New filtering algorithm using observations with one or two-step random delay

This paper discusses the least-squares linear Altering problem of discrete-time signals from observations, perturbed by additive white noise, which can be randomly delayed by one or two sampling times. It is assumed that the Bernoulli random variables modelling the delays are independent and that the delay probabilities are known. Using an innovation approach, a recursive linear filtering algorithm is obtained using only the covariance functions of the signal and the noise, and the delay probabilities. An illustrative example shows the performance of the proposed filtering estimators for different delay probabilities.