1985 Vol. 10, No. 1
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.
Bahnverbesserung ist in die Pre-processing der Satelliten-Laserentfernungsdaten einge-führt.Ein 4-Parameter-Modell der Bahn-verbesserung ist ausgearbeitet and geprüft,um den systematischen Anteil der Residien der Bahnberechnung zu reduzieren.Einzweischrittiges Verfahren ist aufgestellt um die Lösung der Normalgleichungen zu stabilisieren.Zwei Programmsysteme Bind entwickelt,um die LAGEOS-Daten zu prüfen,die Normalpunkte zu berechnen and die Eingnagsdaten für die short-Arc-Punktbestimmung zu vordereiten.Diese Arbeit ist unter der Instruktion and Hilfe von Dr.D.Lelgemann beim Institut für Angewandte Geodäsie,Frankfurt am Main,im Rahmcn dcs Sondcrforschungsbcreichcs 78 Satellitengeodasie der TU München ausgeführt.
In order to test and evaluate correctness and reasonableness the weights,which obtained from direction observations of different classes in astrogeodetic nets of our country,two methods are given;1、Using Helmert's simplified calculated formula,the estimation of variance of observed directions and the best estimated value are made;2、The weight intervals of direction obscrvations of different classes are determined under certain requirement of precision.Through calculation and analysis,we recognized that the weights of direction observations of different classes,which used in astrogeodetic network adjustment,are more appropriate and reasonable.
The concept of weighted generalized inverse matrices is described in this paper,It is shown,from the relationship between weighted generalized inverse and solution of linear equations,that three kinds of rank-defect network adjustment(common used rank-defect network adjustment,quasi-stable adjustment,weighted rank-defect network adjustment) all belong to the weighted rank-defect net adjustment.But different weight matrices are selected in them.Therefore,they can all be explicated with weighted generalized inverse.
The basic principle of array algebra is systematically introduced.The transformation relation between the array and matrix equations,and with the aid of this relation the solution to the least square problem by array algebra are expounded.The application of array algebra to surveying is presented.Finally,the Limitation and the efficiency of the method are explained.
The nested coefficient method for solving two geodetic problems has been developed and the practical formulars of direct and inverse solutions are given.They are suitable well to the electronic computation and can be used to any length from 1 to 20,000 Km.The theoretical accuracy can be over 10-5 sec.for both the latitude and the longitude and 1 mm to the distance respectively.But the practical accruacy of 10-4 sec.and several mm.may be obtained respectively,if the numbers of the effective figures are 10 and the Sharp pc-1500 computher is used.
The probability distribution of the τ variable,the distribution of its limit and the principal numerical characteristics are firstly studied.The method and formulars for calculating the distribution density of the probability of the variable are derived.The distribution of limit of τ variable,being considered as normal-variable,is proved and its-functional value has been calculated.Base on the above theoretical derivation and numerical calculation,the application of the τ variable for the statistical test on outliers and curve fitting are discussed.