Multi-sensor information fusion target tracking method with random variable parameter matrix

Abstract

This invention discloses a multi-sensor information fusion target tracking method with a stochastic variable parameter matrix. The method includes the following steps: 1. Establishing a dynamic model of the tracking target in a multi-sensor target tracking system; 2. Designing the predictor and estimator structures; 3. Calculating the upper bound Θ of the one-step prediction error covariance matrix of the i-th sensor at time k+1. i,k+1|k 4. Calculate the estimated gain matrix K of the i-th sensor at time k+1. i,k+1 And the fusion estimation of the tracking target, part five, K i,k+1 Substituting into step two, we obtain the state estimate of the target tracked by the i-th sensor at time k+1. We then determine whether k+1 has reached the estimated total duration MN. If k+1 < MN, proceed to step six; if k+1 = MN, the process ends after calculating the fusion estimate. Step six: Calculate the upper bound of the estimation error covariance Θ. i,k+1|k+1 Let k = k + 1, and continue in step 2 until k + 1 = MN is satisfied. This invention can effectively estimate the target state and has good robustness.

Description

Technical Field

[0001] This invention relates to a target tracking method, specifically a multi-sensor information fusion target tracking method with a random variable parameter matrix. Background Technology

[0002] Due to the emergence of information fusion technology, the reliability and estimation accuracy of multi-sensor systems are significantly better than those of single-sensor systems. Multi-sensor information state estimation and multi-sensor fusion estimation have always been research hotspots and have wide applications in various fields such as industry, military, and transportation.

[0003] In reality, noise is widespread, including not only ordinary additive noise but also multiplicative noise, which affects the current state observation. In practical engineering, the state of a system is often stochastic and the system is nonlinear, which increases the difficulty of state estimation.

[0004] In multi-sensor systems, measurement loss, packet loss, and random sensor delays are often unavoidable during data transmission due to limitations in storage and communication bandwidth. Specifically, measurement data may be missing during information transmission due to sensor aging or uncertainties in the external environment. To improve the accuracy of estimations, it is crucial to establish a sufficiently accurate model.

[0005] Common fusion estimation methods include distributed fusion estimation, centralized fusion estimation, and sequential fusion estimation. Considering factors such as random variable parameter matrices, multiplicative noise, and nonlinearity, the robust distributed fusion estimation method can guarantee the control performance of the system. Summary of the Invention

[0006] The purpose of this invention is to provide a multi-sensor information fusion target tracking method with a random variable parameter matrix. This method solves the problem that existing multi-sensor information fusion target tracking methods cannot simultaneously handle factors such as random variable parameter matrices, multiplicative noise, measurement loss, and nonlinear functions, which leads to poor robustness of the estimator, insufficient estimation performance of the estimator, and even divergence of the tracking curve.

[0007] The objective of this invention is achieved through the following technical solution:

[0008] A multi-sensor information fusion target tracking method with a random variable parameter matrix includes the following steps:

[0009] Step 1: Establish the following dynamic model of the target being tracked in the multi-sensor target tracking system:

[0010]

[0011] yi,k =λ i,k (B i,k +η i,k C i,k )x k +v i,k

[0012] In the formula, x k+1 To track the target's state information at time k+1; x k To track the target's state information at time k; Let f(x) be the random variable parameter state matrix at time k; k ) is a continuously differentiable nonlinear function; w k The process noise at time k; y i,k Let λ be the measurement output information obtained by the i-th sensor at time k; i,k B is a Bernoulli random variable describing measurement loss. i,k Let C be the measurement matrix of the i-th sensor at time k; i,k Let η be a matrix of appropriate dimension at time k; i,k ν represents the Gaussian white noise of the i-th sensor at time k; i,k Let be the measurement noise of the i-th sensor at time k;

[0013] Step 2: Design the forecaster and estimator structure:

[0014]

[0015]

