A new and fast globally optimal method for triangulation

Aim: The introduction of the full paper points out what we believe to be the shortcomings of the existing two types of triangulation method. So we propose what we believe to be a new triangulation method that is fast and can ensure globally optimal triangulation. Section 1 briefs the error function; in it, eq. (5) describes the error function mathematically. Section 2 explains in some detail our new and fast globally optimal method for triangulation; its core consists of: (A) eq. (6) gives the Hessian matrix of the error function or eq. (5); (B) to verify whether a local minimum solution is globally optimal, it provides a simple and rapid test involving the Hessian matrix of the error function. Section 3 gives a five-step procedure for implementing our globally optimal algorithm. Section 4 presents two sets of experiment with real data to verify the accuracy and speed of the globally optimal algorithm. The experimental results, given in Figs. 3 through 6 and Tables 1 and 2, and their discussions show preliminarily that our algorithm can obtain the globally optimal solution for triangulation and greatly raise the calculation speed compared with the algorithm based on L_∞ norm.