Improving solar radiation pressure modeling for GLONASS satellites

Satellite laser ranging (SLR) to the satellites of the global navigation satellite systems (GNSS) provides substantial and valuable information about the accuracy and quality of GNSS orbits and allows for the SLR-GNSS colocation in space. In the framework of the NAVSTAR-SLR experiment two GPS satellites of Block-IIA were equipped with laser retroreflector arrays (LRAs), whereas all satellites of the GLONASS system are equipped with LRAs in an operational mode. We summarize the outcome of the NAVSTAR-SLR experiment by processing 20 years of SLR observations to GPS and 12 years of SLR observations to GLONASS satellites using the reprocessedmicrowave orbits provided by the center for orbit determination in Europe (CODE). The dependency of the SLR residuals on the size, shape, and number of corner cubes in LRAs is studied. We show that the mean SLR residuals and the RMS of residuals
\ndepend on the coating of the LRAs and the block or type of GNSS satellites. The SLR mean residuals are also a function of the equipment used at SLR stations including the single-photon and multi-photon detection modes.We also showthat the SLR observations to GNSS satellites are important to validate GNSS orbits and to assess deficiencies in the solar radiation pressure models. We found that the satellite signature effect, which is defined as a spread of optical pulse signals due to reflection from multiple reflectors, causes the variations of mean SLR residuals of up to 15mmbetween the observations at nadir angles of 0◦ and 14◦. in case of multiphoton SLR stations. For single-photon SLR stations this effect does not exceed 1 mm. When using the new empirical
\nCODE orbit model (ECOM), the SLR mean residual falls into the range 0.1–1.8 mm for high-performing singlephoton SLR stations observing GLONASS-M satellites with uncoated corner cubes. For best-performing multi-photon stations the mean SLR residuals are between −12.2 and
\n−25.6 mm due to the satellite signature effect.

<p>Numerous active low Earth orbiters (LEOs) and Global Navigation Satellite System (GNSS) satellites, including the Galileo constellation, are equipped with laser retroreflectors used for Satellite Laser Ranging (SLR). Moreover, most of LEOs are equipped with GNSS receivers for precise orbit determination. SLR measurements to LEOs, GNSS, and geodetic satellites vary in terms of the number of registered normal points (NPs) or registered satellite passes. In 2016-2018, SLR measurements to LEOs constituted 81% of all NPs and 59% of all registered satellite passes, whereas 10% of NPs and 30% of satellite passes, respectively, were assigned to GNSS. The remaining SLR measurements were completed by geodetic satellites, including LAGEOS-1/2, and LARES-1.</p><p>In this study, we show that the SLR observations to Galileo, passive geodetic and active LEO satellites together with precise GNSS-based orbits of LEOs and Galileo, can be used for the determination of global geodetic parameters, such as geocenter coordinates (GCC) and Earth rotation parameters (ERPs), i.e. pole coordinates, and length-of-day parameter.</p><p>GCC are typically determined using SLR observations to passive geodetic satellites, such as LAGEOS-1/2. Also, the SLR observations to LAGEOS-1/2 together with GNSS and Very Long Baseline Interferometry data are used for the determination of ERPs. Here, we use SLR observations to Galileo, LAGEOS-1/2, LARES-1, Sentinel-3A, SWARM-A/B/C, TerraSAR-X, Jason-2, GRACE-A/B satellites to investigate whether they can be applied for the reference frame realization and for deriving high-quality global geodetic parameters.</p><p>We present various types of solutions to investigate the best solution set-up. The studied solutions differ in terms of solution lengths, the combination of different sets of satellites and the relative weights for the variance scaling factors of technique and satellite-specific normal equations. We compare our results with the standard LAGEOS-based solutions, the combined EOP-14-C04 products and show the consistency of the results.</p>

