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

arXiv: https://arxiv.org/abs/2007.04587 · HTML: https://mlsanity.com/paper/2007.04587/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2020.

## Built on by (most cited first, 1 of 1)

- [Tempering the Bayes Filter towards Improved Model-Based Estimation](https://mlsanity.com/paper/2512.02823/) (2025)

## Abstract (arXiv)

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.