An Iterative Kalman-Like Algorithm Ignoring Noise and Initial Conditions

We address a p -shift finite impulse response (FIR) unbiased estimator (UE) for linear discrete time-varying filtering ( p =0), p -step prediction ( p >; 0), and p -lag smoothing ( p <; 0) 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 outperform 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. Extensive numerical studies of the FIR UE are provided in Gaussian and non-Gaussian environments with outliers and temporary uncertainties.