A Versatile Algorithm for Local Positioning in Closed Form

This paper presents an algorithm for computing the intersections of three surfaces that are either planes or quadrics of revolution. The algorithm is directly applicable to calculating position from various combinations of range and pseudorange measurements. With a locality assumption, the system is reduced into a simplified form that is easy to solve analytically. The presented algorithm can be used as a preliminary step to obtain an optimal set of starting points for least-squares iteration. The testing section presents an example of how the algorithm can be used to augment the conventional iterative least-squares method in the presence of a two-fold ambiguity.