In this paper, the optimal least-squares state estimation problem is addressed for a class of discrete-time multisensor linear stochastic systems with state transition and measurement random parameter matrices and correlated noises. It is assumed that at any sampling time, as a consequence of possible failures during the transmission process, one-step delays with different delay characteristics may occur randomly in the received measurements. The random delay phenomenon is modelled by using a different sequence of Bernoulli random variables in each sensor. The process noise and all the sensor measurement noises are one-step autocorrelated and different sensor noises are one-step cross-correlated. Also, the process noise and each sensor measurement noise are two-step cross-correlated. Based on the proposed model and using an innovation approach, the optimal linear filter is designed by a recursive algorithm which is very simple computationally and suitable for online applications. A numerical simulation is exploited to illustrate the feasibility of the proposed filtering algorithm.

The design of recursive estimation algorithms in networked systems is an important research challenge from both theoretical and practical perspectives. The growing number of application fields are demanding the development of new mathematical models and algorithms that accommodate the effect of the unavoidable network-induced uncertainties. Special relevance have transmission delays and packet dropouts, which may yield a significant degradation in the performance of conventional estimators. This paper discusses the distributed fusion estimation problem in a class of linear stochastic uncertain systems whose measurement noises are cross-correlated and coupled with the process noise. The uncertainty of the system is not only described by additive noises, but also by multiplicative noise in the state equation and random parameter matrices in the measurement model. Both one-step delays and packet dropouts can randomly occur during the transmission of the sensor measurements to the local processors and a compensation strategy based on measurement prediction is used. Under the least-squares criterion and using an innovation approach, a recursive algorithm for the local filtering estimators is designed. These local estimators are then fused at a processing centre, where the distributed fusion filter is generated as the least-squares matrix-weighted linear combination of the local ones.