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Following several performance enhancements, GPS has provided a stable signal-in-space range error (SISRE) of about 50 cm (RMS) for more than a decade. As of early 2024, a major SISRE reduction by about 30% could be noted that helps to maintain the competitiveness of GPS in comparison with the Chinese BeiDou system and reduces the performance difference with respect to the European Galileo system. Based on analyses of onboard clock stability and broadcast navigation messages, the SISRE enhancement can be attributed to a combination of clock switches on selected satellites as well as an overall reduction of the mean time between navigation data uploads. The additional adoption of new transmit antenna phase center offsets in the control segment has no immediate performance impact but affects the comparison of broadcast and precise orbits. Following the aforementioned operational changes, SISRE values for dual-frequency P(Y)-code positioning with the legacy navigation message (LNAV) were found to decrease to roughly 30 cm from March 2024 onward, and marginally worse results are obtained for users of the civil L1/L2 signals and the L2 civil navigation (CNAV) message. Single-frequency LNAV users, on the other hand, experience only a minor benefit, since orbit and clock information improvements are largely masked by the non-availability of group delay information for the L1 C/A signal relative to the L1 P(Y) signal. [ABSTRACT FROM AUTHOR]

The fifth GLONASS-K1 satellite with space vehicle number R807 was launched in October 2022. It represents the first spacecraft of the K1+ generation, which offers various technical innovations. Compared to previous K1 satellites, R807 also transmits a code-division multiple access (CDMA) signal in the L2 frequency band in addition to L1 and L2 frequency-division multiple access (FDMA) and L3 CDMA signals. Thus, R807 is the first spacecraft of the K1+ generation. A geometry- and ionosphere-free triple carrier combination is used to analyze the GLONASS R807 clock consistency at different frequencies. Significant inconsistencies were found showing up as variations with a peak-to-peak amplitude of up to 40 cm and periods between 15 min and a few days. Whereas the ultimate explanation for these variations is not known, it is likely that they originate from cross-talk of two oscillators with similar frequency. A short-term clock analysis for integration times up to 100 s based on the one-way carrier phase (OWCP) method shows a superior stability of the R807 clock compared to all other GLONASS satellites including the new K2 generation. The Allan deviation computed from 5 s clock estimates confirms this finding for integration times up to 600 s but shows a significant bump at longer integration times due to the periodic variations mentioned above. Single-frequency OWCP processing confirms consistency of the L1 and L2 FDMA signals whereas the L3 CDMA signal shows a slight phase shift. Although the spurious variations mask the true performance of the K1+ atomic frequency standard, its behavior at short integration times points at a new type of GLONASS satellite clock. [ABSTRACT FROM AUTHOR]

K2 is a new generation of GLONASS satellites that provides code division multiple access (CDMA) signals in the L1, L2 and L3 frequency bands in addition to legacy L1 and L2 signals based on frequency division multiple access (FDMA) modulation. The first GLONASS-K2 satellite was launched in August 2023 and started signal transmission in early September 2023. Based on measurements with a 30-m high-gain antenna, spectral characteristics of the various signal components are described and relative power levels are identified. A 3 dB (L1) to 4 dB (L2) higher total power is determined for the CDMA signal compared to the legacy FDMA signal and an equal power of the open service and secured CDMA signal components is found. The ranging code of the L2 channel for service information, which has not been publicly disclosed so far, is identified as a Gold code sequence consistent with the data channel of the L1 open service CDMA signal. The high-gain antenna measurements are complemented by tracking data from terrestrial receivers that enable a first assessment of user performance. An up to 50% improvement in terms of noise and multipath performance is demonstrated for the new L1 and L2 CDMA signals in comparison with their legacy counterpart, but no obvious differences between the different binary phase-shift keying and binary offset carrier modulations of the data and pilot components of these signals could be identified for the test stations. Triple-frequency carrier phase observations from L1, L2, and L3 CDMA signals exhibit good consistency at the noise and multipath level, except for small variations that can be attributed to slightly different antenna phase patterns on the individual frequencies. Overall, the new CDMA signals are expected to notably improve and facilitate precise point positioning applications once fully deployed across the GLONASS constellation. [ABSTRACT FROM AUTHOR]