Since the beginning of the International Global Navigation Satellite System (GLONASS) Experiment, IGEX, in October 1998, the Center for Orbit Determination in Europe (CODE) has acted as an analysis center providing precise GLONASS orbits on a regular basis. In CODE's IGEX routine analysis the Global Positioning System (GPS) orbits and Earth rotation parameters are introduced as known quantities into the GLONASS processing. A new approach is studied, where data from the IGEX network are combined with GPS observations from the International GPS Service (IGS) network and all parameters (GPS and GLONASS orbits, Earth rotation parameters, and site coordinates) are estimated in one processing step. The influence of different solar radiation pressure parameterizations on the GLONASS orbits is studied using different parameter subsets of the extended CODE orbit model. Parameterization with three constant terms in the three orthogonal directions, D, Y, and X (D = direction satellite–Sun, Y = direction of the satellite's solar panel axis), and two periodic terms in the X-direction, proves to be adequate for GLONASS satellites. As a result of the processing it is found that the solar radiation pressure effect for the GLONASS satellites is significantly different in the Y-direction from that for the GPS satellites, and an extensive analysis is carried out to investigate the effect in detail. SLR observations from the ILRS network are used as an independent check on the quality of the GLONASS orbital solutions. Both processing aspects, combining the two networks and changing the orbit parameterization, significantly improve the quality of the determined GLONASS orbits compared to the orbits stemming from CODE's IGEX routine processing.

The Gaussian beam for atmospheric refraction (GBAR) method is used to model the effects of the refractive atmosphere between a global navigation satellite system (GNSS) satellite and a low earth orbit (LEO) satellite in a radio occultation (RO) configuration. The wave transmitted by the GNSS satellite is expanded into Gaussian beams using a multibeam expansion procedure (MEP). The wave is modeled in the troposphere by Gaussian beams, and additional MEPs are processed if needed. The refractive atmosphere is modeled by a grid of rectangular cells within each of which is defined a constant and vertical refractivity gradient. The propagation factor at the LEO satellite is used to retrieve the refractivity profile at the perigees. The inverse method is recalled, and the global spherical symmetry assumption is emphasized. The inversion of the simulated propagation factor amplitude data is tested in two simulations. The first one considers a spherically symmetrical refractive atmosphere characterized by a standard exponential refractivity distribution. The second one uses data from weather research and forecast (WRF) simulations in the Caribbean region. The error brought by the spherical symmetry assumption is investigated. The GBAR method provides a new tool for the remote sensing of planetary atmospheres.

Implementing the International GNSS Service 2021+ Strategic Plan: Vision and Use Cases

The quality of BeiDou Navigation Satellite System (BDS) Geostationary Earth Orbit (GEO) ultra-rapid products is unsatisfactory because GEO satellites are nearly stationary relative to ground stations. To optimize the quality of these ultra-rapid orbit products, we investigated the effects of the fitting arc length, an a priori Solar-Radiation Pressure (SRP) model, and the along-track empirical acceleration on the prediction of BDS GEO satellite orbits. The predicted orbit arcs of 24-h were evaluated through comparisons with the corresponding observed orbit arc and Satellite Laser Ranging (SLR) observations. In both eclipse and non-eclipse seasons, accuracy of the orbit predictions obtained using a 48-h fitting arc length were better than those obtained using 24-h and 72-h fitting arc lengths. Although the overlapping precision of predicted orbits exhibited no obvious improvement when an a priori SRP model was employed, the systematic bias in the SLR residuals was significantly reduced. Specifically, the mean value of SLR residuals decreased from −0.248 m to −0.024 m during non-eclipse seasons and from −0.333 m to −0.041 m during eclipse seasons, respectively. In addition, when an empirical acceleration in the along-track direction was introduced, the three-Dimensional Root-Mean-Square (3D RMS) of overlapping orbits during eclipse seasons decreased from 2.964 to 1.080 m, which is comparable to that during non-eclipse seasons. Furthermore, the Standard Deviation (STD) of SLR residuals decreased from 0.419 to 0.221 m during eclipse seasons. The analysis of SRP estimates shows that the stability of SRP parameters was significantly enhanced after the introduction of along-track empirical acceleration in eclipse seasons. The optimal BDS GEO ultra-rapid orbit prediction products were yielded by using a 48-h fitting arc length, an a priori SRP model and an along-track empirical acceleration.

