Receding-horizon unbiased FIR filters for continuous-time state-space models without a priori initial state information

A receding horizon unbiased finite-impulse response filter (RHUFF) is proposed for continuous-time state space models. Linearity, unbiasedness, finite-impulse response (FIR) structure, and independence of the initial state information will be required in advance, in addition to a performance index of minimum variance. The proposed RHUFF is obtained by directly minimizing the performance index with the unbiasedness constraint. The proposed RHUFF is represented first in a standard FIR form and then in an iterative form. It is shown that the RHUFF is equivalent to the existing receding horizon (RH) Kalman FIR filter. The former is more systematic and logical, while the latter is heuristic due to the handling of infinite covariance of the initial state information.