Cross-track Components Research Articles

Performance Evaluation and Application Field Analysis of Precise Point Positioning Based on Different Real-Time Augmentation Information

The most commonly used real-time augmentation services in China are the International GNSS Service’s (IGS) real-time service (RTS), PPP-B2b service, and Double-Frequency Multi-Constellation (DFMC) service of the BeiDou Satellite-Based Augmentation System (BDSBAS) service. However, research on the performance evaluation, comparison, and application scope of these three products is still incomplete. This article introduces methods for obtaining real-time augmentation information and real-time orbit and clock offset recovery. Based on real-time orbit and clock offset accuracy, positioning accuracy, and positioning availability, this article systematically evaluates the performance and analyzes the application fields of Centre National d’Études Spatiales (CNES), PPP-B2b, and BDSBAS augmentation information. The results of the evaluation revealed that the radial accuracy of the CNES and PPP-B2b real-time orbit product is consistent, and the Root Mean Square (RMS) is better than 5 cm. The CNES real-time orbit product can achieve centimeter-level accuracy in both along-track and cross-track components, surpassing PPP-B2b’s decimeter-level accuracy. Both services demonstrate consistent accuracy in the real-time clock offset, with PPP-B2b showing similar standard deviations (STDs) of 0.16 ns for different satellites. However, for CNES, the STD of the real-time clock offset varies, with values of 0.10 ns, 0.19 ns, and 0.60 ns, respectively, for GPS, BDS-3 Medium Earth Orbit (MEO), and BDS-3 Inclined Geosynchronous Satellite Orbit (IGSO) satellites. Centimeter-level accuracy is achieved after convergence and positioning availability exceeds 99% for CNES and PPP-B2b services. Therefore, the difference between the two services in application areas depends on the acquisition of augmentation information. However, BDSBAS, which concentrates on code observations, demonstrates inferior performance in real-time orbit, clock offset, positioning accuracy, and positioning availability when compared to the other two services. Its primary application is in the aviation and maritime domains, where there is a greater need for service integrity, continuity, and reliability.

Choices for temporal gravity field modeling for precision orbit determination of CryoSat-2

In this paper we review the precision orbit determination (POD) performance of the CryoSat-2 mission where we used all tracking data between June-2010 and Jan-2023; with station and beacon coordinates provided in the ITRF2020 reference system, we use a mean gravity model, and we use spacecraft specific models for modeling drag and radiation pressure. To model time variable gravity (TVG) we distinguish between two components, there is a short term oceanic and atmospheric part for which we use the AOD1B model; for the longer term part we employ GRACE and GRACE-FO monthly potential coefficient solutions. Our experience is that adding TVG information is not necessarily successful during POD, and that attention must be paid to the proper processing of the GRACE and GRACE-FO data. To demonstrate this property we define four runs where we gradually implement TVG information. An evaluation criterion is the level of POD tracking residuals, the level of the empirical accelerations, and a comparison to precision orbit ephemeris provided by the Centre National d’Etudes Spatiales (CNES). Unexplained empirical accelerations found during POD are on the level of 3 nm/s2 for the along-track component and 13 nm/s2 for the cross-track component. The laser residuals converge at approximately 1.02 cm and the Doppler residuals are on the level of 0.406 mm/s, the radial orbit difference to the CNES POE-F (Precision Orbit Ephemeris version F) orbits narrows to 6.5 mm. Tracking residuals are not evenly distributed for DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite) beacons, the South Atlantic Anomaly effect is for instance clearly visible in the first empirical orthogonal function EOF mode of monthly binned DORIS residuals. After consideration of all possible TVG approaches our conclusion is that 3 hourly AOD1B model fields result in a small but visible improvement. The addition of TVG from GRACE and GRACE-FO is implemented in two different ways from which we can select a version that does lead to a reduction in the Doppler tracking residuals and which does reduce the level of solved for empirical accelerations.

