Derivation of linear estimation algorithms from measurements affected by multiplicative and additive noises

This paper addresses the problem of estimating signals from observation models with multiplicative and additive noises. Assuming that the state-space model is unknown, the multiplicative noise is non-white and the signal and additive noise are correlated, recursive algorithms are derived for the least-squares linear filter and fixed-point smoother. The proposed algorithms are obtained using an innovation approach and taking into account the information provided by the covariance functions of the process involved.