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A Kalman filter as a minimax estimator

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Abstract

A minimax terminal state estimation problem is posed for a linear plant and a generalized quadratic loss function. Sufficient conditions are developed to insure that a Kalman filter will provide a minimax estimate for the terminal state of the plant. It is further shown that this Kalman filter will not generally be a minimax estimate for the terminal state if the observation interval is arbitrarily long. Consequently, a subminimax estimate is defined, subject to a particular existence condition. This subminimax estimate is related to the Kalman filter, and it may provide a useful estimate for the terminal state when the performance of the Kalman filter is no longer satisfactory.

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Authors and Affiliations

  1. Department of Engineering and Applied Science, Yale University, New Haven, Connecticut

    Max Mintz (Assistant Professor)

Authors
  1. Max Mintz
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Communicated by J. V. Breakwell

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Mintz, M. A Kalman filter as a minimax estimator. J Optim Theory Appl 9, 99–111 (1972). https://doi.org/10.1007/BF00932347

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  • DOI: https://doi.org/10.1007/BF00932347

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