Robust $q$-LAG Unbiased FIR Smoother for LTV Systems and Recursive Forms

A new robust
$q$
-lag unbiased finite impulse response (UFIR) smoother is obtained in discrete-time state-space in batch and recursive forms for linear time-varying (LTV) systems under arbitrary zero mean noise and uncertainties. It is shown that recursive computation of the error covariance of the UFIR smoother is partly available for LTV systems and fully available for linear time-invariant systems. Examples of a polynomial model with colored noise and an uncertain harmonic process have proved that the
$q$
-lag UFIR smoother outperforms the Rauch-Tung-Striebel or Kalman smoother.