Impact of ITRS 2014 realizations on altimeter satellite precise orbit determination

This paper evaluates orbit accuracy and systematic error for altimeter satellite precise orbit determination on TOPEX, Jason-1, Jason-2 and Jason-3 by comparing the use of four SLR/DORIS station complements from the International Terrestrial Reference System (ITRS) 2014 realizations with those based on ITRF2008. The new Terrestrial Reference Frame 2014 (TRF2014) station complements include ITRS realizations from the Institut National de l’Information Géographique et Forestière (IGN) ITRF2014, the Jet Propulsion Laboratory (JPL) JTRF2014, the Deutsche Geodätisches Forschungsinstitut (DGFI) DTRF2014, and the DORIS extension to ITRF2014 for Precise Orbit Determination, DPOD2014. The largest source of error stems from ITRF2008 station position extrapolation past the 2009 solution end time. The TRF2014 SLR/DORIS complement impact on the ITRF2008 orbit is only 1–2 mm RMS radial difference between 1992–2009, and increases after 2009, up to 5 mm RMS radial difference in 2016. Residual analysis shows that station position extrapolation error past the solution span becomes evident even after two years, and will contribute to about 3–4 mm radial orbit error after seven years. Crossover data show the DTRF2014 orbits are the most accurate for the TOPEX and Jason-2 test periods, and the JTRF2014 orbits for the Jason-1 period. However for the 2016 Jason-3 test period only the DPOD2014-based orbits show a strong and statistically significant margin of improvement. The positive results with DTRF2014 suggest the new approach to correct station positions or normal equations for non-tidal loading before combination is beneficial. We did not find any compelling POD advantage in using non-linear over linear station velocity models in our SLR & DORIS orbit tests on the Jason satellites. The JTRF2014 proof-of-concept ITRS realization demonstrates the need for improved SLR+DORIS orbit centering when compared to the Ries (2013) CM annual model. Orbit centering error is seen as an annual radial signal of 0.4 mm amplitude with the CM model. The unmodeled CM signals show roughly a 1.8 mm peak-to-peak annual variation in the orbit radial component. We find the TRF network stability pertinent to POD can be defined only by examination of the orbit-specific tracking network time series. Drift stability between the ITRF2008 and the other TRF2014-based orbits is very high, the relative mean radial drift error over water is no larger than 0.04 mm/year over 1993–2015. Analyses also show TRF induced orbit error meets current altimeter rate accuracy goals for global and regional sea level estimation.     

Differential code bias estimation based on uncombined PPP with LEO onboard GPS observations

Differential Code Bias (DCB) is an essential correction that must be provided to the Global Navigation Satellite System (GNSS) users for precise position determination. With the continuous deployment of Low Earth Orbit (LEO) satellites, DCB estimation using observations from GNSS receivers onboard the LEO satellites is drawing increasing interests in order to meet the growing demands on high-quality DCB products from LEO-based applications, such as LEO-based GNSS signal augmentation and space weather research. Previous studies on LEO-based DCB estimation are usually using the geometry-free combination of GNSS observations, and it may suffer from significant leveling errors due to non-zero mean of multipath errors and short-term variations of receiver code and phase biases. In this study, we utilize the uncombined Precise Point Positioning (PPP) model for LEO DCB estimation. The models for uncombined PPP-based LEO DCB estimation are presented and GPS observations acquired from receivers onboard three identical Swarm satellites from February 1 to 28, 2019 are used for the validation. The results show that the average Root Mean Square errors (RMS) of the GPS satellite DCBs estimated with onboard data from each of the three Swarm satellites using the uncombined PPP model are less than 0.18 ns when compared to the GPS satellite DCBs obtained from IGS final daily Global Ionospheric Map (GIM) products. Meanwhile, the corresponding average RMS of GPS satellite DCBs estimated with the conventional geometry-free model are 0.290, 0.210, 0.281 ns, respectively, which are significantly larger than those obtained with the uncombined PPP model. It is also noted that the estimated GPS satellite DCBs by Swarm A and C satellites are highly correlated, likely attributed to their similar orbit type and space environment. On the other hand, the Swarm receiver DCBs estimated with uncombined PPP model, with Standard Deviation (STD) of 0.065, 0.037 and 0.071 ns, are more stable than those obtained from the official Swarm Level 2 products with corresponding STD values of 0.115, 0.101, and 0.109 ns, respectively. The above indicates that high-quality DCB products can be estimated based on uncombined PPP with LEO onboard observations.     

