State Estimation Using a Network of Observers: A Distributed Optimization Approach

We introduce a novel dynamic data fusion method for distributed state estimation in multi-agent systems. We consider a scenario where system outputs are measured by sensors distributed across multiple agents. We assume that the local measurement may lack detectability while the joint measurements ensure the detectability of the system. Each node is equipped with an observer that exchanges state estimates with neighboring nodes over a communication network, with the objective of estimating the entire system state locally. Our approach first reconstructs the locally observable portion of the state at each agent and then reformulates the distributed state estimation problem as a distributed online optimization task. By iteratively solving this optimization problem, the proposed scheme enables each agent to estimate the full system state within a bounded error, which depends on the system dynamics and the number of iterations per time step. Simulation results show the effectiveness of the proposed dynamic data fusion method.