A Kalman-like algorithm with no requirements for noise and initial conditions

We address a Kalman-like estimator for solving universally the problems of filtering (p = 0), prediction (p > 0), and smoothing (p < 0) of discrete time-varying state-space models with no requirements for noise and initial conditions. The estimator proposed overperforms the Kalman one when 1) noise covariances and initial conditions are not known exactly, 2) noise constituents are not white sequences, and 3) both the system and measurement noise components need to be filtered out and the deterministic state estimated. Otherwise, the Kalman-like and Kalman filters produce similar errors. A numerical comparison of the Kalman and Kalman-like estimators is provided.