Steady state Kalman Filter behavior for unstabilizable systems

Soura Dasgupta; D. Richard Brown; Rui Wang

doi:10.1109/CDC.2014.7040168

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Conference proceeding

Steady state Kalman Filter behavior for unstabilizable systems

Soura Dasgupta, D. Richard Brown and Rui Wang

53rd IEEE Conference on Decision and Control, Vol.2015-(February), pp.4989-4994

12/2014

DOI: 10.1109/CDC.2014.7040168

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Abstract

Some important textbooks on Kalman Filters suggest that positive semidefinite solutions to the filtering Algebraic Riccati Equation (ARE) cannot be stabilizing should the underlying state variable realization be unstabilizable. We show that this is false. Questions of uniqueness of positive semidefinite solutions of the ARE are also unresolved in the absence of stabilizability. Yet fundamental performance issues in modern communications systems hinge on Kalman Filter performance absent stabilizability. In this paper we provide a positive semidefinite solution to the ARE for detectable systems that are not stabilizabile and show that it is unique if the only unreachable modes are on the unit circle.

Asymptotic stability

Eigenvalues and eigenfunctions

Kalman Filter

Kalman filters

MIMO

Noise

Oscillators

Riccati Equation

Stability

Steady-state

Uniqueness

Details

Title: Subtitle: Steady state Kalman Filter behavior for unstabilizable systems
Creators: Soura Dasgupta - University of Iowa
D. Richard Brown - Worcester Polytechnic Institute
Rui Wang - Worcester Polytechnic Institute
Resource Type: Conference proceeding
Publication Details: 53rd IEEE Conference on Decision and Control, Vol.2015-(February), pp.4989-4994
Publisher: IEEE
DOI: 10.1109/CDC.2014.7040168
ISSN: 0191-2216
eISSN: 2576-2370
Language: English
Date published: 12/2014
Academic Unit: Electrical and Computer Engineering
Record Identifier: 9984197176402771

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