Over the last decade, chip-scale atomic clocks (CSACs) have emerged as stable time and frequency references with small size, weight, and power (SWaP). While the short-term stability of these devices clearly outperforms other oscillators with similar power consumption, their stability over longer time intervals is notably limited by frequency noise. Such long-term deviations can effectively be compensated by disciplining the clock with respect to a stable time and frequency reference such as Coordinated Universal Time (UTC) or a time scale based on GNSS observations. In view of the limited accuracy of GPS pseudorange observations and broadcast ephemerides, the performance of GNSS-disciplined atomic clocks is commonly limited to the few-nanosecond level. For further improvement, this study combines the use of carrier phase-based precise-point-positioning (PPP) techniques and high-performance broadcast ephemerides to discipline the phase of a CSAC with respect to GNSS broadcast time. Making use of a dual-frequency, dual-constellation GPS/Galileo receiver, a sub-nanosecond time interval error with respect to a national UTC timing laboratory is demonstrated over time intervals from 1 s to several days. [ABSTRACT FROM AUTHOR]

Analysis of the bias between Quasi-Zenith Satellite System (QZSS) L5-Q and L5-I pseudoranges reveals decimeter-level variations over the satellite passes, a phenomenon that is not observed on any other GNSS signal. The paper provides a study of this QZSS peculiarity. It is shown that the bias depends on the orientation of the line-of-sight vector with respect to the transmit antenna panel of the QZSS satellite, and that the amplitude of its variation is satellite dependent. The cause of the L5 bias is identified as interference from the L5S signal transmitted by QZSS satellites at the same frequency and from a different antenna. The interference introduces a distortion of the correlation peak dependent on the primary and secondary code selected for the L5 and L5S signals and on the relative delay and phase between the received L5 and L5S signals. This distortion induces tracking biases affecting pseudoranges produced using the pilot signal component. A theoretical model of the interference is provided, and it is shown that the bias variation can be accurately modeled and compensated for if L5 and L5S measurements are available. [ABSTRACT FROM AUTHOR]

While traditional GNSS signals are always modulated with navigation data, various modern signals provide a distinct pilot channel without data modulation to support long coherent integration times. Intra-signal biases between the data and pilot components of such signals are evaluated for satellites of the GPS, Galileo, BeiDou-3, and QZSS constellations using measurements from a dedicated set of receivers. Peak values of about 2 ns are obtained for the GPS L5 signal, while slightly smaller values of up to 1 ns apply for the B1C and B2a signals of BeiDou-3 as well as the QZSS L1C signal. For Galileo E1 and E5a/b, data + pilot biases are confined to less than 0.1–0.3 ns, which is typically less than other pseudorange errors for these signals. Fully negligible values of < 0.05 ns are obtained for the L1C and L2C signals of GPS as well as the L2C signal of QZSS in accord with expectations for time-multiplexed or interlaced modulations. To support consistent processing of multi-GNSS data in heterogeneous networks, biases between combined data + pilot tracking and pilot-only tracking are derived in a dedicated zero-baseline receiver test bed. The analysis confirms the general understanding that biases between combined and pilot-only pseudoranges amount to a fixed fraction of the corresponding data + pilot biases. This fraction depends on the power sharing of the data and pilot component in the respective signals and amounts to 50% in most cases. The results of this study are expected to remove the prevailing problem of two distinct receiver groups in the generation of satellite clock and bias products by the International GNSS Service and to enable a rigorous and consistent use of these products by multi-GNSS users. [ABSTRACT FROM AUTHOR]

Information about satellite antenna phase center offsets (PCOs) is indispensable for high-precision applications of global navigation satellite systems. Pre-flight manufacturer calibrations of the PCOs are available for all individual Galileo satellites and each frequency. So far, geodetic usage of Galileo is focused on the ionosphere-free linear combination of the E1 and E5a signals. In view of the growing number of E5b- and E6-capable receivers and upcoming multi-frequency applications, the consistency of the PCO values for different frequencies becomes a topic of increasing importance. Galileo satellite antenna PCOs have been estimated from the ionosphere-free linear combinations of E1/E5a, E1/E5b, and E1/E6. The mean horizontal PCOs of the different frequencies agree on the few millimeter level. The X-PCOs show a bias of about 1 cm compared to the manufacturer calibrations, whereas the Y-PCOs are free of such a bias. The Z-PCOs have a systematic offset of - 11 to - 15 cm w.r.t. the manufacturer calibrations due to scale inconsistencies of the current version of the International Terrestrial Reference Frame (ITRF2020) and the manufacturer calibrations. The maximum Z-PCO difference between the various linear combinations amounts to 4 cm and provides a measure of the presently achieved consistency of ground and space antenna calibrations across different frequencies. This inconsistency would translate into height differences of about 1.6 mm and associated scale differences of the terrestrial reference frame of 0.25 ppb, when adjusting station coordinates with manufacturer calibrated Galileo PCOs for different frequency pairs. [ABSTRACT FROM AUTHOR]