Estimation of differential code biases with Jason-2/3 onboard GPS observations

With the continuous deployment of Low Earth Orbit (LEO) satellites, the estimation of differential code biases (DCBs) based on GNSS observations from LEO has gained increasing attention. Previous studies on LEO-based DCB estimation are usually using the spherical symmetry ionosphere assumption (SSIA), in which a uniform electron density is assumed in a thick shell. In this study, we propose an approach (named the SHLEO method) to simultaneously estimate the satellite and LEO onboard receiver DCBs by modeling the distribution of the global plasmaspheric total electron content (PTEC) above the satellite orbit with a spherical harmonic (SH) function. Compared to the commonly used SSIA method, the SHLEO model improves the GPS satellite DCB estimation accuracy by 13.46% and the stability by 22.34%, respectively. Compared to the GPS satellite DCBs estimated based on the Jason-3-only observations, the accuracy and monthly stability of the satellite DCBs can be improved by 14.42% and 26.8% when both Jason-2 and Jason-3 onboard observations are jointly processed. Compared with the Jason-2 solutions, the GPS satellite DCB estimates based on the fusion of Jason-2 and Jason-3 observations have an improved consistency of better than 18.26% and 9.71% with the products provided by the Center for Orbit Determination in Europe (CODE) and Chinese Academy of Sciences (CAS). Taking the DCB products provided by the German Aerospace Center (DLR) as references, there is no improvement in accuracy of the GPS satellite DCB estimates based on the fusion of Jason-2 and Jason-3 observations than the Jason-2 solutions alone. A periodic variation is found in the time series of both the Jason-3 and Jason-2 onboard receiver DCB estimates. Preliminary analysis of the PTEC distribution based on the estimated SH coefficients are also presented.     

An improved focusing method for geosynchronous SAR

More and more attention is paid to Geosynchronous Orbit (GEO) Synthetic Aperture Radar (SAR) in recent years due to its fine temporal resolution and large coverage, so that GEO SAR will play an important role in monitoring natural disasters, but its imaging is more difficult compared to lower Earth orbit (LEO) SAR because of the increase of orbit height. This paper mainly studies the coverage property and focusing method in GEO SAR. As is known to us, the coverage of a GEO SAR satellite can reach 1/3 of the whole Earth, and the revisiting time can reduce to 2 h, which will remarkably improve the capability in ocean applications, earth dynamics and natural hazards management and so on. Compared with the imaging in LEO SAR, a problem in GEO SAR is that the linear trajectory model can bring a big error due to the long synthetic aperture time, so that the classical imaging algorithms in LEO SAR cannot be directly applied in GEO SAR. Using the Norm method and Taylor expansion method, this paper gains an accurate slant range model, which can resolve the big error of the linear trajectory at perigee and collapse of the linear trajectory at apogee. Furthermore, this paper deduces a novel imaging algorithm for GEO SAR by means of series reversion, which realizes the focusing on large scene under the synthetic aperture time of 100 s. Finally, the simulation results at apogee and perigee prove the correction of the slant range model and imaging algorithm.     

Improved kHz-SLR tracking techniques and orbit quality analysis for LEO missions

Satellite gravity field missions such as CHAMP, GRACE and GOCE are designed as low Earth orbiting spacecraft (LEO) with orbit heights of about 250–500 km. The challenging mission objectives require a very precise knowledge of the satellite orbit position in space. For these missions precise orbit information is typically provided by GPS satellite-to-satellite tracking (SST) observations supported by satellite laser ranging (SLR).     

