Feedback adaptive IMM filter for heavy tail noise
By introducing feedback adaptive structure and variational Bayesian method into the IMM filter, processing process noise and measuring noise are solved, and the performance degradation of IMM filters and uncertain model probability in heavy tail noise environments is achieved, and a more stable and accurate filtering effect is achieved.
Patent Information
- Application Number
- CN202411551775.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-01
- Publication Date
- 2025-02-25
AI Technical Summary
When handling heavy tail noise, the performance of the IMM filter is degraded and the model probability is uncertain, and the process noise is not effectively processed.
A feedback adaptive IMM filter is proposed, and the adaptive processing of process noise and measurement noise is realized through preliminary fusion, Student-t distribution assumption, variational Bayesian method and maneuverability energization, and the feedback is applied to the IMM framework.
In the nonlinear Markov system, the stability and accuracy of the IMM filter are improved, ensuring stable filtering effect under different degrees of heavy tail noise, and improving the accuracy of model probability.
Smart Images
Figure CN119519662A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the field of state estimation, and in particular to a feedback adaptive IMM filter for heavy-tail noise. Background Art
[0002] State estimation is a key step in the fields of maneuvering target tracking, radar positioning, information fusion, etc. IMM filters have been proven to be able to effectively track maneuvering and non-maneuvering targets using different filter models. However, the accuracy of state estimation methods such as IMM filters depends largely on the prior knowledge of system model parameters and noise model parameters. However, the prior information of maneuvering targets is limited, so the system requires adaptive filtering. Variational Bayesian inference (VB) is a closed-loop iterative method that can transform complex posterior probability density function inference problems into optimization problems between conjugate prior distributions, and is used to estimate noise covariance and system states. However, the heavy-tailed noise generated by tracking maneuvering targets using unreliable sensors can cause the filtering results to jitter or even diverge.
[0003] A large number of robust filters have been proposed to solve the problem of filtering with heavy-tailed noise. The basic robust filtering method assumes that both process noise and measurement noise are Student-t distributed, and uses the VB method to solve the scale matrix and degree of freedom parameters. The posterior probability density function (PDF) is approximately Student-t distributed, thereby solving the problem of heavy-tailed noise. However, the above methods do not consider the impact of system nonlinearity and rapid target maneuvers.
[0004] In order to solve the problem of target flexibility and unreliability of measurement system in the filtering process, heavy-tail noise filtering under jump Markov system has become a research focus. A filtering method with Huber function as the sub-filter is proposed in the IMM framework. The Huber filter (HKF) that minimizes the combined 1 and 2 norms is robust to heavy-tail processes and measurement noise. However, HKF is difficult to solve, resulting in poor IMM fusion effect. The heavy-tail characteristic of student-t distribution is a good way to solve outliers. The filter derived from the state vector and the scale matrix through VB approximation is embedded in the IMM framework, which can solve the target flexibility and handle the heavy-tail noise of the measurement system. The latest method adopts an interactive multi-model fusion framework to promote the collaborative work of the cubature Kalman filter with maximum correlation coefficient (VBMCCKF) and the cubature Kalman filter with maximum correlation criterion (MCCKF) to achieve better results. This solves the coupling problem of estimating the noise covariance matrix and suppressing outliers. The above method uses an IMM filter to perform adaptive filtering in a Markov system containing heavy-tail noise. It only focuses on the handling of target maneuverability and measurement inaccuracy, without handling process noise. It only applies the IMM framework but does not improve the IMM framework against heavy-tail noise. Summary of the invention
[0005] 1. Technical issues to be resolved
[0006] In view of the deficiencies of the prior art, the present invention provides a feedback adaptive IMM filter for heavy-tail noise, which solves the problems raised in the above background technology.
[0007] (II) Technical solution
[0008] In order to achieve the above-mentioned purpose, the present invention specifically adopts the following technical solutions:
[0009] A feedback adaptive IMM filter for heavy-tail noise specifically comprises the following steps:
[0010] S1: Perform a preliminary fusion of the previous estimation results to obtain the initial value of each sub-filter; the sub-filters are combined with the target maneuverability for cubature Kalman filtering and fused into an interactive prediction process;
[0011] S2: Assuming that the process noise and measurement noise conform to the Student-t distribution, the variational inference method is used to estimate the measurement noise and error covariance matrix;
[0012] S3: Based on the inference of process noise and measurement noise, the maneuverability of the target is estimated by combining the measurement prediction residual, and the maneuverability is quantified to realize adaptive filtering.
