关于GPS源定位中解的唯一性的研究：距离与平方距离最小化在二维和三维空间中的有限测量情况
On the Uniqueness of Solutions in GPS Source Localization: Distance and Squared-Distance Minimization under Limited Measurements in Two and Three Dimensions
AI总结：
本文研究了GPS源定位中距离与平方距离最小化问题，在二维和三维空间中探讨了解的唯一性及有限测量下的解数量。
摘要：
源定位问题，对于GPS等应用至关重要，通常被视为在各种噪声存在下的最小化问题。确保GPS技术中的解的唯一性对于应用的可靠性和准确性至关重要，从日常导航到关键的军事行动。在本文中，我们研究了两个关键的最小化问题：一个专注于距离误差，另一个专注于平方距离误差。我们探讨了这些问题在三维空间（标准场景）和二维空间（简化情况）中的情况。此外，我们讨论了当测量数量少于三个时可能的源解数量。
英文摘要：
The source localization problem, fundamental to applications like GPS, is typically approached as a minimization problem in the presence of various types of noise. Ensuring the uniqueness of solutions in GPS technology is vital for the reliability and accuracy of applications, from everyday navigation to critical military operations. In this paper, we examine two key minimization problems: one focused on distance error and the other on squared distance error. We explore these problems in both three-dimensional space, the standard scenario, and in two-dimensional space as a simplified case. Furthermore, we discuss the number of possible source solutions when the number of measurements is fewer than three.
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