A Metropolis–Hastings-within-Gibbs approach for nonlinear state–space system estimation

This paper presents a new Metropolis–Hastings-within-Gibbs (MH–Gibbs) sampling method for state-estimation and parameter-identification in nonlinear state–space systems. Compared to the conventional filtering and smoothing approaches, the proposed method offers substantial improvements in both time efficiency and memory usage, while maintaining effective estimation accuracy. Furthermore, owing to the high efficiency of the proposed state-estimation method, a new approach is proposed to approximate the gradient of the log-likelihood function with respect to the system-parameters, which facilitates parameter-identification. Case studies on three benchmark systems show that: (1) compared to the forward-filtering–backward-smoothing approach, the proposed state-estimation method achieves comparable accuracy with only one-tenth the computational time; and (2) the proposed parameter-identification method has reasonable accuracy.