Fixed window estimation with a worst-case performance measure

We present an estimation scheme with a fixed window for a discrete system with a worst-case performance measure. The relevance of the problem arises from applications where a past state-combination is sought based on the current information. The optimal fixed window estimate is a linear combination of an H_∞ estimator and an H₂ smoother. Differences and comparisons with conventional smoothing and estimation with a worst-case performance measure are drawn. It is shown that as the window-size (delay) goes to zero, the estimator converges to a conventional worst-case estimator