Noise Covariances Identification by MDM: Weighting, Recursion, and Implementation

TL;DR

This paper extends the measurement difference method (MDM) for identifying noise covariance matrices in stochastic linear time-varying models, proposing three techniques with different weighting schemes, recursive forms, and analyzing their performance.

Contribution

It generalizes MDM to time-varying dimensions and introduces three new weighted techniques with recursive implementations for improved noise covariance estimation.

Findings

Techniques differ in estimate quality and computational complexity

Recursive forms enhance efficiency of the proposed methods

Performance analysis through numerical examples demonstrates effectiveness

Abstract

The problem of noise covariance matrix identification of stochastic linear time-varying state-space models is addressed. The measurement difference method (MDM) is generalized to time-varying dimensions of the measurement and control. Three MDM identification techniques that differ in weighting used in the underlying least squares method are proposed. The techniques differ in estimate quality and computational complexity. In addition, recursive forms are designed for two techniques. The performance of the proposed techniques is analyzed using two numerical examples. The implementation of techniques is enclosed with the paper.