Multidimensional GNSS Meta-Signals

Abstract A global navigation satellite system (GNSS) meta-signal is obtained by considering and processing components from different radio frequencies (RFs) as a single entity. While most research on GNSS meta-signals has considered components from only two frequencies, four and five open signals are currently provided by Galileo and the BeiDou satellite navigation system (BDS), respectively. In this paper, multidimensional GNSS meta-signals, with a number of components equal to a power of two, are introduced and described using multicomplex numbers, a multidimensional extension of complex numbers. In this way, single-frequency GNSS signal processing is generalized to the multidimensional case. A multicomplex cross ambiguity function is derived and used for the design of multifrequency acquisition and tracking algorithms. Theoretical results are supported by experiments in which four RF front-ends are used to capture Galileo and BDS signals from different frequencies. The four signals are then jointly processed using the algorithms developed.