Learning Hidden Markov Models for Linear Gaussian Systems with Applications to Event-based State Estimation

TL;DR

This paper introduces a method to approximate linear Gaussian systems with finite-state hidden Markov models using a two-step approach involving state space model identification and quantization, enabling improved event-based state estimation.

Contribution

The paper proposes a novel indirect modeling approach for learning HMMs from Gaussian systems, including algorithms with proven convergence and asymptotic properties.

Findings

The proposed algorithms effectively learn HMM parameters from Gaussian system data.

The learned HMM improves event-triggered state estimation accuracy.

Numerical results validate the approach's effectiveness in model learning and state estimation.

Abstract

This work attempts to approximate a linear Gaussian system with a finite-state hidden Markov model (HMM), which is found useful in solving sophisticated event-based state estimation problems. An indirect modeling approach is developed, wherein 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.