Estimating ambiguity fixed satellite orbit, integer clock and daily bias products for GPS L1/L2, L1/L5 and Galileo E1/E5a, E1/E5b signals

Journal of Geodesy (2021) 95:44 https://doi.org/10.1007/s00190-021-01500-0 ORIGINAL ARTICLE Estimating ambiguity fixed satellite orbit, integer clock and daily bias products for GPS L1/L2, L1/L5 and Galileo E1/E5a, E1/E5b signals Bingbing Duan1 · Urs Hugentobler1 · Inga Selmke1 · Ningbo Wang1 Received: 19 November 2019 / Accepted: 11 March 2021 © The Author(s) 2021 Abstract Ambiguity resolution of a single receiver is becoming more and more popular for precise GNSS (Global Navigation Satellite System) applications. To serve such an approach, dedicated satellite orbit, clock and bias products are needed. However, we need to be sure whether products based on specific frequencies and signals can be used when processing measurements of other frequencies and signals. For instance, for Galileo E5a frequency, some receivers track only the pilot signal (C5Q) while some track only the pilot-data signal (C5X). We cannot compute the differences between C5Q and C5X directly since these two signals are not tracked concurrently by any common receiver. As code measurements contribute equally as phase in the Melbourne-Wuebbena (MelWub) linear combination it is important to investigate whether C5Q and C5X can be mixed in a network to compute a common satellite MelWub bias product. By forming two network clusters tracking Q and X signals, respectively, we confirm that GPS C5Q and C5X signals cannot be mixed together. Because the bias differences between GPS C5Q and C5X can be more than half of one wide-lane cycle. Whereas, mixing of C5Q and C5X signals for Galileo satellites is possible. The RMS of satellite MelWub bias differences between Q and X cluster is about 0.01 wide-lane cycles for both E1/E5a and E1/E5b frequencies. Furthermore, we develop procedures to compute satellite integer clock and narrow-lane bias products using individual dual-frequency types. Same as the finding from previous studies, GPS satellite clock differences between L1/L2 and L1/L5 estimates exist and show a periodical behavior, with a peak-to-peak amplitude of 0.7 ns after removing the daily mean difference of each satellite. For Galileo satellites, the maximum clock difference between E1/E5a and E1/E5b estimates after removing the mean value is 0.04 ns and the mean RMS of differences is 0.015 ns. This is at the same level as the noise of the carrier phase measurement in the ionosphere-free linear combination. Finally, we introduce all the estimated GPS and Galileo satellite products into PPP-AR (precise point positioning, ambiguity resolution) and Sentinel-3A satellite orbit determination. Ambiguity fixed solutions show clear improvement over float solutions. The repeatability of five ground-station coordinates show an improvement of more than 30% in the east direction when using both GPS and Galileo products. The Sentinel-3A satellite tracks only GPS L1/L2 measurements. The standard deviation (STD) of satellite laser ranging (SLR) residuals is reduced by about 10% when fixing ambiguity parameters to integer values. Keywords Integer satellite clock · Ambiguity resolution · Daily code and phase biases · GPS and Galileo signals · Pilot and data 1 Introduction The IGS (International GNSS Service) has been providing GPS satellite orbit and clock products for more than 20 years B Bingbing Duan B Urs Hugentobler 1 Institute for Astronomical and Physical Geodesy, Technical University of Munich, Arcisstr 21, 80333 Munich, Germany (Dow et al. 2009; Johnston et al. 2017). Within the IGS processing, ambiguity parameters are fixed to integer values. The typical approach is to form double-difference between observations that are simultaneously acquired between two satellites and two receivers. Clock errors and biases on both satellite and receiver sides are eliminated, and the doubledifferenced ambiguity parameters can be consequently fixed to integer values (Teunissen et al. 2003). However, satellite clock products need to be estimated by a second run using zero-difference observations (Dach et al. 2009; Prange et al. 2017). In order to make use of the fixed ambiguity parame- 0123456789().: V,-vol 123 44 Page 2 of 14 ters in clock estimation, the GeoForschungsZentrum (GFZ) decomposes each integer double-difference ambiguity into a pseudo zero-difference observation, and then jointly uses them with the real code and phase observations by giving a very tight constraint (Ge et al. 2005; Uhlemann et al. 2015; Deng et al. 2016). Different than fixing double-difference ambiguities, CNES/CLS (Centre National d’Etudes Spatiales/Collecte Localisation Satellites) estimates dedicated satellite orbit, clock and bias products when fixing zero-difference ambiguities to integer values (Loyer et al. 2012). The advantage is that users can also do ambiguity resolution at zero-difference level by making use of the publicly available CNES/CLS products. However, the clock estimates are slightly inconsistent with respect to the IGS products since they are relative to phase measurements (Montenbruck et al. 2018). To avoid such inconsistencies, GFZ and Wuhan University estimate epoch-wise satellite narrow-lane biases separately and provide such biases together with their satellite products to authorized users (Ge et al. 2008; Geng et al. 2012; Li et al. 2016). Instead of providing float clock and epoch-wise narrow-lane bias products, the Center for Orbit Determination in Europe (CODE) determines daily code and phase biases as observable-specific bias (OSB) terms on each signal and estimates ambiguity fixed clock products (Schaer et al. 2018; Villiger et al. 2019). The advantage is that ambiguity fixed satellite clock products show better consistency to the IGS final products. Furthermore, the correction of OSB products on each signal is more straight forward. In December 2019, CODE made their phase bias products publicly available as routine bias products at https://cddis.nasa.gov/. From February 2019, the European Galileo constellation has reached a total of 24 satellites, providing positioning, navigation and timing (PNT) services independently. The Galileo signals are transmitted in four frequency bands: E1, E5a, E5b and E6. The current Galileo satellite orbit and clock products in the MGEX (Multi-GNSS Pilot Project) are based on E1 and E5a signals (Montenbruck et al. 2017; Steigenberger and Montenbruck 2017). Since 2018 CODE and CNES/CLS have extended their ambiguity fixed products to Galileo satellites as well (Schaer et al. 2018; Katsigianni et al. 2019a, b). The performance combining GPS and Galileo satellites together in the PPP-AR applications are analyzed by Paziewski and Wielgosz (2015), Li et al. (2018), Xiao et al. (2019). In fact, for the frequency L5, E5a and E5b, some receivers track only pilot signal Q while some track only pilot-data signal X. These two signals are not tracked concurrently by any common receiver. Therefore, the differences of code and phase biases between Q and X need to be considered in (...truncated)