[0016] In the formula, Let be the one-step prediction value of the target state tracked by the i-th sensor at time k; Let A be the estimated value of the target tracked by the i-th sensor at time k; k for Expectations; B i,k+1 Let be the measurement matrix of the i-th sensor at time k+1; f(x) is a nonlinear function k Updated estimates; For λ i,k Expectations; K i,k+1 y is the estimated gain of the i-th sensor to be designed; i,k+1 This refers to the measurement output information obtained by the i-th sensor at time k+1; in order to process the nonlinear function f(x) k ),exist The Taylor expansion of this part is defined as follows:

[0017]

[0018] in D represents the higher-order terms in a Taylor expansion. i,k E i,k Given a matrix of suitable dimension, and an unknown matrix N. i,k satisfy I is an identity matrix of suitable dimension;

[0019] Step 3: Calculate the upper bound Θ of the one-step prediction error covariance matrix of the i-th sensor at time k+1. i,k+1|k :

[0020]

[0021]

[0022]

[0023]

[0024] In the formula, This indicates taking the expectation of a matrix or function; "∑" is the summation symbol. for Transpose of; for Transpose of; D i,k transpose, For E i,k Transpose of; ξ is a known quantity; i,k It is a constant value. For ξ i,k The inverse; μ1 is a constant. It is the inverse of μ1; express The element in row s and column t; Φ i,k The element in the l-th row and j-th column;

[0025] Step 4: Calculate the estimated gain matrix K of the i-th sensor at time k+1. i,k+1 And the fusion estimation of the tracked target

[0026]

[0027]

[0028]

[0029] In the formula, K i,k+1To estimate the gain matrix; Θ i,k+1|k This is the upper bound of the prediction error covariance; for Transpose of; For B i,k+1 Transpose of; C i,k+1 The transpose of μ; μ2 is a constant. It is the inverse of μ2; For multiplicative noise η i,k The variance; R i,k+1 To measure noise ν i,k+1 The variance;

[0030]

[0031]

[0032]

[0033] In the formula, To fuse the upper bound of the estimated covariance; Θ i,k|k To estimate the upper bound of the error covariance, For Θ i,k|k The reverse; The fusion gain matrix is ​​N; the number of sensors is g. i These are the weighting coefficients; for The reverse;

[0034] Step 5: Place K i,k+1 Substituting into step two, we obtain the state estimate of the target tracked by the i-th sensor at time k+1. Determine whether k+1 reaches the estimated total duration MN. If k+1 < MN, proceed to step six. If k+1 = MN, end the process after calculating the fusion estimate.

[0035] Step 6: Calculate the upper bound of the covariance of the estimation error Θ i,k+1|k+1 :

[0036]

[0037]

[0038] In the formula, I represents an identity matrix of suitable dimension. for Transpose of;

[0039] Let k = k + 1, and proceed to step two until k + 1 = MN is satisfied.

[0040] Compared with the prior art, the present invention has the following advantages:

[0041] 1. This invention proposes a target tracking method with a random variable parameter matrix, which considers the effects of measurement loss, nonlinearity, and multiplicative noise, and designs a recursive estimation method accordingly. A distributed estimation method is employed, and the system is approximated as a linear system using Taylor expansion, utilizing multiple sensors to estimate the tracked target.

[0042] 2. This invention employs an inverse covariance cross-fusion estimation method. Simulation results demonstrate that this method yields more accurate estimation results. Furthermore, compared to common matrix-weighted fusion estimation methods, the method used in this invention has a lower computational burden because it does not require calculating cross-covariance. Attached Figure Description

[0043] Figure 1 This is a flowchart of the multi-sensor information fusion target tracking method with a random variable parameter matrix according to the present invention.

[0044] Figure 2 To track the first component x of the target k,1 A comparison diagram of the actual trajectory and the fused tracking trajectory after passing through the fusion estimator designed in this invention.

[0045] Figure 3 To track the second component x of the target k,2 A comparison diagram of the actual trajectory and the fused tracking trajectory after passing through the fusion estimator designed in this invention.

[0046] Figure 4 To track the first component x of the target k,1 The mean square error of the fusion estimate and x k,1 A comparison of the mean squared errors estimated on the three sensors.

