Posterior Cramer-Rao bounds for discrete-time nonlinear filtering

  • Authors:
  • P. Tichavsky;C.H. Muravchik;A. Nehorai

  • Affiliations:
  • Inst. of Inf. Theory & Autom., Czechoslovak Acad. of Sci., Prague;-;-

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 1998

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Abstract

A mean-square error lower bound for the discrete-time nonlinear filtering problem is derived based on the van Trees (1968) (posterior) version of the Cramer-Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems and is more general than the previous bounds in the literature. The case of singular conditional distribution of the one-step-ahead state vector given the present state is considered. The bound is evaluated for three important examples: the recursive estimation of slowly varying parameters of an autoregressive process, tracking a slowly varying frequency of a single cisoid in noise, and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation