Recursive estimation of discrete-time signals from nonlinear randomly delayed observations

In this paper, one-stage prediction, filtering, and fixed-point smoothing problems are addressed for nonlinear discrete-time stochastic systems with randomly delayed measurements perturbed by additive white noise. The observation delay is modelled by a sequence of independent Bernoulli random variables whose values zero or one indicate that the real observation arrives on time or it is delayed one sampling time and, hence, the available measurement to estimate the signal is not updated. Assuming that the state space model generating the signal to be estimated is unknown and only the covariance functions of the processes involved in the observation equation are available, recursive estimation algorithms based on linear approximations of the real observations are proposed.