Unobservable Systems: No Problem for Noise Identification

TL;DR

This paper introduces a correlation measurement difference method for noise identification in linear time-varying stochastic systems, effective even when the system is unobservable, with implementation in a MATLAB toolbox.

Contribution

It presents a novel noise estimation method applicable to both observable and unobservable systems, ensuring unbiased and consistent results.

Findings

Method provides unbiased, consistent estimates of noise covariances.

Effective for systems with unknown input sequences.

Implemented in a MATLAB toolbox and validated numerically.

Abstract

This paper deals with the noise identification of a linear time-varying stochastic dynamic system described by the state-space model. In particular, the stress is laid on the design of the correlation measurement difference method for estimation of the state and measurement noise covariance matrices for both observable and \textit{unobservable} systems with possibly unknown input sequence. The method provides unbiased and consistent estimates and is implemented in a publicly available MATLAB toolbox and numerically evaluated.