Low Earth Orbit Precise Orbit Determination Research Articles

Performance assessment of multiple ambiguity resolution methods in single LEO precision orbit determination

Low Earth Orbit (LEO) satellites play a vital role in fields of gravity field recovery, meteorological detection, and Precise Point Positioning (PPP) of augmented Global Navigation Satellite Systems (GNSS), which makes the precise orbit determination (POD) of LEO satellites the key to their mission-execution. Ambiguity resolution (AR) is an effective method to improve the orbit accuracy of LEO satellites, among which the Single Difference (SD) AR method requires GNSS hardware bias products. Besides, Track-to-Track (T2T) AR and Single Difference Track-to-Track (SDT2T) AR can be used as the alternative methods in the scenarios without any GNSS bias products. In this study, the reduced dynamic POD (RDPOD) of the GRACE-FO and SWARM constellations from day 001 to 150 of 2020 was performed using the SD AR, T2T AR and SDT2T AR methods. The results showed that the performance of T2T AR is inferior to that of SDT2T AR and SD AR due to the gradual variability in the phase fractional bias of satellites and receivers. By analyzing the relationship between the success rate of T2T AR and the time interval between adjacent ambiguities, it is found that the success rate of T2T AR is higher when the time interval is within 30 minutes. Therefore, it can be assumed that the fractional cycle biases of the receivers remains constant within 30 minutes because the performance of T2T AR highly depends on the stability of the fractional cycle biases of the receivers. With impacts caused by the receiver fractional biases eliminated, SDT2T AR significantly outperforms T2T AR and achieves comparable performance with SD AR. Therefore, in the cases that GNSS bias products are unavailable, SDT2T AR is recommended as the preferred option for single LEO POD.

GPS-Based Precise Orbit Determination of LEO Satellites Using Space-Based Double-Differenced Observations

One of the important GPS applications in space is precise orbit determination (POD) of Low-Earth Orbit (LEO) satellites. Thousands of LEO satellites are currently in orbit. One of the challenges is how to efficiently and precisely determine the orbits to satisfy the relative and absolute accuracy needs of missions. Currently, GPS-based POD of LEO satellites can be performed using either un-differenced (UD) or ground-based double-differenced (DD) observations. The UD POD needs both precise GPS satellite orbits and clocks; the DD POD needs not only the precise orbits, but also global ground reference receivers. Therefore, the GPS-based LEO POD is based on either global ground stations or precise GNSS clocks, which are not convenient for near real-time or real-time data processing. The GPS orbits can be precisely predicted in certain time; the clocks are not. For some formation flying satellite missions (two or more LEO satellites), the absolute orbit accuracy requirements are not as stringent as the relative requirements. The problem is how to perform LEO POD without global station data and precise GPS clocks in near real-time or real-time to achieve the mission orbit accuracy requirement. Based on this motivation, we investigated the GPS-based LEO POD using space-based DD observations without using global ground station GPS data and precise GPS clock products. For this study, we processed the real GPS observations from two LEO satellites. The absolute and relative orbit accuracy is assessed using several tests, including analysis of the orbit fits, external orbit comparisons, Satellite Laser Ranging (SLR) and K-band Ranging (KBR) residuals.

Absolute and relative POD of LEO satellites in formation flying: Undifferenced and uncombined approach

