Precise Orbit Determination of BeiDou Regional Navigation Satellite System Via Double-Difference Observations

Precise Orbit Determination (POD) is an integral part for analyzing measurements from space geodetic techniques such as Satellite Laser Ranging (SLR) and Global Navigation Satellite Systems (GNSS) such as the Global Positioning System (GPS). In the last two decades, POD based on GPS data has furthermore been established as one of the standard techniques to derive trajectories of satellites in the low Earth orbit (LEO) with highest accuracy. Since the launch of dedicated gravity missions, GPS sensors are not only used as a key tracking system for LEO POD, but also for extracting the long wavelength part of the Earth’s gravity field (together with SLR to spherical satellites). This chapter introduces SLR and GNSS measurements collected by the terrestrial networks of the International Laser Ranging Service (ILRS) and the International GNSS Service (IGS) as the observational basis for the realization of a terrestrial reference frame from satellite data. On this foundation, the basic equations and mathematical methods of orbit determination are introduced and extensively discussed. Pseudo-stochastic orbit modeling techniques are eventually presented as a general and efficient concept to determine satellite trajectories of highest quality even in presence of deficient force models, covering the full range between dynamic and purely kinematic solutions. Selected results from the application of the discussed orbit determination techniques are highlighted for GPS LEO data. Special emphasis is also put to present orbit determination in the context of more general orbit determination problems, where satellite trajectories are simultaneously determined with other parameters encompassing (at maximum) all pillars of geodesy, i.e., the shape, rotation, and gravity field of the Earth.

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.

Solar radiation pressure (SRP) is an extremely critical perturbative force that affects the GNSS satellites’ precise orbit determination (POD). Its imperfect modelling is one of the main error sources of POD, whose magnitude is even to10−9 m/s2. The shadow factor (i.e., eclipse factor) is one crucial parameter of SRP, generally estimated by the cylindrical model, the conical model, or shadow models considering the Earth’s oblateness and the atmospheric effect, such as the Perspective Projection Method atmosphere (PPMatm) model and Solar radiation pressure with Oblateness and Lower Atmospheric Absorption, Refraction, and Scattering Curve Fit (SOLAARS-CF) model. This paper applies the former four shadow models to determine the corresponding precise orbit using BeiDou satellites’ ground-based observation, and then compared and assessed the orbit accuracy through Satellite Laser Ranging (SLR) validation and Inter-Satellite Link (ISL) check. The results show that the PPMatm model’s accuracy is equivalent to the SOLAARS-CF model. Compared with the conical shadow model, SLR validations show the orbit accuracy from the PPMatm and SOLAARS-CF model can be generally improved by 2–10 mm; ISL range check shows that the Root Mean Square (RMS) can be decreased by 2–7 mm. These results show that the shadow model in GNSS POD should fully consider the Earth’s oblateness and the atmospheric effect, especially for the perturbative acceleration higher than 10–10 m/s2.Graphical

Though widely used to generate the global navigation satellite system (GNSS) ultra-rapid orbit products for real-time applications, the batch least-squares (LSQ) adjustment and precise orbit determination (POD) prediction is limited for satellites undergoing maneuvers. To generate the truly real-time orbit products, we introduce the square root information filter (SRIF) real-time POD strategy, in which a real-time satellite maneuver handling algorithm that adapts the stochastic model for irregular satellite behaviors is implemented. The performance of the SRIF POD strategy is first evaluated with 1-month of data from multi-GNSS experiment (MGEX) network and BDS experimental tracking stations (BETS). Compared with the MGEX final products provided by GFZ (GBM), the SRIF solutions show higher precision than the ultra-rapid solutions. The averaged 3D RMS of the orbit differences between the SRIF solutions and the GBM final product is about 29.1 cm and 22.5 cm for the BDS IGSO and MEO satellites. The BDS orbits generated by SRIF are continuous over all the time, while the ultra-rapid orbits exhibit obvious jumps and discontinuity at the orbit update time. Validation by satellite laser ranging (SLR) shows that for GEO satellites, the SRIF solutions have better stability and continuity, whereas the GBM final products exhibit obvious accuracy degradation around the day boundary. To evaluate the performance of maneuver handling, the proposed method is further tested on 10 maneuver cases of BDS GEO and IGSO satellites. The start and end time of all maneuver events in different cases are precisely detected, which are consistent with the officially announced ones. Using the proposed strategy, the filter avoids divergence and outputs continuous orbit solutions during the maneuver periods and restores the normal POD within about 7.5 h after the maneuver is finished.

