# Asymptotically Efficient Identification of Known-Sensor Hidden Markov Models

## TL;DR

This paper introduces a two-step estimation method for hidden Markov models with known observation probabilities, demonstrating its theoretical efficiency and computational advantages over traditional approaches.

## Contribution

It proposes a novel two-step estimator combining method of moments and Newton-Raphson, proven to be consistent and asymptotically efficient.

## Key findings

- Estimator is consistent and asymptotically efficient.
- Method reduces computational demand for large data sets.
- Numerical experiments confirm theoretical advantages.

## Abstract

We consider estimating the transition probability matrix of a finite-state finite-observation alphabet hidden Markov model with known observation probabilities. The main contribution is a two-step algorithm; a method of moments estimator (formulated as a convex optimization problem) followed by a single iteration of a Newton-Raphson maximum likelihood estimator. The two-fold contribution of this letter is, firstly, to theoretically show that the proposed estimator is consistent and asymptotically efficient, and secondly, to numerically show that the method is computationally less demanding than conventional methods - in particular for large data sets.