Absolute or relative precise orbit determination (POD) is an essential prerequisite for many low earth orbit (LEO) missions. The POD of LEO satellites typically relays on processing the onboard global navigation satellite system (GNSS) measurements. The absolute POD is usually based on an ionosphere-free (IF) combination, and currently, integer ambiguity resolution (IAR) can be achieved only when external GNSS satellite phase bias (SPB) products are used. The use of these products is not flexible in multi-frequency/multi-constellation scenarios and is difficult to achieve in real-time missions. For relative POD, the double-differenced (DD) with IAR is the most general method. However, the differencing process amplifies observation noise and loses the opportunity to impose dynamic constraints on some eliminated parameters. In this contribution, based on the use of undifferenced and uncombined (UDUC) observations, a new model for both absolute and relative POD is proposed. In this model, the ambiguities of common-view satellites are constructed into DD form, thus IAR can be achieved without any external SPB products. Working with the UDUC observations, multi-frequency scenarios can be easily applied, and residuals can be separated for each frequency. In addition, with precise GNSS satellite clock/orbit products, both the absolute and relative orbits can be derived, which supports absolute and relative LEO POD. Based on onboard GPS observations of T-A and T-B satellites in formation flying, the performance of the UDUC POD model with DD ambiguity was evaluated. With the UDUC algorithm and IAR, the proposed model presented a consistency of 2.8–3.8 cm in 3D with the reference orbits, and the orbit difference was reduced by 16.3% and 10.6% for T-A and T-B compared with the IF-based POD, respectively. In addition, the relative orbit of the two satellites derived from the proposed model showed a consistency of 1.1–1.5 mm, which proved the feasibility of the UDUC POD model with DD ambiguity for formation flying missions.

Improved undifferenced ambiguity resolution for LEO precise orbit determination

Ambiguity resolution (AR) is critical for enhancing the orbit accuracy in precise orbit determination (POD) for low earth orbit (LEO) satellites. While orbit estimation using single-difference (SD) AR has been widely researched, the investigation of orbit estimation using undifferenced (UD) AR for LEO satellites is limited due to time-varying hardware biases at the LEO receiver end. To address this deficiency, we propose an improved UD AR method for LEO satellite orbit determination. The method employs the optimal integer datum ambiguity for a 1-day observation arc, and the random-walk clock model is utilized to transfer the integer ambiguity datum to the other epochs, which enables the arc-wise ambiguities to regain the integer property within the time frame. To validate the effectiveness of our improved method, numerical experiments are conducted. Moreover, we assess the performance of the random-walk clock model for a spaceborne ultra-stable oscillator (USO). The high frequency stability of the USO establishes the satisfactory requirements for this study. Both in the kinematic and dynamic modes, the AR success rates of our improved method are ∼ 2% higher than that of the current SD AR method, and the orbit results indicate a slight improvement. The 3-Dimensional (3D) root-mean-squares (RMS) of the orbit differences between JPL precise science orbits (PSO) and our orbits are reduced by up to 4% and 5% for kinematic and dynamic orbits, respectively. The subtle benefit is also proven by K-band ranging (KBR) system validations. In the case of the Gravity Recovery and Climate Experiment Follow-on (GFO) satellites, the results indicate that the effect of our improved UD AR can be equivalent to that of SD AR. Our improved UD AR method can be a good alternative for its superior ability to generate hardware delay at the LEO receiver end.

Topside Ionospheric Tomography Exclusively Based on LEO POD GPS Carrier Phases: Application to Autonomous LEO DCB Estimation

This paper presents a novel technique to estimate DCBs from GPS transmitters and receivers on-board Low Earth Orbit (LEO) satellites. The technique consists of obtaining the DCBs as residuals from the difference between the ionospheric combination of the code and the associated ionospheric delay. The ionospheric delay is computed with TOMION, a background-model-free ionospheric tomographic technique based on dual-frequency GPS carrier phase data only, and solved with a Kalman filter. Thus, DCBs are also estimated epoch-wise from the LEO Precise Orbit Determination (POD) GPS receiver as a secondary product. The results for GPS satellite DCBs, obtained exclusively from the three MetOp LEO POD GPS receivers over four consecutive weeks, are in full agreement (i.e., at the level of a few tenths of ns) with those reported independently with other techniques from hundreds of ground-based receivers exclusively, by JPL and CODE analysis centers.

