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 or on decentralized schemes. The main advantage of centralized filter (CF) is its ability to provide mean-square optimal estimate of the linear system state. 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). The FFA are computationally simpler and immune to false measurements, however, they generally fail to provide optimal estimates. 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 CF. 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.