The HY-2A satellite is the first ocean dynamic environment monitoring satellite of China. Centimeter-level radial accuracy is a fundamental requirement for its scientific research and applications. To achieve this goal, we designed the strategies of precise orbit determination (POD) in detail. To achieve the relative optimal orbit for HY-2A, we carried out POD using DORIS-only, SLR-only, and DORIS + SLR tracking data, respectively. POD tests demonstrated that the consistency level of DORIS-only and SLR-only orbits with respect to the CNES orbits were about 1.81 cm and 3.34 cm in radial direction in the dynamic sense, respectively. We designed 6 cases of different weight combinations for DORIS and SLR data, and found that the optimal relative weight group was 0.2 mm/s for DORIS and 15.0 cm for SLR, and RMS of orbit differences with respect to the CNES orbits in radial direction and three-dimensional (3D) were 1.37 cm and 5.87 cm, respectively. These tests indicated that the relative radial and 3D accuracies computed using DORIS + SLR data with the optimal relative weight set were obviously higher than those computed using DORIS-only and SLR-only data, and satisfied the requirement of designed precision. The POD for HY-2A will provide the invaluable experience for the following HY-2B, HY-2C, and HY-2D satellites.

Precise orbit determination for geostationary satellites with multiple tracking techniques

Precise orbit determination and rapid orbit recovery supported by time synchronization

The inter-satellite link (ISL) equipment of the third-generation BeiDou Navigation Satellite System (BDS-3) can enhance the accuracy of precise orbit determination (POD) for BDS-3 satellites. However, the hardware delays within ISL observations can impact the measurement accuracy of ISL observations. This study evaluates the characteristics of hardware delays in ISL observations for BDS-3 medium Earth orbit (MEO) satellites and investigates their effects on POD. Analysis shows that most links exhibit slow variations in hardware delays, with standard deviations (STD) of 6.4 cm and 3.6 cm over 45 days for the C19-C25 and C20-C21 links, respectively. Conversely, some links like C30-C23 and C30-C33 show more pronounced variations, with STD values reaching 17.7 cm and 14.1 cm within three days. Links involving satellites C23 and C30 display higher variability and significant jumps in hardware delays compared with other links. The larger variations in hardware delays of these links can be absorbed by other parameters, thereby affecting the accuracy of parameter estimation. To mitigate their impact on POD, a segmented estimation strategy for hardware delays is proposed. This strategy divides a single link into multiple segments based on a set interval length and estimates the hardware delay parameters for each segment separately, thereby absorbing the variations in hardware delays or unmodeled errors. The effectiveness of this strategy is demonstrated through ISL POD residual analysis, comparison with L-band orbit determination results, and validation using Satellite Laser Ranging (SLR) residuals. The root mean square (RMS) of ISL observation residuals decreased by approximately 44.3%, from 6.1 cm to 3.4 cm. Comparisons with L-band orbits confirmed an approximate 28.2% reduction in the 3D RMS of orbit discrepancies, from 26.5 cm to 19.0 cm. Additionally, the RMS of the overall SLR residuals showed a slight decrease. Overall, the improved segmented estimation strategy effectively reduces the influence of hardware delay variations on BDS-3 orbit determination, notably enhancing the orbit determination accuracy of BDS-3 satellites, especially for C23 and C30, which experience larger hardware delay fluctuations.

<p>The Ice, Cloud, and land Elevation Satellite-2 (ICESat-2) mission launched on September 15<sup>th</sup>, 2018, with the primary goal of measuring ice sheet topographic change. The fundamental measurement used to achieve mission science objectives is the geolocation of individual photon bounce points. Geolocation is computed as a function of three complex measurements: (1) the position of the laser altimeter instrument in inertial space, (2) the pointing of each of the six individual laser beams in inertial space, and (3) the photon event round trip travel time observation measured by the Advanced Topographic Laser Altimeter System (ATLAS) instrument. ICESat-2 Precision Orbit Determination (POD) is responsible for computing the first of these; the precise position of the laser altimeter instrument.</p><p>ICESat-2 carries two identical on-board GPS receivers, both manufactured by RUAG Space. Tracking data collected by GPS receiver #1 is used as the primary data source for generating POD solutions. POD is performed using GEODYN, NASA Goddard Space Flight Center’s state-of-the-art orbit determination and geodetic parameter estimation software, and a reduced-dynamic solution strategy is employed. The GPS-based POD solutions are calibrated and validated using independent Satellite Laser Ranging (SLR) data from ground-based tracking stations.</p><p>ICESat-2 mission requirements state that the POD solutions must have a one-sigma radial accuracy of 3 cm over a 24-hour time interval. Here we show that early mission ICESat-2 POD performance is exceeding mission requirements. We describe in-depth the ICESat-2 spacecraft macro-model, used for non-conservative force modeling, and the results from tuning of the associated parameters. Lastly, we show the iterated GPS receiver antenna phase center variation map solution and assess its impact on POD performance.</p>

