Initial Results of Modeling and Improvement of BDS-2/GPS Broadcast Ephemeris Satellite Orbit Based on BP and PSO-BP Neural Networks

With the rapid development and gradual perfection of GNSS in recent years, improving the real-time service performance of GNSS has become a research hotspot. In GNSS single-point positioning, broadcast ephemeris is used to provide a space–time reference. However, the orbit parameters of broadcast ephemeris have meter-level errors, and no mathematical model can simulate the variation of this, which restricts the real-time positioning accuracy of GNSS. Based on this research background, this paper uses a BP (Back Propagation) neural network and a PSO (Particle Swarm Optimization)–BP neural network to model the variation in the orbit error of GPS and BDS broadcast ephemeris to improve the accuracy of broadcast ephemeris. The experimental results showed that the two neural network models in GPS can model the broadcast ephemeris orbit errors, and the results of the two models were roughly the same. The one-day and three-day improvement rates of RMS(3D) were 30–50%, but the PSO–BP neural network model was better able to model the trend of errors and effectively improve the broadcast ephemeris orbit accuracy. In BDS, both of the neural network models were able to model the broadcast ephemeris orbit errors; however, the PSO–BP neural network model results were better than those of the BP neural network. In the GEO satellite outcome of the PSO–BP neural network, the STD and RMS of the orbit error in three directions were reduced by 20–70%, with a 20–30% improvement over the BP neural network results. The IGSO satellite results showed that the PSO–BP neural network model output accuracy of the along- and radial-track directions experienced a 70–80% improvement in one and three days. The one- and three-day RMS(3D) of the MEO satellites showed that the PSO–BP neural network has a greater ability to resist gross errors than that of the BP neural network for modeling the changing trend of the broadcast ephemeris orbit errors. These results demonstrate that using neural networks to model the orbit error of broadcast ephemeris is of great significance to improving the orbit accuracy of broadcast ephemeris.

A Hybrid ECOM Model for Solar Radiation Pressure Effect on GPS Reference Orbit Derived by Orbit Fitting Technique

A hybrid ECOM (Empirical CODE Orbit Model) solar radiation pressure (SRP) model, which is termed ECOMC in this work, is proposed for global navigation satellite system (GNSS) orbit modeling. The ECOMC is mainly parameterized by both ECOM1 and ECOM2 models. The GNSS orbit mainly serves as a reference datum not only for its ranging measurement but also for the so-called precise point positioning (PPP) technique. Compared to a complex procedure of orbit determination with real tracking data, the so-called orbit fitting technique simply uses satellite positions from GNSS ephemeris as pseudo-observations to estimate the initial state vector and SRP parameters. The accuracy of the reference orbit is mainly dominated by the SRP, which is usually handled by either ECOM1 or ECOM2. However, the reference orbit derived by ECOM1 produces periodic variations on orbit differences with respect to International GNSS Service (IGS) final orbit for GPS IIR satellites. Such periodic variations are removed from a reference orbit formed using the ECOM2 model, which, however, yields large cross-track orbit errors for the IIR and IIF satellites. Such large errors are attributed to the fact that the ECOM2 intrinsically lacks 1 cycle per revolution (CPR) terms, which stabilize the estimations of the even-order CPR terms in the satellite-Sun direction when the orbit fitting is used. In comparison, a reference orbit constructed with the ECOMC model is free of both the periodic variations from the ECOM1 and the large cross-track orbit errors from the ECOM2. The above improvements from the ECOMC are associated with (1) the even CPR terms removing the periodic variations and (2) the 1 CPR terms compensating for the force mismodeling at = 90° and 270°, where the is the argument of the latitude of the satellite with respect to the Sun. The parameter correlation analysis also presents that the direct SRP estimation is sensitive to the 1 and 2 CPR terms in the ECOMC case. In addition, the root-mean-square (RMS) of orbit difference with respect to IGS orbit is improved by ~40%, ~10%, and ~50% in the radial, along-track, and cross-track directions, respectively, when the SRP model is changed from the ECOM2 to the ECOMC. The orbit accuracy is assessed through orbit overlaps at day boundaries. The accuracy improvements of the ECOMC-derived orbit over the ECOM2-derived orbit in the radial, along-track, and cross-track directions are 13.2%, 14.8%, and 42.6% for the IIF satellites and 7.4%, 7.7%, and 35.0% for the IIR satellites. The impact of the reference orbit using the three models on the PPP is assessed. The positioning accuracy derived from the ECOMC is better than that derived from the ECOM1 and ECOM2 by approximately 13% and 20%, respectively. This work may serve as a reference for forming the GNSS reference orbit using the orbit fitting technique with the ECOMC SRP model.

