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

In this note, a new receding horizon unbiased finite-impulse response filte r (RHUFF) is proposed for continuous-time state space models. Linearity, un biasedness, finite-impulse response (FIR) structure, and independence of th e Initial state information will be required in advance, in addition to a p erformance index of minimum variance. The proposed RHUFF is obtained by dir ectly minimizing the performance index with the unbiasedness constraint. Th e 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 r eceding horizon (RH) Kalman FIR filter. The former is more systematic and l ogical, while the latter is heuristic due to the handling of infinite covar iance of the initial state information.