[0047] Figure 5 To track the second component x of the target k,2 The mean square error of the fusion estimate and x k,2 A comparison of the mean squared errors estimated on the three sensors.

[0048] Figure 6 To track the first component x of the target k,1 The fusion estimate of the upper bound of the trace and x k,1 A comparison of the traces of the upper bound estimated on the three sensors.

[0049] Figure 7 To track the second component x of the target k,2 The fusion estimate of the upper bound of the trace and x k,2 A comparison of the traces of the upper bound estimated on the three sensors.

[0050] Figure 8A comparison of the trajectories of the upper bound of the fusion estimation for tracking targets under different probabilities of measurement loss. Detailed Implementation

[0051] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0052] This invention provides a multi-sensor information fusion target tracking method with a random variable parameter matrix, such as... Figure 1 As shown, the method includes the following steps:

[0053] Step 1: Establish the following dynamic model of the target being tracked in the multi-sensor target tracking system:

[0054]

[0055] y i,k =λ i,k (B i,k +η i,k C i,k )x k +v i,k

[0056] In the formula, x k+1 To track the target's state information at time k+1; x k To track the target's state information at time k; y i,k This represents the measurement output information obtained by the i-th sensor at time k. B is the random variable parameter state matrix at time k; i,k Let C be the measurement matrix of the i-th sensor at time k; i,k Let η be a matrix of appropriate dimension at time k; i,k Let the expectation of the i-th sensor at time k be zero and its variance be... Gaussian white noise; w k The expected value at time k is zero and the variance is Q. ω Process noise; ν i,k The expected value of the i-th sensor at time k is zero, and the variance is R. i,k Measurement noise; f(x) k ) is a continuously differentiable nonlinear function; λ i,k A Bernoulli random variable to describe measurement loss;

[0057] Random variable parameter matrix It has the following statistical properties:

[0058]

[0059]

[0060] in Cov(a,b) represents taking the expectation of a matrix or function; Cov(a,b) represents taking the covariance of variables a and b; A k for Expectations for The element in the l-th row and j-th column, for The element in the s-th row and t-th column, The quantity is known;

[0061] Bernoulli random variable λ i,k It has the following statistical properties:

[0062]

[0063]

[0064] Where Prob represents probability; For λ i,k The expected value is between 0 and 1;

[0065] Initial state x0 and B i,k ω k ν i,k η i,k , λ i,k They are all uncorrelated and have the following statistical properties:

[0066]

[0067]

[0068] In the formula, P0 is the expected value of the initial state; P0 is the variance of the initial state.

[0069] definition With virtual noise The transformed system model is as follows:

[0070] x k+1 =A k x k +f(x k )+h k

[0071] Virtual noise h k It has the following statistical characteristics:

[0072]

[0073]

[0074] In the formula, For x k Transpose of; For virtual noise h k The transpose of Q h For virtual noise h k variance; Q ω For process noise w k The variance;

[0075] Step 2: Design the forecaster and estimator structure:

[0076]

[0077]

[0078] In the formula, Let be the one-step prediction value of the target state tracked by the i-th sensor at time k; Let be the estimated value of the target tracked by the i-th sensor at time k; f(x) is a nonlinear function k Updated estimate of K; i,k+1 The estimated gain of the i-th sensor to be designed; in order to handle the nonlinear function f(x) k ),exist The Taylor expansion of this part is defined as follows:

[0079]

[0080] in D represents the higher-order terms in a Taylor expansion. i,k E i,k Given a matrix of suitable dimension, and an unknown matrix N. i,k satisfy I is an identity matrix of suitable dimension;

[0081] Step 3: Calculate the upper bound Θ of the one-step prediction error covariance matrix of the i-th sensor at time k+1. i,k+1|k :

[0082]

[0083]

[0084]

[0085]

