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CN-122001336-A - Distributed particle filtering algorithm based on Gaussian mixture and Gossip fusion

CN122001336ACN 122001336 ACN122001336 ACN 122001336ACN-122001336-A

Abstract

The invention discloses a distributed particle filter algorithm based on Gaussian mixture and Gossip fusion, which relates to the technical field of distributed state estimation, and comprises the steps that a sensor node acquires local posterior distribution through local particle filter, based on Gossip protocol, the node exchanges full statistics of GMM with a neighbor node selected randomly, and iteration fusion of the GMM is realized through weighted mixture importance sampling; and finally, optimizing the global state estimation result through a posterior correction step. The invention replaces the transmission of original particles by exchanging only full statistics such as the mixing coefficient, the mean vector, the covariance matrix and the like of a Gaussian Mixture Model (GMM) among nodes, obviously reduces the communication overhead, and the communication complexity linearly grows along with the network scale, and simultaneously simplifies the calculation flow, reduces the calculation load of a single node and adapts the deployment of a large-scale sensor network with limited resources by adopting an adaptive GMM component adjustment, a regularized weighted EM algorithm and an iterative update strategy controlled by a random weight matrix on the premise of ensuring the estimation precision.

Inventors

  • LI XIAOLEI
  • MA JIANING
  • WANG JIANGE
  • LUO XIAOYUAN

Assignees

  • 燕山大学

Dates

Publication Date
20260508
Application Date
20260126

Claims (10)

  1. 1. The distributed particle filtering algorithm based on Gaussian mixture and Gossip fusion is characterized by comprising the following steps of: step one, initializing a system, namely setting parameters of a sensor network, including the number M of nodes, the dimension d of a state space, the maximum component number J_max of the total number R, GMM of particles and a convergence threshold value Each node initializes a local particle set and weights based on the prior distribution. The local posterior GMM approximation, wherein each node acquires local posterior distribution through a prediction-update cycle of local particle filtering, a weighted Expectation Maximization (EM) algorithm is adopted to fit a Gaussian Mixture Model (GMM), and the improved Bayesian Information Criterion (BIC) is utilized to adaptively determine the optimal component quantity of the GMM; the GMM fusion based on Gossip, wherein each node randomly selects neighbor nodes, exchanges sufficient statistics of each GMM, adopts a weighted mixed importance sampling method to realize the fusion of two nodes GMM, generates a new weighted sample set and normalizes weights; Iteration fusion and convergence judgment, namely repeating the GMM fusion step until the GMM of all nodes is converged, wherein the convergence judgment condition is that the difference between the GMM log likelihood values of two adjacent iterations is smaller than a set threshold epsilon Step five, posterior correction, namely respectively extracting samples from prior prediction distribution and post-convergence posterior distribution by each node, calculating corresponding importance weights, normalizing, and re-fitting the GMM through an EM algorithm to obtain corrected global posterior distribution; And step six, outputting state estimation, namely generating a uniformly weighted particle set through resampling based on the corrected GMM, and outputting a global state estimation result.
  2. 2. The distributed particle filter algorithm based on Gaussian mixture and Gossip fusion of claim 1, wherein the improved BIC formula in step 2: Wherein the method comprises the steps of Representing the "number of significant components", which automatically reduces the penalty strength of the weak or overlapping components by means of the exponentiations of the weights, Is a super parameter, is used for controlling the sensitivity of punishment, lambda is a global intensity coefficient, and the value ranges of the lambda and the lambda are (0, 1).
  3. 3. The distributed particle filter algorithm based on Gaussian mixture and Gossip fusion of claim 1, wherein a regularization term is introduced into the covariance matrix to prevent numerical singularities during the M-step updating of the weighted EM algorithm in step 2: Wherein the method comprises the steps of Is a small regularization constant set as , Is an identity matrix.
  4. 4. A distributed particle filter algorithm based on Gaussian mixture and Gossip fusion as recited in claim 1, wherein said sufficient statistics in said step 3 include mixing coefficients of GMM components Average value vector Sum covariance matrix Only the sufficient statistics are exchanged between nodes and not the original particles.
  5. 5. A distributed particle filter algorithm based on Gaussian mixture and Gossip fusion as defined in claim 1, wherein said weighted mixture importance sampling in step 3 is implemented by extracting R/2 samples from local GMM and giving unit weight, extracting R/2 samples from GMM of random neighbor j, and calculating importance weight thereof Wherein In order to achieve a distribution of the objects, To propose a distribution, the sample sets are combined and the weights normalized.
  6. 6. The distributed particle filtering algorithm based on Gaussian mixture and Gossip fusion of claim 1, wherein the step 4 adopts a KL divergence minimization strategy to fine tune the GMM components, in particular to calculate KL divergence among different GMM components: and clustering the matched components according to the KL divergence, and averaging the matched component parameters.
  7. 7. A distributed particle filter algorithm based on Gaussian mixture and Gossip fusion as claimed in claim 1, wherein the posterior update formula of each iteration in step 4 is Wherein As a set of neighbor nodes for node m, For the weight coefficient of node m to node j in the t-th iteration, the following is satisfied =1 And 。
  8. 8. A distributed particle filter algorithm based on Gaussian mixture and Gossip fusion as claimed in claim 1, wherein said a priori prediction distribution in said step 5 is calculated by the Chapman-Kolmogorov formula Wherein The system state at the time k is the system state, Is the cumulative observation up to time k-1.
  9. 9. A sensor network system is characterized by comprising a plurality of sensor nodes, wherein the sensor nodes adopt the algorithm of any one of claims 1-8 to realize distributed state estimation, the sensor network adopts an undirected connected graph topological structure, and the nodes only establish communication connection in a coverage area with a preset radius to support multi-hop routing.
  10. 10. Use of an algorithm according to any of claims 1-8 in object tracking, environmental monitoring or intelligent transportation networks.

