Maneuvering target tracking method based on multi-model filtering
By introducing feedback learning terms and optimizing the Kalman gain matrix in the multi-model filtering method, the problems of slow model switching speed and insufficient estimation accuracy in the prior art are solved, and a higher maneuvering target tracking accuracy is achieved.
Patent Information
- Application Number
- CN202411201897.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-08-29
- Publication Date
- 2025-06-13
AI Technical Summary
The existing interactive multi-model filtering method has a slow switching speed, and the estimation accuracy still needs to be improved.
A maneuver target tracking method based on multi-model filtering is proposed. By establishing the state equation and measurement equation of the tracking system, multi-model interaction is carried out, parallel filtering is carried out, feedback learning terms are introduced, Kalman gain matrix is optimized, and model probability update and state estimation fusion are performed.
It improves the overall performance of the filter and significantly improves the position and speed estimation accuracy of the maneuvering target, especially in noisy environments, and has higher tracking accuracy.
Smart Images
Figure CN120143601A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a maneuvering target tracking method based on multi-model filtering, belonging to the technical field of aircraft control. Background Art
[0002] A maneuvering target refers to a target with a continuously changing motion form. For example, the target changes from uniform motion to accelerated motion, or from linear motion to turning motion.
[0003] As a powerful adaptive estimation algorithm, multi-model estimation is widely used in the tracking of maneuvering targets due to its unique structure, ability to handle parameter uncertainties and model changes, and ability to decompose complex problems into simpler sub-problems. In multi-model estimation, various possible system models are combined together according to different characteristics exhibited by the system to form alternative system models. Based on the selected different system models, a set of filters are used to obtain model-conditioned estimates, and the overall state estimate is a certain form of combination of these model estimates.
[0004] The interacting multiple model filtering method has been proven to be one of the most cost-effective hybrid state estimation schemes. This interacting multiple model filtering method requires multiple filters, each corresponding to a different maneuvering state of the target. Therefore, this algorithm can estimate the state of a system with sudden changes. In the classical interacting multiple model filtering algorithm, the model switching speed is slow, and the final fusion estimate is only used as an output without being fed back to the next moment for state estimation.
[0005] However, in the existing interacting multiple model filtering methods, the model switching speed is slow, and the estimation accuracy still needs to be improved.
[0006] Therefore, it is necessary to conduct a more in-depth study on the existing multi-model filtering methods to solve the above problems. Summary of the Invention
[0007] To overcome the above problems, the inventor of the present invention has conducted in-depth research and proposed a maneuvering target tracking method based on multi-model filtering, including:
[0008] S1. Establish the state equation and measurement equation of the tracking system;
[0009] S2. Perform multi-model interaction according to the interacting multiple model filtering method;
[0010] S3. Perform parallel filtering, use the current moment feedback learning term as a reference item, and obtain the state estimates and error covariance matrices of different models at the next moment;
[0011] S4. Perform model probability update;
[0012] S5. Fusion of the state estimates of each model is performed based on the updated probability to obtain the target state and covariance matrix, and the feedback learning term for the next moment is obtained based on the target state and covariance matrix;
[0013] S6. Repeat S2 - S5 for multiple iterations to achieve tracking of the target at subsequent moments.
[0014] In a preferred embodiment, in S1, the state equation of the tracking system is:
[0015] x(k + 1) = Fx(k) + GW(k)
[0016] where k is the current moment, x(k) represents the motion state vector of the target at moment k, F is the system state transition matrix, G is the system noise driving matrix, and W(k) is the input noise.
[0017] In a preferred embodiment, the measurement equation of the tracking system is:
[0018] Z(k) = h[x(k)] + V(k)
[0019] where Z(k) is the observed quantity of the target at moment k, h is the non - linear observation function, and V(k) is the input noise.
[0020] In a preferred embodiment, in S3, the feedback learning term is obtained based on the final fusion estimate of the traditional interacting multiple model filtering.
[0021] In a preferred embodiment, in parallel filtering, the state estimate of the model at the next moment is expressed as:
[0022]
[0023] where, represents the optimal estimate of the motion state vector of the j - th model at moment k, represents the estimate of the motion state vector of the j - th model at moment k - 1 for moment k, represents the Kalman gain matrix of the j - th model at moment k, z k represents the observed quantity of the target at moment k, represents the observation matrix of the j - th model at moment k, represents the gain parameter of the feedback learning term of the j - th model at moment k, represents the feedback learning term of the j - th model at moment k.
