Long Baseline Underwater Positioning with Fusion of Saved and Current Measurements and Ambiguity Resolution. Part I. Mathematical Formulation

We report a recursive positioning algorithm for an autonomous underwater vehicle (AUV) based on measurements of ranges to acoustic beacons, water speed log and heading indicator data. Two types of desynchronization between the beacon and AUV clocks are considered: random and unknown. The algorithm starts without using AUV a priori coordinates when simultaneous measurements from minimum two or three beacons (depending on the desynchronization type) are first obtained. The newly coming measurements and those saved before the algorithm start are processed in forward and backward time in the same filter. If AUV coordinate estimates are ambiguous, two filters are implemented, which process the same data with different measurement linearization points. Ambiguity is resolved based on the ratio of a posteriori probabilities of hypotheses on AUV position. This ratio is calculated using the filters’ outputs.