Impact of GPS antenna phase center variations on precise orbits of the GOCE satellite

The first European Space Agency Earth explorer core mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) has been launched on March 17, 2009. The 12-channel dual-frequency Global Positioning System receiver delivers 1 Hz data and provides the basis for precise orbit determination (POD) on the few cm-level for such a very low orbiting satellite (254.9 km). As a member of the European GOCE Gravity Consortium, which is responsible for the GOCE High-level Processing Facility (HPF), the Astronomical Institute of the University of Bern (AIUB) provides the Precise Science Orbit (PSO) product for the GOCE satellite. The mission requirement for 1-dimensional POD accuracy is 2 cm. The use of in-flight determined antenna phase center variations (PCVs) is necessary to meet this requirement. The PCVs are determined from 154 days of data and the magnitude is up to 3-4 cm. The impact of the PCVs on the orbit determination is significant. The cross-track direction benefits most of the PCVs. The improvement is clearly seen in the orbit overlap analysis and in the validation with independent Satellite Laser Ranging (SLR) measurements. It is the first time that SLR could validate the cross-track component of a LEO orbit.     

Geosynchronous satellites expanding a future GNSS satellite constellation: A precise orbit determination study

The integration of geosynchronous orbit (GSO) satellites in Global Navigation Satellite Systems (GNSS) is mostly discussed to enable a regional enhancement for tracking. But how do GSO satellites affect the orbit determination of the rest of the constellation? How accurately can these orbits be determined in a future GNSS tracking scenario with optical links? In this simulation study we analyze the benefit of GSO satellites as an expansion of a MEO (Medium Earth Orbit) satellite constellation – we selected the Galileo satellite constellation – for MEO Precise Orbit Determination (POD). We address not only the impact on POD of MEO satellites but also the possibility to precisely determine the GSO satellites – geostationary orbits (GEO) and inclined geosynchronous orbits (IGSO) – in such an expanded MEO constellation. In addition to GNSS microwave observations, we analyze the influence of different optical links between the participating entities: Optical two-way Inter-Satellite Links (OISL) and ground-space oriented Optical Two-Way Links (OTWL). These optical measurements together with the GNSS microwave observations give a remarkable benefit for the POD capability. In the case of GNSS and OTWL, we simulate the measurements with regard to a network of 16 ground stations. We pay great attention to the simulation of systematic effects of all measurement techniques. We discuss the influence on the systematic errors as well as the formal orbit uncertainties. A MEO constellation expanded with GSO satellites as well as the use of optical links together with GNSS observations not only improves the MEO satellite orbits but also the GSOs to a great extent.     

Spectral filter for signal identification in the kHz SLR measurements of the fast spinning satellite Ajisai

The high repetition rate satellite laser ranging (SLR) measurements to the fast spinning satellites contain a frequency signal caused by the rotational motion of the corner cube reflector (CCR) array. The spectral filter, developed here, is based on the Lomb algorithm, and is tested with the simulated and the observed high repetition rate SLR data of the geodetic satellite Ajisai (spin period ∼2 s). The filter allows for the noise elimination from the SLR data, and for identification of the returns from the single CCRs of the array – even for the low return rates. Applying the spectral filter to the simulated SLR data increases the S/N ratio by a factor 40–45% for all return rates. Filtering out the noise from the observed data strengthens the frequency signal by factor of ∼25 for the low return rates, which significantly helps to determine the spin phase of the satellite. The spectral filter is applied to the Graz SLR data and the spin rates of Ajisai are determined by two different methods: the frequency analysis and the phase determination of the spinning retroreflector array.The analysis of more than 8 years of the Graz SLR measurements indicates an exponential spin rate trend: f = 0.67034 exp(−0.0148542 Y) [Hz], RMS = 0.085 mHz, where Y is the year since launch. The highly accurate spin rate information demonstrates periodic changes related to the precession of the orbital plane of Ajisai, as it determines the amount of energy received by the satellite from the Sun. The rate of deceleration of Ajisai is not constant: the half life period of the satellite’s spin oscillates around 46.7 years with an amplitude of about 5 years.     