Enhanced precise orbit determination of BDS-3 MEO satellites based on ambiguity resolution with B1C/B2a dual-frequency combination

Broadcasting the multi-frequency signals is one of the outstanding advantages of BDS-3 (BeiDou Navigation Satellite System). In addition to the legacy signals B1I and B3I, we are interested in the performance of two new signals B1C and B2a. For the purpose of improving the orbit accuracy of BDS-3 backbone MEOs (Medium Earth Orbits), this study focuses on Precise Orbit Determination (POD) using B1C/B2a dual-frequency measurements. First, the performance of POD will be benefit from an increasing observation quantity and qualities. Observations from the public MGEX (Multi-GNSS Experiment) network are statistically collected, and the number of stations able to track B1C and B2a signals is analyzed. In recent years, the sustainable growth number of stations is up to more than one hundred, which brings the new chance to improve the POD accuracy based on B1C/B2a linear combination. Then, the multipath and post-fit residuals of observations are compared between B1C/B2a and B1I/B3I to investigate the observation qualities. Second, as a key strategy, the ambiguities are successfully fixed during POD processing of BDS-3 MEOs. The ambiguity fixing percentage is as high as 93.1% on average using B1C/B2a combination. Compared with float solutions, the improvements of ambiguity fixed orbits reach 36.2%, 19.9% and 36.6% on the radial, along-track and cross-track components, respectively. For the fixed solutions of B1I/B3I and B1C/B2a, it is noticed that the orbits achieve further benefits from B1C/B2a combination for 8.4%, 6.9% and 8.0% on the radial, along-track and cross-track components, respectively. Finally, the performance of B1C/B2a combination POD is validated by orbital overlapping, the orbit signal-in-space range error (SISRE) analysis, independent technology Satellite Laser Ranging (SLR) and Precise Point Positioning (PPP), respectively. SLR residuals show the radial orbital accuracy has an improvement of 8.0% for C20, C21, C29 and C30 on average when employing B1C/B2a measurements. Compared with B1I/B3I, both static and kinematic PPP based on B1C/B2a orbits indicate the improvement on the vertical component. And a faster and more stable convergence performance is also observed using B1C/B2a combination.

Evaluation of BDS-3 B1C/B2b Single/Dual-Frequency PPP Using PPP-B2b and RTS SSR Products in Both Static and Dynamic Applications

The BeiDou Global Navigation Satellite System (BDS-3) can provide PPP-B2b satellite-based Precise Point Positioning (PPP) real-time service to the Asia–Pacific region via PPP-B2b signal transmitted from the three Geostationary Earth Orbit (GEO) satellites. This paper provides a comprehensive evaluation of the accuracies of the satellite’s precise real-time orbit and clock products, including BDS-3 PPP-B2b precise products and the precise real-time products provided by four IGS centers (CAS, DLR, GFZ, and WHU). In addition, the influences of these real-time precise satellite products on the PPP positioning accuracy with single-frequency and dual-frequencies are also studied. Furthermore, the accuracies of broadcast ephemeris and IGS ultra-rapid products are studied, as well as their impact on PPP accuracies. Results illustrate that the orbits accuracies of PPP-B2b orbits are 9.42 cm, 21.26 cm, and 28.65 cm in the radial, along-track, and cross-track components, which are slightly lower than those of real-time orbits provided by the four IGS centers. However, the accuracy of PPP-B2b clock biases is 0.18 ns, which is higher than those provided by IGS Real-Time Service (RTS). In the static positioning test, the 3D positioning accuracy of B1I+B3I dual-frequencies PPP and B1C single-frequency PPP are centimeter-level while using PPP-B2b service, which is slightly lower in horizontal components compared to those obtained based on IGS RTS products. The results of the dynamic vehicle test indicate that the positioning accuracies of B1I+B2b dual-frequency PPP are about 50 cm and 120 cm in horizontal and vertical components, which are close to those of B2b single-frequency PPP using PPP-B2b service. Generally, the PPP-B2b orbit and clock accuracies on real-time PPP present similar performance to that based on IGS RTS.

