The article presents the results of testing the algorithm, considered in the first part, for determining the position of an autonomous underwater vehicle (AUV) based on measurements of ranges to acoustic beacons and on the data from a water-speed log and a heading indicator. Distinctive features of the algorithm are the start without using AUV a priori coordinates and without the set of measurements required for an unambiguous navigation solution, recursive processing, in the same filter, of current measurements and those saved before the algorithm starts, and accounting for the ambiguity of the AUV position and its resolution. The performance of the proposed algorithm is compared with other possible solutions. The results of simulation and field data post-processing have been obtained, which make it possible to estimate the time to get the first unambiguous solution and the accuracy of unambiguous solutions using the developed algorithm with a different number and location of acoustic beacons and the AUV trajectory. The cases are considered when the desynchronization of the beacon and AUV clocks is a random variable and when the desynchronization is unknown; consequently, either range measurements or range-difference measurements are used. The solutions are compared taking into account the measurements saved before the algorithm start and without taking them into account.