Improving Precise Orbit Determination of LEO Satellites Using Enhanced Solar Radiation Pressure Modeling

AbstractPrecise orbit knowledge is a fundamental requirement for low Earth orbit (LEO) satellites. High‐precision non‐gravitational force modeling directly improves the overall quality of LEO precise orbit determination (POD). To address the potential systematic errors in solar radiation pressure (SRP), we introduce observed radiation data and modeled physical effects to describe the real in‐flight environment of satellites. Time‐dependent solar irradiance data and a highly physical shadow model are considered for SRP modeling. We develop an advanced thermal reradiation model for satellite solar panels. A set of improved non‐gravitational force models is performed for LEO POD, and we discuss the benefits of the enhanced dynamic models on orbit quality and dependence on empirical parameters. The Gravity Recovery and Climate Experiment Follow‐On (GRACE‐FO), Jason‐3, and Haiyang‐2B missions are selected for the POD process. Estimated empirical acceleration and scale parameters and independent satellite laser ranging (SLR) are used to validate the final orbit solutions. The magnitude of empirical acceleration estimated in POD is reduced by 19% with the enhanced dynamic modeling, and the estimated scale factor for the SRP converges to stable and reasonable level. Furthermore, the steady‐state temperature model used in thermal reradiation can effectively reduce mismodeled effects in the SRP, and the systematic linear dependency revealed by the SLR residuals is significantly reduced for the GRACE‐C and Jason‐3 satellites, with improvements of approximately 61% and 49%, respectively. Overall, advances are made in the explicit modeling of non‐gravitational forces to pursue superior satellite orbits, suggesting a more dynamic orbit solution.

Integrity monitoring for precise orbit determination of LEO satellites

Due to an increasing requirement for high accuracy orbital information for low Earth orbit (LEO) satellites, precise orbit determination (POD) of LEO satellites is a topic of growing interest. To assure the safety and reliability of the applications requiring high accuracy LEO orbits in near-real-time, integrity monitoring (IM) is an essential operation of the POD process. In this contribution, the IM strategy for LEO POD in both the kinematic and reduced-dynamic modes is investigated. The overbounding parameters of the signal-in-space range error are investigated for the GPS products provided by the International GNSS Service’s Real-Time Service and the Multi-GNSS Advanced Demonstration of Orbit and Clock Analysis service. Benefiting from the dynamic models used and the improved model strength, the test results based on the data of the LEO satellite GRACE FO-1 show that the average-case mean protection levels (PLs) can be reduced from about 3–4 m in the kinematic mode to about 1 m in the reduced-dynamic mode in the radial, along-track and cross-track directions. The overbounding mean values of the SISRE play the dominant role in the final PLs. In the reduced-dynamic mode and average-case projection, the IM availabilities reach above 99% in the radial, along-track and cross-track directions with the alert limit (AL) set to 2 m. The values are still above 98% with the AL set to 4 m, when the duty cycle of tracking is reduced to 40%, e.g., in the case of power limits for miniature satellites such as CubeSats.

Comparison of the real-time precise orbit determination for LEO between kinematic and reduced-dynamic modes

The real-time high-accuracy orbit and clock of the GNSS (Global Navigation Satellite System) are one of the most essential corrections for the real-time kinematic precise orbit determination (POD) mode and reduced-dynamic POD mode for Low Earth Orbit (LEO) satellites. This work is devoted to initially achieve the real-time POD with the two modes and compare their performance. Numerical results showed that (1) the average accuracy improvement of the real-time reduced-dynamic POD relative to the real-time kinematic POD is about 46% on the condition that the number of observable GPS satellites is less than 6; (2) Comparing with the real-time kinematic POD, the real-time reduced-dynamic orbit determination by applying dynamical constraints can improve the accuracy (maximum 12%) of LEO POD and reduce the convergence time (maximum 20%); (3) in most circumstances, the accuracy of real-time kinematic POD and reduced-dynamic POD for LEO are better than 11 cm and 9 cm, respectively, and the reduced-dynamic POD performs more robust against the kinematic POD.

