A Highly Maneuverable Target Tracking Method
By proposing an adaptive TPM iterative formula and interactive multi-model filtering algorithm in the Bayesian framework, the problem of low maneuver target tracking accuracy under insufficient prior information or inaccurate conditions is solved, and high-precision maneuver target tracking and TPM adaptive update are achieved.
Patent Information
- Application Number
- CN202210261738.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-03-17
- Publication Date
- 2025-02-28
- Estimated Expiration
- 2042-03-17
AI Technical Summary
In the case of insufficient or inaccurate prior information, it is difficult to achieve high-precision tracking of maneuverable targets, and the traditional TPM adaptive update method is not effective.
Based on the Bayesian framework, an adaptive TPM iterative formula is proposed, which uses quantitative sequencing sequences to perform adaptive updates of TPM, and tracks high maneuverable targets through interactive multi-model filtering algorithms.
In the case of insufficient or inaccurate prior information, the tracking accuracy of maneuverable targets is improved, the adaptability of TPM and model posterior probability is enhanced, and the filtering accuracy is improved.
Smart Images
Figure CN114611068B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to fields such as communication, radar, measurement and control that require tracking of mobile targets, and specifically to a method for tracking and predicting mobile targets using an interactive multi-model. Background Art
[0002] Maneuvering target tracking is a key and difficult problem in the field of target tracking. Relevant scholars have conducted extensive research on this issue, and have experienced a development process from single model to multiple models. Among the multiple model methods, the Interacting Multiple Model (IMM) is a filtering method with the best cost-effectiveness. It maps the target motion state to many known models, each model corresponds to a filter. In the iterative process, all filters work in parallel, and the switching between models is controlled by the Markov chain. If the constructed multi-motion model matches the target motion trajectory, the IMM algorithm can track any maneuvering target. The traditional method sets the transition probability matrix (TPM) to a fixed main diagonal dominant matrix based on prior information, which leads to a lag in the algorithm model switching and a deterioration in the tracking effect. In addition, if the prior information is insufficient or inaccurate, the use of a fixed TPM often leads to inaccurate estimation of the target state by the system, making it difficult to guarantee the performance of the IMM algorithm. In order to achieve the adaptive update of TPM, the existing methods generally implement the adaptive adjustment of TPM based on the measurement information at the current moment, but this adaptive adjustment is a weak adjustment that does not make full use of the observation sequence, resulting in poor improvement. In addition, existing methods have high requirements for prior information. If the prior information is insufficient or inaccurate, it will lead to reduced tracking accuracy or even filtering divergence.
[0003] In view of the above shortcomings, the present invention provides an adaptive TPM iteration formula based on a Bayesian framework according to the measurement sequence, thereby proposing a high-maneuverability target tracking method when prior information is insufficient or inaccurate. Summary of the invention
[0004] The problem to be solved by the present invention is: how to make full use of the measurement sequence to realize the adaptive update of TPM when the prior information is insufficient or inaccurate, so as to improve the tracking accuracy of the maneuvering target. The method for solving the technical problem is a high maneuvering target tracking method, and the implementation steps are:
[0005] (1) The initial conditions of the algorithm are: there are a total of r (r ≥ 3) system motion models in the algorithm, and the model transition probability matrix Π(0) at time 0 is
[0006]
[0007] Among them, π ij (0) According to the system prior information, i,j = 1, 2, ..., r, model M i For example, given the model M i All initial conditions: The state vector at time 0 is given according to the system prior information and its corresponding estimation error covariance matrix P i (0|0), the covariance matrix Q of the state noise i , the covariance matrix R of the measurement noise i And the model posterior probability μ i (0), the measured value of the system z(0) = [x(0)y(0)z(0)] T , where x(0), y(0), and z(0) represent the position coordinates of the target in the x, y, and z directions at time 0, respectively, and the symbol "T" represents the transpose of a vector or matrix;
