System Identification of Nonlinear Dynamical System with Missing Observations

Abstract

AbstractWe consider a nonlinear state-space model with unknown state transition function and process noise. The state transition function is modeled as a Gaussian process, besides, it is also expressed as basis function expansion. Using the connection to the Gaussian process, the prior of the coefficients of basis function can be obtained. The posterior of the state and unknown coefficients can be obtained through Bayesian inference. Sequential Monte Carlo (Particle Gibbs with ancestor sampling) is used to estimate the states. The coefficients are modeled as random variables related to state statistics. The Markov Chain Monte Carlo (MCMC) method is used to repeated iteratively sample from parameter posterior and state posterior. The problems of missing observations due to sensor failure are often encountered in practical engineering and are taken into consideration in this paper. We propose a learning method for nonlinear dynamical system with missing observations. According to whether the observation data is missing or not, the state and parameters are updated respectively. The proposed nonlinear system identification method is robust to incomplete dataset. A numerical example is used to demonstrate the effectiveness of the proposed method.KeywordsState-space modelSystem identificationBasis function expansionMarkov chain Monte CarloBayesian learning