Model-based adaptive maneuvering target tracking method

Abstract

The application discloses a model self-adaptive maneuvering target tracking method, which combines a Bayesian online change point detection and a model selection method, wherein the Bayesian online change point detection detects a change point of a generated parameter in sequence data in an online manner, so that the change of a target motion state can be perceived in real time; and the model selection method can select a motion model matched with the change of the target motion state from a model set; specifically, the change of the target motion state is detected in real time through the Bayesian online change point detection technology, when the change point is detected, the model selection mechanism is triggered, a suitable motion model is selected according to the current target motion state, and the parameters of a tracking filter are updated, so that the accurate tracking of the maneuvering target is realized. This method not only can adapt to the change of the target motion state, but also can fully utilize the information in the historical data, and improve the robustness and accuracy of the tracking algorithm.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of single-sensor single-maneuvering target tracking subsystems in 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

[0002] Timely and accurate continuous tracking of the position of a maneuvering target by using sensors such as radars and sonars has a very wide application in intelligent security, unmanned driving and other fields. Target maneuvering refers to the sudden change of parameters such as velocity, direction and acceleration during the movement of the target. In the process of tracking a maneuvering target, the movement state of the target 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 constant velocity (CV) model or constant acceleration (CA) model, and these methods can achieve good tracking effect when the movement state of the target is stable, but when the target maneuvers, the mismatch between the model and the actual movement state often leads to a sharp decline in tracking performance.

[0003] In order to solve this problem, researchers have proposed a variety of adaptive maneuvering target tracking methods, which adapt to the changes in the movement state of the target by adjusting the parameters of the tracking filter or switching different motion models in real time. However, these methods still have certain limitations in practical application. For example, although the variable dimension filter can adaptively switch different motion models, it depends on an accurate maneuvering detector, and the performance of the maneuvering detector is often affected by noise and interference; the Singer model algorithm can handle the maneuvering noise of the target, but it assumes that the structure of the target movement state transition model is fixed, and may not be able to effectively cope with complex maneuvering situations. SUMMARY

[0004] In order to solve the problems of low filtering accuracy and untimely maneuvering response in existing maneuvering target tracking methods, the application proposes a maneuvering target tracking method based on model adaptation, which can detect the maneuverability of the target in real time, effectively handle the state estimation problem and improve the performance of maneuvering target tracking.

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

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

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

[0008] Step 2, starting from the current time, the subject obtains measurement data of the target through the sensor, and calculates a posterior predictive probability density of the measurement data at each time according to the target motion state transition model and the target measurement model; the posterior predictive density is conditioned on the target motion state transition model, a running length and measurement data at a previous time;

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

[0010] Step 4, the subject determines a recursive calculation formula of the running length and the target motion state transition model of the to-be-estimated parameters at the current time according to the joint distribution of the running length and the target motion state transition model;

[0011] Step 5, the subject calculates state estimation mean and corresponding estimation covariance of the target motion state transition model by using the recursive calculation formula, so as to obtain a posterior distribution of a target state of the to-be-estimated parameters, the posterior distribution containing estimation mean and estimation covariance of the target at the current time, wherein the estimation mean of the target contains a position estimation of the target, so as to realize tracking of the target.

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

[0013] Step 1.1, introducing a non-negative discrete integer variable r k ∈[1, k] as the change point model to represent a number of time periods experienced since a last change point in a sequence of measurement data to time k, i.e., a running length at time k; r k =1 represents that a change point occurs at time k; and r k =r k-1 +1 represents that no change point occurs at time k, and the sequence of measurement data continues to grow, k and k-1 respectively represent a current time and a previous time;

[0014] Step 1.2, the target motion state transition model set is composed of target motion state transition models; m ka target motion state transition model used at time k;

[0015] The time length between adjacent change points in the measurement data sequence is a run length; in each run length, for the target motion state transition model set The motion state transition model contained Can be uniformly expressed as Wherein, And Respectively represent the model m k And the model m k-1 The target state vector when the run length is r k , r k-1 , contains the position and velocity in the x direction and the position and velocity in the y direction; f m (·) is the state transition function of model m k , Is the process noise of model m k , that is, zero mean Gaussian distributed noise, Is the process noise covariance matrix corresponding to model m k .

[0016] Step 1.3, in the tracking process of the maneuvering target, the raw data obtained by the sensor for the maneuvering target can obtain the measurement data of the target after coordinate conversion and registration and other pretreatments, which can be expressed as Wherein, 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, that is, zero mean Gaussian distributed noise, R k Is the measurement noise covariance matrix.