Modelling and Assessment of BDS-3 Real-time Precise Point Positioning Time Transfer Based on PPP-B2b Service

In 2020, users in and around China had access to a new real-time precise point positioning (RTPPP) service with the BeiDou global navigation satellite system (BDS-3) B2b (PPP-B2b) signal. In this study, the quality of PPP-B2b products is first assessed and compared with the CNAV1 broadcast ephemeris. Then a mode of BDS-3 PPP time transfer with PPP-B2b (B2b-RTPPP) is developed and evaluated in static and kinematic modes. The results demonstrate that the discontinuity of orbit is improved by applying the PPP-B2b, and its root mean square errors (RMSEs) are 0.081 m, 0.165 m, and 0.107 m in the radial, along-track, and cross-track components, respectively. The standard deviation (STD) of the PPP-B2b clock offset is 0.08 ns, greatly better than that of the broadcast clock offset. For time transfer, the type A uncertainty of the B2b-RTPPP solution is approximately 0.1 ns in static mode, and approximately 0.3 ns in kinematic mode. The B1I/B3I B2b-RTPPP time transfer solution performs better than the B1C/B2a solution. For frequency stability, the modified Allan deviation (MDEV) of the B2b-RTPPP solution is comparable to that of the post-processing solution. The B1C/B2a combination has better short-term frequency stability than B1I/B3I, while the long-term frequency stability of B1C/B2a is worse. In addition, the contribution of the differential code bias (DCB) to B2b-RTPPP time transfer is also investigated. The type A uncertainty of the B2b-RTPPP solution without DCB correction is worse than that of the B2b-RTPPP solution with DCB correction. The B1C/B2a B2b-RTPPP solution without DCB correction has better frequency stability than the B1I/B3I B2b-RTPPP solution.

Calibration of GRACE on-board accelerometers for thermosphere density derivation

ABSTRACT Low Earth Orbit satellite on-board accelerometers play an important role in improving our understanding of thermosphere density; however, the accelerometer-derived densities are subject to accelerometer calibration errors. In this study, two different dynamic calibration schemes, the accelerometer parameter-incorporated orbit fitting and precise orbit determination (POD), are investigated with the Gravity Recovery And Climate Experiment (GRACE) satellite accelerometers for thermosphere density derivation during years 2004–2007 (inclusive). We show that the GRACE accelerometer parametrization can be optimized by fixing scale coefficients and estimating biases every 60 min so that the orbit fitting and POD precision can be improved from 10 cm to 2 cm in the absence of empirical acceleration compensations and as a result the integrity of calibration parameters may be reserved. The orbit-fitting scheme demonstrates similar calibration precision with respect to POD. Their bias estimates in the along-track and cross-track components exhibit an offset within 0.1% and a standard deviation (STD) less than 0.3%. Correspondingly, a bias of 2.20% and a STD of 5.75% exists between their thermosphere density estimates. The orbit-fitting and POD-derived thermosphere densities are validated through the comparison against the results published by other institution. The comparison shows that either of them can achieve a precision level at 6%. To derive thermosphere density from the rapid-increasing amount of on-board accelerometer data sets, it is suggested to take full advantage of the orbit-fitting scheme due to its high efficiency as well as high precision.

Real-Time Precise GPS Orbit and Clock Estimation With a Quasi-Orbit-Fixed Solar Radiation Pressure Model

<h3>Abstract</h3> Real-time precise global navigation satellite system (GNSS) orbit and clock products play a key role for real-time GNSS-based applications, both in the scientific and industrial communities. Different from the typical two-step procedure to generate orbit and clock solutions separately, we estimate the real-time orbit and clock products simultaneously using a Kalman filter. For this purpose, we developed a GNSS data processing software that can run in pseudo-real-time mode with RINEX files and is ready to run in real-time mode once given the real-time observation stream. Meanwhile, a quasi-orbit-fixed solar radiation pressure (SRP) model is developed. In order to verify the performance of the software and the new SRP model, several experiments with a global network of 60 tracking stations over a time span of three months were conducted to generate real-time Global Positioning System (GPS) orbit and clock products. Then, the results were assessed in terms of accuracy and efficiency, both critical for real-time precise GNSS applications. Compared to the International GNSS Service (IGS) final orbits, the real-time GPS orbit accuracy was 2.82 cm, 5.45 cm, and 5.47 cm in the radial, along-track, and cross-track components, respectively. The precision of the clock product in terms of standard deviation (STD) value was about 0.1 ns. Moreover, the average execution time per epoch was usually less than 1.0 s, which ensures the high efficiency of the processing.

