Multi-agent Target Position Estimation Using Bearing-only Measurements via Spatial Excitation

This paper solves the problem of estimating a single target position by a group of agents in two-dimensional space. Each agent is assumed to know its own position and to measure only the bearing to the target. We develop a distributed estimation scheme that processes individual bearing measurements by utilizing continuous-time dynamics with communication among the agents. Under the assumption of connectivity on the communication graph, it is shown that, even if each bearing measurement does not satisfy the persistency of excitation condition, each agent is able to estimate the target position provided that the agents are properly positioned. We examine this condition in terms of spatial excitation and its relationship with geometric configuration of the agents. Additionally, we analyze the convergence rate of the estimation error. Simulation results are provided to illustrate the performance of the proposed estimator.