ABSTRACT
The problem of distributed Kalman filtering (DKF) for sensor networks is one of the most fundamental distributed estimation problems for scalable sensor fusion. This chapter addresses the DKF problem by reducing it to two separate dynamic consensus problems in terms of weighted measurements and inverse-covariance matrices. These two data fusion problems are solved is a distributed way using low-pass and band-pass consensus filters. Consensus filters are distributed algorithms that allow calculation of average-consensus of time-varying signals. It is shown that a central Kalman filter for sensor networks can be decomposed into n micro-Kalman filters with inputs that are provided by two types of consensus filters. This network of micro-Kalman filters collectively are capable of providing an estimate of the state of the process (under observation) that is identical to the estimate obtained by a central Kalman filter, given that all the nodes agree on two central sums. Later, we demonstrate that our consensus filters can approximate these sums, and that gives an approximate distributed Kalman filtering algorithm.
In a hi-tech environment, a strict surveillance unit is required for an appropriate supervision. It often utilizes a group of distributed sensors which provide information about the local targets. Compared to the centralized Kalman filtering (CKF), which can be used in mission critical scenarios, where every local sensor is important with its local information, the distributed fusion architecture has many advantages. There is no second thought that in certain scenarios, a centralized Kalman filter plays a major role, and it involves minimum information loss. A general structure for the Distributed Kalman Filter (DKF) can be seen in Figure 4.1.
