A Nonlinear Fixed-Lag Smoother for Finite-State Markov Processes

The fixed-lag smoothing of random telegraph type signals is studied. The smoothers are derived by first obtaining fixed-point smoothing equations and then using a time discretization. Simulation results are described that verify the qualitative carry-over of known results for the linear-Gaussian problem: The greater the lag, the greater the improvement; beyond a certain lag, no further improvement is obtained by the increase of lag; and the higher the signal-to-noise ratio (SNR), the greater is the improvement over filtering obtained through the use of smoothing. Smoothing errors of one-half the corresponding filtering error are demonstrated.