Minimax FIR smoothers for deterministic continuous-time state space models

In order to design a smoother for a deterministic continuous-time state space model, a new performance criterion is proposed, which is given by a ratio of the current estimation error to the weighted energy of the deterministic disturbance applied during the recent finite horizon. Among smoothers with the deadbeat property and finite impulse response (FIR) structure, a minimax FIR smoother (MFS) is obtained to optimize the proposed performance criterion. To begin with, the functional optimization problem is formulated with respect to kernel functions of the MFS and then its solution is explicitly presented. The MFS depends only on inputs and outputs on the finite recent horizon, and is independent of any a priori   state information. The MFS is first represented in an integral form for simple representation and then a differential form is introduced for efficient numerical computation. As in H∞H∞ IIR smoothing and H2H2 IIR filtering, it is shown that the proposed MFS for a deterministic system can be interpreted as the minimum variance unbiased FIR smoother for a stochastic system.