Distributing the Kalman Filter for Large-Scale Systems

This paper derives a near optimal distributed Kalman filter to estimate a large-scale random field monitored by a network of N sensors. The field is described by a sparsely connected dynamical system of high-dimensionality, n. The main contributions of the paper are: (1) distribute the high-dimensional model into N coupled sensor-based reduced models of dimension nl n using a graph-theoretic approach; (2) implement local Kalman filters on the reduced models; (3) fuse the observations and estimates that are common among the local Kalman filters using bipartite fusion graphs and consensus averaging algorithms; (4) invert the error covariances and information matrices of the local filters with a generalized distributed matrix Jacobi algorithm that we introduce and an L−banded matrix inversion theorem. These inversion algorithms compute the submatrices of interest with only local variables of dimension nl, hence, performing the Riccati and Lyapunov equations with only local commun...

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Usman A. Khan, José M. F. Moura
• Keywords: CORR 2007, Education, Implement Local Kalman, Local Kalman filters, Sensor-based Reduced Models