Multilateration - A nondegenerate method of obtaining station coordinates and satellite ephemerides

A technique for the determination of three-dimensional station coordinates and satellite ephemerides is developed which is based on the principle of multilateration. The method makes use of a system of six ground stations which simultaneously measure the slant range between each station and one or two satellites. It is demonstrated that a minimum of six stations is required in order to yield a system which will be free of mathematical degeneracies. It will be seen that the method of multilateration is not dependent upon the position of the satellite or any other dynamical considerations in the equations used to determine the relative station coordinates. In fact, the satellite coordinates are obtained as a direct by-product of the method. Numerical results are presented which indicate that the method of multilateration can determine the relative three-dimensional station coordinates with an accuracy that is limited only by the hardware measurement system. If a highly accurate laser ranging system is used, then accuracies in the 1-cm range can be expected.