Robust fractional order singular Kalman filter

Author:

Nosrati Komeil1ORCID,Belikov Juri2ORCID,Tepljakov Aleksei1ORCID,Petlenkov Eduard1ORCID

Affiliation:

1. Department of Computer Systems Tallinn University of Technology Tallinn Estonia

2. Department of Software Science Tallinn University of Technology Tallinn Estonia

Abstract

AbstractIn this article, the state estimation problem of linear fractional order singular (FOS) systems subject to matrix uncertainties is investigated where a recursive robust algorithm is derived. Considering an uncertain discrete‐time linear FOS system with added process and measurement noises, we aim to design a robust Kalman‐type state estimation algorithm based on an optimal data fitting approach with a given sequence of observations. As a substitute for the stochastic formulation, this general filter is obtained by minimizing a completely deterministic regularized residual norm in its worst‐possible form at each step over admissible uncertainties. Analysis of the algorithm shows that not only does the proposed robust filter cover the traditional robust Kalman filters (KFs), but it also represents an extension of the nominal fractional singular KF (FSKF) when the system is not subject to uncertainties. Furthermore, besides giving a sufficient condition for the existence of the robust filter, we derive conditions for the asymptotic properties of the filter, where we demonstrate that the filter and the Riccati equation are stable and converge when an equivalent system is detectable and stabilizable. A numerical example is included to demonstrate the performance of the introduced filter.

Funder

European Social Fund

Eesti Teadusagentuur

Publisher

Wiley

Subject

Electrical and Electronic Engineering,Industrial and Manufacturing Engineering,Mechanical Engineering,Aerospace Engineering,Biomedical Engineering,General Chemical Engineering,Control and Systems Engineering

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