Multiple Model Algorithm for Single-Beacon Navigation of Autonomous Underwater Vehicle without Its A Priori Position. Part 1. Mathematical Formulation

Abstract

The article considers a problem of autonomous underwater vehicle (AUV) positioning with acoustic measurements of range and possibly radial velocity relative to a single beacon, velocity components and coordinate increments from an inertial navigation system, and the data from a water-speed log or a ground log. Interruptions in acoustic measurements reception are acceptable. Availability of a priori information on relative position of AUV and the beacon is not assumed. In order to solve the problem, the author proposes a multiple model algorithm based on a bank of extended Kalman filters which independently estimate the initial horizontal range and errors of the used data under different hypotheses about a value of AUV initial azimuth relative to the beacon. Current coordinates of AUV are determined by the outputs of filters, taking into account the a posteriori probabilities of the corresponding hypotheses. The algorithm is rather simple for programming and does not require much computational power.