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

A new estimation algorithm from measurements with multiplestep random delays and packet dropouts

The least-squares linear estimation problem using covariance information is addressed in discretetime linear stochastic systems with bounded random observation delays which can lead to bounded packet dropouts. A recursive algorithm, including the computation of predictor, filter, and fixed-point smoother, is obtained by an innovation approach. The random delays are modeled by introducing some Bernoulli random variables with known distributions in the system description. The derivation of the proposed estimation algorithm does not require full knowledge of the state-space model generating the signal to be estimated, but only the delay probabilities and the covariance functions of the processes involved in the observation equation

Derivation of centralized and distributed filters using covariance information

The problem of estimating a degraded image using observations acquired from multiple sensors is addressed when the image degradation is modelled by white multiplicative and additive noise. Assuming the state-space model is unknown, the centralized and distributed filtering algorithms are derived using the information provided by the covariance functions of the processes involved in the measurement equation. The filters obtained are applied to an image affected by multiplicative and additive noise, and the goodness of the centralized and distributed filters is compared by examining the respective filtering error variances.Multiplicative noise Filter Multiple sensors