Inter-satellite link augmented BeiDou-3 orbit determination for precise point positioning

Precise Point Positioning (PPP) requires precise products, including high-accuracy satellite orbit and clock parameters. It is impossible to obtain an orbit solution that is sufficiently accurate for PPP services with a regional tracking network; therefore, satellite orbits are usually estimated by a global tracking network with a large number of ground stations. However, it is expensive to build globally distributed stations. Fortunately, BeiDou-3 satellites carry an Inter-Satellite Link (ISL) payload, which can track the whole arc of the BeiDou-3 satellites and enhance the orbit determination accuracy with regional ground stations. In this contribution, a novel orbit determination strategy for BeiDou-3 PPP is proposed, in which the BeiDou-3 satellite orbits are enhanced by the ISL. First, the generation of precise satellite products is demonstrated in detail. In addition, the products are assessed by Satellite Laser Ranging (SLR) residuals and overlap comparisons. Moreover, the products are used for receivers in mainland China to carry out the static and kinematic modes to research the PPP performance of BeiDou-3′s 3IGSO/24MEO constellation. The SLR validations of the satellite orbits demonstrate an accuracy better than 0.1 m in the radial component, and the orbit overlap comparisons show accuracies of 0.016 m in the radial component, 0.088 m in the along-track component and 0.087 m in the cross-track component. The Standard Deviation (STD) in the differences in overlapping arcs for the estimated satellite clocks is approximately 0.10 ns. The static PPP results demonstrate that the error in both the horizontal and vertical components is smaller than 10 cm after 30 minutes of convergence. After 24 hours of convergence, the errors are 0.70 cm, 0.63 cm and 1.99 cm for the north, east and up components, respectively. The kinematic PPP experiment illustrates that the Root Mean Square (RMS) position errors in the north, east and up components are approximately 3.23 cm, 5.27 cm and 8.64 cm, respectively, after convergence. The obtainable positioning and convergence performances are comparable to those using products generated by global tracking networks.

An analysis of BDS-3 real-time PPP: Time transfer, positioning, and tropospheric delay retrieval

With the development of China’s BDS-3, more studies focused on its performance in precise point positioning (PPP), mainly in post-processing mode. This study conducts a comprehensive investigation of BDS-3 real-time PPP with Centre National d’Etudes Spatiales (CNES) real-time products (SSRA00CNE0) from the perspective of time transfer, positioning, and tropospheric delay retrieval. First, the availability and accuracy of BDS-3 real-time products were evaluated over 41 days. The product availability was about 80%. The accuracy of BDS-3 satellite orbit were 0.060, 0.115 and 0.065 m in the radial, along-track, and cross-track component. In addition, the standard deviation (STD) of satellite clock difference was 0.455 ns. Afterwards, precise time transfer, positioning, and Zenith troposphere delay (ZTD) estimation derived from BDS-3 real-time PPP were assessed with 7-day processing. The root mean square (RMS) of smoothed residuals is 0.020 ns, while it is 0.001 ns for BDS-3 PPP with WUM final products for time transfer. Furthermore, the RMS values of positioning errors derived from real-time static BDS-3 PPP positioning were 0.021, 0.010, and 0.03 m in the east (E), north (N), and up (U) component, respectively. Moreover, the RMS of ZTD estimation is 9.9 mm, which is comparable to GPS real-time PPP solutions.

Investigating the GALILEO and BeiDou orbit accuracy derived from rapid products

In recent years, the advances of the new Global Navigation Satellite System (GNSS) constellations including, Galileo and BeiDou (BDS), have undergone dramatic changes. Some analysis centers (ACs) produce precise orbit and clock products of Galileo and BeiDou constellations. Currently, three types of Galileo and BeiDou satellite orbit and clock products are available &amp;amp;ndash; namely, precise, rapid and ultra-rapid products &amp;amp;ndash;. Ultra-rapid and rapid products are generally used for time-constrained applications. Precise orbit determination (POD) of Galileo and BeiDou is much challenging compared with GPS and GLONASS constellations due to the officially undetermined receiver phase center offset (PCO), variations (PCV) of Galileo and BeiDou constellations and, also some other not well-defined factors such as yaw-attitude models and solar radiation pressure. In this study, GALILEO orbit accuracy is investigated using rapid products produced by Center for Orbit Determination in Europe (CODE) GeoForschungsZentrum (GFZ) and Wuhan University (WUHAN), while GFZ and WUHAN rapid products are used for BeiDou constellation only. One month (January) of data in 2020 is used to compute errors of radial, along-track, and cross-track components of Galileo and BeiDou orbit derived by rapid products compared with the CODE final Multi-GNSS Experiment (MGEX) product which is assumed as the reference product. The results show that no significant differences between the products are found for Galileo orbit. For BeiDou orbit, WUHAN rapid product produced the smaller root mean square errors (RMSEs) of orbit components compared with the GFZ rapid product.

