一种用于重建三维空间中运动点声源的新型采样方法
A novel sampling method for reconstruction of a moving point acoustic source in $\mathbb{R}^3$
浏览论文内容
中文总结 AI 辅助
该研究针对三维空间中未知位置与发射时刻的运动点声源，提出新型采样方法，结合代数与几何理论，仅用5个观测点数据即可完成声源轨迹重建，提升了计算效率、稳定性与抗噪性，经数值实验验证有效。
中文摘要 AI 辅助
本文提出一种新型采样方法，用于重建三维空间（ℝ³）中运动点声源的轨迹，该声源的空间位置和发射时刻均未知。结合代数理论与几何知识，利用5个观测点的测量数据证明声源位置的唯一性。所提采样方法基于到达时间差约束公式的残差在真实声源位置处消失的特性构造指示函数，仅通过5个观测点的数据及其对应的到达时间，即可完成运动点声源的空间位置与发射时刻的重建。该算法不仅减少了所需观测点的数量，还提升了计算效率、稳定性及抗噪性，数值实验验证了该方法的有效性。
英文摘要
In this paper, we introduce a novel sampling method to recovering the trajectory of a moving point source in R^3, where both the spatial location and emission moment of the moving point source are unknown. Combining algebraic theory with geometric knowledge, we prove the uniqueness of the source location by using measured data from five observation points. Our sampling method constructs an indicator function based on the property that the residual of the time difference of arrival constraint formula vanishes at the true source location. It achieves the reconstruction of the spatial positions and emission moments of a moving point source only using data from five observation points and their corresponding arrival times. The algorithm not only reduces the required number of observation points, but also improves computational efficiency, stability, and noise resistance. Numerical experiments verify the effectiveness of the method.
