Abstract
In order to improve the estimation accuracy of particle filter algorithm in a nonlinear system state estimation problem, a new algorithm based on the second-order divided difference filter to generate the proposed distribution and the differential evolution algorithm for resampling is proposed. The second-order divided difference based on Strling’s interpolation formula is used to generate approximations to nonlinear dynamics, which avoids the evaluation of the Jacobian derivative matrix and is easy to implement. Cholesky factorization is used to ensure the positive definiteness of the covariance matrix. The truncated errors of the local linearization are reduced to a certain extent, and the approximation degree of the proposed distribution to the posterior probability of the system state is improved. The differential evolution algorithm is used to replace the traditional resampling algorithm, which effectively mitigates the problem of particle degradation. Monte Carlo simulation experiments show the effectiveness of the new algorithm.
Highlights
Particle filters (PF) are an effective solution to a nonlinear dynamic and/or measurement filtering problem, which has been widely used in many fields such as economics [1, 2], visual tracking [3, 4], navigation position [5], and radio communication [6]. e PF is a recursive Bayesian estimation method based on the Monte Carlo simulation
The estimation performance and computational cost of the proposed particle filters are evaluated on a state estimation problem and compared with that of the standard sampling importance-resampling particle filter (SIR-PF), extended particle filter (EPF), unscented particle filter (UPF), and the second-order divided difference particle filter (DD2PF)
We propose an efficient second-order divided difference particle filter based on differential evolution. e filter adopts the DD2 filter to generate the proposal distribution, and the differential evolution algorithm to optimize the resampling process. e DD2 filter linearizes the nonlinear dynamic model by using a multivariable extension of Stirling’s interpolation formula rather than the derivativebased Taylor series approximation. e filter provides excellent accuracy without the need to analytically calculate Jacobians
Summary
Particle filters (PF) are an effective solution to a nonlinear dynamic and/or measurement filtering problem, which has been widely used in many fields such as economics [1, 2], visual tracking [3, 4], navigation position [5], and radio communication [6]. e PF is a recursive Bayesian estimation method based on the Monte Carlo simulation. E PF is a recursive Bayesian estimation method based on the Monte Carlo simulation It exploits a set of random particles (samples) and their associated weights to represent the posterior probability density function. By linearizing nonlinear functions around the current state at first-order Taylor approximations, extended Kalman filter (EKF) is used to generate the proposal distribution, and the extended particle filter (EPF) is proposed. E unscented particle filter (UPF) [7] utilizes the unscented Kalman filter (UKF) to generate the proposal distribution. E second-order divided difference (DD2) filter [13] is based on a similar linear regression to the UKF, but is able to more accurately estimate the state covariance resulting in a more precise set of weighted sample points to estimate from.
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