Minimax Estimators and Performance Levels

  • Tamer Başar
  • Pierre Bernhard
Part of the Modern Birkhäuser Classics book series (MBC)


In the previous two chapters, in the development of the solutions to the disturbance attenuation problem with imperfect measurements in continuous and discrete time, we have encountered filter equations which resemble the standard Kalman filter when the weighting on the state in the cost function (i.e., Q) is set equal to zero. In this chapter we study such problems directly and show that the appearance of the Kalman filter, or Kalman filter-like structures, is actually not a coincidence. The commonality of the analysis of this chapter with those of the previous ones is again the use of game-theoretic techniques.


Kalman Filter Riccati Equation Attenuation Level Cumulative Error Minimax Estimator 


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Copyright information

© Springer Science+Business Media New York 2008

Authors and Affiliations

  • Tamer Başar
    • 1
  • Pierre Bernhard
    • 2
  1. 1.Coordinated Science LaboratoryUniversity of IllinoisUrbanaUSA
  2. 2.Unité de Recherche Sophia-AntipolisINRIAValbonne CedexFrance

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