Brief paper: On the lower smoothing bound in identification of time-varying systems

  • Authors:
  • Maciej Niedwiecki

  • Affiliations:
  • Department of Automatic Control, Faculty of Electronics, Telecommunications and Computer Science, Gdańsk University of Technology, ul. Narutowicza 11/12, Gdańsk, Poland

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2008

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Abstract

In certain applications of nonstationary system identification the model-based decisions can be postponed, i.e. executed with a delay. This allows one to incorporate in the identification process not only the currently available information, but also a number of ''future'' data points. The resulting estimation schemes, which involve smoothing, are not causal. Assuming that the infinite observation history is available, the paper establishes the lower steady-state estimation bound for any noncausal estimator applied to a linear system with randomly drifting coefficients (under Gaussian assumptions). This lower bound complements the currently available one, which is restricted to causal estimators.