Learning hidden Markov models for linear Gaussian systems with applications to event-based state estimation

This work attempts to approximate a linear Gaussian system with a finite-state hidden Markov model (HMM), which is found useful in dealing with challenges in designing networked control systems An indirect approach is developed, where a state-space model (SSM) is firstly identified for a Gaussian system and the SSM is then used as an emulator for learning an HMM. In the proposed method, the training data for the HMM are obtained from the data generated by the SSM through building a quantization mapping. Parameter learning algorithms are designed to learn the parameters of the HMM, through exploiting the periodical structural characteristics of the HMM. The convergence and asymptotic properties of the proposed algorithms are analyzed. The HMM learned using the proposed algorithms is applied to event-triggered state estimation, and numerical results on model learning and state estimation demonstrate the validity of the proposed algorithms. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This work attempts to approximate a linear Gaussian system with a finite-state hidden Markov model (HMM) and address challenges in designing networked control systems. An indirect approach is developed where a state-space model (SSM) is identified for the Gaussian system and used as an emulator for learning an HMM. Parameter learning algorithms are designed based on the periodic structural characteristics of the HMM, leading to convergence and asymptotic properties of the proposed algorithms. The HMM learned using the proposed algorithms is successfully applied to event-triggered state estimation, demonstrating their validity through numerical results on model learning and state estimation.