Navigation systems based on multiple bearing measurements

This paper presents two navigation filters based on multiple bearing measurements. In the first, the state is augmented and an equivalent linear system is derived, while in the second the output of the system is modified in such a way that the resulting system is linear. In both cases, the design of a filtering solution relies on linear systems theory, in spite of the nonlinear nature of the system, and the resulting error dynamics can be made globally exponentially stable by applying, for example, Kalman filters. The continuous/discrete nature of the different measurement sources is taken into account, with the updates occurring in discrete time, while open-loop propagation is carried out between bearing measurements. Simulation results are presented, including Monte Carlo runs and a comparison with both the extended Kalman filter and the Bayesian Cramér-Rao bound, to assess the performance of the proposed solutions.