Improving Distributed Moving Horizon Estimation Over Wireless Sensor Networks With Application to Mobile Robot Localization

This article investigates the distributed state estimation (DSE) problem for constrained nonlinear systems over wireless sensor networks (WSNs). We propose a novel hybrid distributed moving horizon estimation (DMHE) framework that combines both local measurements and prior estimates from neighboring nodes. The local estimation is performed in real time by solving an optimization problem that fuses these two information sources, thereby enhancing accuracy and robustness. A key advantage of our framework lies in designing the consensus prior weighting parameters offline via linear matrix inequalities (LMIs), providing a more flexible and scalable approach to improving global estimation performance. Furthermore, under disturbance boundedness, collective observability, and network connectivity, we prove that the global estimation error converges exponentially to a well-defined bound. The proposed framework generalizes two distinct DMHE approaches—consensus on prior estimates and consensus on measurements. Numerical results on a mobile robot localization task demonstrate its superior performance, underscoring both its theoretical soundness and practical feasibility.