[0013] S4: Update the model probabilities of each sub-filter of the IMM filtering algorithm in combination with the maneuverability, so that the interactive multi-model filtering algorithm has a more accurate fusion result.
[0014] Furthermore, the preliminary fusion formula of the S1 neutron filter is:
[0015]
[0016]
[0017] where each sub-filter mixture state estimate is and the error covariance matrix is the estimated probability of transferring from model i to model j at time k-1, This is the initial fusion result.
[0018] Filter estimate based on k-1 time and the corresponding error covariance matrix The calculation generates volume points, namely:
[0019]
[0020] is the i-th volume point estimated at time k-1, with a total of 2n volume points, where n represents the dimension of the state vector. i represents a unit vector with 1 at the i-th position and 0 elsewhere.
[0021] Calculate the interactive prediction results under the influence of the target maneuverability:
[0022]
[0023] in, is the state and error covariance matrix obtained by one-step prediction, Indicates the difference between the measured value and the predicted value. K k Depend on and To obtain, and Represents mobility performance Processed system noise covariance matrix and measurement noise covariance matrix.
[0024] Furthermore, the process noise vector w in S2 k and the observation noise vector v k All assume Student-t distribution:
[0025]
[0026] Where St(·; μ,∈,θ) represents the Student-tPDF with mean μ, scale matrix ∈, and degree of freedom parameter θ. β and γ are the degree of freedom parameters, Q k and R k is the scaling matrix of system noise and measurement noise. j (·) represents the probability density function of each variable at the time of model j, j∈N, N={1,2,...,N} is a finite set of models, where j is based on the probability transfer matrix However, since the Student-t PDF is not strictly closed, the closed solution of the posterior PDF cannot be solved. Two integral variables λ and ξ are introduced to convert the Student-t distribution model into a collection of Gaussian distributions. Therefore, the one-step prediction PDF and likelihood PDF are represented by Gaussian sets. For the selection of the above parameters, the variational Bayes method is used to adaptively estimate these parameters. According to the principle of the VB method, it is necessary to find the conjugate prior distribution of the unknown quantity to ensure that the posterior distribution has the same form as the prior distribution of the unknown parameter.
[0027] Furthermore, in S3, the measurement prediction residual is first calculated Combined with the change of noise, the maneuverability of the final tracking target is obtained.
[0028]
[0029] Among them, χ k ∈(0,1] is used to adjust the strength of the scale matrix and the factors affecting mobility. and is the process noise covariance matrix and measurement noise covariance matrix after maneuverability processing, and the feedback effect IMM framework.
[0030] Furthermore, the model probability update in S4 is to calculate the probability that the target is in motion model j at time k. Right now:
[0031]
[0032] in is the model likelihood function, where maneuverability is used in calculating the likelihood function
[0033] (III) Beneficial effects
[0034] Compared with the prior art, the present invention provides a feedback adaptive IMM filter for heavy-tail noise, which has the following beneficial effects:
[0035] In order to solve the problem of performance degradation and model probability uncertainty caused by the heavy-tail process and measurement noise in the IMM algorithm under nonlinear Markov system (JMS), we propose a feedback adaptive IMM filter for heavy-tail noise. The first layer: the initial fused state is pre-filtered with the participation of maneuverability. The second layer: based on the pre-filtering results, the characteristics of Student-t distribution and variational Bayes method are used to infer the system state, degree of freedom parameters, scale matrix, and target maneuverability parameters. The target maneuverability feedback acts on model probability calculation and pre-filtering.
[0036] 1. To address the problem that the adaptive parameters calculated using the variational method cannot be combined with the IMM framework, we designed a two-layer adaptive feedback structure. The variational estimation results are fed back to the IMM framework for prediction, ensuring a stable filtering effect under different degrees of heavy-tailed noise.
[0037] 2. To address the problem of inaccurate filter model selection when the IMM filter tracks maneuvering targets, we use process noise and measurement noise with adaptive capabilities to quantify maneuvering performance parameters and apply them to the model probability update stage to obtain more accurate model probabilities. BRIEF DESCRIPTION OF THE DRAWINGS
[0038] Figure 1 It is a schematic diagram of a feedback adaptive IMM filter for heavy-tail noise of the present invention;
[0039] Figure 2 It is a structural block diagram of the method of the present invention;
[0040] Figure 3 The present invention measures the calculation method of the prediction residual. DETAILED DESCRIPTION
[0041] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0042] Example
[0043] like Figure 1-3As shown, an embodiment of the present invention proposes a feedback adaptive IMM filter for heavy-tail noise. The main body of the filter is the IMM method, and the three sub-filters are cubature Kalman filters. The variational method is used to dynamically estimate the noise and target maneuverability, and the feedback acts on the IMM framework. The maneuverability of the target is quantified by measuring the changes in the prediction residual combination process and the measurement noise. The performance parameters accurately adjust the model probability and affect the pre-filtering results. The structure of variational Bayesian estimation and feedback maneuverability effectively improves the IMM framework to deal with the flexible movement of the target and the heavy-tail noise problem.
