Fusion estimation using measured outputs with random parameter matrices subject to random delays and packet dropouts

• Multi-sensor noisy measurements with random delays and dropouts are considered.
• A recursive least-squares centralized fusion estimation algorithm is proposed.
• Least-squares matrix-weighted distributed fusion estimators are also proposed.
• The algorithms, based on covariances, are derived by an innovation approach.
• Recursive formulas for the estimation error covariance matrices are also proposed.

This paper investigates the centralized and distributed fusion estimation problems for discrete-time random signals from multi-sensor noisy measurements, perturbed by random parameter matrices, which are transmitted to local processors through different communication channel links. It is assumed that both one-step delays and packet dropouts can randomly occur during the data transmission, and different white sequences of Bernoulli random variables with known probabilities are introduced to depict the transmission delays and losses at each sensor. Using only covariance information, without requiring the evolution model of the signal process, a recursive algorithm for the centralized least-squares linear prediction and filtering estimators is derived by an innovation approach. Also, local least-squares linear estimators based on the measurements received by the processor of each sensor are obtained, and the distributed fusion method is then used to generate fusion predictors and filters by a matrix-weighted linear combination of the local estimators, using the mean squared error as optimality criterion. In order to compare the performance of the centralized and distributed fusion estimators, recursive formulas for the estimation error covariance matrices are also derived. A numerical example illustrates how some usual network-induced uncertainties can be dealt with the current observation model with random matrices.