[0017] Further, the step 1 of determining the change point model and the transition probability of the target motion state transition model and the to-be-estimated parameter at the current time comprises:

[0018] Step 1.4, the transition probability of the change point model is set as: the transition probability of the run length r k-1 To r k Is p(r k |r k-1 ), when r k =1, p(r k |r k-1 )=H(r k-1 +1); otherwise, when 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 from the first k-1 time steps. 1：(k-1) With running length r k When the condition is given, model m 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 When = 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; otherwise r k =r k-1 When +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 first k-1 time steps. 1：(k-1) Given a running length r k-1 Time model m k-1 The posterior probability; when the target's motion pattern changes, let r k =1, at which point the measurement data sequence produces a change point; when the target motion pattern does not change, r k =r k-1 +1, and the measurement data sequence continues to grow;

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

[0021] Furthermore, step 2 specifically includes:

[0022] Step 2.1: Calculate the running length r using the motion state transition model from Step 1.2. k Time model mk State prediction mean and the corresponding prediction covariance

[0023]

[0024] in, Representation model m k-1 With a running length of r k-1 The target state vector at that time, It involves finding the sign of the partial derivative; This indicates that the running length from time k-1 to time k is r. k Time model m k State prediction vector, Represents time k-1 The state estimation vector; and The running length at time k-1 is r k-1 m k-1 The state estimate means and corresponding estimated covariance; the superscript T indicates transpose; if r k =1, then It should be reinitialized, which consists of the measurement data at time k-1 and the estimated velocity at time k-1; It should also be reinitialized, and its diagonal elements consist of the measurement noise variance and the estimated velocity variance at time k-1.

[0025] Step 2.2: Calculate the running length r using the target measurement model from Step 1.3. k Time model m k Measurement prediction mean and the corresponding predicted covariance

[0026]

[0027] in, This indicates that the running length from time k-1 to time k is r. k Time model m k Measurement prediction vector; It involves finding the sign of the partial derivative; and These are respectively the model m at time k in step 2.1 with a running length of r. k The state prediction mean and the corresponding prediction covariance;

[0028] Step 2.3, for all target motion state transition models m k and running length r k Calculate measurement data y kThe posterior predicted probability density p(y) k |y 1：(k-1) m k r k ):

[0029]

[0030] in, and These are the predicted covariances corresponding to the predicted mean of the measurements in step 3.2.

[0031] Furthermore, step 3 specifically includes:

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

[0033]

[0034] Where p(y k |y 1：(k-1) m k r k ) represents the posterior predictive probability density of the measurement in step 2; q(m) k |y 1：(k-1) m k-1 r k () is the running length r in step 1.4 k When the condition is given, model m k-1 The transition probability; p(r) k |r k-1 () represents the running length r in step 1.4 k-1 The transition probability; p(y 1：(k-1) r k-1 m k-1 () represents the joint distribution of measurement data, runtime, and model at time k-1;

[0035] Step 3.2, the model transition probability q(m) from step 1.4 is... k |y 1：(k-1) m k-1 r k ) and runtime transition probability p(r) k |r k-1 Substitute into the joint distribution p(y) in step 3.1 1：k r k m k The expression for ) further gives the joint probability p(y) when the change point occurs. 1：k r k =1,m k) and the joint probability p(y 1：k , r k , m k-1 ) at the run length growth time, as follows:

[0036]

[0037] Further, the step 4 specifically comprises:

[0038] Step 4.1, based on the joint distribution p(y 1：k , r k , m k ) in step 3, the marginal likelihood p(y 1：k ) of the measurement data from the initial time to the kth time is calculated:

[0039]

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

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

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

[0043]

[0044] Step 4.4, based on the above model posterior and the measurement data y k from the initial time to the kth time, the run length probability conditioned on the model m k is calculated by the Bayes theorem:

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

[0046] Step 4.5, based on the above-mentioned running length probability and the measurement data y from the initial time to time k. 1：k The probability of the global runtime is calculated using the law of total probability:

[0047]

[0048] Step 4.6: Based on the above model, the joint distribution of runtime, and the global runtime distribution, determine the joint probability formula p(y) for runtime growth in Step 3.2. 1：k r k =r k-1 +1,m k The model transition probability q(m) k-1 |y 1：(k-1) r k-1 The expression for ) is as follows:

[0049]

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

[0051] Furthermore, step 5 specifically includes:

[0052] Step 5.1, using the measurement data y at the current time k. k The running length is calculated to be r. k Time model m k State estimate mean and the corresponding estimated covariance

[0053]

[0054] in, It is a gain matrix, and and These are the state prediction mean, state prediction covariance, measurement prediction mean, and measurement prediction covariance from 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 from step 4.4. kAll runtime probabilities p(r) k |m k y 1：k Sort the probabilities from largest to smallest, and retain the first τ probability lengths.

