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.