A Novel Long Short-Term Memory Predicted Algorithm for BDS Short-Term Satellite Clock Offsets

The satellite clocks carried on the BeiDou navigation System (BDS) are a self-manufactured hydrogen clock and improved rubidium clock, and their on-orbit performance and stabilities are not as efficient as GPS and Galileo satellite clocks caused of the orbital diversity of the BDS and the complexity of the space operating environment. Therefore, the existing BDS clock product cannot guarantee the high accuracy demand for precise point positioning in real-time scenes while the communication link is interrupted. To deal with this problem, we proposed a deep learning-based approach for BDS short-term satellite clock offset modeling which utilizes the superiority of Long Short-Term Memory (LSTM) derived from Recurrent Neural Networks (RNN) in time series modeling, and we call it QPLSTM. The ultrarapid predicted clock products provided by IGS (IGU-P) and four widely used prediction methods (the linear polynomial, quadratic polynomial, gray system (GM (1,1)), and Autoregressive Integrated Moving Average (ARIMA) model) are selected to compare with the QPLSTM. The results show that the prediction residual is lower than clock products of IGU-P during 6-hour forecasting and the QPLSM shows a greater performance than the mentioned four models. The average prediction accuracy has improved by approximately 79.6, 69.2, 80.4, and 77.1% and 68.3, 52.7, 66.5, and 69.8% during a 30 min and 1-hour forecasting. Thus, the QPLSTM can be considered as a new approach to acquire high-precision satellite clock offset prediction.

Performance Analysis of Several GPS/Galileo Precise Point Positioning Models

This paper examines the performance of several precise point positioning (PPP) models, which combine dual-frequency GPS/Galileo observations in the un-differenced and between-satellite single-difference (BSSD) modes. These include the traditional un-differenced model, the decoupled clock model, the semi-decoupled clock model, and the between-satellite single-difference model. We take advantage of the IGS-MGEX network products to correct for the satellite differential code biases and the orbital and satellite clock errors. Natural Resources Canada’s GPSPace PPP software is modified to handle the various GPS/Galileo PPP models. A total of six data sets of GPS and Galileo observations at six IGS stations are processed to examine the performance of the various PPP models. It is shown that the traditional un-differenced GPS/Galileo PPP model, the GPS decoupled clock model, and the semi-decoupled clock GPS/Galileo PPP model improve the convergence time by about 25% in comparison with the un-differenced GPS-only model. In addition, the semi-decoupled GPS/Galileo PPP model improves the solution precision by about 25% compared to the traditional un-differenced GPS/Galileo PPP model. Moreover, the BSSD GPS/Galileo PPP model improves the solution convergence time by about 50%, in comparison with the un-differenced GPS PPP model, regardless of the type of BSSD combination used. As well, the BSSD model improves the precision of the estimated parameters by about 50% and 25% when the loose and the tight combinations are used, respectively, in comparison with the un-differenced GPS-only model. Comparable results are obtained through the tight combination when either a GPS or a Galileo satellite is selected as a reference.

Performance Analysis of Several GPS/Galileo Precise Point Positioning Models

This paper examines the performance of several precise point positioning (PPP) models, which combine dual-frequency GPS/Galileo observations in the un-differenced and between-satellite single-difference (BSSD) modes. These include the traditional un-differenced model, the decoupled clock model, the semi-decoupled clock model, and the between-satellite single-difference model. We take advantage of the IGS-MGEX network products to correct for the satellite differential code biases and the orbital and satellite clock errors. Natural Resources Canada’s GPSPace PPP software is modified to handle the various GPS/Galileo PPP models. A total of six data sets of GPS and Galileo observations at six IGS stations are processed to examine the performance of the various PPP models. It is shown that the traditional un-differenced GPS/Galileo PPP model, the GPS decoupled clock model, and the semi-decoupled clock GPS/Galileo PPP model improve the convergence time by about 25% in comparison with the un-differenced GPS-only model. In addition, the semi-decoupled GPS/Galileo PPP model improves the solution precision by about 25% compared to the traditional un-differenced GPS/Galileo PPP model. Moreover, the BSSD GPS/Galileo PPP model improves the solution convergence time by about 50%, in comparison with the un-differenced GPS PPP model, regardless of the type of BSSD combination used. As well, the BSSD model improves the precision of the estimated parameters by about 50% and 25% when the loose and the tight combinations are used, respectively, in comparison with the un-differenced GPS-only model. Comparable results are obtained through the tight combination when either a GPS or a Galileo satellite is selected as a reference.

