Particle Filter Grey Wolf Optimization for Parameter Estimation of Nonlinear Dynamic System

Particle filter samplers, Markov chain Monte Carlo (MCM-C)samplers, and swarm intelligence can be used for parameter estimation with posterior probability distribution in nonlinear dynamic system. However the global exploration capabilities and efficiency of the sampler rely on the moving step of particle filter sampler. In this paper, we presented a mixing sampler algorithm: particle filter grey wolf optimization sampler(PF -GWO). PF-GWO sampler is operated by combining grey wolf optimization with Metropolis ratio into framework of particle filter, which is suitable to estimate unknown static parameters of nonlinear dynamic models. Based on Bayesian framework, parameter estimation of Lorenz model shows that PF -GWO sampler is superior to other combined particle filter sampler algorithms with large range prior distribution.

1. Introduction

Algorithms of parameter estimation have been advanced for increasing computer computation capability in recent years. From Markov chain Monte Carlo (MCMC) algorithms such as Gibbs sampling, Metropolis algorithm, random walk Metropolis (RWM) algorithm [1], to improved adaptive Metropolis (AM) algorithm [2], differential evolution Markov chain (DE-MC) algorithm [2], particle filter sampler algorithm [3], swarm intelligence([4]), these algorithms can be used for uncertainty estimation and unknown parameters estimation of nonlinear dynamic systems. Among them, Bayesian inference provides an basic framework for assessing parameters by considering observation and model structure.