Accurate Solution of Adjustment Models of 3D Control Network

Abstract

The spatial Three-Dimensional (3D) edge network is one of the typical rank-lossless networks. The current network adjustment usually uses Least Squares (LS) algorithm, which has the complexity of linearization derivation, computational volume and other problems. It is based on high-precision ranging values. This study aims to minimize the sum of the difference between the inverse distance of the control point coordinates and the observation distance, the composition of the non-linear system of equations to build a functional model. Considering the advantages of the intelligent optimization algorithm in the non-linear equation system solving method, such as no demand derivation and simple formula derivation, the Particle Swarm Optimization (PSO) algorithm is introduced and the improved PSO algorithm is constructed; at the same time, the improved Gauss-Newton (G-N) algorithm is studied for the calculation of the 3D control network adjustment function model to solve the problems of computational volume and poor convergence performance of the algorithm with large residuals of the unknown parameters. The results show that the improved PSO algorithm and the improved G-N algorithm can guarantee the accuracy of the solution results. Compared with the traditional PSO algorithm, the improved PSO algorithm has a faster optimization speed. When the residuals of the unknown parameters are too large, the improved G-N algorithm is more stable than the improved PSO algorithm, which not only provides a new way to solve the spatial 3D network, but also provides theoretical support for the establishment of the spatial 3D network.