Fixed-interval smoothing problem from uncertain observations with correlated signal and noise

Abstract

This paper presents recursive filtering and fixed-interval smoothing algorithms from observations corrupted by additive and multiplicative noises. Additive noise is a white process correlated with the signal, and multiplicative noise is modelled by a sequence of independent Bernoulli random variables. It is assumed that both, autocovariance function of signal and crosscovariance function about signal and observation noise, are expressed in a semi-degenerate kernel form. The algorithms are obtained by an innovation approach, without using the state-space model, but only covariance information of signal and observation noise, and probability that signal exists in the observed values.