论文标题
超越凸出船体TOA的本地化的迭代rndop-oftimal锚固位置：性能界限和启发式算法
Iterative RNDOP-Optimal Anchor Placement for Beyond Convex Hull ToA-based Localization: Performance Bounds and Heuristic Algorithms
论文作者
论文摘要
在锚凸面外部的定位目标是在以车辆为中心，基于无人机和自我定位应用程序中进行的研究局度研究但普遍的情况。考虑到这种情况，本文研究了最佳的锚定位置问题（基于到达时间（TOA）的基于时间（TOA）的定位方案，因此将最坏的精度稀释（DOP）最小化。在基于凸出船体TOA本地化的DOP缩放定律的先前结果的基础上，我们提出了一个新颖的度量标准，称为范围差异DOP（RNDOP）。我们表明，最差的DOP-最佳锚定位置问题简化为Min-Max RNDOP最佳锚定位置问题。不幸的是，这种配方在现实的约束下导致了一个非凸面和棘手的问题。为了克服这一点，我们提出了迭代锚添加方案，这导致了可拖延的问题，尽管是非凸面问题。通过利用由此产生的Rank-1更新产生的结构，我们设计了三个启发式方案，具有不同的性能复杂性权衡。此外，我们还为场景中的上限和下限得出了锚点以优化最坏情况（a）3D定位误差和（b）2D定位误差。我们以这些结果为基础，以设计一个具有凝聚力的迭代算法框架，以用于稳健的锚定位置，表征锚位置不确定性的影响，然后讨论所提出的方案的计算复杂性。使用数值结果，我们验证了理论结果的准确性。我们还提出了全面的蒙特卡洛模拟结果，以比较每个迭代方案的定位错误和执行时间性能，讨论权衡并为超越凸出赫尔本地化方案提供宝贵的系统设计见解。
Localizing targets outside the anchors' convex hull is an understudied but prevalent scenario in vehicle-centric, UAV-based, and self-localization applications. Considering such scenarios, this paper studies the optimal anchor placement problem for Time-of-Arrival (ToA)-based localization schemes such that the worst-case Dilution of Precision (DOP) is minimized. Building on prior results on DOP scaling laws for beyond convex hull ToA-based localization, we propose a novel metric termed the Range-Normalized DOP (RNDOP). We show that the worst-case DOP-optimal anchor placement problem simplifies to a min-max RNDOP-optimal anchor placement problem. Unfortunately, this formulation results in a non-convex and intractable problem under realistic constraints. To overcome this, we propose iterative anchor addition schemes, which result in a tractable albeit non-convex problem. By exploiting the structure arising from the resultant rank-1 update, we devise three heuristic schemes with varying performance-complexity tradeoffs. In addition, we also derive the upper and lower bounds for scenarios where we are placing anchors to optimize the worst-case (a) 3D positioning error and (b) 2D positioning error. We build on these results to design a cohesive iterative algorithmic framework for robust anchor placement, characterize the impact of anchor position uncertainty, and then discuss the computational complexity of the proposed schemes. Using numerical results, we validate the accuracy of our theoretical results. We also present comprehensive Monte-Carlo simulation results to compare the positioning error and execution time performance of each iterative scheme, discuss the tradeoffs, and provide valuable system design insights for beyond convex hull localization scenarios.