Precise Orbit Determination for LEO Satellites With Ambiguity Resolution: Improvement and Comparison

AbstractPrecise knowledge of orbit represents a fundamental requirement for the earth observing satellite missions to achieve their advanced objectives. The integer ambiguity resolution (IAR) has proved to be a key to utmost accuracy in space navigation. Generally, there are two typical IAR methods widely used in the orbit determination of low Earth orbit (LEO) satellites, the classical double‐difference (DD) IAR and new single‐difference (SD) IAR. Based on one‐year observations of Gravity Recovery and Climate Experiment Follow‐On (GRACE‐FO) and Sentinel‐3 missions, this study is dedicated to a comprehensive analysis of the differences of the products used, implementation details and ambiguity fixing performance for different IAR methods in LEO precise orbit determination (POD), and discusses how these differences influence the orbit solutions. The results show that the orbit accuracy improvement contributed by the ambiguity fixing varies with the adopted IAR methods. SD IAR can contribute to a representative reduction of 1–4 mm in satellite laser ranging (SLR) residuals compared to the float solutions. The application of bias products from different analysis centers leads to marginal differences for the ambiguity fixing. For DD IAR method, the different ways to form the double‐difference ambiguity yield different performances in POD. The DD IAR of space‐ground baselines can achieve a comparable performance to SD IAR, while the benefit of ambiguity fixing is largely weakened when forming space‐space baseline. Furthermore, we also analyze the contribution of the ambiguity fixing to the accuracy and robustness of the kinematic orbit and discuss its great potential for the future applications.

LEO-Constellation-Augmented BDS Precise Orbit Determination Considering Spaceborne Observational Errors

The precise orbit determination (POD) accuracy of the Chinese BeiDou Navigation Satellite System (BDS) is still not comparable to that of the Global Positioning System because of the unfavorable geometry of the BDS and the uneven distribution of BDS ground monitoring stations. Fortunately, low Earth orbit (LEO) satellites, serving as fast moving stations, can efficiently improve BDS geometry. Nearly all studies on Global Navigation Satellite System POD enhancement using large LEO constellations are based on simulations and their results are usually overly optimistic. The receivers mounted on a spacecraft or an LEO satellite are usually different from geodetic receivers and the observation conditions in space are more challenging than those on the ground. The noise level of spaceborne observations needs to be carefully calibrated. Moreover, spaceborne observational errors caused by space weather events, i.e., solar geomagnetic storms, are usually ignored. Accordingly, in this study, the actual spaceborne observation noises are first analyzed and then used in subsequent observation simulations. Then, the observation residuals from the actual-processed LEO POD during a solar storm on 8 September 2017 are extracted and added to the simulated spaceborne observations. The effect of the observational errors on the BDS POD augmented with different LEO constellation configurations is analyzed. The results indicate that the noise levels from the Swarm-A, GRACE-A, and Sentinel-3A satellites are different and that the carrier-phase measurement noise ranges from 2 mm to 6 mm. Such different noise levels for LEO spaceborne observations cause considerable differences in the BDS POD solutions. Experiments calculating the augmented BDS POD for different LEO constellations considering spaceborne observational errors extracted from the solar storm indicate that these errors have a significant influence on the accuracy of the BDS POD. The 3D root mean squares of the BDS GEO, IGSO, and MEO satellite orbits are 1.30 m, 1.16 m, and 1.02 m, respectively, with a Walker 2/1/0 LEO constellation, and increase to 1.57 m, 1.72 m, and 1.32 m, respectively, with a Walker 12/3/1 constellation. When the number of LEO satellites increases to 60, the precision of the BDS POD improves significantly to 0.89 m, 0.77 m, and 0.69 m for the GEO, IGSO, and MEO satellites, respectively. While 12 satellites are sufficient to enhance the BDS POD to the sub-decimeter level, up to 60 satellites can effectively reduce the influence of large spaceborne observational errors, i.e., from solar storms.

