Least-Squares Filtering Algorithm in Sensor Networks with Noise Correlation and Multiple Random Failures in Transmission

This paper addresses the least-squares centralized fusion estimation problem of discrete-time random signals from measured outputs, which are perturbed by correlated noises. These measurements are obtained by different sensors, which send their information to a processing center, where the complete set of data is combined to obtain the estimators. Due to random transmission failures, some of the data packets processed for the estimation may either contain only noise (uncertain observations), be delayed (randomly delayed observations), or even be definitely lost (random packet dropouts). These multiple random transmission uncertainties are modelled by sequences of independent Bernoulli random variables with different probabilities for the different sensors. By an innovation approach and using the last observation that successfully arrived when a packet is lost, a recursive algorithm is designed for the filtering estimation problem. The proposed algorithm is easily implemented and does not require knowledge of the signal evolution model, as only the first- and second-order moments of the processes involved are used. A numerical simulation example illustrates the feasibility of the proposed estimators and shows how the probabilities of the multiple random failures influence their performance.