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Session P6: Present and Emerging Applications and Techniques for Time and Frequency using GNSS/RNSS/LEO and Optics

Exploring the Technical Limits of GNSS-based Frequency Transfer
Thomas Krawinkel, Ahmed Elmaghraby, Steffen Schön, Leibniz University Hannover, Germany
Location: Beacon A

GNSS-based frequency transfer (FT) involves two GNSS receivers each connected to a local frequency standard or another type of atomic clock whose frequencies should be compared. Typically, the recorded GNSS data are analyzed using the precise point positioning (PPP) method. From the difference of the obtained receiver clock error time series of both receivers, usually the modified Allan deviation serves as a measure for the instability of the actual FT. Currently, an instability range smaller than 1E-16 is reached by means of PPP with integer ambiguity resolution. On the side of the receivers, the stability of the internal hardware delays is the most crucial factor for the achievable FT instability. This includes delay variations in each receiver itself as well as different behaviors of these variations between the two receivers. In theory, if all error sources were eliminated or well controlled, the instability of GNSS-based FT should only be dominated by white frequency noise at the level of the noise of the GNSS observation type in use. When using modern, state-of-the-art GNSS receivers, this limit would be in the range of 1-3 mm.
In our contribution, we will present a study investigating the technical limits such receivers impose on GNSS FT by means of a dedicated experiment conducted at Germany's national metrology institute (PTB). For this purpose, we used four geodetic receivers, two of the same type each (2 JAVAD OMEGA, 2 Septentrio PolaRx5TR), that were all connected to the same frequency signal of the locally generated approximation of Coordinated Universal Time (UTC), referred to as UTC(PTB). In the first ten days of the latter, all receivers were also connected to the same Leica AR20 antenna, i.e. forming a zero-baseline (ZB), common-clock (CC) measurement configuration. This was changed afterward to a short-baseline setup by connecting one receiver of each type to a second antenna of the same type that was installed two meters apart from the first one. The signal paths from the antenna to each receiver were identical to ensure identical delays. We analyze the data in a standard PPP approach as well as by means of forming single differences (SDs) between a pair of receivers at a time. The PPP method represents a typical use case for GNSS FT, whereas the SD analysis is used to determine the minimum achievable frequency instability between these receivers. In the ZB configuration, this is possible since virtually all error sources cancel out by forming SDs. Thus, only the carrier phase ambiguities for each satellite and a relative clock offset between the receivers remain as unknowns. Due to the fact that the observation geometries for both receivers are virtually the same, ambiguity resolution is a relatively trivial task and can be achieved by means of rounding to the nearest integer value. From this best-case measurement scenario, we progress to the short-baseline part of the experiment by applying the same analysis strategy. Although there are only small differences in geometry between the two antennas, we anticipate results that are deviating from the ZB results mainly because of different multipath effects in both stations.
In PPP, we apply a linearized Kalman filter with forward-backward smoothing, which estimates the receiver coordinates together with the clock error, a residual tropospheric delay as well as float carrier phase ambiguities for each satellite in view. For all four receivers, we compute the same continuous ten-day PPP solution for different ionosphere-free (IF) observables. The basis are GPS L1(C/A), L2W, L2C and L5 as well as Galileo E1, E5a and E5a+b observation data. The SD analysis also uses the same IF observables, but in comparison the algorithm is simpler to this point since almost all error sources cancel out when forming the SDs between two receivers. We assess the instability of three different receiver combinations: two using the same receiver type (intra-receiver) and one using different receiver types (inter-receiver). For the zero-baseline measurements, our findings are as follows. In both PPP and SD analysis, the intra-receiver pairs reach lower instability values faster than the inter-receiver combination, which is in part caused by the different signal tracking modes of the JAVAD and Septentrio receivers. Regarding the PPP results, an instability level below 1E-16 is reached after about one day of averaging time. There are only slight differences detectable when using different observation types. However, in this case study, Galileo signals lead to better FT performance than GPS signals, overall. When using the latter, with modern L2C signals we obtain instability values that are at least comparable to those based on legacy L2 P-code observations, although fewer satellites transmit the L2C signal. Due to the very specific measurement configuration, the instability values derived from the SD analysis are significantly smaller as compared to the PPP results. To be specific, the intra-receiver pairs reach the 1E-18 instability range after approximately an averaging time of one day, whereas the inter-receiver combination already hits its noise floor at about 1.5E-17. The use of different observation type combinations only leads to small differences regarding the link instability.
In conclusion, we can state that, today, GNSS-based frequency transfer aiming for instability values below 5E-17 should not be limited by the GNSS equipment if modern, state-of-the-art instruments are being used. We will extend our methodology to the analysis of the short-baseline experiment, where we expect a certain degradation in frequency instability due to signal errors that are affecting the receiver involved differently. Furthermore, we will also discuss the promising impact of physically meaningful receiver clock modeling on the PPP results. Preliminary findings show that this approach can improve the frequency instability by up to one order of magnitude. In this case, different error sources shall be rigorously modeled, where this improves the performance of the GNSS FT.



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