[0056] Step 5.3, the model m at time k can be obtained through weighted fusion. k State estimate mean and the corresponding estimated covariance

[0057]

[0058] in, At time k, in a running length of r k Time model m k The corresponding weights are expressed as follows:

[0059]

[0060] p(r k |m k y 1：k The probability of the running length after pruning in step 5.2 is denoted as ). and For step 5.2, at time k after pruning, the running length is r k Time model m k The corresponding state estimates are the mean and covariance.

[0061] Step 5.4, select model m from step 4.3 k Posterior p(m) k |y 1：k The model at its maximum The model The mean of the state estimate determined in step 5.3 and the corresponding estimated covariance That is, the target state vector x k The estimated mean μ(x) k|k ), estimate the covariance ∑(x k|k ), where μ(x) k|k It includes the required position estimates of the maneuvering target in the x and y directions, thereby enabling the tracking of the maneuvering target;

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

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

[0064] A computer readable storage medium, the medium storing a computer program; the computer program is executed by a processor to implement the model-based adaptive maneuvering target tracking method.

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

[0066] The maneuvering target tracking method provided by the present application is based on model adaptation, and simultaneously performs state estimation and variable point detection by using Bayesian online variable point detection and a multi-model estimator. The method divides time series data into non-overlapping observation sets based on run length, that is, uses run length to model variable point positions, and the time of generating a variable point is the time when a target maneuvers, so that a non-stationary process in a maneuvering target tracking scenario is converted into a partitioned stationary process. For each partitioned stationary process, the most likely model in a model set is selected to model the partitioned time series stationary process, thereby improving the performance of maneuvering target tracking. The simulation scenarios of six groups of Benchmark air targets in Matlab show that the method has the advantages of high tracking accuracy and robust tracking effect compared with the existing interactive multi-model based method. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 The figure is a flowchart of the method of the present application;

[0068] Figures 2-7 The figures are target motion trajectory graphs of the embodiment scenarios S1-S6 of the present application;

[0069] Figures 8-13 The figures are target position RMSE curve graphs in different model sets in the embodiment scenarios S1-S6 of the present application, and the process noise sets of the model sets from left to right are η=[16, 14, 60] / 10, η=[16, 40, 60], and η=[16, 40, 60]×10, respectively. DETAILED DESCRIPTION

[0070] Considering the combination of the Bayesian online change point detection technique and the model selection method, the application proposes a model adaptive maneuvering target tracking method; the Bayesian online change point detection technique detects the mutation point of the generated parameter in the sequence data in an online manner, that is, the change point, so as to realize the real-time sensing of the change of the target motion state. The model selection method can select the motion model matched with the change of the target motion state in the model set. Specifically, the Bayesian online change point detection technique is used to detect the change of the target motion state in real time, when the change point is detected, the model selection mechanism is triggered, 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 realize the accurate tracking of the maneuvering target. This method not only can adapt to the change of the target motion state, but also can make full use of the information in the historical data, and improve the robustness and accuracy of the tracking algorithm. The maneuvering target in the application includes a moving object such as a ship, a vehicle, an airplane and the like which can be detected by a sensor (such as a radar).

[0071] Referring to the accompanying drawings Figure 1 , the application provides a model adaptive maneuvering target tracking method, a subject applying 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 target estimated position, and 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 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 motion mode of the target changes, and determines the transition probability of the change point model and the target motion state transition model; specifically as follows:

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

[0074] Step 1.2, the target motion state transition model set is composed of the motion state transition models of the target; wherein the motion state transition models usually include constant speed models, turning models, uniform acceleration models and the like; m k represents the motion state transition model used at time k;

[0075] The time length between adjacent change points in the measurement data sequence is a running length; in each running length, for the target motion state transition model set The motion state transition model contained therein Can be uniformly represented as Wherein, And Respectively represent the model m k And the model m k-1 The target state vector when the running length is r k , r k-1 , contains the position and velocity in the x direction and the position and velocity in the y direction; f m (·) is the state transition function of model m k , which is specifically a uniform speed, uniform acceleration, turning, etc. State transition function; Is the process noise of model m k , that is, zero-mean Gaussian distributed noise, Is the process noise covariance matrix corresponding to model m k .

