Fractal Patterns in Long-term Behavior of GPS and GLONASS Orbits

In this paper we analyze repetitive patterns in GLONASS and GPS satellite orbits for the time span of 1 year using fractal dimension computation. A number of different statistical phenomena for such repetitive patterns at various dimension scales are reported. As we demonstrate below, the expected local dimension 6 does not hold for 1-year sets of GNSS satellite orbits, these sets have much smaller dimensions. The histograms of distributions of the orbit clusters collected in the process of computation of the fractal dimension show remarkable “resonances” for some special values of the box size.