Unbiased FIR smoother for discrete time-variant systems with backward structure

This paper is concerned with the q-lag smoothing problem for linear discrete time-variant state space models without any requirement for initial conditions and zero mean noise. A new unbiased finite impulse response (UFIR) smoother is proposed in a batch form, and further realized iteratively for fast computation. Compared with the Kalman smoother, the initial state and noise statistics are not required. Compared with the existing UFIR smoothers, the proposed method uses a backward pass that projects from the estimate at the last time step to obtain the smoothed state. In this way, any point between the initial and final times can be estimated. Finally, some numerical examples are given to demonstrate the applicability of the results.