A Kalman-like FIR estimator ignoring noise and initial conditions

A p-shift finite impulse response (FIR) unbiased estimator (UE) is addressed for linear discrete time-varying filtering (p = 0), p-step prediction (p > 0), and p-lag smoothing (p <; 0) of signal models in state space with no requirements for initial conditions and zero mean noise. A solution is found in a batch form and represented in a computationally efficient iterative Kalman-like one. It is shown that the Kalman-like FIR UE is able to overperform the Kalman filter if the noise covariances and initial conditions are not known exactly, noise is not white, and both the system and measurement noise components need to be filtered out. Otherwise, the errors are similar.