Assessment of single-difference and track-to-track ambiguity resolution in LEO precise orbit determination

Single-difference (SD) ambiguity resolution (AR) and track-to-track (T2T) AR are two typical AR methods in precise orbit determination (POD) for Low Earth Orbit (LEO) satellites, which could improve the accuracy of orbits greatly. In this study, SD AR and T2T AR methods are introduced and analyzed. The performance of these two methods is assessed by three months of GPS observations from the Gravity Recovery and Climate Experiment Follow On (GRACE-FO) twin satellites. Results show that T2T AR is highly dependent on the stability of receiver hardware delays, while SD AR requires Fractional Cycle Bias (FCB) or Integer Recovery Clock (IRC) products. We find that these two methods have comparable performance in Reduced Dynamic Precise Orbit Determination (RDPOD), while SD AR slightly outperforms T2T AR in Kinematic Precise Orbit Determination (KPOD). We also find that SD AR has a higher AR success rate than T2T AR. Therefore, we recommend SD AR as the top choice in LEO orbit determination, and T2T AR can be a good alternative when FCB or IRC products are not available.

A More Reliable Orbit Initialization Method for LEO Precise Orbit Determination Using GNSS

Precise orbit determination (POD) using GNSS has been rapidly developed and is the mainstream technology for the navigation of low Earth orbit (LEO) satellites. The initialization of orbit parameters is a key prerequisite for LEO POD processing. For a LEO satellite equipped with a GNSS receiver, sufficient discrete kinematic positions can be obtained easily by processing space-borne GNSS data, and its orbit parameters can thus be estimated directly in iterative manner. This method of direct iterative estimation is called as the direct approach, which is generally considered highly reliable, but in practical applications it has risk of failure. Stability analyses demonstrate that the direct approach is sensitive to oversized errors in the starting velocity vector at the reference time, which may lead to large errors in design matrix because the reference orbit may be significantly distorted, and eventually cause the divergence of the orbit parameter estimation. In view of this, a more reliable method, termed the progressive approach, is presented in this paper. Instead of estimating the orbit parameters directly, it first fits the discrete kinematic positions to a reference ephemeris in the form of the GNSS broadcast ephemeris, which construct a reference orbit that is smooth and close to the true orbit. Based on the reference orbit, the starting orbit parameters are computed in sufficient accuracy, and then the final orbit parameters are estimated with a high accuracy by using discrete kinematic positions as measurements. The stability analyses show that the design matrix errors are reduced in the progressive approach, which would assure more robust orbit parameter estimation than the direct estimation approach. Various orbit initialization experiments are performed on the KOMPSAT-5 and FY3C satellites. The results have fully verified the high reliability of the proposed progressive approach.

Dynamic GPS-based LEO orbit determination with 1 cm precision using the Bernese GNSS Software

The Astronomical Institute of the University of Bern (AIUB) has been performing GPS-based Precise Orbit Determination (POD) for a large variety of Low Earth Orbit (LEO) satellites since two decades. Traditionally, LEO orbits have been generated by a reduced-dynamic POD strategy using the Bernese GNSS Software, replacing an explicit modeling of non-gravitational forces by dedicated empirical orbit parametrizations. This LEO POD strategy can be advanced by two main developments: on the one hand, use is made of the GNSS Observation-Specific Bias (OSB) and clock products provided by the Center for Orbit Determination in Europe (CODE), allowing for the resolution of single-receiver GNSS carrier-phase ambiguities. On the other hand, the main focus of this article, a refined satellite non-gravitational force modeling strategy is constructed to reduce the amount of empirical parameters used to compensate for force modeling deficiencies. LEO POD is first performed for Sentinel-3, a satellite formation currently consists of two identical satellites −3A and −3B, which experience a similar in-flight environment and allow for direct POD performance comparisons. A third satellite Swarm-C, which flies at a lower altitude and has a more sophisticated surface geometry, is selected to validate the robustness of the new POD strategy. As a result, both the internal consistency checks and external orbit validations suggest superior orbit quality obtained for the three satellites for a time span of 1.5 years (7 June, 2018 to 31 December, 2019). The ambiguity resolution adds strong constraints to the orbits and the satellite non-gravitational force modeling leads to more tightly constrained (towards zero) pseudo-stochastic empirical parameters. The final orbit solutions agree with external orbit solutions and independent satellite laser ranging measurements at levels of sub-cm, indicating approximately 20% improvement w.r.t. the nominal reduced-dynamic orbit solutions. This suggests potential benefits to the space geodesy community that always pursues best-possible satellite orbits.