The application of inter-satellite links connectivity schemes in various satellite navigation systems for orbit and clock corrections determination: simulation study

Inter-Satellite Links (ISLs) are intended to improve precision of orbit determination and satellite clock estimation. The ISLs provide a precise pseudorange measurements between satellites in a specific constellation. The study is a preparatory assessment of exploitation of seven connectivity schemes in the terms of the precise orbit determination for three types of constellations—Galileo-like with 24 satellites on three orbital planes, GPS-like with 24 satellites on six orbital planes, and GPS with real positions. The first part of the study focused on detailed analysis of the various ISL connectivity schemes, considering the geometry of ISL observations. The selected results of ranging were examined in the context of the precise orbit determination based on weighted least squares adjustment. The second part of the analysis was based on simulated measurements with two approaches. First approach focuses on geometrical dependencies and the second is performed with ISL measurement biases estimation. It was found that the use of the ISL technique with GNSS measurements in orbit determination improves the results by reducing the RMS error in the along-track and cross-track components. Choice of connectivity schemes does not have a significant impact on the total results of orbit determination, but give different contribution to particular components. Introducing constant bias in ISL measurements occurs in slightly worse estimation results. However, the relations between connectivity schemes is very similar to approach without simulation of ISL bias, the differences are at the level of 10%. Satellite and station clock estimation errors are almost equal for all used connectivity schemes. Results of clocks are also not influenced by ISL bias. This study showed that the ISL technique is a highly promising addition for future generations of satellite navigation systems and that sequential and ring connectivity schemes can be recommended for use in future navigation constellations.

Tilt-to-Length Coupling in the GRACE Follow-On Laser Ranging Interferometer

The Laser Ranging Interferometer onboard the Gravity Recovery and Climate Experiment Follow-On satellites is the first laser interferometer in space measuring satellite-to-satellite distance variations. One of its main noise sources at low frequencies is the so-called tilt-to-length coupling, caused by satellite pointing variations. This error is estimated by fitting a linear coupling model, making use of the so-called center-of-mass calibration maneuvers. These maneuvers are performed regularly for the original purpose of center-of-mass determination. Here, the results of the tilt-to-length estimations for the Laser Ranging Interferometer are presented in terms of coupling factors, which are all within and thus meet the requirements. From these parameters, estimations of nadir and cross-track components of the spacecraft center-of-mass positions with respect to the interferometer reference point are derived, providing an additional method to track center-of-mass movement over time.

LEO constellation-augmented multi-GNSS for rapid PPP convergence

The fast motion of low earth orbit (LEO) satellite contributes to the geometric diversity, allowing for rapid convergence of precise point positioning (PPP). In this contribution, we investigate the PPP performance of the LEO constellation-augmented full operational capability (FOC) multi-GNSS. We design six LEO constellations with different satellite numbers, orbit altitudes and orbit types, together with the FOC multi-GNSS constellations, and then simulate both the onboard LEO and ground-based observations. The multi-GNSS POD result shows much better orbit accuracy of 3.3, 2.7 and 2.6 cm in radial, along-track and cross-track components, respectively, compared with that of 10.3, 9.2 and 8.9 cm for GPS-only POD. Furthermore, the performance of LEO-augmented multi-GNSS PPP is evaluated. With the augmentation of 60-, 96-, 192- and 288-satellite LEO constellation, the multi-GNSS PPP convergence time can be shortened from 9.6 to 7.0, 3.2, 2.1 and 1.3 min, respectively, in midlatitude region. For LEO-augmented GPS- and BDS-only PPP, the improvement is more significant with the convergence time dramatically shortened by 90% from about 25 to within 3 min with 192- or 288-satellite constellation. The augmentation capability is also found to be associated with station latitude, and the higher latitude, the better performance. To enable about more than 70% significant reduction on convergence time, as well as considering the cost, the 192-satellite LEO constellation scheme is suggested. In terms of orbit altitude, the scheme of 1000 km presents better performance than that of 600 km. As for orbit type, the performances are comparable for polar and sun-synchronous orbits. Additionally, LEO-only PPP can be achieved with the convergence time of about 6.5 min.

