Federated Kalman filtering via formation of relation equations in augmented state space

A new approach to the synthesis of federated filters used in the solution of multisensor system state estimation problems is considered. The method is based on two principles. The principle of state vector augmentation makes it possible to substitute a solution of an optimal estimation problem using a centralized Kalman filter for bias error measurement processing for an optimal estimation problem solution in the augmented state space. The equivalence of estimation results is achieved by a certain adjustment of focal filters and formation of additional error-free pseudomeasurements. The principle of rejection of part of the information contained in the relation equations makes it possible to establish a relation between federated filtering and filtering in the augmented state space, between weighting of local estimates and processing of pseudomeasurements, and, as a result, to reveal the reasons for the loss of optimality of federated filters. It is emphasized that at a certain adjustment, the covariance matrix calculated in the master filter is an upper bound for a real covariance matrix of a global estimate, and it can be used as an accuracy characteristic of the parameters estimated. The results of a simulation are given to illustrate the approach.