大地高程误差对卫星网与地面网联合平差的影响

在地面网与卫星网的联合平差中,地面网大地高程的精度对于平差方法的选择具有重要意义。本文从两网联合平差的基本数学模型出发,导出了地面网点大地坐标的微变化对联合平差后相应坐标平差值影响的一般表达式。并利用模拟同分别计算了表征大地经纬度和高程的变化对联合平差后大地坐标影响的相应系数矩阵。该系数矩阵表明,如果地面网大地坐标各分量的精度相近,则它们通过联合平差各自引起的大地纬度平差值的残差将保持同一数量级。根据对模拟网的数值计算结果得出的结论是:在三维坐标系进行联合平差时,高程和平面位置的精度具有同样重要意义,但并不意味着要求两者的精度相当,重要的问题在于可靠地获得它们各自的精度信息。即使大地高程的精度较低,只要能可靠地确定它们的方差与协方差,仍以在三维系统进行联合平差为宜。而当大地高程精度难以可靠地确定时,赋以大地高程较小的权可明显地减弱其对平差结果的不利影响,虽然这样在一定程度上损失了大地高程所提供的有用信息,但此之在二维平差中,放弃大地高程这一分量是更为适宜的。

The Effects of the Errors of Geodetic Heights on the Results of Combined Satellite and Terrestrial Net Adjustment

The accuracies of geodetic heights of terrestrial net are important for selecting of the approch of combined satellite and terrestrial net adjustment.Starting from the basic mathematical model for the combined adjustment of two nets,a general expression for the effects of small changes in the initial values of geodetic coordinates of terrestrial net on the corresponding adjusted values of the coordinates in the combined adjustment has been derived in this paper.By using a simulative net,the authors computed the corresponding coefficient matrices which represent the effects of the changes in geodetic latitudes,longitudes,and heights on the adjusted values in the combined adjustment.The matrices show that if the accuracies of the components of geodetic coordinates of terrestrial net are nearly on a level with each other,through the combined adjustment the residuals of the adjusted geodetic latitudes induced respectively by the standard errors of the components are held in the same magnitudes.According to the results of the numerical calculations and analyses on the simulative net,it comes to the conclusions that the accuracies of either heights or positions in two-dimensinnal space are of the same significance for the combined adjustment in three-dimensional coordinate system,however,it does not mean that the same magnitude of accuracies of the heights and the positions are required.An important problem lies in reliable acquisition of the information about their accuracies.It is preferable that the combined adiustment should be carried out in three-dimensional coordinate system provided the accuracies of geodetic heights can be reliablely determined,even though the accuracies of geodetic heights are low.When the determination of the reliable accuracies of heights is difficult,the assignment of a smaller weignt to geodetic heights may significantly weaken the unfavorable effects on the results of the adjustment.It is likely more appropreate to perform the combined adjustment in three-dimensional coordinate system than in two-dimensional space where the components of the heights are abandoned,though the useful irformation contributed by heights to the adjustment would be lost in a certain extent.