Sea Surface Current Estimation Using Airborne Circular Scanning SAR with a Medium Grazing Angle

Circular scanning synthetic aperture radar (SAR) is a novel imaging mode wherein the radar antenna rotates from 0 degrees to 360 degrees along the platform flight direction, providing us with a potentially effective technique to estimate the sea surface current velocity. In this paper, we propose a novel method to estimate the sea surface current velocity utilizing the Doppler centroid shifts of different scan angles over 360 degrees after the airborne platform motion compensation. In this method, the Doppler centroid shifts of the sea clutter at different scan angles are first extracted, and the corresponding compensation errors caused by the azimuth pointing and the incidence angle of the radar beam are considered. Finally, the least squares (LS) technique is applied to estimate the along-track velocity component and the cross-track velocity component of the sea surface current. The effectiveness of the proposed method is verified by the real data recorded by an airborne circular scanning SAR system.

An Adjoint-Based Forecast Impact from Assimilating MISR Winds into the GEOS-5 Data Assimilation and Forecasting System

This study examines the benefit of assimilating cloud motion vector (CMV) wind observations obtained from the Multiangle Imaging SpectroRadiometer (MISR) within a Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2), configuration of the Goddard Earth Observing System-5 (GEOS-5) model data assimilation system (DAS). Available in near–real time (NRT) and with a record dating back to 1999, MISR CMVs boast pole-to-pole coverage and geometric height assignment that is complementary to the suite of atmospheric motion vectors (AMVs) included in the MERRA-2 standard. Experiments spanning September–November of 2014 and March–May of 2015 estimated relative MISR CMV impact on the 24-h forecast error reduction with an adjoint-based forecast sensitivity method. MISR CMV were more consistently beneficial and provided twice as large a mean forecast benefit when larger uncertainties were assigned to the less accurate component of the CMV oriented along the MISR satellite ground track, as opposed to when equal uncertainties were assigned to the eastward and northward components as in previous studies. Assimilating only the cross-track component provided 60% of the benefit of both components. When optimally assimilated, MISR CMV proved broadly beneficial throughout the Earth, with the greatest benefit evident at high latitudes where there is a confluence of more frequent CMV coverage and gaps in coverage from other MERRA-2 wind observations. Globally, MISR represented 1.6% of the total forecast benefit, whereas regionally that percentage was as large as 3.7%.

National BDS Augmentation Service System (NBASS) of China: Progress and Assessment

Abstract: In this contribution, the processing strategies of real-time BeiDou System (BDS) precise orbits, clocks, and ionospheric corrections in the National BDS Augmentation Service System (NBASS) are briefly introduced. The Root Mean Square (RMS) of BDS predicted orbits are better than 10 cm in radial and cross-track components, and the accuracy of the BDS real-time clock is better than 0.5 ns for Inclined Geosynchronous Orbit (IGSO) and Mid Earth Orbit (MEO) satellites. The accuracy of BDS Geostationary Earth Orbit (GEO) orbits and clocks are worse than the IGSO and MEO satellites due to its poor geometry conditions. The real-time ionospheric correction is evaluated by cross-validation, and the average accuracy in the vertical direction is about 4 TECU. With these real-time corrections, the overall single and dual-frequency kinematic precise point positioning (PPP) performance in China are evaluated in terms of positioning accuracy at the 95% confidence level and convergence time. The BDS PPP positioning accuracy shows significant regional characteristics due to the geometry distribution of BDS satellites and the accuracy of ionospheric model in different regions. The BDS dual-frequency PPP positioning accuracy in high-latitude and western fringe region is about 0.5 m and 1.0 m in the horizontal and vertical component, respectively, while the horizontal accuracy is better than 0.2 m and the vertical accuracy is better than 0.3 m in the midlands. The convergence time of the BDS PPP is much longer than the GPS PPP and it needs more than 60 min to achieve the accuracy better than 10 cm in both horizontal and vertical directions for dual-frequency PPP. Similar with dual-frequency PPP, the positioning accuracy of the BDS single-frequency PPP in the fringe region is worse than other regions. The positioning in the midlands can achieve 0.5 m in horizontal component and 1.0 m in the vertical component. In addition, when GPS and BDS are combined, the positioning performance of both single-frequency and dual-frequency PPP can be greatly improved.