[0024] In a preferred embodiment, in parallel filtering, the error covariance matrix of the model at the next moment is expressed as:
[0025]
[0026] Among them, is the error covariance matrix of the j-th model at time k, I represents the identity vector, represents the estimation of the error covariance matrix of the j-th model at time k - 1 for time k, represents the feedback learning term of the j-th model at time k.
[0027] In a preferred embodiment, in parallel filtering, the feedback learning term is used to correct the Kalman gain matrix which is expressed as:
[0028]
[0029] Among them, represents the covariance matrix of the j-th model at time k, represents the observation noise variance of the j-th model at time k.
[0030] The beneficial effects of the present invention include:
[0031] (1) By introducing the feedback learning term and using the final fusion estimation as a reference term for the state estimation at the next moment, this mechanism enables the fusion estimation not only to be the output at the current moment but also to provide guidance for the estimation at subsequent moments, improving the overall performance of the filter;
[0032] (2) Redesigning the Kalman gain matrix further optimizes the estimation process;
[0033] (3) There are significant improvements in both the position estimation and speed estimation accuracy of maneuvering targets, especially in a noisy environment where the tracking accuracy is higher. BRIEF DESCRIPTION OF THE DRAWINGS
[0034] Figure 1 shows a schematic flowchart of a maneuvering target tracking method based on multi-model filtering according to a preferred embodiment of the present invention;
[0035] Figure 2 shows the simulation diagrams of the tracking trajectories of Example 1 and Example 1 and the true target trajectory;
[0036] Figure 3 shows the root mean square error results of the positions of Example 1 and Example 1;
[0037] Figure 4 shows the root mean square error results of the speeds of Example 1 and Example 1. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0038] The present invention will be further described in detail below with reference to the drawings and embodiments. Through these descriptions, the features and advantages of the present invention will become clearer and more definite.
[0039] As used herein, the term "exemplary" means "serving as an example, embodiment, or illustration". Any embodiment described herein as "exemplary" is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings are not necessarily drawn to scale unless otherwise specified.
[0040] A maneuvering target tracking method based on multi-model filtering provided by the present invention, as Figure 1 shown, includes:
[0041] S1. Establish the state equation and measurement equation of the tracking system;
[0042] S2. Perform multi-model interaction according to the interacting multiple model filtering method;
[0043] S3. Perform parallel filtering, use the feedback learning term at the current moment as a reference item, and obtain the state estimate and error covariance matrix of the next moment for different models;
[0044] S4. Update the model probabilities;
[0045] S5. Based on the updated probabilities, fuse the state estimates of each model to obtain the target state and covariance matrix, and obtain the feedback learning term at the next moment based on the target state and covariance matrix;
[0046] S6. Repeat S2 to S5 for multiple iterations to achieve the tracking of the target at subsequent moments.
[0047] In S1, the state equation of the tracking system is:
[0048] x(k + 1) = Fx(k) + GW(k)
[0049] where k is the current moment, x(k) represents the motion state vector of the target at moment k, F is the system state transition matrix, G is the system noise driving matrix, and W(k) is the input noise.
[0050] The measurement equation of the tracking system is:
[0051] Z(k) = h[x(k)] + V(k)
[0052] where Z(k) is the observed quantity of the target at moment k, h is the non-linear observation function, and V(k) is the input noise.
[0053] Preferably, the input noises W(k) and V(k) are both white noises subject to Gaussian distribution with a mean of 0.
[0054] In S2, through multi-model interaction, obtain the optimal state estimate of each model at moment k - 1 and covariance matrix In the present invention, this process is exactly the same as the multi-model interaction in traditional multi-model filtering and will not be elaborated in the present invention.
[0055] The parallel filtering process means that within each time step, for each model, state prediction and update are independently performed. This parallel processing method allows the filter to simultaneously consider the influence of multiple models on the system state, thereby improving the accuracy and robustness of the estimation.
[0056] According to the present invention, in the parallel filtering process, the unscented Kalman filter (UKF) is adopted. The unscented transformation method can more effectively handle nonlinear problems and has higher estimation accuracy and stability compared to the traditional extended Kalman filter (EKF).
[0057] The unscented Kalman filter is a commonly used filtering method in the art. In the present invention, the specific process of filtering will not be elaborated.
