Recursive fixed-interval smoother with correlated signal and noise in presence of uncertain observations

A recursive filter and fixed-interval smoother are presented in this paper, using observations which are affected by additive and multiplicative noises; additive noise is a white process correlated with signal and multiplicative one is modelled by independent Bernoulli random variables. It is used an innovation approach and assumed that the autocovariance function of signal and the crosscovariance function about signal and observation noise are expressed in a semidegenerate kernel form. The algorithms are obtained using covariance information of signal and observation noise, without using the state-space model.