[0008] (2) Calculate the mixing probability μ i|j (n-1|n-1), after the measurement sequence Z is obtained n-1 And the n-time model M j Under valid conditions, model M i The mixing probability at time n-1 is
[0009]
[0010] Among them, the measurement sequence Z n-1 represents the set of all measurements before time n {z(1),z(2),…,z(n-1)}, μ i (n-1) means that in a given measurement sequence Z n-1 Under the condition of n-1 time model M i The posterior probability of
[0011] μ i (n-1) = P{M i (n-1)|Z n-1}
[0012] π ij (n-1) represents the model transition probability at time n-1, that is
[0013] π ij (n-1) = P{M j (n)|M i (n-1),Z n-1}
[0014] (3) Model interaction, the model M before the interaction at time n-1 i The state vector and its corresponding estimation error covariance matrix Pi (n-1|n-1), and according to the mixing probability μ at time n-1 i|j (n-1|n-1), calculate the model M after interaction j The state vector and its corresponding estimation error covariance matrix P oj (n-1|n-1)
[0015]
[0016] (4) Use the basic Kalman filter algorithm to filter all r filters in parallel, with model M j For example, j = 1, 2, ..., r, estimate the state vector at time n and its corresponding estimation error covariance matrix P j (n|n), and the innovation process a j (n) and its corresponding covariance matrix A j (n):
[0017] Step 1: Prediction: Based on model M j The state transition matrix F j and the state noise covariance matrix Q j , calculate the predicted value of the state vector at time n-1 and the predicted value P of the corresponding estimation error covariance matrix oj (n|n-1)
[0018]
[0019] P oj (n|n-1)=F j P oj (n-1|n-1)(F j ) T +Q j
[0020] The second step is to update the estimate: based on the measurement value z(n) at time n and the measurement matrix H j (n) Calculate the new information process a j (n), and the measurement noise covariance matrix R j Calculate the covariance matrix A of the innovation process at time n j (n), and further calculate the Kalman gain K j (n), the final estimated state vector at time n and its corresponding estimation error covariance matrix P j (n|n), and the calculation formulas are
[0021]
[0022] A j (n) = H j (n)P oj (n|n-1)[H j (n)] T +R j
[0023] K j (n) = P oj (n|n-1)[H j (n)] T [A j (n)] -1
[0024]
[0025] P j (n|n)=[IK j (n)H j (n)]P oj (n|n-1)[IK j (n)H j (n)] T +K j (n)R j [K j (n)] T
[0026] Where I represents the unit matrix, whose dimension is the same as P oj (n|n-1) is consistent, and the symbol "-1" means to find the inverse of a matrix;
[0027] (5) Model posterior probability μ j (n) Update
[0028]
[0029] Among them, Λ j (n) represents the model M at time n j The likelihood function is calculated as
[0030]
[0031] Among them, |A j (n) means to find A j The determinant of (n);
[0032] (6) Model transition probability π ij Adaptive update of (n):
[0033] The first step is to define the one-step prediction value π of the model transition probability at time n-1 ij (n-1|n)
[0034]
[0035] Among them, the likelihood function Λ ij (n) is calculated as
[0036]
[0037] Among them, a ij (n), A ij (n) represents the model M at time n j The innovation process and its corresponding covariance matrix;
[0038] The second step is to establish π ij (n-1|n) and the model transition probability π at time n ij (n), according to the model transition probability π at time n ij (n), it is difficult to obtain the model M i (n) to model M j (n+1) transition probability, so it is considered that for the same measurement sequence Z n , the model transition probability from time n to time n+1 is unchanged, that is,
[0039] P{M j (n+1)|M i (n),Z n}≈P{M j (n)|M i (n-1),Z n}
[0040] So the model transition probability π at time n ij The final calculation expression of (n) is
[0041]
[0042] (7) State fusion output, estimate the state vector of the system at time n and its corresponding estimation error covariance matrix P(n|n), and its update formulas are
[0043]
[0044] It should be noted that the state fusion output is not part of the algorithm iteration, but is only used to output the system estimation results to the outside of the iterative system;
[0045] (8) Take time n=n+1 and repeat steps (2) to (6) to achieve position tracking of high-maneuverability targets.
