Linear estimation based on covariances for networked systems featuring sensor correlated random delays

This article is concerned with the least-squares (LS) linear estimation problem of discrete-time signals from noisy measurements coming from multiple randomly delayed sensors with different delay characteristics. It is assumed that the Bernoulli random variables characterising the measurement delays are correlated at consecutive sampling times. Using an innovation approach, recursive linear filtering and smoothing (fixed-point and fixed-interval) algorithms are obtained without requiring the state-space model generating the signal, but only the covariance functions of the signal and the noise, the delay probabilities and the correlation function of the Bernoulli variables. Also, recursive formulas for filtering and fixed-point smoothing error covariance matrices are obtained to measure the goodness of the proposed estimators.