Research of Nonrecursive Federated Filtering Algorithms Under Non-White Noise Measurement Errors

Abstract

The paper considers the design of the algorithms estimating the dynamic system state under the presence of non-white noise measurement errors. The estimators can be based on centralized processing, when all available measurements are fed to one centralized computer, or on decentralized schemes. The main advantage of centralized architecture is its ability to provide mean-square optimal estimate of the linear system state using the linear measurements with Gaussian system noise and measurement errors, however, this architecture features low reliability and high computational load.

The described decentralized processing methods are based on federated filtering algorithms (FFA), where the state vector of dynamic system is estimated by weighting the estimates of the local filters (LF), processing the local measurements, in the master filter (MF). Decentralized methods based on FFA have become widespread and also often applied to navigation of different robot-aided systems. The federated filtering algorithms are computationally simpler and immune to false measurements, however, they generally fail to provide optimal estimates, and the calculated accuracy characteristic is not a real error covariance matrix of the generated estimate.

The proposed FFA is based on nonrecursive processing of measurements in LF. It has been shown that when LF tuning conditions are met, the MF estimates and covariance matrices coincide with the estimates and covariance matrices for the optimal centralized Kalman filter. It has been noted that the use of a nonrecursive measurement processing scheme creates a good background for applying factor graph optimization (FGO) methods in the problem of nonlinear measurements processing using FFA.

The obtained results are illustrated by the example of navigation system correction.