[0058] Different from the traditional interacting multiple model filtering method, in the present invention, a feedback learning term is set in the parallel filtering process.
[0059] The said feedback learning term is obtained based on the final fusion estimation of the traditional interacting multiple model filtering. The inventor found that in the traditional interacting multiple model filtering method, the final fusion estimation is only used as an output. However, the final fusion estimation often has higher estimation accuracy than the estimations depending on each mode. Using it as a reference for the state estimation of each model can more accurately estimate the state of different models at the next moment.
[0060] Furthermore, in the present invention, no limitation is imposed on the initial setting value of the feedback learning term, and those skilled in the art can freely set it according to actual needs.
[0061] Furthermore, after introducing the feedback learning term, the state estimation of the model at the next moment is expressed as:
[0062]
[0063] Wherein, represents the optimal estimation of the motion state vector of the j-th model at time k, represents the estimation of the motion state vector of the j-th model at time k - 1 for time k, represents the Kalman gain matrix of the j-th model at time k, z k represents the observed value of the target at time k, represents the observation matrix of the j-th model at time k, represents the gain parameter of the feedback learning term of the j-th model at time k, represents the feedback learning term of the j-th model at time k.
[0064] Different from the traditional unscented Kalman filter, preferably, a feedback learning term is also used to correct the Kalman gain matrix which is expressed as:
[0065]
[0066] wherein, represents the covariance matrix of the j-th model at the k-th moment, represents the observation noise variance of the j-th model at the k-th moment.
[0067] By correcting the Kalman gain matrix through the feedback learning term, the estimation process is further optimized and the estimation accuracy is improved.
[0068] According to the present invention, the error covariance matrix of the model at the next moment is expressed as:
[0069]
[0070] wherein, is the error covariance matrix of the j-th model at the k-th moment, I represents the unit vector, represents the estimation of the error covariance matrix of the j-th model at the k-th moment from the (k - 1)-th moment, represents the feedback learning term of the j-th model at the k-th moment.
[0071] In the present invention, the processes of steps S4 to S6 are the same as those of the traditional interacting multiple model filtering method and will not be elaborated herein.
[0072] It should be understood that various forms of the flow shown above can be used, steps can be reordered, added or deleted. For example, the steps recorded in the disclosure of the present invention can be executed in parallel, sequentially or in a different order, as long as the desired results of the technical solution disclosed in the present invention can be achieved, and no limitation is imposed herein.
[0073] Embodiment
[0074] Embodiment 1
[0075] A simulation experiment is carried out for maneuvering target tracking based on multiple model filtering, including:
[0076] S1. Establish the state equation and measurement equation of the tracking system;
[0077] S2. Perform multiple model interactions according to the interacting multiple model filtering method;
[0078] S3. Perform parallel filtering, use the current moment feedback learning term as a reference item, and obtain the state estimation and error covariance matrix of different models at the next moment;
[0079] S4. Update the model probability;
[0080] S5. Based on the updated probability, fuse the state estimates of each model to obtain the target state and covariance matrix, and obtain the feedback learning term at the next moment based on the target state and covariance matrix;
[0081] S6. Repeat S2 - S5 for multiple iterations to achieve the tracking of the target at subsequent moments.
[0082] In S1, the state equation of the tracking system is:
[0083] x(k + 1) = Fx(k) + GW(k)
[0084] The measurement equation of the tracking system is:
[0085] Z(k) = h[x(k)] + V(k)
[0086] In S3, after introducing the feedback learning term, the state estimate of the model at the next moment is expressed as:
[0087]
[0088] The error covariance matrix of the model at the next moment is expressed as:
[0089]
[0090] The feedback learning term is used to correct the Kalman gain matrix which is expressed as:
[0091]
[0092] During the simulation process, the target acceleration is modeled as a discrete - time three - state homogeneous Markov chain, and the value set of the acceleration is {(0,0) T ,(5,10) T ,(-5,-10) T};
[0093] In S1, the parameters are set as:
[0094]
[0095] where T is the sampling time interval, and the sampling time interval is taken as 1 during the simulation process; I 2 is the two - dimensional identity matrix; represents the Kronecker product.
[0096] The process noise w k is modeled as zero - mean Gaussian white noise and has a known covariance matrix as follows:
[0097]
[0098] where λ is the process noise intensity, and λ is taken as 2 in the simulation;
[0099] The measurement equation of the sensor includes distance and azimuth, that is
[0100]
[0101] where: v k is zero-mean Gaussian white noise, and the covariance matrix
[0102] R = diag(40 2 , 0.002 2 ).
