Hybrid positioning algorithm based on least squares and LM for 3D cluster networks

Abstract

This paper proposes a hybrid positioning algorithm, LS-LM, based on least squares (LS) and Levenberg–Marquardt (LM) for position estimation of low-cost and miniaturized unmanned cluster networks in the absence of GPS. The LS method is first used to obtain an initial solution of position estimation, and the LM algorithm to iteratively refine the solution. The LS-LM algorithm has the advantages of simple computation, no complicated communication, and full distribution. It has high accuracy in the coordinated positioning algorithm without coordinate matching. In evaluating its efficacy,we have compared the root mean square error of the LS-LM algorithm to that of the LS method, tetrahedron shape measurement (TSM) algorithm and improved trilateration localization method with minimum uncertainty propagation and optimized selection of anchor nodes (ITL-MEPOSA) method. The simulation results demonstrate a varying degree of reduction in error with the application of the LS-LM algorithm.