Earth\u2019s gravity field modelling based on satellite accelerations derived from onboard GPS phase measurements

GPS data collected by satellite gravity missions can be used for extracting the long-wavelength part of the Earth’s gravity field. We propose a new data processing method which makes use of the ‘average acceleration’ approach to gravity field modelling. In this method, satellite accelerations are directly derived from GPS carrier phase measurements with an epoch-differenced scheme. As a result, no ambiguity solutions are needed and the systematic errors that do not change much from epoch to epoch are largely eliminated. The GPS data collected by the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite mission are used to demonstrate the added value of the proposed method. An analysis of the residual accelerations shows that accelerations derived in this way are more precise, with noise being reduced by about 20 and 5% at the cross-track component and the other two components, respectively, as compared to those based on kinematic orbits. The accelerations obtained in this way allow the recovery of the gravity field to a slightly higher maximum degree compared to the solution based on kinematic orbits. Furthermore, the gravity field solution has an overall better performance. Errors in spherical harmonic coefficients are smaller, especially at low degrees. The cumulative geoid height error is reduced by about 15 and 5% up to degree 50 and 150, respectively. An analysis in the spatial domain shows that large errors along the geomagnetic equator, which are caused by a high electron density coupled with large short-term variations, are substantially reduced. Finally, the new method allows for a better observation of mass transport signals. In particular, sufficiently realistic signatures of regional mass anomalies in North America and south-west Africa are obtained.

Assessment of MISR Cloud Motion Vectors (CMVs) Relative to GOES and MODIS Atmospheric Motion Vectors (AMVs)

AbstractCloud motion vector (CMV) winds retrieved from the Multiangle Imaging SpectroRadiometer (MISR) instrument on the polar-orbiting Terra satellite from 2003 to 2008 are compared with collocated atmospheric motion vectors (AMVs) retrieved from Geostationary Operational Environmental Satellite (GOES) imagery over the tropics and midlatitudes and from Moderate Resolution Imaging Spectroradiometer (MODIS) imagery near the poles. MISR imagery from multiple view angles is exploited to jointly retrieve stereoscopic cloud heights and motions, showing advantages over the AMV heights assigned by radiometric means, particularly at low heights (&lt;3 km) that account for over 95% of MISR CMV sampling. MISR–GOES wind differences exhibit a standard deviation ranging with increasing height from 3.3 to 4.5 m s−1 for a high-quality [quality indicator (QI) ≥ 80] subset where height differences are &lt;1.5 km. Much of the observed difference can be attributed to the less accurately retrieved component of CMV motion along the direction of satellite motion. MISR CMV retrieval is subject to correlation between error in retrieval of this along-track component and of height. This manifests as along-track bias varying with height to magnitudes as large as 2.5 m s−1. The cross-track component of MISR CMVs shows small (&lt;0.5 m s−1) bias and standard deviation of differences (1.7 m s−1) relative to GOES AMVs. Larger differences relative to MODIS are attributed to the tracking of cloud features at heights lower than MODIS in multilayer cloud scenes.

