This paper presents a novel filtering technique to estimate the position of a moving target based on discrete-time direction and velocity measurements. The velocity is assumed to be corrupted by an unknown constant bias, which is explicitly estimated in the process. A nonlinear system is first designed, describing the dynamics and observations associated to the target, followed then by a state augmentation that yields an equivalent linear time-varying system. An observability analysis for the latter is conducted based on necessary and sufficient conditions that are related to the target's motion. The final estimation solution resorts to a Kalman Filter with globally exponentially stable error dynamics. Its performance is assessed via realistic numerical simulations, including Monte Carlo runs and a comparison with both the standard extended Kalman filter and the Bayesian Cramer-Rao bound. A set of experimental results achieved within the scope of a realistic underwater mission scenario is also presented that allows to further assess the proposed technique.