Abstract
In this article, the least-squares νth-order polynomial fixed-point smoothing problem of uncertainly observed signals is considered, when only some information about the moments of the processes involved is available. For this purpose, a suitable augmented observation equation is defined such that the optimal polynomial estimator of the original signal is obtained from the optimal linear estimator of the augmented signal based on the augmented observations and, hence, a recursive algorithm for this linear estimator is deduced. The proposed estimator does not require the knowledge of the state-space model of the signal, but only the moments (up to the 2νth one) of the signal and observation noise, as well as the probability that the signal exists in the observations.
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