The unexpected signal in GRACE estimates of $$C_{20}$$

For science applications of the gravity recovery and climate experiment (GRACE) monthly solutions, the GRACE estimates of \(C_{20}\) (or \(J_{2}\)) are typically replaced by the value determined from satellite laser ranging (SLR) due to an unexpectedly strong, clearly non-geophysical, variation at a period of \(\sim \)160 days. This signal has sometimes been referred to as a tide-like variation since the period is close to the perturbation period on the GRACE orbits due to the spherical harmonic coefficient pair \(C_{22}/S_{22}\) of S2 ocean tide. Errors in the S2 tide model used in GRACE data processing could produce a significant perturbation to the GRACE orbits, but it cannot contribute to the \(\sim \)160-day signal appearing in \(C_{20}\). Since the dominant contribution to the GRACE estimate of \(C_{20}\) is from the global positioning system tracking data, a time series of 138 monthly solutions up to degree and order 10 (\(10\times 10\)) were derived along with estimates of ocean tide parameters up to degree 6 for eight major tides. The results show that the \(\sim \)160-day signal remains in the \(C_{20}\) time series. Consequently, the anomalous signal in GRACE \(C_{20}\) cannot be attributed to aliasing from the errors in the S2 tide. A preliminary analysis of the cross-track forces acting on GRACE and the cross-track component of the accelerometer data suggests that a temperature-dependent systematic error in the accelerometer data could be a cause. Because a wide variety of science applications relies on the replacement values for \(C_{20}\), it is essential that the SLR estimates are as reliable as possible. An ongoing concern has been the influence of higher degree even zonal terms on the SLR estimates of \(C_{20}\), since only \(C_{20}\) and \(C_{40}\) are currently estimated. To investigate whether a better separation between \(C_{20}\) and the higher-degree terms could be achieved, several combinations of additional SLR satellites were investigated. In addition, a series of monthly gravity field solutions (\(60\times 60\)) were estimated from a combination of GRACE and SLR data. The results indicate that the combination of GRACE and SLR data might benefit the resonant orders in the GRACE-derived gravity fields, but it appears to degrade the recovery of the \(C_{20}\) variations. In fact, the results suggest that the poorer recovery of \(C_{40}\) by GRACE, where the annual variation is significantly underestimated, may be affecting the estimates of \(C_{20}\). Consequently, it appears appropriate to continue using the SLR-based estimates of \(C_{20}\), and possibly also \(C_{40}\), to augment the existing GRACE mission.

GLACIER VOLUME CHANGE ESTIMATION USING TIME SERIES OF IMPROVED ASTER DEMS

Volume change data is critical to the understanding of glacier response to climate change. The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) system embarked on the Terra (EOS AM-1) satellite has been a unique source of systematic stereoscopic images covering the whole globe at 15m resolution and at a consistent quality for over 15 years. While satellite stereo sensors with significantly improved radiometric and spatial resolution are available to date, the potential of ASTER data lies in its long consistent time series that is unrivaled, though not fully exploited for change analysis due to lack of data accuracy and precision. Here, we developed an improved method for ASTER DEM generation and implemented it in the open source photogrammetric library and software suite MicMac. The method relies on the computation of a rational polynomial coefficients (RPC) model and the detection and correction of cross-track sensor jitter in order to compute DEMs. ASTER data are strongly affected by attitude jitter, mainly of approximately 4 km and 30 km wavelength, and improving the generation of ASTER DEMs requires removal of this effect. Our sensor modeling does not require ground control points and allows thus potentially for the automatic processing of large data volumes. &amp;lt;br&amp;gt;&amp;lt;br&amp;gt; As a proof of concept, we chose a set of glaciers with reference DEMs available to assess the quality of our measurements. We use time series of ASTER scenes from which we extracted DEMs with a ground sampling distance of 15m. Our method directly measures and accounts for the cross-track component of jitter so that the resulting DEMs are not contaminated by this process. Since the along-track component of jitter has the same direction as the stereo parallaxes, the two cannot be separated and the elevations extracted are thus contaminated by along-track jitter. Initial tests reveal no clear relation between the cross-track and along-track components so that the latter seems not to be easily modeled analytically from the first one. We thus remove the remaining along-track jitter effects in the DEMs statistically through temporal DEM stacks to finally compute the glacier volume changes over time. Our method yields cleaner and spatially more complete elevation data, which also proved to be more in accordance to reference DEMs, compared to NASA’s AST14DMO DEM standard products. &amp;lt;br&amp;gt;&amp;lt;br&amp;gt; The quality of the demonstrated measurements promises to further unlock the underused potential of ASTER DEMs for glacier volume change time series on a global scale. The data produced by our method will help to better understand the response of glaciers to climate change and their influence on runoff and sea level.