Discrete-Time Filtering for Linear Systems in Correlated Noise with Non- Gaussian Initial Conditions: Asymptotic Behavior of the Difference Between the MMSE and LMSE Estimates.

摘要

We consider the one-step prediction problem for discrete-time linear systems in correlated plant and observation noises, and non-Gaussian initial conditions. We investigate the asymptotic behavior of the expected square Et of the difference between the MMSE and LMMSE (or Kalman) estimates of the state given past observations. We characterize the hrnit of the error seqnence (Et, t = 0,1,...) and obtain some related rates of convergence, with complete analysis being provided for the scalar case. The discussion is based on the explicit representations which were obtained by the authors for the MMSE and LMMSE estimates, and which explicitly display the dependence of these quantities on the initial distribution.