The radar imaging satellite mission TerraSAR-X requires precisely determined satellite orbits for validating geodetic remote sensing techniques. Since the achieved quality of the operationally derived, reduced-dynamic (RD) orbit solutions limits the capabilities of the synthetic aperture radar (SAR) validation, an effort is made to improve the estimated orbit solutions. This paper discusses the benefits of refined dynamical models on orbit accuracy as well as estimated empirical accelerations and compares different dynamic models in a RD orbit determination. Modeling aspects discussed in the paper include the use of a macro-model for drag and radiation pressure computation, the use of high-quality atmospheric density and wind models as well as the benefit of high-fidelity gravity and ocean tide models. The Sun-synchronous dusk-dawn orbit geometry of TerraSAR-X results in a particular high correlation of solar radiation pressure modeling and estimated normal-direction positions. Furthermore, this mission offers a unique suite of independent sensors for orbit validation. Several parameters serve as quality indicators for the estimated satellite orbit solutions. These include the magnitude of the estimated empirical accelerations, satellite laser ranging (SLR) residuals, and SLR-based orbit corrections. Moreover, the radargrammetric distance measurements of the SAR instrument are selected for assessing the quality of the orbit solutions and compared to the SLR analysis. The use of high-fidelity satellite dynamics models in the RD approach is shown to clearly improve the orbit quality compared to simplified models and loosely constrained empirical accelerations. The estimated empirical accelerations are substantially reduced by 30% in tangential direction when working with the refined dynamical models. Likewise the SLR residuals are reduced from $$-3\,\pm \,17$$ to $$2\,\pm \,13$$ mm, and the SLR-derived normal-direction position corrections are reduced from 15 to 6 mm, obtained from the 2012-2014 period. The radar range bias is reduced from $$-10.3$$ to $$-6.1$$ mm with the updated orbit solutions, which coincides with the reduced standard deviation of the SLR residuals. The improvements are mainly driven by the satellite macro-model for the purpose of solar radiation pressure modeling, improved atmospheric density models, and the use of state-of-the-art gravity field models. [ABSTRACT FROM AUTHOR]

The carrier signals of the first two Galileo satellites, IOV-1 and IOV-2, exhibit subtle phase variations, which may cause high-rate oscillations in carrier phase measurements of geodetic-grade receivers as well as associated Doppler measurement errors. The carrier phase oscillations slightly exceed the noise level of the measurements and have been attributed to a subtle cross talk of signals from two active atomic frequency standards in the clock monitoring and control unit (CMCU). This cross talk is only present in the first two IOV satellites, and its practical implications have partly been compensated by now through a suitable configuration of the CMCU. Nevertheless, a proper understanding of the phenomenon is deemed relevant to the interpretation of Galileo IOV measurements collected with global ground networks in the 2012 to early 2015 time frame. Also, the data collected so far offer valuable insight into the tracking of high-frequency signal variation of geodetic receivers that are of interest for applications such as structural monitoring or earthquake research. We present practical measurements from zero-baseline tests of common geodetic receivers with data rates of 1/30-1 Hz as well as dedicated tests with high-rate (50-100 Hz) receivers to evidence the phenomenon. Efforts are made to understand the different response of specific receivers based on generic receiver tracking and measurement generation concepts. [ABSTRACT FROM AUTHOR]

Satellite antenna phase center offsets for the Galileo In-Orbit Validation (IOV) and Full Operational Capability (FOC) satellites are estimated by two different analysis centers based on tracking data of a global GNSS network. The mean x- and y-offsets could be determined with a precision of a few centimeters. However, daily estimates of the x-offsets of the IOV satellites show pronounced systematic effects with a peak-to-peak amplitude of up to 70 cm that depend on the orbit model and the elevation of the Sun above the orbital plane. For the IOV y-offsets, no dependence on the orbit model exists but the scatter strongly depends on the elevation of the Sun above the orbital plane. In general, these systematic effects are significantly smaller for the FOC satellites. The z-offsets of the two analysis centers agree within the 10-15 cm level, and the time series do not show systematic effects. The application of an averaged Galileo satellite antenna model obtained from the two solutions results in a reduction of orbit day boundary discontinuities by up to one third-even if an independent software package is used. [ABSTRACT FROM AUTHOR]

