Algorithms that enable acoustic sensing vehicles to autonomously map acoustic fields are being developed, but some require an analytical representation of the data collected from the acoustic field with specific continuity properties. One optimal control technique that has these requirements and has been used in autonomous acoustic sensing algorithms is Pontryagin’s Maximum Principle (PMP). Given that most real-world fields are modeled by numerical methods, the need to create continuous analytical representations from data is a hurdle in realistic applications of these autonomous algorithms. In this work, finite series of basis functions are used to solve this problem. The basis functions are selected to meet the criteria of the PMP, and are used to approximate the field from the data collected. While this approach meets the criteria of the algorithm, it can be a computationally expensive approach for complex fields and large datasets. This paper looks at the trade off between accuracy and computational time, for different frequencies and levels of field complexity. A previously published ocean profile developed from data taken off the island of Elba is used in the normal mode software, Kraken, to generate the acoustic fields used to test this method. The candidate basis functions considered are trigonometric functions analogous to finite Fourier series, and Legendre polynomials. The Legendre polynomials are shown to have higher accuracy when used with a dynamically selected exclusion range at low frequencies and a cubic spline interpolation method for generating intermediate data points at higher frequencies. Run times are calculated and while both candidate basis functions are shown to meet the requirements of the PMP algorithm, the Legendre polynomials require the least amount of run time.

中文翻译：

---

用于自动驾驶汽车应用的具有有限基函数级数的近似海洋声场

正在开发使声学传感车辆能够自主映射声场的算法，但有些算法需要对从声场收集的具有特定连续性属性的数据进行分析表示。具有这些要求并已用于自主声学传感算法的一种最佳控制技术是 Pontryagin 的最大原理 (PMP)。鉴于大多数现实世界的领域都是通过数值方法建模的，因此需要从数据中创建连续的分析表示是这些自主算法在实际应用中的障碍。在这项工作中，使用有限系列的基函数来解决这个问题。选择基函数以满足 PMP 的标准，并用于从收集的数据中逼近场。虽然这种方法符合算法的标准，但对于复杂的字段和大型数据集来说，它可能是一种计算量大的方法。本文着眼于不同频率和场复杂度级别的精度和计算时间之间的权衡。以前发布的从厄尔巴岛获取的数据开发的海洋剖面用于正常模式软件 Kraken，以生成用于测试该方法的声场。考虑的候选基函数是类似于有限傅里叶级数的三角函数和勒让德多项式。当与动态选择的低频排除范围和用于在较高频率生成中间数据点的三次样条插值方法一起使用时，勒让德多项式显示具有更高的精度。