Estimating the Fractional Cycle Biases for GPS Triple-Frequency Precise Point Positioning with Ambiguity Resolution Based on IGS Ultra-Rapid Predicted Orbits

We investigate the estimation of the fractional cycle biases (FCBs) for GPS triple-frequency uncombined precise point positioning (PPP) with ambiguity resolution (AR) based on the IGS ultra-rapid predicted (IGU) orbits. The impact of the IGU orbit errors on the performance of GPS triple-frequency PPP AR is also assessed. The extra-wide-lane (EWL), wide-lane (WL) and narrow-lane (NL) FCBs are generated with the single difference (SD) between satellites model using the global reference stations based on the IGU orbits. For comparison purposes, the EWL, WL and NL FCBs based on the IGS final precise (IGF) orbits are estimated. Each of the EWL, WL and NL FCBs based on IGF and IGU orbits are converted to the uncombined FCBs to implement the static and kinematic triple-frequency PPP AR. Due to the short wavelengths of NL ambiguities, the IGU orbit errors significantly impact the precision and stability of NL FCBs. An average STD of 0.033 cycles is achieved for the NL FCBs based on IGF orbits, while the value of the NL FCBs based on IGU orbits is 0.133 cycles. In contrast, the EWL and WL FCBs generated based on IGU orbits have comparable precision and stability to those generated based on IGF orbits. The use of IGU orbits results in an increased time-to-first-fix (TTFF) and lower fixing rates compared to the use of IGF orbits. Average TTFFs of 23.3 min (static) and 31.1 min (kinematic) and fixing rates of 98.1% (static) and 97.4% (kinematic) are achieved for the triple-frequency PPP AR based on IGF orbits. The average TTFFs increase to 27.0 min (static) and 37.9 min (kinematic) with fixing rates of 97.0% (static) and 96.3% (kinematic) based on the IGU orbits. The convergence times and positioning accuracy of PPP and PPP AR based on IGU orbits are slightly worse than those based on IGF orbits. Additionally, limited by the number of satellites transmitting three frequency signals, the introduction of the third frequency, L5, has a marginal impact on the performance of PPP and PPP AR. The GPS triple-frequency PPP AR performance is expected to improve with the deployment of new-generation satellites capable of transmitting the L5 signal.

Assessment of COSMIC-2 reduced-dynamic and kinematic orbit determination

<p>The Constellation Observing System for Meteorology, Ionosphere, and Climate 2 (COSMIC-2) mission was launched on June 25, 2019 into six evenly spaced circular orbital planes of 24° inclination with initial altitudes of 725 km. By February 2021 the COSMIC-2 satellites will be lowered to an operational altitude of about 520 km. The satellites carry an advanced Tri‐GNSS (Global Navigation Satellite System) Radio-occultation System (TGRS) instrument to provide high vertical resolution profiles of atmospheric bending angle and refractivity, as well as measurements of ionospheric total electron content, electron density, and scintillation. The TGRS payload tracks GPS and GLONASS signals on two upward looking antennas used for precise orbit determination (POD). We compute one- and two-antenna GPS and GPS+GLONASS POD solutions at both orbit altitudes and assess the orbit quality and systematic orbit errors using different metrics. In particular, we also use different POD setups to compute kinematic solutions employing single-receiver ambiguity fixing and test their contribution to selected months of gravity field recovery based on Swarm GPS data.</p>

Millimeter-accuracy SLR bias determination using independent multi-LEO DORIS and GNSS-based orbits

