带有部分不确定性的平差算法在GPS高程拟合中的应用

观测数据中常包含统计信息未知的不确定性,可能导致所建立的函数模型产生病态,影响参数估计的准确性和可靠性。文中研究GPS高程拟合模型的不确定性,将系数矩阵进行分块,对含有不确定性的区块加以限制,并将不确定度融入函数模型,利用min-max准则,运用带部分不确定性的平差算法(PULS,Least-Squares with Part of Uncertainty)解算拟合参数。实验中选取均匀分布的模拟点坐标及其高程异常值,分别运用最小二乘(LeastSquares,LS)、总体最小二乘(Total Least-Squares,TLS)以及PULS对拟合参数进行解算,结果表明,PULS得到的拟合参数精度高于LS和TLS,说明PULS在GPS高程拟合中应用的有效性。

Application of least-squares with part of uncertainty to GPS height fitting

Measurement data usually contains many uncertainties whose statistics information are unknown, which may cause morbid theory model and affect accuracy and reliability of parameter estimation. This paper makes a research on uncertainties of GPS height fitting model,partitions the coefficient matrix and constricts the blocks containing uncertainties. The fitting parameters are calculated by least-squares with part of uncertainty,which involves uncertainty and using min-max criterion. In experiment,this paper selects coordinates of simulated points which have uniform distribution and their height anomaly,and calculates fitting parameters by using least-squares,total least-squares and PULS respectively. The result shows that the precision of fitting parameters by PULS is higher than those by LS or TLS,and indicates the effectiveness of application in GPS height fitting by using PULS.