A navigation algorithm to navigate an AUV within a charted environment is presented. The algorithm uses sonar range measurements and incorporates them with a potential function which defines the map of the operation area. Extended Kalman filtering is used in the algorithm. Least squares techniques are used in the estimation of system parameters. The algorithm is tested by both computer generated data and actual data collected from the vehicle NPS AUVII during tests in a water tank. Fixed interval smoothing is applied in order to smooth the estimates produced by the Kalman filter. The effects of currents in the operation area are sought. An approach based on backpropagation neural networks for the navigation algorithm is also presented. Throughout the simulation studies the algorithm yields a robust and reliable solution to the navigation problem of AUV's.