Optimal and robust noncausal filter formulations

The paper describes an optimal minimum-variance noncausal filter or fixed-interval smoother. The optimal solution involves a cascade of a Kalman predictor and an adjoint Kalman predictor. A robust smoother involving H_∞ predictors is also described. Filter asymptotes are developed for output estimation and input estimation problems which yield bounds on the spectrum of the estimation error. These bounds lead to a priori estimates for the scalar γ in the H_∞ filter and smoother design. The results of simulation studies are presented, which demonstrate that optimal, robust, and extended Kalman smoothers can provide performance benefits.