Asymptotic stability of the MMSE linear filter for systems with uncertain observations (Corresp.)

Sufficient conditions for uniform asymptotic stability in the large of the optimal minimum mean-square error (MMSE) linear filter are developed for discrete linear systems whose observations may contain noise alone and where only the probability of occurrence of such cases is known to the estimator. Conditions for existence, uniqueness, and stability of the steady-state optimal filter are also considered for the case when the system is time-invariant.