Optimal decentralized Kalman filter

The Kalman filter is a powerful state estimation algorithm which incorporates noise models, process model and measurements to obtain an accurate estimate of the states of a process. Implementation of conventional Kalman filter algorithm requires a central processor that harvests measurements from all the sensors in the field. Central algorithms have some drawbacks such as reliability, robustness and high computation which result in a need for non-central algorithms. This study takes optimality in decentralized Kalman filter (DKF) as its focus and derives the optimal decentralized Kalman filter (ODKF) algorithm, in case the network topology is provided to every node in the network, by introducing global Kalman equations. ODKF sets a lower bound of estimation error in least squares sense for DKF.