###### L. Aardoom

**Publications on Geodesy 19** (Vol. 5 Nr. 2).

Delft, 1972. 23 pagina's. ISBN-13: 978 90 6132 219 1. ISBN-10: 90 6132 219 7.

## Summary

Multiple-station very long baseline interferometry (VLBI) is considered from a geodetic point of view. An approach is outlined to deal with relative phase delay data as obtained from measurements on both artificial radio sources at finite range and natural sources at infinity, observed in the simultaneous mode. The approach is basically a range-differences method and allows a treatment in theoretically convenient steps to which the several groups of parameters are primarily confined. This paper deals mainly with the interstation geometry of the VLBI-net.

Attention is drawn to the possible occurrence of singular geometric situations of stations and sources for which no unique solution for the interstation geometry is possible in spite of the presence of an in general sufficient amount of measurement data. For a family of idealized model four-station VLBI-nets a numerical estimate is made of the accuracy likely attainable for the interstation distances, using two hypothetical observation programmes with sources at infinity in supposedly unknown directions. It was found that there is no unique solution if only one natural source is used. In the other programme two natural sources are used and variance-covariance matrices have been estimated with conventional least squares techniques. A variety of declination differences, VLBI-net orientations and maximum zenith distances is considered. It was found that the ratio between estimated standard deviations of the interstation distances and the range-difference measurements lies between 5 and 25 if 9 range-difference measurements are extracted from one pass of each of the two sources, provided cases of marginal observability of one of the sources are avoided and if it is assumed that the directions to the sources are not restricted to zenith distances below 55. Station clocks are supposed to be perfectly synchronized.

## Contents

Summary 4

- Introduction 5
- Interstation geometry and relative clock-offsets 6
- Some simulation calculations 14

Acknowledgement 23

References 23