[0076] Step 1.3, in the tracking process of the maneuvering target, the raw data obtained by the sensor for the maneuvering target can obtain the measurement data of the target after coordinate conversion and registration and other pretreatments, which can be expressed as Wherein, 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, that is, zero-mean Gaussian distributed noise, R k Is the measurement noise covariance matrix.

[0077] Step 1.4, determine the running length transition probability p(r k |r k-1 ) and the 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 as: the transition probability of the running length r k-1 to r k is p(r k |r k-1 ), when r k =1, p(r k |r k-1 )=H(r k-1 +1); otherwise, when r k =r k-1 +1, p(r k |rk-1 ) = 1 - H(r k-1 ); H(·) denotes the risk function of the change-point model.

[0079] The transition probability of the target motion state transition model is: 1：(k-1) , given the measurement data y k , and the running length r k-1 k k 1：(k-1) k-1 k k k 1：(k-1) k-1 k k k k k k-1 k 1：(k-1) k-1 k k-1 1：(k-1) k-1 k-1 1：(k-1) k-1 1：(k-1) k-1 k-1 k k k-1

[0080] Step 1.5, select (x k , r k , m k ) as the to-be-estimated parameters at the kth moment, x k is the target state vector to be estimated at the current kth moment, representing the position and velocity of the target in the x direction and the position and velocity in the y direction; r k represents the running length at the current kth moment, and m k represents the target motion state transition model used at the current kth moment.

[0081] ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​Step 2: Starting from the current time k, the subject acquires the target's measurement data through the sensor. Based on the target motion state transition model and target measurement model defined in Step 1, the subject adjusts all motion state transition models m at each time step. k and running length r k Calculate measurement data y k The posterior predicted probability density p(y) k |y 1：(k-1) m k r k The posterior predicted density is transferred to the target motion state model m. k , running length rk and previous k-1 Measurement data y at each moment 1：(k-1) The conditions are as follows:

[0082] Step 2.1: Calculate the running length r using the motion state transition model from Step 1.2. k Time model m k State prediction mean and the corresponding predicted covariance

[0083]

[0084] in, Representation model m k-1 With a running length of r k-1 The target state vector at that time, It involves finding the sign of the partial derivative; This indicates that the running length from time k-1 to time k is r. k Time model m k State prediction vector, Represents time k-1 The state estimation vector; and The running length at time k-1 is r k-1 m k-1 The state estimates are the mean and corresponding estimated covariance; the superscript T indicates transpose. If r k =1, then It should be reinitialized, which consists of the measurement data at time k-1 and the estimated velocity at time k-1; It should also be reinitialized, and its diagonal elements consist of the measurement noise variance and the estimated velocity variance at time k-1.

[0085] Step 2.2: Calculate the running length r using the target measurement model from Step 1.3. k Time model m k Measurement prediction mean and the corresponding prediction covariance

[0086]

[0087] in, This indicates that the running length from time k-1 to time k is r. k Time model m k Measurement prediction vector; It involves finding the sign of the partial derivative; and These are respectively the model m at time k in step 2.1 with a running length of r. k The state prediction mean and the corresponding prediction covariance.

[0088] Step 2.3, for all target motion state transition models m k and running length r k Calculate measurement data y k The posterior predicted probability density p(y) k |y 1：(k-1) m k r k ):

[0089]

[0090] in, and These are the predicted covariances corresponding to the predicted mean of the measurements in step 3.2.

[0091] Step 3: Based on the variable point model in Step 1, the main body calculates the measurement data y from the initial time to time k. 1：k Running length r k and target motion state transition model m k The joint distribution p(y) 2：k r k m k The details are as follows:

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

[0093]

[0094] Where p(y k |y 1：(k-1) m k r k ) represents the posterior predictive probability density of the measurement in step 2; q(m) k |y 1：(k-1) mk-1 r k () is the running length r in step 1.4 k When the condition is given, model m k-1 The transition probability of p(r) k |r k-1 () represents the running length r in step 1.4 k-1 The transition probability; p(y) 1：(k-1) r k-1 m k-1 ) represents the joint distribution of measurement data, running length, and model at time k-1.