Single event upset investigations on the “Flying Laptop” satellite mission

The radiation effects in electronic parts are called single-event effects, which are deemed to be critical for space missions. This paper presents the Single Event Upsets that were observed in an onboard memory device of the Low Earth Orbit “Flying Laptop” satellite mission during its in-orbit operation. The Single Event Upsets were carefully mapped on the satellite orbital space itself and their root causes were investigated together with their rates of occurrence. Subsequently, the events were traced to show several root cause sources such as (i) trapped energetic protons leaking to low altitudes within the South Atlantic Anomaly, (ii) Solar Energetic Particles emitted by an impulsive event on 10 September 2017, and (iii) Galactic Cosmic Rays. A profound analysis was carried out on the observed flight data, and its corresponding results are actually in agreement with the standard energetic particle models. The presented results provide another important insight on the Single Event Upsets for future Low Earth Orbit satellite missions.     

The multi-source data fusion global ionospheric modeling software—IonoGim

We introduce a new global ionospheric modeling software—IonoGim, using ground-based GNSS data, the altimetry satellite and LEO (Low Earth Orbit) occultation data to establish the global ionospheric model. The software is programmed by C++ with fast computing speed and highly automatic degree, it is especially suitable for automatic ionosphere modeling. The global ionospheric model and DCBs obtained from IonoGim were compared with the CODE (Center for Orbit Determination in Europe) to verify its accuracy and reliability. The results show that IonoGim and CODE have good agreement with small difference, indicating that IonoGim owns high accuracy and reliability, and can be fully applicable for high-precision ionospheric research. In addition, through comparison between only using ground-based GNSS observations and multi-source data model, it can be demonstrated that the space-based ionospheric data effectively improve the model precision in marine areas where the ground-based GNSS tracking station lacks.     

GRO和LRO掩星事件模拟研究

GRO（Global Navigation Satellite System Radio Occultation）和LRO（Low Earth Orbit Radio Occultation）联合组网探测地球大气是无线电掩星探测技术的主要发展方向.本文根据掩星事件的数学判据,仿真分析了LEO卫星主要轨道参数对GRO和LRO掩星事件数量和全球分布情况的影响.研究表明:卫星轨道越低GRO掩星事件越多;轨道倾角在30°和75°之间时,GRO掩星事件较多,全球覆盖率也较大;利用极轨卫星进行LRO掩星探测时,LRO掩星事件较均匀地分布在各纬度带.研究成果对GRO和LRO联合星座设计具有参考价值.      

Autonomous broadcast ephemeris improvement for GNSS using inter-satellite ranging measurements

This paper discusses the concept of using inter-satellite ranging (ISR) measurements of the satellites of a Global Navigation Satellite System (GNSS) for autonomous broadcast ephemeris improvement. Firstly the inter-satellite ranging is modeled to obtain the clock and orbit error observables. The orbit error observable is analyzed and its observation equation is provided. Both least-squares estimation and Kalman Filter approach are proposed to estimate satellite clock errors, while solely the Kalman Filter is used to estimate the orbit errors. All these algorithms are validated using true broadcast ephemeris and precise ephemeris of GPS along with the simulated ranging noise. Based on the settings adopted in the test, the result shows that the orbit accuracy of the precise ephemeris using the proposed method is around 20–50 cm and the accuracy of the satellite clock can reach 20 cm while ranging noise is assumed to be 0.45 m (1σ). The User Ranging Error (URE) is improved from 1.05 m to 0.34 m, which is comparable to other sources of precise ephemeris or even better, while the proposed approach has many advantages such as compatibility and accessibility. It is also noted that the proposed method may provide useful functions in determining inter-constellation coordinate and time differences autonomously for better interoperability and interchangeability in the multi GNSS operation era.     

Towards accurate atmospheric mass density determination Using precise positional information of space objects

This paper presents a new method of deriving atmospheric mass densities with a high temporal resolution from precise orbit data of low earth orbiting (LEO) space objects. This method is based on the drag perturbation equation of the semi-major axis of the orbit of LEO space objects which relates the change rate of the semi-major axis to the atmospheric mass density. The effectiveness of the new method is evaluated using the GFZ-ISDC GPS rapid science orbit (RSO) products of the CHAMP satellite over a time period of 3 months. The densities derived using this new method and obtained from accelerometer data are compared and good agreements are achieved. An example of using the derived density to generate good orbit prediction for CHAMP is presented.     

