统一约束几何构型优化用于源定位系统：一种基于黎曼流形的方法
Unified Constrained Geometric Configuration Optimization for Source Localization Systems: A Riemannian Manifold-Based Approach
- College of Information Science and Engineering, Hohai University（河海大学信息科学与工程学院）
- School of Information and Communication Engineering, Hainan University（海南大学信息与通信工程学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出基于黎曼流形的统一约束几何构型优化算法（RM-CGCOA），用于优化五种源定位系统的传感器几何构型，在满足距离和角度约束下显著降低位置误差界并提升运行效率。
AI中文摘要：
到达时间（TOA）、到达时间差（TDOA）、接收信号强度（RSS）、接收信号强度差（RSSD）和到达角（AOA）是源定位中常用的技术。这些系统的定位精度在很大程度上取决于传感器的几何构型，而该构型通常受到实际条件的约束。本文提出一个统一框架，用于优化所有五种定位系统的传感器几何构型，明确纳入传感器位置的距离和角度约束。首先，将这些系统的克拉美-罗下界（CRLBs）进行变换以获得统一表达式。基于该表达式，构建了一个统一的约束几何构型优化问题。随后，通过用方向矩阵替代传感器-目标角度，将该问题简化为紧凑形式。接着，提出一种基于黎曼流形的约束几何构型优化算法（RM-CGCOA），用于优化传感器-目标距离和方向矩阵。该算法将方向矩阵投影到单位圆的乘积流形上。进一步提出一种自适应回拉（adaptive pullback）方法，以严格强制执行与角度相关的不等式约束，确保在通过黎曼梯度更新方向矩阵时所有迭代点保持可行。在RM-CGCOA中，为TOA、TDOA、RSS和AOA推导了解析最优距离，而对于RSSD，距离则使用投影梯度下降（PGD）与方向矩阵一起更新。实验结果表明，与现有策略相比，所提出的RM-CGCOA始终实现显著更低的位置误差界（PEB），并与近最优搜索算法获得相似的PEB，但运行时间快得多。
英文摘要：
Time of arrival (TOA), time difference of arrival (TDOA), received signal strength (RSS), received signal strength difference (RSSD) and angle of arrival (AOA) are commonly used techniques for source localization. The positioning accuracy of these systems depends heavily on the geometric configuration of sensors, which is typically constrained by practical conditions. This paper presents a unified framework for optimizing sensor geometry across all five localization systems, explicitly incorporating both distance and angle constraints on sensor positions. First, the Cramér-Rao lower bounds (CRLBs) of these systems are transformed to obtain a unified expression. Based on this expression, a unified constrained geometric configuration optimization problem is formulated. The problem is then simplified into a compact form by replacing the sensor-target angles with an orientation matrix. Subsequently, a Riemannian manifold-based constrained geometric configuration optimization algorithm (RM-CGCOA) is proposed to optimize the sensor-target distances and the orientation matrix. This algorithm casts the orientation matrix onto a product manifold of unit circles. An adaptive pullback is further proposed to strictly enforce angle-related inequality constraints, ensuring that all iterates remain feasible when updating the orientation matrix via the Riemannian gradient. Within RM-CGCOA, analytical optimal distances are derived for TOA, TDOA, RSS and AOA, whereas for RSSD, the distances are updated using projected gradient descent (PGD) together with the orientation matrix. Experimental results demonstrate that the proposed RM-CGCOA consistently achieves a significantly lower position error bound (PEB) compared with the existing strategies and yields a similar PEB to the near-optimal search algorithm, but with a much faster running time.
