Cramér-Rao-type bound for state estimation in linear discrete-time system with unknown system parameters

Tracking problems are usually investigated using the Bayesian approach. Many practical tracking problems involve some unknown deterministic nuisance parameters such as the system parameters or noise statistical parameters. This paper addresses the problem of state estimation in linear discrete-time dynamic systems in the presence of unknown deterministic system parameters. A Cramér-Rao-type bound on the mean-sqaure-error (MSE) of the state estimation is introduced. The bound is based on the concept of risk-unbiasedness and can be computed recursively. It allows evaluating the optimality of the estimation procedure. Some sequential estimators for this problem are proposed such that the estimation procedure can be considered an on-line technique. Simulation results show that the proposed bound is asymptotically achieved by the considered estimators.