The University of Montana
Department of Mathematical Sciences

Technical report #32/2008

A Matrix Theoretic Derivation of the Kalman Filter

John Bardsley
University of Montana


We present a matrix theoretic derivation of the Kalman filter—motivated by the statistical technique of minimum variance estimation—in order to make its theoretical underpinnings accessible to a broader audience. Standard derivations of the filter utilize probabilistic arguments that are less familiar to the matrix analyst and computational mathematician.


AMS Subject Classification: 15A99, 65C60

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