Navigation and source localization based on single pseudo-ranges

This paper presents a novel estimation solution for the problems of navigation and source localization based on pseudo-range measurements to a single pinger. In particular, the distance measurements are assumed to be corrupted by an unknown constant bias, which is explicitly taken into consideration in the design. First, the equivalence between the problems of navigation and source localization is established, as well as cooperative navigation of two vehicles in tandem. Then, an augmented system is derived and its observability is carefully studied. The analysis is constructive, in the sense that the means to design an observer for the new system dynamics with globally exponentially stable error dynamics are readily available, resorting to linear systems theory. Moreover, the new augmented system is shown to be equivalent to the original. Finally, simulations results are presented and discussed to assess the performance of the proposed solution in the presence of sensor noise.