Extension of the repro3 ANTEX file with BeiDou and QZSS satellite antenna pattern

<p>During the preparations for the International GNSS Service (IGS) contribution to the next reference frame, called repro3, the disclosed pre-launch chamber calibrated Galileo satellite antenna pattern were analyzed. Those tests revealed a discrepancy between the GPS and GLONASS z-component of the phase center offsets (PCO), aligned to the IGS14 scale, and the calibrated Galileo z-PCOs. In order to make the PCOs compatible to the repro3 it was decided to rely on the calibrated Galileo pattern and adjust the GPS and GLONASS PCOs accordingly. Combined with multi-GNSS receiver calibrations for all systems the repro3 might contribute to the scale determination for the next reference frame.</p><p>As the repro3 is based on GPS, GLONASS, and Galileo only those three systems have been analyzed leading to the repro3 ANTEX file, containing all used antenna pattern, which is aligned to the Galileo induced scale. In order to extend the repro3 ANTEX file with satellite calibrations for BeiDou and QZSS a dedicated reprocessing based on CODEs MGEX solution is made to assess the available PCOs for those satellites and tests their consistency with the repro3 scale. The results should allow to extend the repro3 ANTEX with the BDS and QZSS pattern for experimental purposes.</p>

General Relativistic effects acting on GNSS orbits with a focus on Galileo satellites launched into incorrect orbital planes

<p>Three orbital effects emerging from general relativity are typically considered for Earth-orbiting satellites: the Schwarzschild effect, Lense-Thirring effect or frame-dragging, and the de Sitter or geodetic precession effect. For circular orbits and short satellite orbital arcs, the dominating Schwarzschild effect is difficult to determine, because it causes a constant radial acceleration which can be absorbed by a small modification in the gravitational constant GM term or a constant offset in the estimated semi-major axis of a satellite orbit. To separate the effects caused by the Schwarzschild effect from other orbital effects, especially those emerging from orbit modeling issues of non-gravitational accelerations, eccentric satellite orbits should be employed.</p><p>The first pair of satellites belonging to the Galileo satellite system was accidentally launched into non-circular orbits with height variations between from 17,180 km for the perigee to 26,020 km for the apogee. The eccentric orbits introduced new opportunities for the verification of the effects emerging from general relativity when employing the Galileo constellation. Galileo satellites are equipped with two techniques for precise orbit determination: microwave GNSS antennas and SLR retroreflectors which allow for deriving their orbits of superior quality.</p><p>In this study, we discuss effects in GNSS orbits emerging from general relativity. We concentrate on those effects that exceed the value of 1 mm over 1 day, thus are of fundamental importance for precise orbit determination in satellite geodesy and precise high-quality products of the International GNSS Service. We show that the semi-major axis of Galileo satellites in eccentric orbits varies between -29 mm in perigee to -9 mm in apogee due to the Schwarzschild term. For GNSS geostationary satellites with the inclination angle close to zero, the omission of the de Sitter effect may cause an error of the determination of the right ascension of ascending node exceeding the value of 1 meter after 1 day. Finally, we discuss the suitability of using GPS, GLONASS, and Galileo satellite orbits to determine the values of the Post-Newtonian Parameters γ and β and all limitations related to the observability of these parameters at GNSS heights and systematic errors emerging from non-gravitation orbit perturbations.</p>

Terrestrial frame solutions from the IGS third reprocessing

<p>The International GNSS Service (IGS) recently finalized its third reprocessing campaign (repro3). Ten Analysis Centers (ACs) reanalyzed the history of GPS, GLONASS and Galileo data collected by a global tracking network over the period 1994-2020. Combinations of the daily repro3 AC terrestrial frame solutions constitute the IGS contribution to the next release of the International Terrestrial Reference Frame, ITRF2020.</p><p>Compared to the previous IGS reprocessing campaign (repro2), a number of new models and strategies have been implemented in repro3, including the new IERS linear pole model, the new IERS-recommended sub-daily EOP tide model, and rotations of phase center corrections for tracking antennas not oriented North. Besides, a new set of satellite antenna phase center offsets was adopted in repro3, based on the published pre-flight calibrations of the Galileo satellite antennas. As a consequence, the IGS contribution to ITRF2020 provides for the first time an independent Galileo-based realization of the terrestrial scale, instead of being conventionally aligned in scale to the previous ITRF.</p><p>In this presentation, quality metrics from the daily repro3 terrestrial frame combinations are first introduced and compared to those from repro2. The impacts of the newly adopted models are then assessed and discussed. The terrestrial scale realized by the IGS repro3 solutions is in particular confronted to independent estimates from SLR and VLBI. The precision of the IGS repro3 station position time series is finally compared to that of the IGS repro2 series as well as of station position time series from independent groups.</p>