[0086] In the formula, “∑” represents the summation symbol; Θi,k+1|k This is the upper bound of the covariance of the one-step prediction error; for Transpose of; for Transpose of; D i,k transpose, For E i,k Transpose of; ξ is a known quantity; i,k constant value For ξ i,k The inverse; μ1 is a constant. It is the inverse of μ1; express The element in row s and column t; Φ i,k The element in the l-th row and j-th column;

[0087] Step 4: Calculate the estimated gain matrix K of the i-th sensor at time k+1. i,k+1 And the fusion estimation of the tracked target

[0088]

[0089]

[0090]

[0091] In the formula, K i,k+1 To estimate the gain matrix; Θ i,k+1|k This is the upper bound of the prediction error covariance; for Transpose of; For B i,k+1 Transpose of; C i,k+1 The transpose of μ; μ2 is a constant. It is the inverse of μ2; For multiplicative noise η i,k The variance; R i,k+1 To measure noise ν i,k+1 The variance;

[0092]

[0093]

[0094]

[0095] In the formula, To fuse the upper bound of the estimated covariance; Θi,k|k To estimate the upper bound of the error covariance, For Θ i,k|k The reverse; The fusion gain matrix; N is a positive integer representing the number of sensors; g i These are the weighting coefficients; for The reverse;

[0096] Step 5: Place K i,k+1 Substituting into step two, we obtain the state estimate of the target tracked by the i-th sensor at time k+1. Determine whether k+1 reaches the estimated total duration MN. If k+1 < MN, proceed to step six. If k+1 = MN, end the process after calculating the fusion estimate.

[0097] Step 6: Calculate the upper bound of the covariance of the estimation error Θ i,k+1|k+1 :

[0098]

[0099]

[0100] In the formula, I represents an identity matrix of suitable dimension. for Transpose of;

[0101] Let k = k + 1, and proceed to step two until k + 1 = MN is satisfied.

[0102] Example:

[0103] The system used in this embodiment has three local sensors and one information fusion center, where x k =[x k, 1x k,2 ] T This indicates the target's status information.

[0104] The system matrix of the three sensors is as follows:

[0105] B 1,k = [0.31 0.38], B 2,k = [0.28 0.25], B 3,k = [0.12 0.15], C 1,k = [0.78 0.76], C 2,k = [0.85 0.87], C 3,k =[1.1 1.2].

[0106] The nonlinear function is as follows:

[0107]

[0108] The other parameters are selected as follows:

[0109] I2 is a 2-dimensional identity matrix, Q w =0.01I2,R 1,k =0.065, R 2,k =0.063, R 3,k =0.062, μ1 = 1, μ2 = 1, D i,k =0.2I²,E i,k =0.2I2, P0 = P i,0|0 =Θ i,0|0 =2I2.

[0110] Simulation results:

[0111] Figure 2 , Figure 3 The actual state trajectories of the two components of the tracked target and the estimated state trajectories after fusion estimator designed in this invention are presented. A comparison of the two curves in the figure shows that the fusion estimator designed in this invention can effectively resist multiplicative noise and obtain more accurate state estimation trajectories.

[0112] Figure 4 , Figure 5 The mean square error trajectories of the fusion estimation of the two components of the tracked target and the mean square error trajectories of the estimation of the three local sensors are presented. A comparison of the four curves in the figure shows that the fusion estimator designed in this invention can achieve a smaller mean square error, and experimental results verify the effectiveness of the proposed method.

[0113] Figure 6 , Figure 7 The traces of the upper bounds of the fusion estimation of the two components of the tracked target and the traces of the upper bounds of the estimation of the three local sensors are given. A comparison of the four curves in the figure shows that the fusion estimator designed in this invention has better accuracy.

[0114] Figure 8 Different probabilities are given The trajectory of the tracked target is estimated by fusion, with an upper bound. Scenario 1: Scenario 2: Scenario 3: By comparing the trajectories of the target fusion estimation upper bound under these three scenarios, it was found that the probability... The larger the upper bound, the smaller the trace.

[0115] In summary, the multi-sensor information fusion target tracking method with random variable parameter matrix proposed in this invention can effectively estimate the target state and has good robustness.

