Nonlinear Adjustment of GPS Observations of Type Pseudo-Ranges

Abstract

The nonlinear adjustment of GPS observations of type pseudo-ranges is performed in two steps. In step one a combinatorial minimal subset of observations is constructed which is rigorously converted into station coordinates by means of Groebner basis algorithm or the multipolynomial resultant algorithm. The combinatorial solution points in a polyhedron are reduced to their barycentric in step two by means of their weighted mean. Such a weighted mean of the polyhedron points in ℝ³ is generated via the Error Propagation law/variance-covariance propagation. The Fast Nonlinear Adjustment Algorithm (FNon Ad Al) has been already proposed by Gauss whose work was published posthumously and Jacobi (1841). The algorithm, here referred to as the Gauss-Jacobi Combinatorial algorithm, solves the over-determined GPS pseudo-ranging problem without reverting to iterative or linearization procedure except for the second moment (Variance-Covariance propagation). The results compared well with the solutions obtained using the linearized least squares approach giving legitimacy to the Gauss-Jacobi combinatorial procedure. © 2002 Wiley Periodicals, Inc.