A general p-shift linear optimal finite impulse response (FIR) estimator is proposed for filtering (p D 0), p-lag smoothing (p < 0), and p-step prediction (p > 0) of discrete time-varying state-space models. An optimal solution is found in the batch form with the mean square initial state function self-determined by solving the discrete algebraic Riccati equation. An unbiased batch solution is shown to be independent on noise and initial conditions. The mean square errors in both the optimal and unbiased estimates have been determined along with the noise power gain and estimate error bound. The following important inferences have been made on the basis of numerical simulation. Unlike the time-invariant Kalman filter, the relevant optimal FIR one is very less sensitive to noise, especially when N 1. Both time varying, the optimal FIR and Kalman estimates trace along almost the same trajectories with similar errors and sensitivities to noise. Overall, the optimal FIR estimator demonstrates better robustness than the Kalman one against faults in the noise description.

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