# Performance Limits of GNSS Code-based Precise Positioning: GPS, Galileo & Meta-Signals
## 1 Introduction
RTK requires the use of a reference station with a communication link between the two receivers, and is only valid for short ranges from the base-station to ensure that the two receivers observe the same propagation errors. PPP techniques allow us to get rid of the reference station but to reach decimetric precision in turn need: (i) precise carrier phase measurements, which is not the case in harsh propagation conditions; (ii) high accuracy satellite orbits, clock, and propagation (ionospheric and tropospheric) error corrections; and/or (iii) multi-frequency/multi-system architectures to compensate propagation effects. The price to be paid is the need to access a network broadcasting precise corrections (i.e., International GNSS Service (IGS) products), and a long convergence time of tens of minutes. As stated in [12], these drawbacks limit the use of PPP for real-time applications. Then, the fundamental question that ignited this work is: _Can we obtain a GNSS code-only precise positioning solution and under which conditions_? GNSS positioning being mainly an estimation problem, the optimal performance is given by the well-known Cramer-Rao bound (CRB) [13], which provides an accurate lower bound on the mean square error (MSE) sense under certain conditions (for instance, in the high SNR regime of the conditional signal model [14; 15], of interest in this contribution because it is linked to the optimality of the two-step solution). In the GNSS context, this bound is particularly interesting because the synchronization process is based on the ML principle under Gaussian noise assumptions, which is known to reach the CRB (the ML estimator in this case is asymptotically efficient) [15]. In a recent contribution [16], we derived a new compact closed-form CRB for the time-delay estimation of a generic band-limited signal, which is directly computed from the signal samples and perfectly fits the GNSS problem. In addition, in this contribution, we provide a new joint time-delay and phase estimation CRB to support the discussion. In this article we exploit the time-delay CRB expression to compare the achievable synchronization performance with different GPS and Galileo signals, namely: the GPS L1 C/A, L1C, and L5 signals; the Galileo E1 OS, E6B, E5b-I, and E5 signals; and the Galileo E5b/E6 and E5a/E6 meta-signals. Such comprehensive performance analysis from an optimal estimation point of view is not available in the literature, being an important missing point. In addition, the analysis also provides which is the performance threshold that implies a need of carrier phase-based positioning. The article is organized as follows. Section 2 presents the basic GNSS signal model. Section 3 introduces the time-delay CRB for band-limited signals along with the MLE and a new joint time-delay and phase estimation CRB. Section 4 presents an overview of the GPS civil signals. A complete overview of the Galileo signals is provided in Section 5. The concept of GNSS meta-signals together with the signal structure for the most representative cases is given in Section 6. Section 7 summarizes the main results. Conclusion are drawn in Section 8.