Distributed state estimation for uncertain linear systems: A regularized least-squares approach

This paper addresses the state estimation problem for a discrete-time uncertain system with a network of sensors, where the system is not necessarily observable by each sensor and deterministic uncertainties exist in the system matrices. A new robust estimator is designed for each sensor, using only its own and neighbor’s information, which is fully distributed. Moreover, a novel information fusion strategy is developed to guarantee the estimation performance, based on the collective observability of the sensor network, which greatly relaxes the technical assumption of the proposed estimator. Theoretically, it can be ensured that if the observed system is time-varying, the gains of the estimator will be bounded. Furthermore, if the system is time-invariant, these gains will be convergent. Subsequently, the estimation error covariance will be ultimately bounded if the observed system is quadratically bounded. In the end, the superiority of the proposed robust distributed state estimation algorithm is illustrated by several numerical simulation examples.