In this letter, we propose a new multi-step maximum likelihood predictor with a finite impulse response (FIR) structure for discrete-time state-space signal models. This predictor is called a maximum likelihood FIR predictor (MLFP). The MLFP is linear with the most recent finite outputs and does not require a prior initial state information on a receding horizon. It is shown that the proposed MLFP possesses the unbiasedness property and the deadbeat property. Simulation study illustrates that the proposed MLFP is more robust against uncertainties and faster in convergence than the conventional multi-step Kalman predictor.

In this letter, we propose a new H2 smoother (H2S) with a finite impulse response (FIR) structure for discrete-time state-space signal models. This smoother is called an H2 FIR smoother (H2FS). Constraints such as linearity, quasi-deadbeat property, FIR structure, and independence of the initial state information are required in advance to design H2FS that is optimal in the sense of H2 performance criterion. It is shown that H2FS design problem can be converted into the convex programming problem written in terms of a linear matrix inequality (LMI) with a linear equality constraint. Simulation study illustrates that the proposed H2FS is more robust against uncertainties and faster in convergence than the conventional H2S.

This letter propose a new H∞ smoother (HIS) with a finite impulse response (FIR) structure for discrete-time state-space models. This smoother is called an H∞ FIR smoother (HIFS). Constraints such as linearity, quasi-deadbeat property, FIR structure, and independence of the initial state information are required in advance. Among smoothers with these requirements, we choose the HIFS to optimize H∞ performance criterion. The HIFS is obtained by solving the linear matrix inequality (LMI) problem with a parametrization of a linear equality constraint. It is shown through simulation that the proposed HIFS is more robust against uncertainties and faster in convergence than the conventional HIS.

In this paper, a new maximum likelihood filter with finite impulse response (FIR) structures is proposed for state space signal models with both system and observation noises. This filter is called the maximum likelihood FIR (MLF) filter. The proposed MLF filter doesn't require a priori information of the window initial state and processes the finite observations on the most recent window linearly. The proposed MLF filter is first represented in a batch form, and then in an iterative form for computational advantage. The proposed MLF filter has good inherent properties such as time-invariance, unbiasedness, deadbeat, robustness. The validity of the proposed MLF filter is illustrated by a computer simulation on a sinusoidal signal.