Distributed Kalman Filters in Sensor Networks: Bipartite Fusion Graphs

We study the distributed Kalman filter in sensor networks where multiple sensors collaborate to achieve a common objective. Our motivation is to distribute the global model that comes from the state-space representation of a sparse and localized large-scale system into reduced coupled sensor-based models. We implement local Kalman filters on these reduced models, by approximating the Gaussian error process of the Kalman filter to be Gauss-Markov, ensuring that each sensor is involved only in reduced-order computations and local communication. We propose a generalized distributed Jacobi algorithm to compute global matrix inversion, locally, in an iterative fashion. We employ bipartite fusion graphs in order to fuse the shared observations and shared estimates across the local models.