.1, joint distribution y(y 1：k , r k , m k ) can be expressed recursively as: p(r k |r k-1 )p(y 1:(k-1) ,r k-1 ,m k-1 )} Among them, p(y k |y 1：(k-1) , m k , r k ) is the measured posterior prediction probability density in step 2; q(m k |y 1:(k-1) , m k-1 , r k ) is the run length r in step 1.4 k When the model is conditional k-1 The transition probability p(r k |r k-1 ) is the run length r in step 1.4 k-1 The transition probability p(y 1：(k-1) , r k-1 , m k-1 ) is the joint distribution of the k-1 time measurement data, run length and model; Step 3.2: Transform the model transfer probability q(m k |y 1：(k-1) , m k-1 , r k ) and the run length transition probability p(r k |r k-1 ) into the joint distribution p(y 1：k , r k , m k ) expression, and then give the joint probability p(y 1：k , r k =1,m k ) and the joint probability p(y 1：k , r k =r k-1 +1, m k ) is calculated as follows:

6. The method for tracking a maneuvering target based on model adaptation according to claim 5, characterized in that: The step 4 specifically includes: Step 4.1, based on the joint distribution p(y 1：k , r k , m k ), calculate the marginal likelihood p(y 1：k ): Step 4.2, based on the marginal likelihood of the above measurement and the measurement data y from the initial moment to the k moment 1：k , according to Bayes' theorem, the model m is calculated k and run length r k The joint distribution of: p(r k ,m k |y 1：k )=p(y 1：k ,r k ,m k ) / p(y 1：k ) Step 4.3, based on the above joint distribution and the measured data y from the initial moment to the k moment 1：k , the model m is calculated by the total probability theorem k Posterior: Step 4.4, based on the above model posterior and the measured data y from the initial moment to the k moment 1：k , calculated by Bayesian theorem with model m k The run length probability conditional on: p(r k |m k ,y 1：k )=p(r k ,m k |y 1：k ) / p(m k |y 1：k ) Step 4.5, based on the above run length probability and the measured data y from the initial time to time k 1：k , calculate the global run length probability by the total probability theorem: Step 4.6, based on the above model and the joint distribution of run lengths and the global run length distribution, determine the joint probability formula p(y) when the run length increases in step 3.2 1：k , r k =r k-1 +1, m k ) in the model transition probability q(m k-1 |y 1：(k-1) , r k-1 ) is as follows: Among them, p(r k-1 , m k-1 |y 1：(k-1) ) is the model m calculated according to step 5.2 k-1 and run length r k-1 The joint distribution of k-1 |y 1：(k-1) ) is the global run length probability at time k-1 calculated according to step 5.

4.

7. The method for tracking a maneuvering target based on model adaptation according to claim 6, characterized in that: The step 5 specifically includes: Step 5.1, through the measurement data y at the current k moment k , calculate the run length as r k Time Model k The state estimate mean and the corresponding estimated covariance in, is the gain matrix, and and are the state prediction mean, state prediction covariance, measurement prediction mean and measurement prediction covariance in steps 2.1 and 2.2 respectively, As given in step 2.2, I represents the identity matrix; Step 5.2, pruning: Given a threshold τ, prune the model m in step 4.4 k The probability of all run lengths p(r k |m k ,y 1：k ) Sort from large to small, retaining the first τ run length probabilities; Step 5.3: Through weighted fusion, we can get the k-time model m k The state estimate mean and the corresponding estimated covariance in, For time k in a run of length r k Time Model k The corresponding weight expression is as follows: p(r k |m k ,y 1：k ) is the run length probability after pruning in step 5.2; and After pruning in step 5.2, the kth time is in the running length r k Time Model k The corresponding state estimated mean and estimated covariance; Step 5.4, select the model m in step 4.3 k The posterior p(m k |y 1：k ) model when the maximum The Model The state estimate mean determined in step 5.3 and the corresponding estimated covariance That is, as the target state vector x k The estimated mean μ(x k|k ), estimated covariance∑(x k|k ), where μ(x k|k ) contains the required x-direction and y-direction position estimation of the maneuvering target, thereby achieving tracking of the maneuvering target; Determine whether the measurement data at time k is the measurement data of the sensor at the last moment; if so, end the tracking; otherwise, jump to step 2.

8. A terminal device comprising a processor, a memory and a computer program stored in the memory; characterized in that: When the processor is executed by a computer, the model-adaptive-based maneuvering target tracking method is implemented.

9. A computer-readable storage medium, wherein a computer program is stored in the medium; characterized in that: When the computer program is executed by the processor, the model-adaptive-based maneuvering target tracking method is implemented.

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