Claims

1. A multi-sensor information fusion target tracking method with a random variable parameter matrix, characterized in that... The method includes the following steps: Step 1: Establish a dynamic model of the target being tracked in the multi-sensor target tracking system. y i,k =λ i,k (B i,k +n i,k C i,k )x k +v i,k In the formula, x k+1 To track the target's state information at time k+1; x k To track the target's state information at time k; Let f(x) be the random variable parameter state matrix at time k; k ) is a continuously differentiable nonlinear function; w k The process noise at time k; y i,k Let λ be the measurement output information obtained by the i-th sensor at time k; i,k B is a Bernoulli random variable describing measurement loss. i,k Let C be the measurement matrix of the i-th sensor at time k; i,k Let be a matrix of appropriate dimension at time k; η i,k ν represents the Gaussian white noise of the i-th sensor at time k; i,k Let be the measurement noise of the i-th sensor at time k; Step 2: Design the forecaster and estimator structure: In the formula, Let be the one-step prediction value of the target state tracked by the i-th sensor at time k; Let A be the estimated value of the target tracked by the i-th sensor at time k; k for Expectations; B i,k+1 Let be the measurement matrix of the i-th sensor at time k+1; f(x) is a nonlinear function k Updated estimates; For λ i,k Expectations; K i,k+1 y is the estimated gain of the i-th sensor to be designed; i,k+1 This represents the measurement output information obtained by the i-th sensor at time k+1; To handle nonlinear functions f(x) k ),exist The Taylor expansion of this part is defined as follows: in D represents the higher-order terms in a Taylor expansion. i,k E i,k Given a matrix of suitable dimension, and an unknown matrix N. i,k satisfy I is an identity matrix of suitable dimension; Step 3: Calculate the upper bound Θ of the one-step prediction error covariance matrix of the i-th sensor at time k+1. i,k+1|k : In the formula, This indicates taking the expectation of a matrix or function; "∑" is the summation symbol. for Transpose of; for Transpose of; D i,k transpose, For E i,k Transpose of; ξ is a known quantity; i,k It is a constant value. For ξ i,k The inverse; μ1 is a constant. It is the inverse of μ1; express The element in row s and column t; Φ i,k The element in the l-th row and j-th column; Step 4: Calculate the estimated gain matrix K of the i-th sensor at time k+1. i,k+1 And the fusion estimation of the tracked target In the formula, K i,k+1 To estimate the gain matrix; Θ i,k+1|k This is the upper bound of the prediction error covariance; for Transpose of; For B i,k+1 Transpose of; C i,k+1 The transpose of μ; μ2 is a constant. It is the inverse of μ2; For multiplicative noise η i,k The variance; R i,k+1 To measure noise ν i,k+1 The variance; In the formula, To fuse the upper bound of the estimated covariance; Θ i,k|k To estimate the upper bound of the error covariance, For Θ i,k|k The reverse; The fusion gain matrix is ​​N; the number of sensors is g. i These are the weighting coefficients; for The reverse; Step 5: Place K i,k+1 Substituting into step two, we obtain the state estimate of the target tracked by the i-th sensor at time k+1. Determine whether k+1 reaches the estimated total duration MN. If k+1 < MN, proceed to step six. If k+1 = MN, end the process after calculating the fusion estimate. Step 6: Calculate the upper bound of the covariance of the estimation error Θ i,k+1|k+1 : In the formula, I represents an identity matrix of suitable dimension. for Transpose of; Let k = k + 1, and proceed to step two until k + 1 = MN is satisfied.

2. The multi-sensor information fusion target tracking method with a random variable parameter matrix according to claim 1, characterized in that... The It has the following statistical properties: Where Cov(a,b) represents the covariance of variables a and b; for The element in the l-th row and j-th column, for The element in the s-th row and t-th column, The quantity is known.

3. The multi-sensor information fusion target tracking method with a random variable parameter matrix according to claim 1, characterized in that... The λ i,k It has the following statistical properties: Where Prob represents probability.

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