Two methods to determine scale-independent GPS PCOs and GNSS-based terrestrial scale: comparison and cross-check

The GPS satellite transmitter antenna phase center offsets (PCOs) can be estimated in a global adjustment by constraining the ground station coordinates to the current International Terrestrial Reference Frame (ITRF). Therefore, the derived PCO values rest on the terrestrial scale parameter of the frame. Consequently, the PCO values transfer this scale to any subsequent GNSS solution. A method to derive scale-independent PCOs without introducing the terrestrial scale of the frame is the prerequisite to derive an independent GNSS scale factor that can contribute to the datum definition of the next ITRF realization. By fixing the Galileo satellite transmitter antenna PCOs to the ground calibrated values from the released metadata, the GPS satellite PCOs in the z-direction (z-PCO) and a GNSS-based terrestrial scale parameter can be determined in GPS + Galileo processing. An alternative method is based on the gravitational constraint on low earth orbiters (LEOs) in the integrated processing of GPS and LEOs. We determine the GPS z-PCO and the GNSS-based scale using both methods by including the current constellation of Galileo and the three LEOs of the Swarm mission. For the first time, direct comparison and cross-check of the two methods are performed. They provide mean GPS z-PCO corrections of $$- 186 \pm 25$$ - 186 ± 25 mm and $$- 221 \pm 37$$ - 221 ± 37 mm with respect to the IGS values and $$+ 1.55 \pm 0.22$$ + 1.55 ± 0.22 ppb (parts per billion) and $$+ 1.72 \pm 0.31$$ + 1.72 ± 0.31 in the terrestrial scale with respect to the IGS14 reference frame. The results of both methods agree with each other with only small differences. Due to the larger number of Galileo observations, the Galileo-PCO-fixed method leads to more precise and stable results. In the joint processing of GPS + Galileo + Swarm in which both methods are applied, the constraint on Galileo dominates the results. We discuss and analyze how fixing either the Galileo transmitter antenna z-PCO or the Swarm receiver antenna z-PCO in the combined GPS + Galileo + Swarm processing propagates to the respective freely estimated z-PCO of Swarm and Galileo.

GNSS scale determination using calibrated receiver and Galileo satellite antenna patterns

The reference frame of a global terrestrial network is defined by the origin, the orientation and the scale. The origin of the ITRF2014 is defined by the ILRS long-term solution, the orientation by no-net rotation conditions w.r.t. the previous reference frame (ITRF2008), and the scale by the mean values from global VLBI and SLR solution series (Altamimi et al. in J Geophys Res Solid Earth 121:6109–6131, 2016). With the release of the Galileo satellite antenna phase center offsets (PCO) w.r.t. the satellites center of mass (GSA in Galileo IOV and FOC satellite metadata, 2019) and the availability of new ground antenna calibrations for GNSS receivers, based on anechoic chamber measurements or on robot calibrations, GNSS global network solutions qualify to contribute to the scale determination of terrestrial networks, as well. Our analysis is based on global multi-GNSS solutions of the years 2017 and 2018 and may be seen as “proof of concept” for the contribution of GNSS data to the scale determination of the terrestrial reference frame. In a first step, the currently used Galileo PCO estimations (Steigenberger et al. in J Geod 90:773–785, 2016) are compared to the released PCO values, which show discrepancies on the decimeter-level. Eventually, the published Galileo PCOs are used in an experimental solution as known values. GNSS-specific PCOs are estimated, as well, for GPS and GLONASS, together with the “standard” parameters set up in global GNSS solutions. From the estimated network coordinates, a time series of daily scale parameters of the terrestrial network is extracted, which shows an offset of the order of 1 ppb (parts per billion, corresponding to a height difference of 6.4 mm on the Earth’s surface) w.r.t. to the ITRF2014 network and an annual variation with an amplitude of about 0.3 ppb.