Noncausal Estimation Research Articles

Minimax estimation of continuous time deterministic signals in colored noise

This paper considers continuous time estimation of non-random data corrupted by random noise. The strategy employed is to find a linear noncausal estimator whose performance is best over a pre-designated class of signals. This estimator will minimize the maximum normalized mean square error over input signals belonging to a subset of square-integrable functions on [0, T]. Simple suboptimal estimators are introduced and are shown to behave optimally as the observation interval becomes unbounded. An expression for the asymptotic minimax estimation error is developed.