Robust Estimation of ARX Models With Time Varying Time Delays Using Variational Bayesian Approach

This paper is concerned with robust identification of processes with time-varying time delays. In reality, the delay values do not simply change randomly, but there is a correlation between consecutive delays. In this paper, the correlation of time delay is modeled by the transition probability of a Markov chain. Furthermore, the measured data are often contaminated by outliers, and therefore, t-distribution is adopted to model the measurement noise. The variational Bayesian (VB) approach is applied to estimate the model parameters along with time delays. Compared with the classical expectation-maximization algorithm, VB approach has the advantage of capturing the uncertainty of the estimated parameter and time delays by providing their full probabilities. The effectiveness of the proposed method is demonstrated by both a numerical example and a pilot-scale hybrid-tank experiment.