[0044] S101, calculating the initial state of each sub-filter in this cycle according to the previous fusion state result and model probability;
[0045] The formula for calculating the mixing probability is:
[0046]
[0047] where c j is the normalization constant, is the probability that the model is i at time k-1, is the estimated probability of transferring from model i to model j at time k-1.
[0048] According to the variational Bayesian approximation method, the components of the state space Θ = {x, Σ, R, σ, v} are independent, and the joint prior probability density function at time k-1 can be expressed as a single summation term approximation:
[0049]
[0050] The noise degree of freedom parameters based on the weighted Kullback-Leibler (KL) divergence property matching are as follows:
[0051]
[0052] Each sub-filter mixture state is estimated and the error covariance matrix The initialization calculation formula is as follows:
[0053]
[0054] in and are the state estimate and error covariance matrix of the i-th model filter at time k-1 respectively.
[0055] S102, each sub-filter combines the target maneuverability with the cubature Kalman filter to perform interactive prediction, including:
[0056] S1021: The mixed initial state and error covariance matrix obtained by initialization cannot cope with nonlinear situations and lack stability. We take 2n volume points for prediction processing and receive feedback of the target maneuvering parameters to implement the parameters obtained by the variational Bayesian method to act on the IMM framework for adaptive filtering. The process of maneuvering parameter processing and measurement noise is as follows:
[0057]
[0058] in and Represents mobility performance The processed system noise covariance matrix and measurement noise covariance matrix. The adaptive principle of process noise and measurement noise on volume point filtering is similar to Kalman filtering.
[0059] S1022: Take the posterior probability of the previous moment to calculate the volume point
[0060] Filter estimate based on k-1 time and the corresponding error covariance matrix The calculation generates volume points, namely:
[0061]
[0062] is the i-th volume point estimated at time k-1, with a total of 2n volume points, where n represents the dimension of the state vector. i represents a unit vector with 1 at the i-th position and 0 elsewhere.
[0063] S1023: One-step prediction
[0064] Using the above points to make a one-step forecast, calculate the mean after one-step forecast and the corresponding error covariance matrix, that is:
[0065]
[0066] S1024: Take the current moment prior (predicted value) to calculate the volume point
[0067] According to the prediction and corresponding error covariance matrix calculated by the above formula, the predicted volume point is calculated again, that is:
[0068]
[0069] S1025: Measurement Update
[0070] In obtaining measurement information k After that, the estimated value is calculated using the new volume point, the Kalman coefficient is calculated to determine the proportional relationship between the predicted value and the measured value, and the filtering calculation is updated, that is:
[0071]
[0072] After the interactive prediction process, the state estimates and covariances of each model at the previous moment are combined with the state transfer matrix, the model probability of each filter, and the model mixing probability, and finally the mixed state estimates and mixed covariance matrices required for the next step of each model filtering are calculated. The mixed result is used as the initial output result of the IMM filter for volume point selection, and the adaptive filtering is performed in combination with the maneuvering parameters. The weighted KLD approximation is used to infer the mixed process and measurement noise parameters to prepare for variational inference. This operation receives the parameters fed back by the variational Bayesian estimation and applies them to the IMM filtering framework.
[0073] S103, assuming that the process noise and measurement noise conform to the Student-t distribution, use the variational method to infer the noise state;
[0074] The output result of the interactive prediction is used as the initial value of the fusion output, which is the state input Covariance The purpose of the fusion output step is to pass the posterior probability density function p j (Θ k |z 1:k )calculate However, since the parameters such as the scale matrix to be solved are coupled and unknown, it is impossible to obtain an analytical solution. We can obtain the scale matrix and degree of freedom parameters through variational methods.
