A solution of the smoothing problem for linear dynamic systems

Authors:
D. Q. Mayne
Affiliations:
Department of Electrical Engineering, Imperial College, London UK
Venue:
Automatica (Journal of IFAC)
Year:
1966

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Abstract

A method for obtaining optimal estimates of the states of a linear system given a record of observations is derived. The method uses Kalman's filtering theory to obtain an estimate using 'past' observations, and optimal control theory to obtain an estimate using 'future' observations, and shows how the two estimates can be combined to give a solution to the smoothing or interpolation problem. The method also yields the variance of the estimate. The method is illustrated by means of a numerical example.