Minimum covariance, minimax and minimum energy linear estimators

  • Arthur J. Krener
Part II: Research Reports
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 16)


The estimators which minimize the error covariance for the filtering, prediction and smoothing of linear plants with Gaussian initial conditions and noises are well-known. We show that these same estimators arise when one seeks to minimize the maximum error assuming that initial conditions and noises are bounded in norm in an appropriate Hilbert space (minimax estimator). They also arise when one seeks the trajectory of least energy necessary to produce the given observations (minimum energy estimate).


Minimum Energy Observation Noise Imum Energy Gaussian Random Vector Minimax Estimate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. Gelb, ed., Applied Optimal Estimation, M.I.T. Press, Cambridge, 1974.Google Scholar
  2. [2]
    A. J. Krener, The Kalman-Bucy filter: an old answer to some new questions in linear filtering, 1978.Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Arthur J. Krener
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaDavisUSA

Personalised recommendations