In underwater navigation, the global positioning system is unavailable; hence, other solutions must be pursued in the development of navigation systems. In this paper, filters for the position, linear velocity, and acceleration of underwater vehicles are derived by combining a long baseline acoustic positioning system with an inertial navigation system. A dynamic model is devised via state augmentation, including the bias of the pseudo-ranges, which accounts for the effect of the unknown offset between the emitters’ and receivers’ clocks. With this technique, the resulting dynamics are linear, in spite of the original nonlinear nature of the problem. The proposed solution, which includes the explicit dynamic estimation of the bias of the pseudo-ranges, is a linear Kalman filter. The observability of the system is assessed, which allows to establish globally exponentially stable error dynamics. The performance of the solution is evaluated with realistic simulation results, considering sensor noise and discrete-time measurements. Finally, the comparison with the extended Kalman filter (EKF), the unscented Kalman filter (UKF), and the Bayesian Cramér–Rao bound is presented, including Monte Carlo simulations. This comparison shows the goodness of the proposed solution, which converges for all initial conditions and exhibits performance comparable to the EKF and the UKF, whereas the EKF and UKF are shown to lack global convergence.