The challenge of precise orbit determination for STSAT-2C using extremely sparse SLR data

ADEOS-II precise orbit determinations with GPS and SLR

Geostationary satellites (GEOs) play a significant role in the regional satellite navigation system. Simulation experiments show that the clock corrections could be mitigated through a single strategy or double differencing strategies for a navigation constellation, but for the mode of individual GEO orbit determination, high precision orbit and clock correction could not be obtained in the orbit determination based on the pseudorange data. A new GEO combined precise orbit determination (POD) strategy is studied in this paper, which combines pseudorange data and C-band transfer ranging data. This strategy overcomes the deficiency of C-band transfer ranging caused by limited stations and tracking time available. With the combination of transfer ranging and pseudorange data, clock corrections between the GEO and the stations can be estimated simultaneously along with orbital parameters, maintaining self-consistency between the satellite ephemeris and clock correction parameters. The error covariance analysis is conducted to illuminate the contributions from the transfer ranging data and the psudoranging data. Using data collected for a Chinese GEO satellite with 3 C-band transfer ranging stations and 4 L-band pseudorange tracking stations, POD experiments indicate that a meter-level accuracy is achievable. The root-mean-square (RMS) of the post-fit C-band ranging data is about 0.203 m, and the RMS of the post-fit pseudorange is 0.408 m. Radial component errors of the POD experiments are independently evaluated with the satellite laser ranging (SLR) data from a station in Beijing, with the residual RMS of 0.076 m. The SLR evaluation also suggests that for 2-h orbital predication, the predicted radial error is about 0.404 m, and the clock correction error is about 1.38 ns. Even for the combination of one C-band transfer ranging station and 4 pseudorange stations, POD is able to achieve a reasonable accuracy with the radial error of 0.280 m and the 2-h predicted radial error of 0.888 m. Clock synchronization between the GEO and tracking stations is achieved with an estimated accuracy of about 1.55 ns, meeting the navigation service requirements.

GMV is developing FocusPOD, a suite of tools for POD and geodesy, powered by GMV MAORI, a new GMV in-house Flight Dynamics & Geodesy library, written from scratch in modern C++ and python. FocusPOD supports several projects led by GMV, including the operational provision of Precise Orbit Determination (POD) products of the Copernicus Sentinel satellites in the frame of the CPOD Service, the simulation of tracking data for Galileo 2nd Generation (G2G) System Test Bed, and other space debris and flight dynamics activities.FocusPOD is currently capable of processing GNSS data, with a focus on on-board receivers to support POD, and Satellite Laser Ranging (SLR), mostly used in CPOD as an external orbit validation source. Capabilities to process DORIS have been recently added, also targeting POD applications as a first step. GMV’s roadmap for FocusPOD include processing VLBI in addition to these 3 techniques, with the target of becoming a reference software for the geodesy community.This contribution intends to present FocusPOD roadmap to incorporate VLBI processing capabilities, describing the modelling challenges that have been identified and the various steps that will be taken to finally be able to process VLBI and provide VLBI-based ITRF products. As part of this roadmap, other parallel activities to tie together the rest of the techniques will also be undertaken and described, mostly related to the ground-based processing of GNSS, SLR and DORIS data.

TianQin project, a Chinese initiative in space gravitational wave detection, demands high precision in satellite orbit during both entry and scientific operations. As means of developmental maturation, ground-based measurements play a vital role in ensuring the smooth execution of TianQin satellite’s detection mission. This paper conducts a simulation analysis by utilizing various ground-based measurement data, including the China Deep Space Network (CDSN), S/Ka-band ranging system, and Satellite Laser Ranging (SLR). The main focus is to explore the distinctions in Precise Orbit Determination (POD) capabilities among different methods and to enhance POD accuracy through the integration of multiple techniques for TianQin satellites. The results indicate: (1) Leveraging a strategically positioned station distribution, CDSN stations offer extended observation time, averaging 17.3 h per satellite daily, compared to S/Ka’s 10.5 h. (2) In single-measurement POD scenarios, S/Ka proves superior, achieving accuracy better than 10 m and 0.4 mm s−1 for TianQin satellites with a 7-day orbit arc length. This superiority is attributed to its exceptional observational accuracy, outperforming CDSN’s 40 m and 2.2 mm s−1 for POD accuracy. (3) By integrating high-precision SLR data on the foundation of CDSN or S/Ka observations, the POD accuracy of TianQin satellites is further enhanced, despite the limited SLR data quantity.

Precise orbit and Earth parameter determination supported by LEO satellites, inter-satellite links and synchronized clocks of a future GNSS