Second-order polynomial estimators from uncertain observations using covariance information

摘要

This paper presents recursive least mean-squared error second-order polynomial filtering and fixed-point smoothing algorithms to estimate a signal, from uncertain observations, when only the information on the moments up to fourth-order of the signal and observation noise is available. The estimators require the autocovariance and crosscovariance functions of the signal and their second-order powers in a semidegenerate kernel form, and the probability that the signal exists in the observed values.