Precise Orbit Determination for Climate Applications of GNSS Radio Occultation including Uncertainty Estimation

Global Navigation Satellite System (GNSS) Radio Occultation (RO) is a highly valuable remote sensing technique for probing the Earth’s atmosphere, due to its global coverage, high accuracy, long-term stability, and essentially all-weather capability. In order to ensure the highest quality of essential climate variables (ECVs), derived from GNSS signal tracking by RO satellites in low Earth orbit (LEO), the orbit positions and velocities of the GNSS transmitter and LEO receiver satellites need to be determined with high and proven accuracy and reliability. Wegener Center’s new Reference Occultation Processing System (rOPS) hence aims to integrate uncertainty estimation at all stages of the processing. Here we present a novel setup for precise orbit determination (POD) within the rOPS, which routinely and in parallel performs the LEO POD with the two independent software packages Bernese GNSS software (v5.2) and NAPEOS (v3.3.1), employing two different GNSS orbit data products. This POD setup enables mutual consistency checks of the calculated orbit solutions and is used for position and velocity uncertainty estimation, including estimated systematic and random uncertainties. For LEOs enabling laser tracking we involve position uncertainty estimates from satellite laser ranging. Furthermore, we intercompare the LEO orbit solutions with solutions from other leading orbit processing centers for cross-validation. We carefully analyze multi-month, multi-satellite POD result statistics and find a strong overall consistency of estimates within LEO orbit uncertainty target specifications of 5 cm in position and 0.05 mm/s in velocity for the CHAMP, GRACE-A, and Metop-A/B missions. In 92% of the days investigated over two representative 3-month periods (July to September in 2008 and 2013) these POD uncertainty targets, which enable highly accurate climate-quality RO processing, are satisfied. The moderately higher uncertainty estimates found for the remaining 8% of days (∼5–15 cm) result in increased uncertainties of RO-retrieved ECVs. This allows identification of RO profiles of somewhat reduced quality, a potential benefit for adequate further use in climate monitoring and research.

LEO Precise Orbit Determination with Inter-satellite Links

Traditional precise orbit determination (POD) for low Earth orbit (LEO) satellites relies on observations from ground stations and onboard receivers. Although the accuracy can reach centimeter level, there are still problems such as insufficient autonomous operation capability. The inter-satellite link (ISL) is a link used for communication between satellites and has a function of dual-way ranging. Numerous studies have shown that observational data using ISLs can be adopted for POD of navigation satellites. In this contribution, we mainly focus on LEO satellites POD with ISLs. First, we design LEO constellations with different numbers of satellites and ISL measurements, based on which the constellations are simulated. Then rough tests of POD using different link topologies are carried out. The results show that in the 60-LEO constellation the average 3-dimensional (3D) orbital errors are 0.112 m using “4-connected” link topology with constant 4 links per satellite and 0.069 m using “all-connected” link topology with theoretically maximum numbers of links. After that, we carry out refined POD experiments with several sets of satellite numbers and different observation accuracy. The results show the higher link ranging accuracy and the more numbers of links bring higher POD precision. POD with ISLs gets bad performance in the case of center of gravity reference when link ranging accuracy is poor and numbers of links are small. When the link accuracy is 40 cm, average 3D orbital errors of 60-LEO constellation are 0.358 m, which can only meet the demand of autonomous navigation. With the constraint of the right ascension of the ascending node (RAAN), POD using ISLs reaches an extremely high precision when adopting a spatial reference provided by navigation satellites. For 120-LEO constellation, the average 3D orbital errors are 0.010 m; for 192-LEO constellation, the errors are 0.006 m.