LEO enhanced Global Navigation Satellite System (LeGNSS) for real-time precise positioning services

Global Navigation Satellite System (GNSS) has been widely used in many geosciences areas with its Positioning, Navigation and Timing (PNT) service. However, GNSS still has its own bottleneck, such as the long initialization period of Precise Point Positioning (PPP) without dense reference network. Recently, the concept of PNTRC (Positioning, Navigation, Timing, Remote sensing and Communication) has been put forward, where Low Earth Orbit (LEO) satellite constellations are recruited to fulfill diverse missions. In navigation aspect, a number of selected LEO satellites can be equipped with a transmitter to transmit similar navigation signals to ground users, so that they can serve as GNSS satellites but with much faster geometric change to enhance GNSS capability, which is named as LEO constellation enhanced GNSS (LeGNSS). As a result, the initialization time of PPP is expected to be shortened to the level of a few minutes or even seconds depending on the number of the LEO satellites involved. In this article, we simulate all the relevant data from June 8th to 14th, 2014 and investigate the feasibility of LeGNSS with the concentration on the key issues in the whole data processing for providing real-time PPP service based on a system configuration with fourteen satellites of BeiDou Navigation Satellite System (BDS), twenty-four satellites of the Global Positioning System (GPS), and sixty-six satellites of the Iridium satellite constellations. At the server-end, Precise Orbit Determination (POD) and Precise Clock Estimation (PCE) with various operational modes are investigated using simulated observations. It is found out that GNSS POD with partial LEO satellites is the most practical mode of LeGNSS operation. At the user-end, the Geometry Dilution Of Precision (GDOP) and Signal-In-Space Ranging Error (SISRE) are calculated and assessed for different positioning schemes in order to demonstrate the performance of LeGNSS. Centimeter level SISRE can be achieved for LeGNSS.     

基于单频星载GPS数据的低轨卫星精密定轨

为满足搭载单频GPS接收机低轨卫星的精密定轨需求以及深化单频定轨研究,文中解决了单频星载GPS数据的周跳探测问题,并利用“海洋二号”（HY-2A）卫星及“资源三号”（ZY-3）卫星的单频星载GPS实测数据采用两种方法确定了二者的简化动力学轨道,并通过观测值残差分析、与双频精密轨道比较、激光测卫数据检核等方法对所得轨道精度进行评定。结果表明,在不考虑电离层延迟影响的情况下,HY-2A卫星定轨精度为2~3dm,ZY-3卫星为1m左右;而采用半和改正组合消除电离层延迟一阶项影响后,二者定轨精度均显著提高,HY-2A卫星三维精度提高至1dm左右,ZY-3卫星提高至1~2dm。文章的研究成果表明,搭载单频GPS接收机的低轨卫星也可获得厘米级的定轨精度。     

Near real-time BDS GEO satellite orbit determination and maneuver analysis with reversed point positioning

The Geostationary Earth Orbit (GEO) satellite is a crucial part of the BeiDou Navigation Satellite System (BDS) constellation. However, due to various perturbation forces acting on the GEO satellite, it drifts gradually over time. Thus, frequent orbit maneuvers are required to maintain the satellite at its designed position. During the orbit maneuver and recovery periods, the orbit quality of the maneuvered satellite computed with broadcast navigation ephemeris will be significantly degraded. Furthermore, the conventional dynamic Precise Orbit Determination (POD) approach may not work well, because of a lack of publicly available satellite information for modeling the thrust forces. In this paper, a near real-time approach free of thrust forces modeling is proposed for BDS GEO satellite orbit determination and maneuver analysis based on the Reversed Point Positioning (RPP). First, the station coordinates and receiver clock offsets are estimated by GPS/BDS combined Single Point Positioning (SPP) with single-frequency phase-smoothed pseudorange observations. Then, with the fixed station coordinates and receiver clock offsets, the RPP method can be conducted to determine the GEO satellite orbits. When no orbit maneuvers occur, the proposed method can obtain orbit accuracies of 0.92, 2.74, and 8.30?m in the radial, along-track, and cross-track directions, respectively. The average orbit-only Signal-In-Space Range Error (SISRE) is 1.23?m, which is slightly poorer than that of the broadcast navigation ephemeris. Using four days of GEO maneuvered datasets, it is further demonstrated that the derived orbits can be employed to characterize the behaviors of GEO satellite maneuvers, such as the time span of the maneuver as well as the satellite thrusting accelerations. These results prove the efficiency of the proposed method for near real-time GEO satellite orbit determination during maneuvers.     

