Robust Interpretable and Adaptive Identification Approach for Wiener System with Incomplete Outputs

Abstract

This paper addresses robust parameter estimation for Wiener systems with outliers and randomly missing outputs. A unified Student’s t-based identification method is developed within the expectation-maximization framework. The scale-mixture representation of the Student’s t-distribution provides a posterior precision weight for each observed sample. It assigns relatively high weights to clean samples and down-weights outliers without requiring a predefined noise mixture structure. The method infers missing outputs while jointly estimating the model parameters, noise scale and degrees-of-freedom parameter. Key-term separation removes the inherent gain ambiguity and yields a pseudo-linear parameterization when the intermediate signal is fixed. An auxiliary model estimates the unmeasurable intermediate signal and constructs the required regressors. Under the stated regularity and compactness conditions, the observed-data log-likelihood is non-decreasing and bounded above. Hence, the likelihood sequence converges and every interior limit point of the parameter sequence is stationary. Numerical and Monte Carlo studies together with mass–spring–damper and continuous stirred-tank reactor examples demonstrate the accuracy and stability of the proposed method.