Relative motion and visibility evaluation in GNSS constellation: A projection method

Using crosslinks to network the satellites in a GNSS constellation has been regarded as one of the most important trends for the GNSS modernisation. The motion and visibility of the satellites w.r.t. each other in the constellation have to be evaluated as an prerequisite to many tasks, especially to the inter-satellite network design, measurement scheduling and pointing-related issues. Thus far, very few analytical studies have been done on this issue for GNSS constellations. In this paper, a projection method is proposed to evaluate the relative motion and visibility. By projecting the relative trajectory orthogonally onto the orbital plane of the base satellite, it is much easier to study the geometric characteristics of the relative motion and the effect of constellation parameters and field-of-view constraint on the relative visibility. Given that GNSS constellations are designed based on Walker constellation, the relative motion pattern is explored algorithmically with index mapping techniques and the always visible relationship is visually modelled using a graph which in most cases shows a symmetry structure when the vertices are placed in a proper order. As demonstration of our method, a thorough experimental validation on the nominal GPS, GLONASS, Galileo and BeiDou-M constellation is proposed. The result explicitly reveals that the relative motion and visibility varies according to the parameters of the constellations.