Advanced ARIMA model for clock bias prediction

Abstract

The study presented in this document addresses aspects of the satellite clock prediction issue inside the Global Navigation Satellite System (GNSS) world. Here, different solutions will be analyzed, compared and proposed with the idea of improving the performance of the current method.
Precise timing, with accuracy to the nanosecond, is an absolutely necessary element in the GNSS architecture. So much so that the cornerstone of the GNSS observations,
known as the pseudorange, is basically a measurement of the time difference between the emission of a signal from a GNSS satellite and the reception of that signal at the user’s antenna. In an ideal world, where all clocks measure the same time, the product of this time difference and the speed of light in a vacuum gives the geometric distance between the satellite antenna and the user’s antenna but the reality is not so straightforward. There are several elements which can alter this perfect relationship between distance, velocity and time. Some of them are related to the Earth’s atmosphere, such as the tropospheric delay, others are related to relativistic aspects and, of course, one of these factors is the satellite clock bias (SCB).
The perfect clock measure does not exist (and neither the perfect clock, which is basically an oscillator). Every single one of them possesses measurement errors inherent
to the nature of their way of measuring time. The satellite clock bias is the difference between the time according to a clock reference (we can understand it as an extremely
accurate clock on the ground) and to the on-board clock of the GNSS satellite. Although an atomic clock is highly stable, its complete synchronization is impossible to achieve. There are external factors, such as solar radiation, third-body perturbation, non-spherical
Earth gravity field, etc. which can alter the time measurement of the atomic clock. There are several GNSS constellations: GPS, Galileo, GLONASS, etc. and each one
has its own reference timescale. For constellations such as GPS or Galileo, the satellite clock bias might vary from several nanoseconds to several milliseconds. If the satellite clock bias was unaccounted for, we would be adding a distance error ...d = c · .... , which can take values around 300 km for a ... = 1 ms. As a consequence, the aatellite clock error must be considered and modelled in each case, given that it is intrinsically linked
to the pseudorange measurement. Depending on the number of available measurements and the geometry, pseudorange errors alter directly the GNSS-based position, velocity and time solutions. The main goal of this thesis is the performance characterization of the AutoRegressive Integrated Moving Average (ARIMA) and the seasonal ARIMA (SARIMA) methods in
the satellite clock bias prediction, comparing it with the quadratic model performance (the method used most frequently). The ARIMA and SARIMA models are the most
complete models for forecasting time series. They are intended to fit data series either to better understand the nature of the time series or to predict the behavior of it, which is what is of interest to GNSS applications.