[0095] Step 3.2, the model transition probability q(m) from step 1.4 is... k |y 1：(k-1) m k-1 r k ) and runtime transition probability p(r) k |r k-1 Substitute into the joint distribution p(u) in step 3.1 1：k r k m k The expression for ) further gives the joint probability p(y) when the change point occurs. 1：k r k =1,m k The joint probability p(y) and the length of the running process as the running length increases. 1：k r k =r k-1 +1,m k The formula for calculating ) is as follows:

[0096]

[0097] Step 4, the main body follows the joint distribution p(y) from step 3. 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 transition model m k The recursive calculation formula is as follows:

[0098] Step 4.1, based on the joint distribution p(y) in Step 3 1：k r k m k ), calculate the marginal likelihood p(y) of the measurement data from the initial time to time k. 1：k ):

[0099]

[0100] Step 4.2, based on the marginal likelihood of the above measurements and the measurement data y from the initial time to time k.1：k , m according to Bayes' theorem k and run length r k : p(y

[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 measurement data y 1：k from the initial time to the k-th time, calculate the model m k posterior from the total probability theorem:

[0103]

[0104] Step 4.4, based on the above model posterior and the measurement data y 1：k from the initial time to the k-th time, calculate the run length probability conditioned on the model m k from Bayes' theorem:

[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 measurement data y 1：k from the initial time to the k-th time, calculate the global run length probability from the total probability theorem:

[0107]

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

[0109]

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

[0111] Step 5: The main body uses the recursive calculation formula from Step 4 to calculate model m. k The mean and corresponding covariance of the state estimates are used to obtain the target state x, the parameter to be estimated. k posterior distribution Where μ(x) k|k ) and ∑(x k|k The estimated mean and estimated covariance of the target at time k are respectively, as follows:

[0112] Step 5.1, using the measurement data y at the current time k. k The running length is calculated to be r. k Time model m k State estimate mean and the corresponding estimated covariance

[0113]

[0114] in, It is a gain matrix, and and These are the state prediction mean, state prediction covariance, measurement prediction mean, and measurement prediction covariance from 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 from step 4.4. k All runtime probabilities p(r) k |m k y 1：k Sort the probabilities from largest to smallest, and retain the first τ running length probabilities to reduce computational complexity;

[0116] Step 5.3, the model m at time k can be obtained through weighted fusion. k State estimate mean and the corresponding estimated covariance

[0117]

[0118] in, r k r k r

[0119]

[0120] r k r k r 1：k r k r k

[0121] k k 1：k k k|k k|k k|k

[0122]

[0123]

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

[0125] I. Scenario 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 for the time period k ∈ [1, 60); when the time k ∈ [60, 80), k ∈ [110, 130], the target makes a turning motion with an acceleration of 2g, 3g (g is the acceleration of gravity), respectively; the target continues to fly at a constant speed during other time periods.

[0127] ​​​​​​​​​​​​​​​​​Scenario 2 (S2): The second target represents a small and agile 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 e [1, 30); when time k e [30, 50), the target makes a 90° turn motion with an acceleration of 2.5g (g is the gravitational acceleration); when time k e [100, 115), the target makes a turn motion with an acceleration of 4g (g is the gravitational acceleration); and the target continues to fly at a constant speed in other time periods.

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

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

[0130] Scenario 5 (S5): The fifth target represents a fighter aircraft. The target initially flies at a constant speed; next, at time k e [30, 40), k e [60, 70), k e [115, 170), the target makes turn motions with accelerations of 5g, 7g, 6g (g is the gravitational acceleration), respectively; and the target flies at a constant speed in other time periods.

[0131] Scenario 6 (S6): The sixth target also represents a fighter aircraft. The target keeps flying at a constant speed with an initial speed of 426 m / s for a time period of 30s; next, at time k e [30, 40), k e [70, 85), k e [115, 125), k e [125, 155], the target makes turn motions with accelerations of 7g, 6g, 6g, 7g (g is the gravitational acceleration); and the target keeps flying at a constant speed and heading in other time periods.

[0132] II. Method-related configurations

[0133] The uniform motion model is used as the target motion state transition model, and the target maneuver is captured by different model process noises. Then the motion state transition model contained in the model set can be expressed as

[0134]

[0135] where k and k-1 represent the current time and the last time respectively; and represent the target state vector of model m with the running length of r k and r k-1 , which contains the position and velocity in x direction and the position and velocity in y direction; F k is the state transition matrix of the model, and since all the models in the model set are selected as the uniform motion model, the F k of all the models are the same; is the process noise of model m, which is the zero-mean Gaussian distributed noise, is the process noise covariance matrix corresponding to model m. The state transition matrix F k and the process noise covariance matrix are as follows:

[0136]

[0137] where I2 represents the 2x2 unit matrix, represents the process noise coefficient of model m, T represents the sensor sampling period, is the Kronecker product operator. Considering that these models include different motion modes from near constant velocity (NCV) to high maneuver, three models in the model set are selected as follows: η = [η1, η2, η3] = [16, 40, 60], and η is reduced by 10 times and enlarged by 10 times respectively, and three model set conditions are considered in total.

