Fixed-interval smoother from randomly delayed observations

This paper presents a recursive algorithm for the least-squares linear fixed-interval smoothing problem of discrete-time signals using randomly delayed measurements perturbed by an additive white noise. It is assumed that the autocovariance function of the signal is expressed in a semi-degenerate kernel form and the delay is modelled by a sequence of independent Bernoulli random variables, which indicate if the measurements are up-to-date or delayed by one sampling time. The estimators do not use the state-space model of the signal but only the covariance information about the signal and the additive noise in the observations and the delay probabilities.