Signal polynomial smoothing from correlated interrupted observations based on covariances

The least-squares polynomial smoothing problem of discrete-time signals from uncertain observations is addressed, when the variables describing the uncertainty are correlated at consecutive sampling times. Defining suitable augmented signal and observation vectors, the polynomial estimation problem is reduced to the linear estimation problem of the augmented signal. By an innovation approach, recursive algorithms are derived for the augmented linear estimators without requiring the knowledge of the state-space model generating the signal, but only covariance information of the processes involved.