Abstract
This contribution analyzes the fundamental performance limits of traditional two-step Global Navigation Satellite System (GNSS) receiver architectures, which are directly linked to the achievable time-delay estimation performance. In turn, this is related to the GNSS baseband signal resolution, i.e., bandwidth, modulation, autocorrelation function, and the receiver sampling rate. To provide a comprehensive analysis of standard point positioning techniques, we consider the different GPS and Galileo signals available, as well as the signal combinations arising in the so-called GNSS meta-signal paradigm. The goal is to determine: (i) the ultimate achievable performance of GNSS code-based positioning systems; and (ii) whether we can obtain a GNSS code-only precise positioning solution and under which conditions. In this article, we provide clear answers to such fundamental questions, leveraging on the analysis of the Cramér–Rao bound (CRB) and the corresponding Maximum Likelihood Estimator (MLE). To determine such performance limits, we assume no external ionospheric, tropospheric, orbital, clock, or multipath-induced errors. The time-delay CRB and the corresponding MLE are obtained for 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. The results show that AltBOC-type signals (Galileo E5 and meta-signals) can be used for code-based precise positioning, being a promising real-time alternative to carrier phase-based techniques.
Highlights
Synchronization is a key first stage in many applications, e.g., radar, sonar, communications, or navigation, to name a few [1,2,3,4,5]
Global Navigation Satellite System (GNSS) positioning being mainly an estimation problem, the optimal performance is given by the well-known Cramér–Rao bound (CRB) [13], which provides an accurate lower bound on the mean square error (MSE) sense under certain conditions
A GNSS meta-signal is the combination of two different GNSS signals transmitted at two different carrier frequencies which can be expressed as a single Alternate Binary Offset Carrier (AltBOC) modulated signal [32]
Summary
Synchronization is a key first stage in many applications, e.g., radar, sonar, communications, or navigation, to name a few [1,2,3,4,5]. The asymptotic region is characterized considering only the thermal noise and a high signal-to-noise (SNR) ratio to ensure the efficient behavior of the ML estimator These external errors are the same whatever the processing, so that we do not need to consider them with an aim of comparing SPP and Precise Point Positioning (PPP) schemes. GNSS positioning being mainly an estimation problem, the optimal performance is given by the well-known Cramér–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).
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