Precise Orbit Determination for the FY-3C Satellite Using Onboard BDS and GPS Observations from 2013, 2015, and 2017

Using the FengYun-3C (FY-3C) onboard BeiDou Navigation Satellite System (BDS) and Global Positioning System (GPS) data from 2013 to 2017, this study investigates the performance and contribution of BDS to precise orbit determination (POD) for a low-Earth orbit (LEO). The overlap comparison result indicates that code bias correction of BDS can improve the POD accuracy by 12.4%. The multi-year averaged one-dimensional (1D) root mean square (RMS) of the overlapping orbit differences (OODs) for the GPS-only solution is 2.0, 1.7, and 1.5 cm, respectively, during the 2013, 2015, and 2017 periods. The 1D RMS for the BDS-only solution is 150.9, 115.0, and 47.4 cm, respectively, during the 2013, 2015, and 2017 periods, which is much worse than the GPS-only solution due to the regional system of BDS and the few BDS channels of the FY-3C receiver. For the BDS and GPS combined solution (also known as the GC combined solution), the averaged 1D RMS is 2.5, 2.3, and 1.6 cm, respectively, in 2013, 2015, and 2017, while the GC combined POD presents a significant accuracy improvement after the exclusion of geostationary Earth orbit (GEO) satellites. The main reason for the improvement seen after this exclusion is the unfavorable satellite tracking geometry and poor orbit accuracy of GEO satellites. The accuracy of BDS-only and GC combined solutions have gradually improved from 2013 to 2017, thanks to improvements in the accuracy of International GNSS Service (IGS) orbit and clock products in recent years, especially the availability of a high-frequency satellite clock product (30 s sampling interval) since 2015. Moreover, the GC POD (without GEO) was able to achieve slightly better accuracy than the GPS-only POD in 2017, indicating that the fusion of BDS and GPS observations can improve the accuracy of LEO POD. GC combined POD can significantly improve the reliability of LEO POD, simply due to system redundancy. An increased contribution of BDS to LEO POD can be expected with the launch of more BDS satellites and with further improvements in the accuracy of BDS satellite products in the near future.

Improving LEO precise orbit determination with BDS PCV calibration

As the new members of the Chinese Fengyun-3 meteorological satellites series, the Fengyun-3C (FY-3C) and Fengyun-3D (FY-3D) satellites were launched in 2013 and 2017, respectively. For the first time, both FY-3C and FY-3D satellites carry a high-precision BDS and GPS dual-system space-borne receiver to fulfill their stringent requirement of precise orbit determination (POD). The fusion of BDS and GPS onboard observations can significantly improve the spatial geometry, robustness and reliability of low earth orbit (LEO) POD. In order to achieve high-quality orbit recovery from the onboard GNSS observations, the in-flight calibration of phase center variation (PCV) is a prerequisite. In this contribution, we calibrate the BDS PCV for improving the orbit precision of both FY-3C and FY-3D satellites for the first time. The results show that with the GPS PCV corrections, the residuals of GPS carrier phase observations present a reduction of about 17.6% and 21.9% for FY-3C and FY-3D satellites, respectively, and overlap differences of the GPS-only orbit are reduced on average by 3 and 5 mm. After correcting for BDS PCV, the GPS and BDS combined (GC) POD achieves a better orbit precision for both FY-3C and FY-3D satellites. The application of BDS PCV corrections can contribute to a reduction of up to 12% in BDS phase residuals and a decrease of up to 3 mm in orbit overlap differences in 1-dimension. It indicates that the introduction of the BDS PCV model can significantly improve the orbit precision. Similar orbit precision can be achieved when using the GPS PCV model to replace the BDS PCV model in the GC POD. It demonstrates that for onboard receivers, the GPS PCV model can be used to correct PCV errors of BDS signals, which is commonly used in precise point positioning of ground stations when the BDS PCV is not available. Furthermore, we find that it is feasible to generate an integrated PCV model from both onboard BDS and GPS observations. After application of the integrated PCV model, the FY-3C and FY-3D orbits of GC POD present a better precision than the solution using the single-system PCV model and the largest precision improvement of about 1 mm can be recognized in the radial component. With such a high-quality orbit, FY-3C and FY-3D satellites can be expected to make more contributions to meteorological studies and applications.