<p>Satellite Laser Ranging (SLR), i.e., the optical distance measurement to satellites equipped with laser retro-reflectors, has become an invaluable core technique in numerous geodetic applications. For instance, SLR measurements to spherical geodetic satellites, such as LAGEOS-1/2 or Etalon-1/2, form an essential contribution for the determination of geocenter coordinates and global scale in the International Terrestrial Reference Frame (ITRF) realizations.</p><p>SLR measurements to active satellites in Low Earth Orbit (LEO) are, on the other hand, up to now mostly used for an independent validation of orbit solutions, usually derived by microwave tracking techniques based on Global Navigation Satellite Systems (GNSS) or <span>Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS). This allows for the analysis of systematic orbit errors (e.g., originating from poorly known satellite center of mass locations or sensor offsets) not only in radial direction, but in t</span><span>h</span><span>ree dimensions. A high level of radial orbit reliability is, e.g., key to satellite altimetry applications.</span></p><p><span>For many of these geodetic SLR applications a mm accuracy and 0.1 mm/year stability is required or at least desired. Unavoidable SLR station biases are a major error source and obstacle to reach the aforementioned accuracy and stability goals. Among the stations of the International Laser Ranging Service (ILRS) there is a large diversity of biases and measurement qualities, and the calibration of these biases for all stations is key to further exploit SLR data for present and future geodetic applications.</span></p><p><span>In this presentation we demonstrate that the analysis of SLR data to active LEO satellites equipped with GNSS or DORIS receivers is a promising means to analyze SLR biases and their stability. </span><span>Using three independent selections of Earth observation missions in LEOs with three different SLR analysis software packages (Bernese GNSS Software, Zoom, Napeos), we estimate SLR range biases for all involved tracking stations on a yearly basis. We find that for many of the stations the three independently estimated sets of biases agree on a few-mm level</span><span> and that the inclusion of satellites from multiple missions allows to render the bias estimation more robust and in particular less prone to geographically correlated orbit errors. This shows that microwave-derived orbits of active LEO satellites, nowadays of very high quality due to numerous advances in modeling and an</span><span>alysis</span><span> techniques, can serve as interesting source</span><span>s</span><span> for SLR station calibration in </span><span>demanding</span><span> geodetic applications like, e.g., future ITRF realizations.</span></p>

Covariance Analysis of Real-Time Precise GPS Orbit Estimated from Double-Differenced Carrier Phase Observations

The covariance of real-time global positioning system (GPS) orbits has been drawing attention in various fields such as user integrity, navigation performance improvement, and fault detection. The international global navigation satellite system (GNSS) service (IGS) provides real-time orbit standard deviations without correlations between the axes. However, without correlation information, the provided covariance cannot assure the performance of the orbit product, which would, in turn, causes significant problems in fault detection and user integrity. Therefore, we studied real-time GPS orbit covariance characteristics along various coordinates to effectively provide conservative covariance. To this end, the covariance and precise orbits are estimated by means of an extended Kalman filter using double-differenced carrier phase observations of 61 IGS reference stations. Furthermore, we propose a new method for providing covariance to minimize loss of correlation. The method adopted by the IGS, which neglects correlation, requires 4.5 times the size of the covariance to bind orbit errors. By comparison, our proposed method reduces this size from 4.5 to 1.3 using only one additional parameter. In conclusion, the proposed method effectively provides covariance to users.

Precise Onboard Real-Time Orbit Determination with a Low-Cost Single-Frequency GPS/BDS Receiver

