Squaring and cross-correlation codeless tracking: analysis and generalisation

In this study, squaring and cross-correlation codeless phase lock loops (PLLs) for global navigation satellite systems (GNSS) applications are at first reviewed. It is shown that the discriminators of squaring and cross-correlation PLLs are special solutions of the maximum likelihood (ML) equation for the estimation of the L2 P(Y) signal phase. A generalised codeless PLL (GCPLL), combining squaring and cross-correlation processing, is then derived as general solution of the ML equation. Approximate expressions for the tracking jitter of the considered codeless techniques are provided and validated using Monte Carlo simulations. The analysis is further supported by results obtained using live global positioning system (GPS) L1 and L2 signals.