Model Distribution for Distributed Kalman Filters: A Graph Theoretic Approach

This paper discusses the distributed Kalman filter problem for the state estimation of sparse large-scale systems monitored by sensor networks. With limited computing resources at each sensor, no sensor has the ability to replicate locally the entire large-scale state-space model. We investigate techniques to distribute the model, i.e., to have at each sensor low-dimensional coupled local models that are computationally viable and provide accurate representation of the local states. We implement local Kalman filters over these coupled reduced models. We use system digraphs and cut-point sets for model distribution. Under certain conditions, the local Kalman filters asymptotically guarantee the performance of the centralized Kalman filter.