For precise orbit determination (POD) and precise applications with POD products, one of the critical issues is the modeling of non-conservative forces acting on satellites. Since the official publication of Galileo satellite metadata in 2017, analytical models including the box-wing model and thermal thrust models have been established to absorb a substantial amount of solar radiation pressure (SRP) and thermal thrust. These models serve as the foundation for the best overall modeling approach, combining the analytical box-wing model and thermal thrust model with parameterization of the remaining non-conservative perturbing forces using various optimized Empirical CODE Orbit Models (ECOMs) of the Center for Orbit Determination in Europe (CODE). Firstly, we have demonstrated the significance of the second-order signals in the D direction and the first-order signals in the B direction through spectral analyses of the pure box-wing model, which are consistent with the currently recommended 7-parameter Empirical CODE Orbit Model 2 (ECOM2). In spite of this, we still found that degradation in orbit accuracy frequently occurs during deep eclipse seasons when using the ECOM2 model. We confirm a high-frequency signal existing in the fluctuating orbit overlap differences through the spectral analysis. Considering this, the ECOM2 force model should be extended to higher order and adapted to absorb the remaining effects of potential perturbing forces. After extending the ECOM2 force model to the sixth order in the Sun direction, we demonstrated the significance of fourth- and sixth-order sine terms for deep eclipses. Due to the higher-order periodic terms, the averaged RMS values of orbit overlap difference over deep eclipses can be reduced from 5.3, 10.8, and 23.8 cm to 3.2, 3.9, and 9.9 cm for in-orbit validation (IOV) satellites, from 5.0, 8.6, and 17.7 cm to 3.0, 3.0, and 7.1 cm for the first generation of full operational capability (FOC-1) satellites, and from 5.4, 8.6, and 19.0 cm to 3.6, 3.6, and 7.4 cm for the second generation of FOC (FOC-2) satellites, in the radial, cross-track, and along-track directions, respectively. Fluctuations with a peak amplitude of approximately 0.4 nm/s2 in the bias in the solar panel axis (Y) direction (Y-bias) are effectively mitigated by the higher-order terms. Due to the higher-order terms, the vertical positioning errors during kinematic precise point positioning (PPP) convergence can be improved from 42.3 to 37.1 cm at the 95.5% confidence level. Meanwhile, a low correlation level of up to 0.02 is found between the newly introduced higher-order parameters and earth rotation parameters (ERPs).

Many sophisticated Global Navigation Satellite System (GNSS ) applications require high-precision satellite orbit and clock products. The GNSS orbits and clocks are usually derived from the analysis of tracking data collected by a globally distributed GNSS receiver network. The estimation process adjusts parameters for the satellite orbits, transmitter and receiver clocks, station positions, tropospheric delays, Earth orientation, intersystem and interfrequency biases, and carrier-phase ambiguities. The estimation requires detailed modeling of geophysical processes, atmospheric and relativistic effects, receiver tracking modes, antenna phase centers, spacecraft properties, and attitude control algorithms. This chapter describes precise orbit and clock determination of the GNSS constellations as performed by the analysis centers of the International GNSS Service, including models, estimation strategies, products, and the combination of orbit and clock solutions.

To achieve an accurate and robust localization result under Global Navigation Satellite System (GNSS) denied environment, coupling GNSS with other sensors tends to be a promising solution, also known as the sensor fusion system. One of the most challenging scenarios in sensor fusion is to couple vision navigation system with GNSS, especially the tightly-coupled fusion. Compared with those loosely coupled ones, it performs the information fusion on a more intrinsic level, which can benefit the accuracy and robustness of the system. However, the major barrier lying in front of tightly coupling method is the way to unify the heterogeneous and asynchronous GNSS observations with vision observations. To solve this problem, we start from the Vison Simultaneous Localization and Mapping (V-SLAM) method, which has already become the mainstream in vision navigation domain. By utilizing existing attempts on graph-optimization-based GNSS data processing, we propose a joint graph optimization combining vision-SLAM with GNSS pseudorange. It is a tightly coupled fusion of GNSS and stereo camera, implemented by considering GNSS satellites as vision feature points. Based on the framework of mature state-of-art pose-graph SLAM, a graph optimization is applied simultaneously on GNSS and vision positioning, to achieve a robust, accurate, yet versatile fusion system.

