无线信号交汇定位的奇异解问题表征与解决

Representation and solution of singular positioning issues from wireless signal intersection location technology

无线信号交汇定位是最常见的几何定位技术,在通信与定位领域具有广泛的应用.然而人们对无线信号交汇定位所产生的奇异解问题本质认识不足,对相关解决方法缺少基础和深入的研究.针对上述问题,本文基于最小二乘法推导了相关一维/二维/三维定位的解析式,从新的角度发现了用来表征奇异解的八条几何拓扑约束关系,并提出了参数微调法和空时自调节法来解决奇异解相关问题.实验结果表明所提出的几何拓扑约束关系是可信的,使奇异解问题易表征、可解释;此外,所提出的解决方法可实现对奇解问题的高效解决,且有高精度定位近似解.总之,该工作对几何定位、基站布设、奇异解表征和鲁棒定位算法设计等提供了有益指导.

The wireless signal intersection location is the most common geometric positioning technology, with several applications in communication and positioning. However, it is difficult to understand the singular solution issues generated by the wireless signal intersection location. Additionally, there are limited basic and in-depth research studies on the related solutions. To solve the above issues, we derive the analytic expressions of the relevant one-, two-, and three-dimensional positioning based on the least squares method and discover eight geometric topological constraints to characterize the singular solution from a new perspective. Besides, we propose fine-tuning the parameters and space-time self-adjustment methods to solve the singular related issues. The results show that the proposed geometric topology constraints are credible, easing the characterization and explanation of the singular solution problem. Besides, the proposed solution can realize an efficient solution to the singular solution issues with high precision location results. This study provides useful guidance for geometric positioning,base station layout, singular solution characterization, and robust positioning algorithm.