Brief paper: Unbiased minimum-variance input and state estimation for linear discrete-time systems

Authors:
Steven Gillijns;Bart De Moor
Affiliations:
SCD-SISTA, ESAT, K.U. Leuven, Kasteelpark Arenberg 10, 3001 Leuven, Belgium;SCD-SISTA, ESAT, K.U. Leuven, Kasteelpark Arenberg 10, 3001 Leuven, Belgium
Venue:
Automatica (Journal of IFAC)
Year:
2007

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Abstract

This paper addresses the problem of simultaneously estimating the state and the input of a linear discrete-time system. A recursive filter, optimal in the minimum-variance unbiased sense, is developed where the estimation of the state and the input are interconnected. The input estimate is obtained from the innovation by least-squares estimation and the state estimation problem is transformed into a standard Kalman filtering problem. Necessary and sufficient conditions for the existence of the filter are given and relations to earlier results are discussed.