The Global Navigation Satellite System (GNSS) provides a continuous, high precision, global, real-time, and all weather navigation and positioning, which powerfully contributes to all scientific questions related to precise positioning on Earth’s surface. Recently, the reflected and refracted signals from GNSS satellites resulted in many new applications in environmental remote sensing. The GNSS refracted signals from Radio Occultation satellites together with ground GNSS observations have produced wide applications in atmospheric remote sensing, including global monitoring of tropospheric water vapour, temperature and pressure, tropopause parameters and ionospheric parameters as well as ionospheric irregularities. The GNSS reflected signals from the ocean and land surface could determine the wave height, wind speed and wind direction of ocean surface and land surface conditions. In this paper, GNSS remote sensing applications in the atmosphere, oceans, land and hydrology are presented as well as recent results. With more and more GNSS satellite constellations in coming years, it is expected more and wider applications in various environment remote sensing.

Due to the continued development of the GLONASS satellites, precise orbit determination (POD) still poses a series of challenges. This study examines the impact of introducing the analytical tube-wing model for GLONASS-M and the box-wing model for GLONASS-K in a series of hybrid POD strategies that consider both the analytical model and a series of empirical parameters. We assess the perturbing accelerations acting on GLONASS spacecraft based on the analytical model. All GLONASS satellites are equipped with laser retroreflectors for satellite laser ranging (SLR). We apply the SLR observations for the GLONASS POD in a series of GNSS + SLR combined solutions. The application of the box-wing model significantly improves GLONASS orbits, especially for GLONASS-K, reducing the STD of SLR residuals from 92.6 to 27.6 mm. Although the metadata for all GLONASS-M satellites reveal similar construction characteristics, we found differences in empirical accelerations and SLR offsets not only between GLONASS-M and GLONASS-M+ but also within the GLONASS-M+ series. Moreover, we identify satellites with inferior orbit solutions and check if we can improve them using the analytical model and SLR observations. For GLONASS-M SVN730, the STD of the SLR residuals for orbits determined using the empirical solution is 48.7 mm. The STD diminishes to 41.2 and 37.8 mm when introducing the tube-wing model and SLR observations, respectively. As a result, both the application of the SLR observations and the analytical model significantly improve the orbit solution as well as reduce systematic errors affecting orbits of GLONASS satellites.

Aiming at the Terrestrial Water Storage(TWS) changes in the Amazon River basin, this article uses the coordinate time series data of the Global Navigation Satellite System (GNSS), adopts the Variational Mode Decomposition and Bidirectional Long and Short Term Memory(VMD-BiLSTM) method to extract the vertical crustal deformation series, and then adopts the Principal Component Analysis(PCA) method to invert the changes of terrestrial water storage in the Amazon Basin from July 15, 2012 to July 25, 2018. Then, the GNSS inversion results were compared with the equivalent water height retrieved from Gravity Recovery and Climate Experiment (GRACE) data. The results show that (1) the extraction method proposed in this article has better denoising effect than the traditional method; (2) the surface hydrological load deformation can be well calculated using GNSS coordinate vertical time series, and then the regional TWS changes can be inverted, which has a good consistency with the result of GRACE inversion of water storage, and has almost the same seasonal variation characteristics; (3) There is a strong correlation between TWS changes retrieved by GNSS based on surface deformation characteristics and water mass changes calculated by GRACE based on gravitational field changes, but GNSS satellite’s all-weather measurement results in a finer time scale compared with GRACE inversion results. In summary, GNSS can be used as a supplementary technology for monitoring terrestrial water storage changes, and can complement the advantages of GRACE technology.

The impact of L‐band equatorial ionospheric scintillation on Global Navigation Satellite Systems (GNSS) receivers is investigated in this paper using both real and synthetic scintillation data. To this end, various low‐latitude data sets, recorded during the most recent solar maximum, are exploited in post‐processing to develop and verify realistic simulation tools and evaluate GNSS receiver performance. A scintillation simulation model is implemented based on the phase screen formulation of Dr. Charles Rino (1979, 1982, and 2011) which allows oblique signal propagation in an anisotropic propagation medium with multiple irregularity layers (or phase screens) for multiple GNSS frequencies. The observed real scintillation parameters are used to drive GNSS signal simulations. The subsequent simulated GNSS signal time series are verified through comparison with real data for different signal tracking states including the most severe and challenging tracking scenarios. Using both real and synthetic data sets, the impact of scintillation on observation quality and receiver performance is evaluated in terms of probability of loss of phase and frequency lock, as well as the correlation of disturbed L‐band signals transmitted by GNSS satellites on the same transionsopheric path.