[0046] The beneficial effect of the present invention is that even when the prior information is insufficient or inaccurate, the TPM and model posterior probability of the present invention have good adaptive effects and the filtering accuracy is higher than the existing method. The present invention can be applied to fields such as communication, radar, measurement and control that require mobile target tracking. BRIEF DESCRIPTION OF THE DRAWINGS
[0047] Figure 1 It is a general step diagram of a high maneuverable target tracking method;
[0048] Figure 2 It is a structural block diagram of a high maneuverable target tracking method. DETAILED DESCRIPTION
[0049] First, the spatial position coordinates of the maneuvering target are obtained by radar measurement, and then a high-maneuvering target tracking method is used to complete the position tracking of the maneuvering target based on the system motion model. The overall steps are as follows: Figure 1 As shown, the structural block diagram is as follows Figure 2 The specific implementation steps are as follows:
[0050] (1) The initial conditions of the algorithm are: there are a total of r (r ≥ 3) system motion models in the algorithm, and the model transition probability matrix Π(0) at time 0 is
[0051]
[0052] Among them, π ij (0) According to the system prior information, i,j = 1, 2, ..., r, model M i For example, given the model M i All initial conditions: The state vector at time 0 is given according to the system prior information and its corresponding estimation error covariance matrix P i (0|0), the covariance matrix Q of the state noise i , the covariance matrix R of the measurement noise i And the model posterior probability μ i (0), the measured value of the system z(0) = [x(0)y(0)z(0)] T , where x(0), y(0), and z(0) represent the position coordinates of the target in the x, y, and z directions at time 0, respectively, and the symbol "T" represents the transpose of a vector or matrix;
[0053] (2) Calculate the mixing probability μ i|j (n-1|n-1), after the measurement sequence Z is obtained n-1 And the n-time model M j Under valid conditions, model M i The mixing probability at time n-1 is
[0054]
[0055] Among them, the measurement sequence Z n-1 represents the set of all measurements before time n {z(1),z(2),…,z(n-1)}, μ i (n-1) means that in a given measurement sequence Z n-1 Under the condition of n-1 time model M i The posterior probability of
[0056] μ i (n-1) = P{M i (n-1)|Z n-1}
[0057] π ij (n-1) represents the model transition probability at time n-1, that is
[0058] π ij (n-1) = P{M j (n)|M i (n-1),Z n-1}
[0059] (3) Model interaction, the model M before the interaction at time n-1 i The state vector and its corresponding estimation error covariance matrix P i (n-1|n-1), and according to the mixing probability μ at time n-1 i|j (n-1|n-1), calculate the model M after interaction j The state vector and its corresponding estimation error covariance matrix P oj (n-1|n-1)
[0060]
[0061] (4) Use the basic Kalman filter algorithm to filter r filters in parallel, with model M j For example, j = 1, 2, ..., r, estimate the state vector at time n and its corresponding estimation error covariance matrix P j (n|n), and the innovation process a j (n) and its corresponding covariance matrix A j (n):
[0062] Step 1: Prediction: Based on model M j The state transition matrix F j and the state noise covariance matrix Q j , calculate the predicted value of the state vector at time n-1 and the predicted value P of the corresponding estimation error covariance matrix oj (n|n-1)
[0063]
[0064] P oj (n|n-1)=F j P oj (n-1|n-1)(F j ) T +Q j
[0065] Among them, the state noise covariance matrix Q j The specific calculation formula is:
[0066]
[0067] in They represent the variance of pseudo acceleration in the x, y, and z directions respectively. A is different for the uniform motion model and the uniform acceleration motion model, and are
[0068]
[0069] The second step is to update the estimate: based on the measurement value z(n) at time n and the measurement matrix H j (n) Get the new information process a j (n), and the measurement noise covariance matrix R j Calculate the covariance matrix A of the innovation process at time n j (n), and further calculate the Kalman gain K j (n), the final estimated state vector at time n and its corresponding estimation error covariance matrix P j (n|n), and the calculation formulas are
[0070]
[0071] A j (n) = H j (n)P oj (n|n-1)[H j (n)] T +R j
[0072] K j (n) = P oj (n|n-1)[H j (n)] T [A j (n)] -1
[0073]
[0074] P j (n|n)=[IK j (n)H j (n)]P oj (n|n-1)[IK j (n)H j (n)] T +K j (n)R j [K j (n)] T
[0075] Where I represents the unit matrix, whose dimension is the same as P oj (n|n-1) is consistent, the symbol "-1" means to find the inverse of a matrix, the measurement matrix H j The expression is
[0076]
[0077] (5) Model posterior probability μ j (n) Update
[0078]
[0079] Among them, Λ j (n) represents the model M at time n j The likelihood function is calculated as
[0080]
[0081] Among them, |A j (n)| means to find A j The determinant of (n);
[0082] (6) Model transition probability π ij Adaptive update of (n):
[0083] The first step is to define the one-step prediction value π of the model transition probability at time n-1 ij (n-1|n)
[0084]
[0085] Among them, the likelihood function Λ ij The calculation method of (n) is
[0086]
[0087] Among them, a ij (n), A ij(n) represents the model M at time n j The innovation process and its corresponding covariance matrix;
[0088] The second step is to establish π ij (n-1|n) and the model transition probability π at time n ij (n), according to the model transition probability π at time n ij (n), it is difficult to obtain the model M i (n) to model M j (n+1) transition probability, so it is considered that for the same measurement sequence Z n , the model transition probability from time n to time n+1 is unchanged, that is,
[0089] P{M j (n+1)|M i (n),Z n}≈P{M j (n)|M i (n-1),Z n}
[0090] So the model transition probability π at time n ij The final calculation expression of (n) is
[0091]
[0092] (7) State fusion output, estimate the state vector of the system at time n and its corresponding estimation error covariance matrix P(n|n), and its update formulas are
[0093]
[0094] It should be noted that the state fusion output is not part of the algorithm iteration, but is only used to output the system estimation results to the outside of the iterative system;
[0095] (8) Take time n=n+1 and repeat steps (2) to (6) to achieve position tracking of high-maneuverability targets.