The low-cost single-frequency GNSS receiver is one of the most economical and affordable tools for the onboard real-time navigation of numerous remote sensing small/micro satellites. We concentrate on the algorithm and experiments of onboard real-time orbit determination (RTOD) based on a single-frequency GPS/BDS receiver. Through various experiments of processing the real single-frequency GPS/BDS measurements from the Yaogan-30 (YG30) series and FengYun-3C (FY3C) satellites of China, some critical aspects of the onboard RTOD are investigated, such as the optimal force models setting, the effect of different measurements, and the impact of GPS/BDS fusion. The results demonstrate that a gravity model truncated to 55 × 55 order/degree for YG30 and 45 × 45 for FY3C and compensated with an optimal stochastic modeling of empirical accelerations, which minimize the onboard computational load and only result in a slight loss of orbit accuracy, is sufficient to obtain high-precision real-time orbit results. Under the optimal force models, the real-time orbit accuracy of 0.4–0.7 m for position and 0.4–0.7 mm/s for velocity is achievable with the carrier-phase-based solution, while an inferior real-time orbit accuracy of 0.8–1.6 m for position and 0.9–1.7 mm/s for velocity is achieved with the pseudo-range-based solution. Furthermore, although the GPS/BDS fusion only makes little change to the orbit accuracy, it increases the number of visible GNSS satellites significantly, and thus enhances the geometric distribution of GNSS satellites that help suppress the local orbit errors and improves the reliability and availability of the onboard RTOD, especially in some anomalous arcs where only a few GPS satellites are trackable.

Improving the Performance of Multi-GNSS (Global Navigation Satellite System) Ambiguity Fixing for Airborne Kinematic Positioning over Antarctica

Conventional relative kinematic positioning is difficult to be applied in the polar region of Earth since there is a very sparse distribution of reference stations, while precise point positioning (PPP), using data of a stand-alone receiver, is recognized as a promising tool for obtaining reliable and accurate trajectories of moving platforms. However, PPP and its integer ambiguity fixing performance could be much degraded by satellite orbits and clocks of poor quality, such as those of the geostationary Earth orbit (GEO) satellites of the BeiDou navigation satellite system (BDS), because temporal variation of orbit errors cannot be fully absorbed by ambiguities. To overcome such problems, a network-based processing, referred to as precise orbit positioning (POP), in which the satellite clock offsets are estimated with fixed precise orbits, is implemented in this study. The POP approach is validated in comparison with PPP in terms of integer ambiguity fixing and trajectory accuracy. In a simulation test, multi-GNSS (global navigation satellite system) observations over 14 days from 136 globally distributed MGEX (the multi-GNSS Experiment) receivers are used and four of them on the coast of Antarctica are processed in kinematic mode as moving stations. The results show that POP can improve the ambiguity fixing of all system combinations and significant improvement is found in the solution with BDS, since its large orbit errors are reduced in an integrated adjustment with satellite clock offsets. The four-system GPS+GLONASS+Galileo+BDS (GREC) fixed solution enables the highest 3D position accuracy of about 3.0 cm compared to 4.3 cm of the GPS-only solution. Through a real flight experiment over Antarctica, it is also confirmed that POP ambiguity fixing performs better and thus can considerably speed up (re-)convergence and reduce most of the fluctuations in PPP solutions, since the continuous tracking time is short compared to that in other regions.

Demonstration of Time-Series InSAR Processing in Beijing Using a Small Stack of Gaofen-3 Differential Interferograms

More and more synthetic aperture radar (SAR) satellites in orbit provide abundant data for remote sensing applications. In August 2016, China launched a new Earth observation SAR satellite, Gaofen-3 (GF-3). In this paper, we utilize a small stack of GF-3 differential interferograms to map land subsidence in Beijing (China) using the time-series SAR interferometry (InSAR) technique. The small stack of differential interferograms is generated with 5 GF-3 SAR images from March 2017 to January 2018. Orbit errors are carefully addressed and removed during differential InSAR (DInSAR) processing. Truncated singular-value decomposition (TSVD) is applied to strengthen the robustness of deformation rate estimation. To validate the results of GF-3 data, an additional deformation measurement using 26 Sentinel-1B images from March 2017 to February 2018 is carried out using the persistent scatterer interferometry (PSI) technique. By implementing a cross-comparison, we find that the retrieved results from GF-3 images and Sentinel-1 images are spatially consistent. The standard deviation of vertical deformation rate differences between two data stacks is 11.24 mm/y in the study area. The results shown in this paper demonstrate the reasonable potential of GF-3 SAR images to monitor land subsidence.