Isolated Kalman filtering: theory and decoupled estimator design

In this paper, we propose a state decoupling strategy for Kalman filtering problems, when the dynamics of individual estimates are decoupled and their outputs are sparsely coupled. The algorithm is termed Isolated Kalman Filtering (IsoKF) and exploits the sparsity in the output coupling by applying approximations that mitigate the need for non-involved estimates. We prove that the approximations made during the isolated coupling of estimates are based on an implicit maximum determinant completion of the incomplete a priori covariance matrix. The steady state behavior is studied on eleven different observation graphs and a buffering scheme to support delayed (i.e. out-of-order) measurements is proposed. We discussed handling of delayed measurements in both, an optimal or a suboptimal way. The credibility of the isolated estimates are evaluated on a linear and nonlinear toy example in Monte Carlo simulations. The presented paradigm is made available online to the community within a generic C++ estimation framework supporting both, modular sensor fusion and collaborative state estimation.