Best linear unbiased estimation filters with FIR structures for state space signal models

In this paper, a new best linear unbiased estimation (BLUE) finite impulse response (FIR) filter called the BLUE FIR filter is proposed for discrete-time state space signal models with system noises and inputs. The proposed BLUE FIR filter is a linear function of only the finite measurements and inputs on the most recent horizon, does not require a priori information about the horizon initial state, and has both unbiasedness and efficiency properties. The proposed BLUE FIR filter has time-invariance and dead-beat properties. The proposed BLUE FIR filter is represented in batch form and then iterative form for computational advantage. It is shown to be equivalent to the existing receding horizon (RH) FIR filter with completely unknown horizon initial state, whose efficiency was difficult to obtain and was thus unknown.