Real-time Orbit Determination Research Articles

Performance evaluation of real-time orbit determination for LUTAN-01B satellite using broadcast earth orientation parameters and multi-GNSS combination

Real-time orbit determination (RTOD) for spacecraft using the space-borne GNSS technique needs earth orientation parameters (EOPs) for the required coordinate transformation between earth-fixed and inertial reference frames. GPS and BDS transmit EOPs in modernized navigation messages, which enables GNSS-equipped spacecraft to update EOPs onboard and improves the RTOD automaticity. However, the impact of broadcast EOP errors on RTOD has not yet been evaluated. With the GPS and BDS-3 observations collected from a Chinese low-earth orbit (LEO) mission, the LUTAN-01B satellite, we analyze the LEO RTOD performance with broadcast EOPs and GPS/BDS-3 combination for the first time. In RTOD, we parameterize the ephemeris signal-in-space range error (SISRE) to account for its slow-varying signature and to compensate for the EOP errors. Without estimating SISRE, the RTOD precision using broadcast EOPs is 70.1 cm with only GPS observations and 42.4 cm with only BDS-3, revealing degradations of 5.1 cm (7.8%) and 3.3 cm (8.4%) compared to those using the precise C04 EOPs, respectively. With SISRE estimated, the impact of broadcast EOP error is compensated and the RTOD precisions with broadcast EOPs show identical results to those with C04, reaching 36.3 cm with GPS and 25.8 cm with BDS-3. Combining GPS and BDS-3 further improves the RTOD precision to 23.9 cm. Furthermore, we show that the RTOD precision can be further improved by using GPS and BDS broadcast EOPs’ differences to correct ephemeris rotation errors. With this correction, the precision improvement of BDS-3 independent and GPS/BDS-3 combined RTOD increases significantly when BDS-3 broadcast EOPs suffer large errors due to long update intervals. During the experiment period, their maximum orbital improvements reach 10.2 and 7.7 cm, respectively, while the average improvements are both around 1.5 cm.

An improved approach for rapid filter convergence of GNSS satellite real-time orbit determination

Introduction: The real-time precise satellite orbit of Global Navigation Satellite System (GNSS) usually takes a long time to converge to a stable state using the filter method. The ultra-rapid orbit products are helpful to improve convergence speed by introducing them as external constraints. Reasonably determination of stochastic model of the constraint equation from the ultra-rapid products is the key for a better performance of convergence whereas it has not been well solved.Methods: We propose to establish the stochastic model of the orbit constraint equation by analyzing the differences between the predicted part of the ultra-rapid orbit and the filter orbit after convergence. To improve the orbit accuracy during the convergence, the constant stochastic model of the constraint equation is first determined for each system by averaging the root mean square (RMS) time-series of the differences between predicted orbit from the ultra-rapid products and the SRIF orbit after convergence in different time ranges. Besides, a time-dependent stochastic model of the constraint equation is then determined by analyzing the variation of the RMS time-series. To validate the proposed method, a month of multi-constellation data collected from 80 globally distributed stations is processed using the Square Root Information Filter (SRIF) algorithm.Results: Orbit results without introducing external orbit constraints show that the convergence time in the radial direction is 13.75, 15.25 and 17.75 h for GPS, Galileo and BDS-3 satellite, respectively. For the scheme of constant stochastic model using the average RMS over 6 h, results show that there is no significant convergence phenomenon for each system in all directions. The one-dimensional (1D) RMS during the constraint period is improved by 86.5%, 84.8%, 96.8% for GPS, Galileo and BDS-3 satellites when compared to the results without introducing external orbit constraints. As for the scheme of time-dependent stochastic model, results show that the quadratic function is suitable for modeling the RMS time-series for each system, and the accuracy of results during the constraint period has a further improvement of 1.3%, 3.7% in 1D direction for GPS, BDS-3 satellites when compared to the constant stochastic model using the average RMS over 6 h. In addition, the orbit accuracy with external orbit constraint is slightly better than those without external orbit constraint after the constraint period.Discussion: The above results show that when introducing the ultra-rapid product as the external constraint, there is basically no convergence phenomenon for GNSS satellite, while the orbit accuracy for time-dependent stochastic model has further improvement than constant stochastic model. These results indicate that the proposed method can significantly improve the convergence performance without damaging the orbit accuracy after convergence, and time-dependent stochastic model is better than constant stochastic model.

