Limiting performance of optimal linear filters

Authors:
Julio H. Braslavsky;Mara M. Seron;David Q. Mayne;Petar V. Kokotovi
Affiliations:
Centre for Integrated Dynamics and Control, The University of Newcastle, NSW 2308, Australia;Centre for Integrated Dynamics and Control, The University of Newcastle, NSW 2308, Australia;Department of Electrical & Electronic Engineering, Imperial College, Exhibition Road, London SW7 2BT, UK;Center for Control Engineering and Computation, University of California, Santa Barbara, CA 93106-9560, USA
Venue:
Automatica (Journal of IFAC)
Year:
1999

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Abstract

We study the lowest achievable mean-square estimation error in two limiting optimal linear filtering problems. First, when the intensity of the process noise tends to zero, the lowest achievable mean-square estimation error is a function of the unstable poles of the system. Second, when the intensity of the measurement noise tends to zero, the lowest achievable mean-square estimation error is a function of the nonminimum phase zeros of the system. We link these results with Bode integral characterisations of performance limitations in linear filtering.