Decentralised navigation systems for bearing-based position and velocity estimation in tiered formations

This paper presents a novel decentralised navigation system based on bearing measurements for tiered vehicle formations. In the proposed framework, some vehicles have access to measurements of their own position, whereas others have access to bearing measurements to one or more neighbouring vehicles. Depth measurement may also be available. Local observers for the position and fluid velocity are designed based on the derivation of an equivalent observable linear time-varying system, thus yielding globally exponentially stable error dynamics. The local observers rely on local measurements, as well as limited communications between the vehicles. The stability of the system as a whole is analysed by studying the robustness of the local observers to exponentially decaying perturbations. Thorough Monte Carlo simulations are presented and discussed to compare the performance of the proposed solution with the extended Kalman filter, the unscented Kalman filter, and the Bayesian Cramér-Rao bound.