GNSS global real-time augmentation positioning: Real-time precise satellite clock estimation,prototype system construction and performance analysis

Lots of ambiguities in un-differenced (UD) model lead to lower calculation efficiency, which isn’t appropriate for the high-frequency real-time GNSS clock estimation, like 1 Hz. Mixed differenced model fusing UD pseudo-range and epoch-differenced (ED) phase observations has been introduced into real-time clock estimation. In this contribution, we extend the mixed differenced model for realizing multi-GNSS real-time clock high-frequency updating and a rigorous comparison and analysis on same conditions are performed to achieve the best real-time clock estimation performance taking the efficiency, accuracy, consistency and reliability into consideration. Based on the multi-GNSS real-time data streams provided by multi-GNSS Experiment (MGEX) and Wuhan University, GPS + BeiDou + Galileo global real-time augmentation positioning prototype system is designed and constructed, including real-time precise orbit determination, real-time precise clock estimation, real-time Precise Point Positioning (RT-PPP) and real-time Standard Point Positioning (RT-SPP). The statistical analysis of the 6 h-predicted real-time orbits shows that the root mean square (RMS) in radial direction is about 1–5 cm for GPS, Beidou MEO and Galileo satellites and about 10 cm for Beidou GEO and IGSO satellites. Using the mixed differenced estimation model, the prototype system can realize high-efficient real-time satellite absolute clock estimation with no constant clock-bias and can be used for high-frequency augmentation message updating (such as 1 Hz). The real-time augmentation message signal-in-space ranging error (SISRE), a comprehensive accuracy of orbit and clock and effecting the users’ actual positioning performance, is introduced to evaluate and analyze the performance of GPS + BeiDou + Galileo global real-time augmentation positioning system. The statistical analysis of real-time augmentation message SISRE is about 4–7 cm for GPS, whlile 10 cm for Beidou IGSO/MEO, Galileo and about 30 cm for BeiDou GEO satellites. The real-time positioning results prove that the GPS + BeiDou + Galileo RT-PPP comparing to GPS-only can effectively accelerate convergence time by about 60%, improve the positioning accuracy by about 30% and obtain averaged RMS 4 cm in horizontal and 6 cm in vertical; additionally RT-SPP accuracy in the prototype system can realize positioning accuracy with about averaged RMS 1 m in horizontal and 1.5–2 m in vertical, which are improved by 60% and 70% to SPP based on broadcast ephemeris, respectively.     

On the usefulness of atmospheric and oceanic angular momentum in recovering polar motion and gravity field variations in a unified process

Earth rotation parameters (ERPs) are excited by variations in the mass distribution on the Earth’s surface and the exchange of angular momentum between the atmosphere and oceans and the solid Earth. The same mass redistribution causes temporal changes in the gravity field coefficients with the second degree harmonics related to the rotational deformation and hence to changes in the Earth’s inertial tensor. If precise models of the atmospheric and oceanic angular momentum (AM) are available solution for polar motion and degree 2 Stokes harmonics can be unified. In this study we utilize SLR tracking of LAGEOS to compare (i) degree 2 harmonics from ERPs and gravitation, and (ii) LAGEOS excitation functions and geophysical data (mass + motion). Finally, we investigate to what extent a unified approach is possible with current models for AM data and gravity mass change estimated from ERP within orbit determinations.     

全球个人卫星移动通信系统

全球个人通信系统（ＰＣＳ）是一个发展中的新概念。１９９０年初开始提出利用静止轨道以外的其他轨道通信卫星的设想,最好是利用低轨道（ＬＥＯ）卫星。使用低轨道卫星就像把地面蜂窝网搬到天上,并能提供与之相仿的业务。文章评价了利用移动的和个人终端的通信卫星网;给出了未来低轨道卫星网的前景;对其中一些有关问题作了归纳。同时,描述了个人通信系统的功能性构成,并对一些网络的主要技术参数作表比较。