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 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.