A linear estimation problem of decentralized processing of measurements is considered, which involves the estimate of the state vector of a dynamic system by fusion of the estimates generated in local filters using the data from distributed (separate) sensors. The conditions are discussed that ensure the coincidence of the estimates and calculated covariance matrices of estimation errors generated in this way with the results obtained in the optimal centralized Kalman filter. The features of these conditions for recursive and nonrecursive schemes are analyzed. The comparison of two schemes is illustrated using an example of random walk estimation.

Two schemes of suboptimal estimation algorithms synthesized using the Bayesian approach and based on the linearization of functions describing the behavior of the estimated state vector and measurement model are compared for one class of nonlinear estimation problems. One of them is traditional, in which the estimate is found recursively with respect to measurements, and the other one, nonrecursive, involves the simultaneous use of the full set of all available measurements. The advantages and disadvantages of the analyzed algorithms are discussed and illustrated by an example.