Sensor fault estimation in Markov jump linear system: A Bayesian perspective

Abstract

Existing fault estimation methods for Markov jump linear systems, particularly the interacting multiple model approaches, heavily rely on pre-defined fault model banks. This reliance renders them ineffective against faults with unknown or time-varying dynamics. Conversely, emerging Bayesian estimation approaches are typically confined to single-mode systems and fail to accommodate stochastic mode switching. To bridge this gap, this paper proposes a novel Bayesian framework for the real-time joint estimation of system states, hidden modes, and mode-dependent faults without requiring prior fault dynamic knowledge. In particular, an adaptive fault update mechanism based on innovation moments is introduced to address the trend discontinuity of fault signals caused by mode transitions, a challenge not addressed by standard recursive Bayesian estimators. Results from a numerical simulation example and a fermentation process simulation case study show improved robustness and estimation accuracy over traditional methods. The adaptive fault update also tracks abrupt fault changes while reducing fluctuations when the fault signal varies slowly.