<p>Knowledge of the ionospheric electron density is essential for a wide range of applications, e.g., telecommunications, satellite positioning and navigation, and Earth observation from space. Therefore, considerable efforts have been concentrated on modeling this ionospheric parameter of interest. Ionospheric electron density is characterized by high complexity and is space−and time−varying, as it is highly dependent on local time, latitude, longitude, season, solar cycle and activity, and geomagnetic conditions. Daytime disturbances cause periodic changes in total electron content (diurnal variation) and additionally, there are multi-day periodicities, seasonal variations, latitudinal variations, or even ionospheric perturbations that cause fluctuations in signal transmission.</p><p>Because of its multiple band frequencies, the current Global Navigation Satellite Systems (GNSS) offer an excellent example of how we can infer ionosphere conditions from its effect on the radiosignals from different GNSS band frequencies. Thus, GNSS techniques provide a way of directly measuring the electron density in the ionosphere. The main advantage of such techniques is the provision of the integrated electron content measurements along the satellite-to-receiver line-of-sight at a large number of sites over a large geographic area.</p><p>Deep learning techniques are essential to reveal accurate ionospheric conditions and create representations at high levels of abstraction. These methods can successfully deal with non-linearity and complexity and are capable of identifying complex data patterns, achieving accurate ionosphere modeling. One application that has recently attracted considerable attention within the geodetic community is the possibility of applying these techniques in order to model the ionosphere delays based on GNSS satellite signals.</p><p>This paper deals with a modeling approach suitable for predicting the ionosphere delay at different locations of the IGS network stations using an adaptive Convolutional Neural Network (CNN). As experimental data we used actual GNSS observations from selected stations of the global IGS network which were participating in the still-ongoing MGEX project that provides various satellite signals from the currently available multiple navigation satellite systems. Slant TEC data (STEC) were obtained using the undifferenced and unconstrained PPP technique. The STEC data were provided by GAMP software and converted to VTEC data values. The proposed CNN uses the following basic information: GNSS signal azimuth and elevation angle, GNSS satellite position (x and y). Then, the adaptive CNN utilizes these data inputs along with the predicted VTEC values of the first CNN for the previous observation epochs. Topics to be discussed in the paper include the design of the CNN network structure, training strategy, data analysis, as well as preliminary testing results of the ionospheric delays predictions as compared with the IGS ionosphere products.   </p>

Text: Positioning, timing and navigation (PNT) with Satellite Navigation Systems like GPS, GLONASS, Beidou and Galileo are more and more widespread and used in very different types of applications including core telemetry applications. Global Navigation Satellite Systems (GNSS) receivers in Safety Critical Applications such as landing airplanes, Critical Infrastructure or Remote Sensing missions e.g. Earth Observing Satellites need to be very robust and reliable under a variety of environmental conditions, sometimes very harsh ones outside the atmosphere. Timing is critical in communication between satellite ground stations and the satellites, e.g. telemetry tracking and command, or communication protocols using Time Division Multiple Access. Thus, it is crucial to test GNSS receivers thoroughly under a variety of different conditions, also extreme conditions like very high dynamics or unhealthy GNSS satellites. For this purpose GNSS RF signal simulators are a versatile and flexible tool. The tests can be repeated as many times as necessary with identical conditions. Besides this a simulator offers complete control across the scenario, every single detail can be controlled and changed. In RF simulators comprehensive error models are available for satellite signals and clocks, satellite orbits and health flags, obscuration and multipath, atmospheric conditions, antenna characteristics, vehicle dynamics, leap seconds, jamming and aiding Inertial sensors. Each of them can be controlled individually. For some tests, like unhealthy satellites or future constellations RF, simulators are the only way for testing, as future signals, for example, are not available in live sky test. In this paper, we will introduce the capabilities of GNSS simulators with a wide range of different error conditions and show several telemetry use cases.