Mapping Problems of Geophysical Fields in Ocean and Extremum Problems of Underwater Objects Navigation

Abstract

Abstract The paper focuses on mathematical and technical problems of navigation and control of unmanned underwater vehicles (AUV). Such problems arise during geophysical fields mapping, development of map-aided navigation methods, and optimal routes finding. To address map creation problem, the results of measurements on trajectory were used; then the field map reconstruction in fixed frame of a reference followed. The paper discusses optimization of the survey routes and optimization of measurements of the parameters of local fields and their anomalies on trajectory of an AUV. The field map reconstruction methods based on measurement results on trajectory are considered. Some mathematical problems of navigation by geophysical field maps are discussed. More specifically, matching algorithms for fragment taken in motion with a reference map are studied, the problem of the best reference map approximation for data compression on the AUV board is considered, the field informativity criterion is offered, and the problem of optimal route construction on the basis of such criterion is solved. The estimates obtained in the paper are based on theoretical studies, the results of simulation experiments, and field experimental trials of the AUV systems.