[0138] For the target measurement model, it is assumed that the position measurement of the target can be obtained after the original measurement data obtained by the sensor is preprocessed by coordinate conversion and registration, and it can be expressed according to the characteristics of the measurement data of the target after preprocessing as follows:

[0139]

[0140] where k represents the current time. represents the target state of model m k with the running length of r k , y k is the measurement value; H k is the measurement matrix constructed according to the measurement characteristics of the sensor; is the measurement noise of the sensor, which is the zero-mean Gaussian distributed noise, and R​k is the measurement noise covariance matrix. In this embodiment, the obtained measurements are the position in x direction and the position in y direction, and the measurement matrix and the measurement noise covariance matrix are set as follows:

[0141]

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

[0143] The initial value of the given running length is r1=1; the initial value of the given model prior is q(m1), and since there are 3 models in the model set, q(m1)=1 / 3 is set. The initial joint distribution p(y 1：1 , r1, m1) = 1 is given for the measurement data, the running length and the model; the risk function H is given, and H(·)=1 / 10 is set.

[0144] III. Evaluation of the maneuvering target tracking situation:

[0145] The maneuvering filtering effect of the interactive multiple model filtering method (IMM) is compared and evaluated as follows.

[0146] In the method of the present application, 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 radial distance of the target. The smaller the RMSE, the better the filtering effect.

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

[0148] Referring to the 6 sets of Benchmark data in MATLAB, six single-target tracking scenarios of variable acceleration maneuvers are considered. The total step length of each tracking scenario is k total =187s, and the sensor sampling period is G=1s. Considering the case where the noise covariance is known, the model process noise coefficients in the model set are set as η=[η1, η2, η3]=[16, 40, 60], and the model set η of the BOCPDMS algorithm and the IMM algorithm for comparison is reduced by 10 times and increased by 10 times respectively, and a total of three model set conditions are considered.

[0149] Table 1 Average position RMSE statistical table of each method under different model domains in different scenarios

[0150]

[0151] Figures 2-7 The target motion trajectory graphs of scenarios S1-S6 are shown in Figs. 1-6 respectively, Figures 8-13Figures are target position RMSE curves of scenarios S1-S6 under different model sets, and each group of figures from left to right, the process noise set of model set is η=[16, 40, 60] / 10, η=[16, 40, 60], η=[16, 40, 60]×10 respectively. It can be seen from the target position RMSE curve that the RMSE value of the algorithm of the scheme is less than that of the comparative algorithm IMM, which indicates that the tracking effect of the algorithm of the scheme is better. And when η m of the model set is reduced, that is, the model set is incomplete, the tracking error of the algorithm of the scheme is significantly less than that of the comparative algorithm. Table 1 is the average position RMSE of scenarios S1-S6 under different model sets. From the numerical results of the table, it can be seen that when η m of the model set is increased, the value of RMSE will also increase, because when η m increases, high maneuvering behavior can be captured, but tracking uncertainty will also increase, and tracking precision will decrease, so the tracking precision of the algorithm of the scheme and the comparative algorithm decreases, but the RMSE of the algorithm of the scheme is still less than that of the comparative algorithm; when η m of the model set is reduced, that is, the model set is incomplete, the RMSE value of the algorithm of the scheme is significantly less than that of the comparative algorithm. The tracking results of different model sets show that the algorithm of the scheme can maintain effective tracking when the model set is incomplete, and its tracking performance is more robust compared with IMM.

[0152] The above examples are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing examples, or make equivalent replacements for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be included in the protection scope of the present application.

Claims

1. A model-based adaptive method of maneuvering target tracking, characterized in that, The method comprises the following steps: Step 1, the subject constructs a target motion state transition model set and a target measurement model to respectively represent possible motion modes of a maneuvering target and measurement data obtained by a sensor, and constructs a change point model to represent a time when the motion mode of the target changes, determines transition probabilities of the change point model and the target motion state transition model and to-be-estimated parameters at a current time; Step 2, starting from the current time, the subject obtains measurement data of the target through the sensor, and according to the target motion state transition model and the target measurement model, calculates a posterior predictive probability density of the measurement data at each time for all motion state transition models and running lengths; the posterior predictive density is conditioned on the target motion state transition model, the running length and measurement data at a previous time; Step 3, the subject calculates a joint distribution of the measurement data, the running length and the target motion state transition model from an initial time to the current time according to the change point model; Step 4, the subject determines a recursive calculation formula of the running length and the target motion state transition model of the to-be-estimated parameters at the current time according to the joint distribution of the running length and the target motion state transition model; Step 5, the subject calculates state estimation mean and corresponding estimation covariance of the target motion state transition model by using the recursive calculation formula, so as to obtain a posterior distribution of the target state of the to-be-estimated parameters, and the posterior distribution comprises an estimation mean and an estimation covariance of the target at the current time, wherein the estimation mean of the target comprises an estimation of a position of the target, so that tracking of the target is realized.