[0096] The present invention can realize the position tracking of highly maneuverable targets when the prior information is insufficient or inaccurate; the present invention can be applied to fields such as communication, radar, measurement and control that have a demand for maneuverable target tracking.
Claims
1. A high maneuverability target tracking method, the implementation steps are: (1) The initial conditions of the algorithm are: there are a total of r (r ≥ 3) system motion models in the algorithm, and the model transition probability matrix Π(0) at time 0 is in, π ij (0) According to the system prior information, i,j = 1, 2, ..., r, model M i For example, given the model M i All initial conditions: The state vector at time 0 is given according to the system prior information and its corresponding estimation error covariance matrix P i (0|0), the covariance matrix Q of the state noise i , the covariance matrix R of the measurement noise i And the model posterior probability μ i (0), the measured value of the system z(0) = [x(0)y(0)z(0)] T , where x(0), y(0), and z(0) represent the position coordinates of the target in the x, y, and z directions at time 0, respectively, and the symbol "T" represents the transpose of a vector or matrix; (2) Calculate the mixing probability μ i|j (n-1|n-1), after the measurement sequence Z is obtained n-1 And the n-time model M j Under valid conditions, model M i The mixing probability at time n-1 is Among them, the measurement sequence Z n-1 represents the set of all measurements before time n {z(1),z(2),...,z(n-1)}, μ i (n-1) means that in a given measurement sequence Z n-1 Under the condition of n-1 time model M i The posterior probability of μ i (n-1)=P{M i (n-1)|Z n-1 } π ij (n-1) represents the model transition probability at time n-1, that is π ij (n-1)=P{M j (n)|M i (n-1),Z n-1 } (3) Model interaction, the model M before the interaction at time n-1 i The state vector and its corresponding estimation error covariance matrix P i (n-1|n-1), and according to the mixing probability μ at time n-1 i|j (n-1|n-1), calculate the model M after interaction j The state vector and its corresponding estimation error covariance matrix P oj (n-1|n-1) (4) Use the basic Kalman filter algorithm to filter all r filters in parallel, with model M j For example, j = 1, 2, ..., r, estimate the state vector at time n and its corresponding estimation error covariance matrix P j (n|n), and the innovation process a j (n) and its corresponding covariance matrix A j (n): Step 1: Prediction: Based on model M j The state transition matrix F j and the state noise covariance matrix Q j , calculate the predicted value of the state vector at time n-1 and the predicted value P of the corresponding estimation error covariance matrix oj (n|n-1) P oj (n|n-1)=F j P oj (n-1|n-1)(F j ) T +Q j The second step is to update the estimate: based on the measurement value z(n) at time n and the measurement matrix H j (n) Calculate the new information process a j (n), and the measurement noise covariance matrix R j Calculate the covariance matrix A of the innovation process at time n j (n), and further calculate the Kalman gain K j (n), the final estimated state vector at time n and its corresponding estimation error covariance matrix P j (n|n), and the calculation formulas are A j (n)=H j (n)P oj (n|n-1)[H j (n)] T +R j K j (n)=P oj (n|n-1)[H j (n)] T [A j (n)] -1 P j (n|n)=[I-K j (n)H j (n)]P oj (n|n-1)[I-K j (n)H j (n)] T +K j (n)R j [K j (n)] T Where I represents the unit matrix, whose dimension is the same as P oj (n|n-1) is consistent, the symbol "-1" means to find the inverse of a matrix; (5) Model posterior probability μ j (n) Update Among them, Λ j (n) represents the model M at time n j The likelihood function is calculated as Among them, |A j (n) means to find A j The determinant of (n); (6) Model transition probability π ij Adaptive update of (n): The first step is to define the one-step prediction value π of the model transition probability at time n-1 ij (n-1|n) Among them, the likelihood function Λ ij (n) is calculated as Among them, a ij (n), A ij (n) represents the model M at time n j The innovation process and its corresponding covariance matrix; The second step is to establish π ij (n-1|n) and the model transition probability π at time n ij (n), according to the model transition probability π at time n ij (n), it is difficult to obtain the model M i (n) to model M j (n+1) transition probability, so it is considered that for the same measurement sequence Z n , the model transition probability from time n to time n+1 is unchanged, that is, P{M j (n+1)|M i (n),Z n }≈P{M j (n)|M i (n-1),Z n } So the model transition probability π at time n ij The final calculation expression of (n) is (7) State fusion output, estimate the state vector of the system at time n and its corresponding estimation error covariance matrix P(n|n), and its update formulas are It should be noted that the state fusion output is not part of the algorithm iteration, but is only used to output the system estimation results to the outside of the iterative system; (8) Take time n=n+1 and repeat steps (2) to (6) to achieve position tracking of high-maneuverability targets.