Auto-localization in Local Positioning Systems: A closed-form range-only solution

This paper studies the problem of determining the position of beacon nodes in Local Positioning Systems, for which there is no inter-node distance measurements available. Also, neither the mobile node nor any of the stationary nodes have positioning or odometry information. The common solution is implemented using a mobile node capable of measuring its distance to the stationary beacon nodes within a sensing radius. Many authors had implemented heuristic methods based on optimization algorithms to solve the problem, however such techniques can fail if the range measurements doesn´t provide enough information to obtain a unique solution. Equally, the actual methods require a good initial estimation of the node positions in order to find the correct solution. In this paper we use rigidity theory to determine the necessary conditions in which such problem is solvable for Local Positioning Systems. We also a present a new method to calculate the inter-beacon distances based in the linearization of the trilateration equations. This method doesn´t require any initial estimation of the nodes position. The simulation results show a good estimation of the beacon nodes position without using any optimization algorithm.