Distributed Kalman Filtering for Sensor Networks With Time-Varying Coordinate Frames

In this article, distributed Kalman filters are designed for a discrete and stochastic sensor network where each sensor holds a time-varying and local coordinate frame. Several stability conditions for the distributed Kalman filtering algorithms are derived by using the Lyapunov method. Then, for the information fusion of affine-transformed innovations from neighbors, a consensus-based distributed Kalman filter is proposed for heterogeneous processes over a digraph. We further consider the existence of transformation uncertainties and translation measurement noises, where a robust weighted consensus-based distributed Kalman filter is developed and a uniform upper bound of the estimation error is established. To show the effectiveness and robustness of the proposed filtering algorithms, a group of automatic guided vehicles is applied to achieve cooperative localization in simulation examples.