An efficient two‐stage algorithm for parameter identification of non‐linear state‐space models‐based on Gaussian process regression

Abstract

Abstract This paper aims to improve the efficiency of parameter identification of the nonlinear state‐space model (SSM). The commonly used particle Markov chain Monte Carlo (PMCMC) method is time‐consuming. The surrogate model is a useful acceleration strategy, but it is expensive to establish a global high‐precision surrogate model. This paper proposes an efficient algorithm that gradually estimates the unknown parameters in two stages. In the first stage, a reduced region is established based on the latest method. We train a local Gaussian Process regression (GPR) of the likelihood function in the reduced region based on the optimum Latin hypercube design (OLHD). In the second stage, we identify the unknown parameters more accurately based on the MCMC method. When the proposal sample is in the reduced region, we use GPR to estimate the likelihood; otherwise, BPF is used to estimate the likelihood. The reduced region is usually the high probability density region, which is why the algorithm is efficient. It is proved that the acceptance rate of any two samples based on the proposed algorithm is theoretically convergent to that of the PMCMC algorithm. Two examples demonstrate that the proposed method performs well in accuracy and efficiency.

Keywords

• Gaussian processes
• Markov chain Monte Carlo
• non‐linear state‐space models
• parameter identification
• particle filter