Information form distributed Kalman filtering (IDKF) with explicit inputs

With the ubiquity of information distributed in networks, performing recursive Bayesian estimation using distributed calculations is becoming more and more important. There are a wide variety of algorithms catering to different applications and requiring different degrees of knowledge about the other nodes involved. One recently developed algorithm is the distributed Kalman filter (DKF), which assumes that all knowledge about the measurements, except the measurements themselves, are known to all nodes. If this condition is met, the DKF allows deriving the optimal estimate if all information is combined in one node at an arbitrary time step. In this paper, we present an information form of the distributed Kalman filter (IDKF) that allows the use of explicit system inputs at the individual nodes while still yielding the same results as a centralized Kalman filter.