Joint Identification of Linear Dynamics and Noise Covariance via Distributional Estimation

TL;DR

This paper introduces a new framework for jointly estimating system dynamics and noise covariance in linear systems with non-Gaussian noise, using distributional shape information for improved accuracy.

Contribution

It proposes a novel parameterization of the state-transition distribution and introduces MLE and SME estimators with theoretical analysis and superior simulation performance.

Findings

Proposed estimators outperform OLS baseline in simulations.

The framework effectively estimates dynamics and noise covariance under general noise distributions.

Rigorous analysis of statistical properties and sample complexity of the estimators.

Abstract

In this paper, we propose a novel framework for the joint identification of system dynamics and noise covariance in linear systems, under general noise distributions beyond Gaussian. Specifically, we would like to simultaneously estimate the dynamical matrix $A$ and the noise covariance matrix $\varSigma$ using state transition data. The formulation builds upon a novel parameterization of the state-transition distribution, which enables more effective use of distributional "shape" information for improved identification accuracy. We introduce two practical estimators, namely the maximum likelihood estimator (MLE) and the score-matching estimator (SME), to solve the joint dynamics-covariance identification problem, and provide rigorous analysis of their statistical properties and sample complexity. Simulation results show that the proposed estimators outperform the ordinary least squares (OLS) baseline.