[0075] Based on the mean field theorem, the joint posterior probability density function of unrelated variables can be decomposed into the form of probability density product, and the approximate value of the posterior probability density function is expressed as:
[0076] Q j (Φ k |z 1:k )=q j (x k )q j (Σ k )q j (R k )q j (σ k )q j (v k )q j (λ k )q j (ξ k ) (42)
[0077] Use the method of minimizing KL divergence to calculate the posterior probability density function p j (Θ k |z1:k ) is an approximate value of .
[0078]
[0079] Among them, p j (Θ k |z 1:k ) is the posterior probability density function of the model at time j. The optimal solution is:
[0080]
[0081] S104, inferring the maneuverability of the target using the change of noise;
[0082] z k is the measured value at time k, and the state value obtained by interactive prediction Then the influencing factor of maneuverability under model j is expressed as: The result of N fixed-point iterations in variational inference can roughly represent the changes in process noise and measurement noise. We combine the influencing factors of maneuverability with the changes in noise to derive the maneuverability of the final tracking target.
[0083]
[0084] Among them, χ k ∈(0,1] is used to adjust the strength of the scale matrix and the factors affecting mobility. and is the process noise covariance matrix and measurement noise covariance matrix after maneuverability processing, and the feedback effect IMM framework.
[0085] S105, calculating the likelihood function of each model according to the target maneuverability;
[0086] Model probability update is to calculate the probability that the target is in motion model j at time k Right now:
[0087]
[0088] in is the model likelihood function, lnp j (z k ∣z 1:k-1 ) is rewritten as lnp j (z k ∣z 1:k-1 )=L(Φ)+KLD(Φ‖p j (Θ|z 1:k )), L(Φ) is the lower bound of the function. Since the second term on the right side of the above equation is minimized through iteration of VB reasoning, Can be Calculated.
[0089]
[0090]
[0091] S106, each sub-filter fuses and outputs a state estimation result;
[0092] Fusion output refers to the calculation of the fusion estimation value and the fusion estimation error covariance matrix at time k based on the output of each sub-filter. The specific calculation formula is as follows:
[0093]
Claims
1. A feedback adaptive IMM filter for heavy-tail noise, characterized in that: Specifically include the following steps: S1: Improve the IMM filter structure, apply the estimation of the target state maneuverability to the input interaction and model filtering stages, and merge them into an interactive prediction process; S2: Assuming that the process noise and measurement noise conform to the Student-t distribution, the variational inference method is used to estimate the measurement noise and error covariance matrix; S3: Based on the inference of process noise and measurement noise, the maneuverability of the target is estimated by combining the measurement prediction residual, and the maneuverability is quantified to realize adaptive filtering. S4: Update the model probabilities of each sub-filter of the IMM filtering algorithm in combination with the maneuverability, so that the interactive multi-model filtering algorithm has a more accurate fusion result.
2. The filtering method according to claim 1 is characterized in that: The target maneuverability in S1 acts on the model prediction stage in the IMM filtering framework. The model prediction stage of the present invention uses cubature Kalman filtering to form a preliminary prediction result. The formula for the target maneuverability is: and is the process noise and measurement noise processed by the maneuverability, is the volume point; It is a process quantity for estimating the error covariance matrix and the measurement covariance matrix.
3. The filtering method according to claim 1 is characterized in that: The formula for estimating the covariance matrix of process noise and measurement noise in S2 is: Where St(·; μ,∈,θ) represents the Student-tPDF with mean μ, scale matrix ∈, and degree of freedom parameter θ; β and γ are the degree of freedom parameters, Q k and R k is the scale matrix of system noise and measurement noise; p j (·) represents the probability density function of each variable at the time j of the model, j∈N, N={1,2,...,N} is a finite set of models, where j is based on the probability transfer matrix Obtain.
4. The filtering method according to claim 1 is characterized in that: The quantification method of the target maneuverability in S3 is: z k is the measured value at time k, and the state value obtained by interactive prediction The influencing factor of maneuverability under the j model is expressed as χ k ∈(0,1] is used to adjust the scale matrix and the strength of the factors affecting maneuverability, the error covariance scale matrix Noise covariance matrix 5. The filtering method according to claim 1 is characterized in that: The formula for updating the model probability method based on maneuverability in S4 is: and is the process noise covariance matrix and measurement noise covariance matrix after maneuverability processing, where is the model likelihood function, lnp j (z k ∣z 1:k-1 ) is rewritten as lnp j (z k ∣z 1:k-1 )=L(Φ)+KLD(Φ‖p j (Θ|z 1:k )), L(Φ) is the lower bound of the function. The probability that the target is in motion model j