Uncovering Process Noise in LTV Systems via Kernel Deconvolution

TL;DR

This paper introduces a novel kernel deconvolution approach to accurately identify process noise density in linear time-varying systems, improving upon existing measurement difference methods with automatic parameter selection.

Contribution

It presents a new method combining refined measurement difference calculations with kernel density deconvolution for process noise estimation in LTV systems.

Findings

Effective in numerical simulations

Automated deconvolution parameter selection

MATLAB implementation provided

Abstract

This paper focuses on the identification of the process noise density of a linear time-varying system described by the state-space model with the known measurement noise density. A novel method is proposed that enhances the measurement difference method (MDM). The proposed method relies on a refined calculation of the MDM residue, which accounts for both process and measurement noises, as well as constructing the kernel density of the residue sample. The process noise density is then estimated by the density deconvolution algorithm utilising the Fourier transform. The method is supplemented with automatic selection of the deconvolution parameters based on the method of moments. The performance of process noise density estimation is evaluated in numerical examples and the paper is supplemented with a MATLAB implementation.