Observer/Kalman-Filter Time-Varying System Identification
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An algorithm for computation of the generalized Markov parameters of an observer or Kalman filter for discretetimevarying systems from input-output experimental data is presented. Relationships between the generalized observer Markov parameters and the system Markov parameters are derived for the time-varying case. The generalized system Markov parameters thus derived are used by the time-varying eigensystem realization algorithm to obtain a time-varying discrete-time state-space model. Aqualitative relationship of the time-varying observer with the Kalman filter in the stochastic environment and an asymptotically stable realized observer are discussed briefly to develop insights for the analyst. The minimum number of repeated experiments for accurate recovery of the system Markov parameters is determined from these developments. The time-varying observer gains realized in the process are subsequently shown to be in consistent coordinate systems for observer state propagation. It is also demonstrated that the observer gain sequence realized in the case of the minimum number of experiments corresponds naturally to a time-varying deadbeat observer. Numerical examples demonstrate the utility of the concepts developed in the paper. Copyright 2009.
