Nonlinear Adjustment of GPS Observations of Type Pseudo-Ranges
Nonlinear Adjustment of GPS Observations of Type Pseudo-Ranges
复制标题
伪距型GPS观测的非线性平差
DOI：
10.1007/pl00012914
复制
发表时间：
2002
期刊：
影响因子：
4.9
通讯作者：
E. Grafarend
中科院分区：
文献类型：
--
作者：
J. Awange;E. Grafarend
伪距GPS观测值的非线性平差分两步进行。在第一步中，构造观测值的组合极小子集，并利用Groebner基算法或多项式结式算法将其严格转换为站坐标。利用多面体中组合解点的加权平均值，将多面体中的组合解点归结为其重心。通过误差传播规律/方差-协方差传播来生成ℝ3中的多面体点的这种加权平均值。快速非线性调整算法(FNon Ad Al)已由Gauss和Jacobi(1841)提出。该算法在这里称为Gauss-Jacobi组合算法，解决了超定GPS伪距问题，除了二阶矩(方差-协方差传播)外，不需要恢复到迭代或线性化过程。计算结果与线性化最小二乘法得到的解进行了比较，证明了Gauss-Jacobi组合方法的合理性。©2002威利期刊公司。
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 ℝ3is 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.