Range difference multilateration for obtaining precision geodetic and trajectory measurements

Abstract

The theoretical aspects of a new multilateration technique suitable for precision geodesy and orbit determination applications are examined. The multilateration technique considered herein makes use of the differential time of arrival of signals at an ensemble of ground stations from a spacecraft or aircraft as the fundamental data type. It is demonstrated that simultaneous measurements give rise to a system of equations which upon solution permits the determination of the three-dimensional vehicle coordinates plus the three-dimensional coordinates of the station net relative to an arbitrarily adopted origin (which may be taken to be one of the stations). A solution to these equations can be obtained without any a priori knowledge of the locations of the stations and vehicle. The necessary conditions for obtaining all of these coordinates in the same solution are discussed, and it is indicated that at least five stations are required in the station ensemble.