Least-Squares Linear Smoothers from Randomly Delayed Observations with Correlation in the Delay

This paper discusses the least-squares linear filtering and smoothing (fixed-point and fixed-interval) problems of discrete-time signals from observations, perturbed by additive white noise, which can be randomly delayed by one sampling time. It is assumed that the Bernoulli random variables characterizing delay measurements are correlated in consecutive time instants. The marginal distribution of each of these variables, specified by the probability of a delay in the measurement, as well as their correlation function, are known. Using an innovation approach, the filtering, fixed-point and fixed-interval smoothing recursive algorithms are obtained without requiring the state-space model generating the signal; they use only the covariance functions of the signal and the noise, the delay probabilities and the correlation function of the Bernoulli variables. The algorithms are applied to a particular transmission model with stand-by sensors for the immediate replacement of a failed unit. key words: least-squares estimation, innovation process, filtering and smoothing, randomly delayed observations, covariance information