Geometry-based Multi-beam Survey Line Layout Problem

TL;DR

This paper develops a geometric and algorithmic approach to optimize multi-beam survey line layouts for underwater terrain detection, improving measurement accuracy and coverage efficiency.

Contribution

It introduces a mathematical model linking survey parameters with terrain measurement, and proposes an optimal survey line layout strategy using greedy algorithms and binary search.

Findings

Mathematical model for survey line coverage and overlap ratio.

Optimal survey line layout strategy using greedy algorithm.

Enhanced accuracy and efficiency in underwater terrain detection.

Abstract

The multi-beam measurement system plays a crucial role in ocean mapping and underwater terrain detection. By simultaneously transmitting multiple beams, the system can accurately receive sound waves reflected from the seabed, providing more precise and comprehensive water depth information while effectively revealing the complexity and characteristics of underwater terrain. Building upon the background and application provided by Question B of the 2023 National Mathematical Contest in Modeling for College Students, this paper investigates the relationship between ocean floor width measurement and factors such as beam position, angle, and slope. Utilizing geometric relations, trigonometric similarity, and sine theorem, a mathematical model is established to determine adjacent strip coverage width and overlap ratio. Furthermore, an optimal strategy is determined using a greedy algorithm, while binary search backtracking is employed to derive the interval of the next adjacent survey line with the required overlap ratio in order to obtain an optimal terrain detection strategy.