A virtual receiver concept and its application to curved aircraft-landing procedures and advanced LEO positioning

Kinematic positioning of highly dynamic platforms by a global navigation satellite system (GNSS) often suffers from fast-changing satellite visibility and signal obstruction. This is especially true for curved landing approaches of aircrafts or low earth orbit (LEO) satellites. In order to improve this situation, we present a mathematical concept that combines GNSS observations of multiple optimally installed antenna–receiver pairs mounted on a single rigid platform into one enhanced positioning solution. We call this concept “Virtual Receiver” as the position of the final solution can be chosen arbitrarily on the rigid platform. The location and orientation of the antennas are selected in such a way that their combined antenna field of view is enlarged with respect to each single, contributing antenna, thus improving the navigation performance. It will be shown that the concept can be applied for code-only navigation as well as for static and kinematic positioning with PPP. Using real data of a highly dynamic flight experiment, the performance of the virtual receiver positioning solution is compared against a single antenna positioning solution. We found that the satellite availability and the precision of the virtual receiver positioning solution significantly outperform the positioning solution of a co-located single antenna. The 95% error bound is reduced by up to 25%. The integrity is assessed by means of the internal reliability and the Stanford diagram, where a better or equally good integrity monitoring availability is found for the virtual receiver with respect to the single antenna. In particular, the vertical receiver autonomous integrity monitoring (RAIM) availability percentage is remarkably high, being 89.4% for this highly dynamic flight. This methodology for single-frequency code-based positioning is extended to precise point positioning (PPP) and applied for a static experiment and LEO precise orbit determination. Thus, the virtual receiver concept is an interesting possibility to improve the navigation performance parameters.

Phase center modeling for LEO GPS receiver antennas and its impact on precise orbit determination

Most satellites in a low-Earth orbit (LEO) with demanding requirements on precise orbit determination (POD) are equipped with on-board receivers to collect the observations from Global Navigation Satellite systems (GNSS), such as the Global Positioning System (GPS). Limiting factors for LEO POD are nowadays mainly encountered with the modeling of the carrier phase observations, where a precise knowledge of the phase center location of the GNSS antennas is a prerequisite for high-precision orbit analyses. Since 5 November 2006 (GPS week 1400), absolute instead of relative values for the phase center location of GNSS receiver and transmitter antennas are adopted in the processing standards of the International GNSS Service (IGS). The absolute phase center modeling is based on robot calibrations for a number of terrestrial receiver antennas, whereas compatible antenna models were subsequently derived for the remaining terrestrial receiver antennas by conversion (from relative corrections), and for the GNSS transmitter antennas by estimation. However, consistent receiver antenna models for space missions such as GRACE and TerraSAR-X, which are equipped with non-geodetic receiver antennas, are only available since a short time from robot calibrations. We use GPS data of the aforementioned LEOs of the year 2007 together with the absolute antenna modeling to assess the presently achieved accuracy from state-of-the-art reduced-dynamic LEO POD strategies for absolute and relative navigation. Near-field multipath and cross-talk with active GPS occultation antennas turn out to be important and significant sources for systematic carrier phase measurement errors that are encountered in the actual spacecraft environments. We assess different methodologies for the in-flight determination of empirical phase pattern corrections for LEO receiver antennas and discuss their impact on POD. By means of independent K-band measurements, we show that zero-difference GRACE orbits can be significantly improved from about 10 to 6 mm K-band standard deviation when taking empirical phase corrections into account, and assess the impact of the corrections on precise baseline estimates and further applications such as gravity field recovery from kinematic LEO positions.