Discovery and Theory of the Shadow Reference Points

Abstract

The triangulation location is the same mathematical principles of the Global Navigation Satellite Systems (GNSSs) and the double-star positioning system, and the range between the navigation satellite and the user has to be measured. The three-dimensional position and clock offset can be solved by GNSS, while only the three-dimensional position can be gotten by the double-star positioning system. The position error is advanced by increasing the navigation satellite number generally. In this paper, the range calculation model of relay navigation is given. Based on the model, we present a theory on how the points with the known distance to the user are discovered in space, and the points are called the shadow reference points. Moreover, the error function of the relay range is analyzed. The shadow reference points can be applied as navigation satellite in order to improve the position error. Especially, the relay distance between the shadow reference points and the user is not needed to be measured, it can be obtained by calculation.