Weighted Free Adjustment of GPS Three.dimensional Network

Abstract

We have some advantages in GPS survey to develop network adjustment with aid of geocentric rectangular coordinates, because not only some results of survey are given directly based on WGS-84 geocentric rectangular coordinate but also theoretical considerations are much simplified. We developed weighted free adjustment of GPS three-dimensional network with observed baseline vectors or observed spatial distances as well as some formula that are required to discuss the vertical and horizontal displa cement of GPS stations from the results of rectangular coordinates adjustment. Constraint equation of the type CX=0 is generally applied for solution of rank deficient normal equation, where C is constraint matrix and X is estimated parameter matrix. This constraint equation is further extended to be CMX=0, where M is interpreted to be a weight matrix to X. We can estimate M with the conventional free adjustment or with some geophysical informations. The solution with constraint of this type can also include so called classical free adjustment such as the case with one fixed station and one fixed direction or with two fixed stations and so on as some special cases.