[0103] In addition, the probability transition matrix of the Markov chain is taken as
[0104]
[0105] The initial state of the target is x 0 = (5000, -45, 500, 10) T , and the target movement time is 100 s.
[0106] During the simulation process, the root mean square error of position and velocity is used as the performance index for comparison. For example, the position and root mean square error in the X direction at time k are defined as
[0107]
[0108] where and respectively represent the true state of the target movement in the X direction and the filtered estimated state obtained from the i-th Monte Carlo run at time k; K represents the number of Monte Carlo runs, and during the simulation process, K = 100 is set.
[0109] Comparative Example 1
[0110] The same experiment as in Example 1 is carried out, except that the traditional interacting multiple model filtering method is used.
[0111] Comparing the simulation results of Example 1 and Comparative Example 1, as Figures 2 - 4 shown, where Figure 2 shows the simulation diagram of the tracking trajectory and the target true trajectory. It can be seen from the figure that both Example 1 and Comparative Example 1 can accurately track the maneuvering target with two turns.
[0112] Figure 3 shows the root mean square error result of the position, Figure 4The root mean square error results of the speed are shown. It can be seen from the figure that in the case where the tracking environment contains noise, the tracking accuracy in Embodiment 1 is significantly better than that in Comparative Example 1.
[0113] The present invention has been described in conjunction with preferred embodiments, but these embodiments are merely exemplary and only serve an illustrative purpose. On this basis, various substitutions and improvements can be made to the present invention, and these all fall within the protection scope of the present invention.
Claims
1. A maneuvering target tracking method based on multi-model filtering, characterized in that: include: S1. Establish the state equation and measurement equation of the tracking system; S2, performing multi-model interaction according to the interactive multi-model filtering method; S3, perform parallel filtering, use the current moment feedback learning item as a reference item, and obtain the state estimation and error covariance matrix of different models at the next moment; S4, updating the model probability; S5. Based on the updated probability, the state estimation of each model is integrated to obtain the target state and covariance matrix, and the feedback learning item at the next moment is obtained based on the target state and covariance matrix; S6. Repeat S2 to S5 for multiple iterations to achieve tracking of the target at subsequent moments.
2. The method for tracking a maneuvering target based on multi-model filtering according to claim 1, characterized in that: In S1, the state equation of the tracking system is: x(k+1)=Fx(k)+GW(k) Where k is the current moment, x(k) represents the motion state vector of the target at moment k, F is the system state transfer matrix, G is the system noise driving matrix, and W(k) is the input noise.
3. The method for tracking a maneuvering target based on multi-model filtering according to claim 1, characterized in that: The measurement equation of the tracking system is: Z(k)=h[x(k)]+V(k) Among them, Z(k) is the observation value of the target at time k, h is the nonlinear observation function, and V(k) is the input noise.
4. The method for tracking a maneuvering target based on multi-model filtering according to claim 1, characterized in that: In S3, the feedback learning item is obtained based on the final fusion estimation of traditional interactive multi-model filtering.
5. The method for tracking a maneuvering target based on multi-model filtering according to claim 4, characterized in that: In parallel filtering, the state estimation of the model at the next moment is expressed as: in, represents the optimal estimate of the motion state vector of the jth model at time k, represents the j-th model's estimate of the motion state vector at time k at time k-1, represents the Kalman gain matrix of the jth model at time k, z k represents the observation of the target at time k, represents the observation matrix of the jth model at time k, represents the gain parameter of the feedback learning item of the j-th model at time k, Represents the feedback learning item of the j-th model at time k.
6. The method for tracking a maneuvering target based on multi-model filtering according to claim 4, characterized in that: In parallel filtering, the error covariance matrix of the model at the next moment is expressed as: in, is the error covariance matrix of the jth model at time k, I represents the unit vector, represents the estimation of the error covariance matrix of the jth model at time k-1 for time k, Represents the feedback learning item of the j-th model at time k.
7. The method for tracking a maneuvering target based on multi-model filtering according to claim 4, characterized in that: In parallel filtering, the Kalman gain matrix is adjusted by using feedback learning terms It has been corrected and expressed as: in, represents the covariance matrix of the jth model at time k, represents the observation noise variance of the j-th model at time k.