Description

Distributed particle filtering algorithm based on Gaussian mixture and Gossip fusion Technical Field The invention relates to the technical field of distributed state estimation, in particular to a distributed particle filter algorithm based on Gaussian mixture and Gossip fusion. Background Particle Filtering (PF) is a recursive bayesian estimation method with significant advantages in state estimation of nonlinear, non-gaussian systems. The traditional centralized particle filtering needs to collect all sensor data to a fusion center for processing, and has the problems of high communication overhead, unbalanced network load, high single-point fault risk and the like, so that the centralized particle filtering is difficult to be suitable for a large-scale sensor network. The Distributed Particle Filter (DPF) autonomously performs local estimation through each node and realizes global consensus through network exchange information, so that the defect of a centralized architecture is effectively overcome. The existing DPF algorithm is mainly divided into three types, namely weight-based algorithm, likelihood-based algorithm and posterior distribution-based algorithm, wherein the weight-based algorithm requires synchronization of random number generators among nodes, communication cost is high, the likelihood-based algorithm is limited by noise distribution homogeneity assumption, flexibility is poor, the posterior distribution-based algorithm approximates local posterior through parameterization and exchanges statistical descriptors, communication cost is reduced, but the traditional method has insufficient approximation precision when processing complex multimodal distribution, and the fusion process depends on global network information and has poor expandability. The Gaussian Mixture Model (GMM) can flexibly represent complex multimodal distribution and provides an effective tool for posterior distribution approximation. However, the existing distributed particle filtering algorithm based on the GMM has the defects that the number of GMM components is fixed and cannot adapt to the dynamic change of local state distribution, an average consistency protocol is adopted in the fusion process, global synchronization is needed, communication overhead and calculation complexity are high, performance is easily affected when the network scale is expanded, and robustness is insufficient. Therefore, there is a need for a distributed particle filter algorithm that can adaptively adjust GMM structure, reduce communication overhead, and improve scalability and estimation accuracy. Disclosure of Invention The invention aims to provide a distributed particle filtering algorithm based on Gaussian mixture and Gossip fusion, so as to solve the problems in the background art. In order to solve the technical problems, the invention adopts the following technical scheme: A distributed particle filtering algorithm based on gaussian mixture and Gossip fusion, comprising the steps of: step one, initializing a system, namely setting parameters of a sensor network, including the number M of nodes, the dimension d of a state space, the maximum component number J_max of the total number R, GMM of particles and a convergence threshold value Each node initializes a local particle set and weights based on the prior distribution. The local posterior GMM approximation, wherein each node acquires local posterior distribution through a prediction-update cycle of local particle filtering, a weighted Expectation Maximization (EM) algorithm is adopted to fit a Gaussian Mixture Model (GMM), and the improved Bayesian Information Criterion (BIC) is utilized to adaptively determine the optimal component quantity of the GMM; the GMM fusion based on Gossip, wherein each node randomly selects neighbor nodes, exchanges sufficient statistics of each GMM, adopts a weighted mixed importance sampling method to realize the fusion of two nodes GMM, generates a new weighted sample set and normalizes weights; Iteration fusion and convergence judgment, namely repeating the GMM fusion step until the GMM of all nodes is converged, wherein the convergence judgment condition is that the difference between the GMM log likelihood values of two adjacent iterations is smaller than a set threshold epsilon Step five, posterior correction, namely respectively extracting samples from prior prediction distribution and post-convergence posterior distribution by each node, calculating corresponding importance weights, normalizing, and re-fitting the GMM through an EM algorithm to obtain corrected global posterior distribution; And step six, outputting state estimation, namely generating a uniformly weighted particle set through resampling based on the corrected GMM, and outputting a global state estimation result. The technical scheme of the invention is further improved in that the improved BIC formula in the step 2 is as follows: Wherein the method comprises the steps of R