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

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.