Signal estimation with nonlinear uncertain observations using covariance information

Abstract

This paper addresses the signal estimation problem in situations where the observations are nonlinear functions of the signal and the measure mechanism is prone to failure or some observations are accidentally lost (uncertain observations). A recursive filtering and fixed-point smoothing algorithm is proposed assuming that the Bernoulli random variables describing the uncertainty in the observations are independent and the state-space model generating the signal is unknown and only the covariance functions of the processes involved in the observation equation are available. A numerical simulation example concerning the phase modulation problem shows the effectiveness of the proposed algorithm.