Mobile Positioning Problem in Manhattan-Like Urban Areas: Uniqueness of Solution, Optimal Deployment of BSs, and Fuzzy Implementation

In this paper, the problem of mobile positioning in a Manhattan-like urban area is considered. For this area, the involved base stations (BSs) try to use the received distance data to position the mobile station (MS) of interest, which naturally leads to an algebraic problem. However, the concerned problem is analyzed from a geometrical point of view. Using this approach, it is found that the ability to uniquely determine the location of the MS by the knowledge of the positions of BSs and the received Manhattan distances is closely related to the positions of the MS and BSs. The uniqueness issue of mobile position is then discussed in detail, and the optimal deployment of BSs is proposed mathematically in the sense that the MS can be uniquely positioned most of the time. Under the optimal deployment, a fuzzy-based estimator for positioning is developed geometrically. This estimator is simple and can work without the knowledge of noise statistics.