2. The model-based adaptive maneuvering target tracking method according to claim 1, wherein, The step 1 comprises the following steps: Step 1.1, introducing non-negative discrete integer variable r k ∈ [1, k] as a change-point model, to represent the number of time points experienced since the last change-point in the sequence of measurement data to time k, i.e., the run length at time k; r k = 1 indicates that there is a change-point at time k; while r k = r k-1 + 1 indicates that there is no change-point at time k, the sequence of measurement data continues to grow, k and k-1 represent the current time and the last time, respectively; Step 1.2, target motion state transition model set comprises target motion state transition models; m k denotes a target motion state transition model used at time k The time length between adjacent change points in the measurement data sequence is a run length; in each run length, for the target motion state transition model set The motion state transition model contained Can be uniformly represented as Wherein, And Respectively represent the model m k And the model m k-1 When the run length is r k , r k-1 The target state vector, which contains the position and velocity in the x direction and the position and velocity in the y direction; f m (·) is the state transition function of the model m k , The process noise of the model m k , that is, the zero-mean Gaussian distribution noise, The corresponding process noise covariance matrix of the model m k ; Step 1.3, in the process of tracking the maneuvering target, the raw data acquired by the sensor for the maneuvering target can obtain the measurement data of the target after the pre-processing such as coordinate conversion and registration, which can be expressed as where y k is the measurement data of the target state, h(·) is a measurement function constructed according to the measurement characteristics of the sensor; is the measurement noise of the sensor, i.e. zero-mean Gaussian distributed noise, R k is the measurement noise covariance matrix.

3. The model-based adaptive maneuvering target tracking method according to claim 2, wherein, The step 1 comprises the following steps: Step 1.4, transition probability of change-point model is set as: run length r k-1 to r k 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 change-point model; The transition probability of the target motion state transition model is: based on the measurement data y from the first k-1 time steps. 1：(k-1) With running length r k When the condition is given, model m 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 When = 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; otherwise r k =r k-1 When +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 first k-1 time steps. 1：(k-1) Given a running length r k-1 Time model m k-1 The posterior probability; when the target's motion pattern changes, let r k =1, at which point the measurement data sequence produces a change point; when the target motion pattern does not change, r k =r k-1 +1, and 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 time k, representing the position and velocity in the x direction, and the position and velocity in the y direction.

4. The model-based adaptive maneuvering target tracking method according to claim 3, wherein, The step 2 comprises the following steps: Step 2.

1. Calculate the run length r from the motion state transition model in Step 1.2 k the state prediction mean k of model m and the corresponding prediction covariance where denotes the model m k-1 at time k - 1 with running length r k-1 and target state vector is the partial derivative symbol; denotes the state prediction vector of model m k at time k - 1 with running length r k from time k - 1 to time k denotes the state estimation vector at time k - 1 ; and are the state estimation mean and the corresponding estimation covariance of m k-1 at time k - 1 with running length r k-1 , respectively; the superscript T denotes the transpose; if r k = 1, then should be reinitialized, which consists of the measurement data at time k - 1 and the estimated velocity at time k - 1 should also be reinitialized, whose diagonal elements consist of the measurement noise variance and the estimated velocity variance at time k - 1 at time k - 1. Step 2.

2. Calculate run length r from the target metrology model in step 1.3 k the metrology prediction mean k of model m and the corresponding prediction covariance wherein represents the state prediction mean and the corresponding prediction covariance of model m k at time k with run length r k at time k with run length r is the sign of the partial derivative; and represents the state prediction mean and the corresponding prediction covariance of model m k at time k with run length r Step 2.

3. Compute the posterior predictive probability density p(y | y, m, r ) for all target motion state transition models m k and run lengths r k Compute the measurement data y k Compute the posterior predictive probability density p(y | y, m, r ) for all target motion state transition models m k |y 1：(k-1) , m k , r k ) where and are the prediction covariances corresponding to the measurement prediction mean in step 3.2, respectively.

