An innovation approach to the smoothing problem from uncertain observations with correlated signal and noise

This paper treats the least mean‐squared error linear fixed‐point and fixed‐lag smoothing problems from uncertain observations, when the variables describing the uncertainty are independent, and the signal and observation white noise are correlated. Using an innovation approach, recursive algorithms are derived for both estimators without requiring the whole knowledge of the state‐space model generating the signal, but only covariance information of the signal and the observation noise, as well as the probability that the signal exists in the observed values. Copyright © 2005 John Wiley & Sons, Ltd.