# Identification of Markov Jump Autoregressive Processes from Large Noisy Data Sets

## TL;DR

This paper presents a new method for identifying Markov jump autoregressive models from large, noisy datasets, accurately estimating system dynamics, switching behavior, and noise parameters even with high noise levels.

## Contribution

It introduces a novel identification approach that handles large measurement noise and Markov switching, improving accuracy in complex noisy environments.

## Key findings

- Effective even with high noise-to-output ratios
- Performs well with large datasets
- Accurately estimates switching dynamics and noise parameters

## Abstract

This paper introduces a novel methodology for the identification of switching dynamics for switched autoregressive linear models. Switching behavior is assumed to follow a Markov model. The system's outputs are contaminated by possibly large values of measurement noise. Although the procedure provided can handle other noise distributions, for simplicity, it is assumed that the distribution is Normal with unknown variance. Given noisy input-output data, we aim at identifying switched system coefficients, parameters of the noise distribution, dynamics of switching and probability transition matrix of Markovian model. System dynamics are estimated using previous results which exploit algebraic constraints that system trajectories have to satisfy. Switching dynamics are computed with solving a maximum likelihood estimation problem. The efficiency of proposed approach is shown with several academic examples. Although the noise to output ratio can be high, the method is shown to be extremely effective in the situations where a large number of measurements is available.