This paper introduces a new approach for modeling solar radiation pressure (SRP) effects on Global Navigation Satellite Systems (GNSSs). It focuses on the Galileo In-Orbit Validation (IOV) satellites, for which obvious SRP modeling deficits can be identified in presently available precise orbit products. To overcome these problems, the estimation of empirical accelerations in the Sun direction (D), solar panel axis (Y) and the orthogonal (B) axis is complemented by an a priori model accounting for the contribution of the rectangular spacecraft body. Other than the GPS satellites, which comprise an almost cubic body, the Galileo IOV satellites exhibit a notably rectangular shape with a ratio of about 2:1 for the main body axes. Use of the a priori box model allows to properly model the varying cross section exposed to the Sun during yaw-steering attitude mode and helps to remove systematic once-per-revolution orbit errors that have so far affected the Galileo orbit determination. Parameters of a simple a priori cuboid model suitable for the IOV satellites are established from the analysis of a long-term set of GNSS observations collected with the global network of the Multi-GNSS Experiment of the International GNSS Service. The model is finally demonstrated to reduce the peak magnitude of radial orbit errors from presently 20 cm down to 5 cm outside eclipse phases. [ABSTRACT FROM AUTHOR]

The first two Galileo In-Orbit Validation satellites were launched in October 2011 and started continuous signal transmission on all frequencies in early 2012. Both satellites are equipped with two different types of clocks, namely rubidium clocks and hydrogen masers. Based on two test periods, the quality of the Galileo orbit determination based on Global Navigation Satellite System (GNSS) and Satellite Laser Ranging (SLR) observations is assessed. The estimated satellite clock parameters are used as quality indicator for the orbits: A bump at orbital periods in the Allan deviation indicates systematic errors in the GNSS-only orbit determination. These errors almost vanish if SLR observations are considered in addition. As the internal consistency is degraded by the combination, the offset of the SLR reflector is shifted by +5 cm, resulting in an improved orbit consistency as well as accuracy. Another approach to reduce the systematic errors of the GNSS-only orbit determination employs constraints for the clock estimates with respect to a linear model. In general, one decimeter orbit accuracy could be achieved. [ABSTRACT FROM AUTHOR]

China is currently focussing on the establishment of its own global navigation satellite system called Compass or BeiDou. At present, the Compass constellation provides four usable satellites in geostationary Earth orbit (GEO) and five satellites in inclined geosynchronous orbit (IGSO). Based on a network of six Compass-capable receivers, orbit and clock parameters of these satellites were determined. The orbit consistency is on the 1-2 dm level for the IGSO satellites and on the several decimeter level for the GEO satellites. These values could be confirmed by an independent validation with satellite laser ranging. All Compass clocks show a similar performance but have a slightly lower stability compared to Galileo and the latest generation of GPS satellites. A Compass-only precise point positioning based on the products derived from the six-receiver network provides an accuracy of several centimeters compared to the GPS-only results. [ABSTRACT FROM AUTHOR]

GIOVE-B is one of two test satellites for the future European Global Navigation Satellite System Galileo. The Cooperative Network for GIOVE Observation (CONGO) is a global tracking network of GIOVE-capable receivers established by Deutsches Zentrum für Luft- und Raumfahrt (DLR) and Bundesamt für Kartographie und Geodäsie (BKG). This network provides the basis for the precise orbit determination of the GIOVE-B satellite for the time period 29 June till 27 October 2009 with a modified version of the Bernese GPS Software. Different arc lengths and sets of orbit parameters were tested. These tests showed that the full set of nine radiation pressure parameters resulted in a better performance than the reduced set of five parameters. An internal precision of about one to two decimeters could be demonstrated for the central day of 5-day solutions. The orbit predictions have a precision of about 1 m for a prediction period of 24 h. External validations with Satellite Laser Ranging (SLR) show residuals on the level of 12 cm. The accuracy of the final orbits is expected to be on the few decimeter level. [ABSTRACT FROM AUTHOR]