5. The model-based adaptive maneuvering target tracking method according to claim 4, wherein, The step 3 comprises the following steps: Step 3.1, joint distribution y(y 1：k , r k , m k ) can be recursively represented as: p(r k |r k-1 )p(y 1:(k-1) ,r k-1 ,m k-1 )} Where p(y k |y 1：(k-1) m k r k ) represents the posterior predictive probability density of the measurement in step 2; q(m) k |y 1:(k-1) m k-1 r k () is the running length r in step 1.4 k When the condition is given, model m k-1 The transition probability; p(r) k |r k-1 () represents the running length r in step 1.4 k-1 The transition probability; p(y 1：(k-1) r k-1 m k-1 () represents the joint distribution of measurement data, runtime, and model at time k-1; Step 3.2, the model transition probability q(m) from step 1.4 is... k |y 1：(k-1) m k-1 r k ) and runtime transition probability p(r) k |r k-1 Substitute into the joint distribution p(y) in step 3.1 1：k r k m k The expression for ) further gives the joint probability p(y) when the change point occurs. 1：k r k =1,m k The joint probability p(y) and the length of the running process as the running length increases. 1：k r k =r k-1 +1,m k The formula for calculating ) is as follows:

6. The model-based adaptive maneuvering target tracking method according to claim 5, wherein, The step 4 comprises the following steps: Step 4.1, based on the joint distribution p(y) in Step 3 1：k r k m k ), calculate the marginal likelihood p(y) of the measurement data from the initial time to time k. 1：k ): Step 4.2, based on the marginal likelihood of the measurements and the measurements y from time 0 to time k 1：k , compute the joint distribution of the model m k and the run length r k according to Bayes' theorem: 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 measurement data y from the initial time to time k. 1：k Model m is calculated using the law of total probability. k Posterior: Step 4.4, based on the model posterior above and the measurement data y from time 0 to time k 1：k The run length probability given the model m k is computed from Bayes' rule: 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 probabilities and the measurement data y from the initial time to time k 1：k Compute global run length probabilities from the total probability theorem: Step 4.6: Based on the above model, the joint distribution of runtime, and the global runtime distribution, determine the joint probability formula p(y) for runtime growth in Step 3.

2. 1：k r k =r k-1 +1,m k The model transition probability q(m) k-1 |y 1：(k-1) r k-1 The expression for ) is as follows: Where p(r) k-1 m k-1 |y 1：(k-1) (m) is the model calculated according to step 5.

2. k-1 and running length r k-1 The joint distribution of p(r) k-1 |y 1：(k-1) The probability of the global running length at time k-1 is calculated according to step 5.

4.

7. The model-based adaptive maneuvering target tracking method according to claim 6, wherein, The step 5 comprises the following steps: Step 5.1, compute the state estimation mean k and the corresponding estimation covariance k of the model m k with running length r using the measurement data y wherein is a 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, is given in step 2.2, and I denotes the identity matrix; Step 5.2, Pruning: Given a threshold τ, prune the model m from step 4.

4. k All runtime probabilities p(r) k |m k y 1：k Sort the probabilities from largest to smallest, and retain the first τ probability lengths. Step 5.

3. Obtain the model m at time k by weighted fusion k of the state estimation mean and the corresponding estimation covariance wherein, is the running length of r k model m k corresponding weight, the expression is as follows: p(r k ) k , y 1：k ) is the run length probability after pruning in step 5.2; and are the state estimation mean and estimation covariance of model m k at time k with run length r k after pruning in step 5.

2. Step 5.

4. Select the model m from step 4.3 with the highest posterior p(m k ) k |y 1：k )max The model The state estimate mean determined by step 5.3 and the corresponding estimate covariance i.e. the estimate mean μ(x k ), estimate covariance ∑(x k|k ) of the target state vector x k|k ), where μ(x k|k ) contains the desired position estimates in x and y directions of the maneuvering target, thus achieving tracking of the maneuvering target; It is judged whether the measurement data at the k time is measurement data at a last time of the sensor; if yes, the tracking is ended, otherwise, the step 2 is jumped to. 8.A terminal device, comprising a processor, a memory, and a computer program stored in the memory; characterized in that, The processor is executed by a computer, and the model adaptive maneuvering target tracking method is realized.

9. A computer readable storage medium having stored therein a computer program; characterized in that, The computer program is executed by the processor, and the model adaptive maneuvering target tracking method is realized.

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