In previous work by the authors a novel estimator was introduced, with asymptotic stability guarantees, for the problems of source localization and navigation based on single range measurements. The aim of this paper is to further study these problems in terms of the performance of the proposed estimators and the trajectories that yield best results. To that purpose, the achievable performance with the proposed estimator is compared with the Bayesian Cramér-Rao Bound (BCRB) for different trajectories of the agent and, in addition, the estimates provided by the Extended Kalman Filter are also computed. It is revealed that the performance of the estimator is close to the BCRB theoretical lower bound and some insight is provided on the effect of the agent trajectory on the estimation performance.