Robust identification for input non‐uniformly sampled Wiener model by the expectation‐maximisation algorithm

Abstract

Abstract The problems of inconsistent data sampling frequency, outliers, and coloured noise often exist in system identification, resulting in unsatisfactory identification results. In this study, a novel identification method of input non‐uniform sampling Wiener model with a coloured heavy‐tailed noise is proposed. The lifted Wiener model with coloured noise and outlier value disturbed is constructed. Under the expectation‐maximisation (EM) algorithm framework, the student's t‐distribution is introduced to model the contaminated output data. The variance scale is regarded as a unique latent variable, and the iterative parameter estimation formula of the non‐uniform sampling Wiener model is derived. The idea of the auxiliary model is applied to acquire the unmeasured middle variable and handle the coloured noise variable in the non‐uniformly sampled Wiener model. The Differential Evolution algorithm is used to calculate the intractable part of the Q‐function. The convergence analysis of the proposed algorithm is given. Two numerical examples and one water tank simulation are employed to indicate the effectiveness of the proposed method.

Keywords

• coloured heavy‐tailed noise
• DE algorithm
• EM algorithm
• non‐linear system
• non‐uniformly sampled
• parameter estimation