Integrated Navigation and Communication Service for LEO Satellites Based on BDS-3 Global Short Message Communication

Massive global Low Earth Orbit (LEO) constellations have been developed rapidly with the characteristics of larger number and shorter orbital periods of LEO satellites in recent years. The increasing requirements of real-time orbit determination and emergency data transfer in full arc can hardly meet the traditional strategies based on regional ground stations. An integrated communication and navigation service architecture based on the third phase of the BeiDou system (BDS-3) Global Short Message Communication (GSMC) is proposed, which enables global coverage and random access. The GSMC downlink single-frequency signal is used for real-time orbit determination, and is further combined with B1C navigation signal for real-time dual-frequency high-precision orbit determination. Considering fast moving of LEO satellites and short burst of uplink messages, the uplink BDS-3 satellite selection strategy based on carrier-to-noise ratio, and uplink high-precision compensation of frequency shift are adopted to increase the communication success rate. The service architecture proposed can improve the precision of the autonomous orbit determination and enhance the capability of real-time command transmission of LEO satellites even without the traditional ground stations involved. Integrated communication and navigation service has been validated by simulation and on-board BDS-3 GSMC test data. The precision of single-frequency real-time orbit determination can reach 2.86m, and the precision of dual-frequency can reach 0.26m. The average time delay of communication is about 11.45s, and the success rate is about 99.8%. The method may provide alternative means of real-time high-precision orbit determination and emergency data transfer of LEO satellites.

Performance assessment of real-time orbit determination for the Haiyang-2D using onboard BDS-3/GPS observations

The Global Navigation Satellite System (GNSS) receivers equipped on the Haiyang-2D (HY-2D) satellite is capable of tracking the signals of both the third generation of BeiDou satellite navigation System (BDS-3) and the Global Positioning System (GPS), which make it feasible to assess the performance of real-time orbit determination (RTOD) for the HY-2D using onboard GNSS observations. In this study, the achievable accuracy and convergence time of RTOD for the HY-2D using onboard BDS-3 and GPS observations are analyzed. Benefiting from the binary-offset-carrier (BOC) modulation, the BDS-3 C1X signal includes less noise than the GPS C1C signal, which has the same signal frequency and chipping rate. The root mean squares (RMS) of the noises of C1X and C1C code measurements are 0.579 m and 1.636 m, respectively. Thanks to a ten-times higher chipping rate, the code measurements of BDS-3 C5P, GPS C1W and C2W are less noisy. The RMS of code noises of BDS-3 C5P, GPS C1W, and C2W are 0.044 m, 0.386 m, and 0.272 m, respectively. For the HY-2D orbit, the three-dimensional (3D) and radial accuracies can reach 31.8 cm and 7.5 cm with only BDS-3 observations, around 50 % better than the corresponding accuracies with GPS. Better performance of the BDS-3 in RTOD for the HY-2D is attributed to the high quality of its broadcast ephemeris. When random parameters are used to absorb ephemeris errors, substantial improvement is seen in the accuracy of HY-2D orbit with either BDS-3 or GPS. The 3D RMS of HY-2D orbit errors with BDS-3 and GPS are enhanced to 23.1 cm and 33.6 cm, and the RMS of the radial components are improved to 6.1 cm and 13.3 cm, respectively. The convergence time is 41.6 and 75.5 min for the RTOD with BDS-3 and GPS, while it is reduced to 39.2 and 27.4 min after the broadcast ephemeris errors are absorbed by random parameters. Overall, the achievable accuracy of RTOD with BDS-3 reaches decimeter level, which is even better than that with GPS, making real-time navigation using onboard BDS-3 observations a feasible choice for future remote sensing missions.

Multi-GNSS products and services at iGMAS Wuhan Innovation Application Center: strategy and evaluation

Over the past years the International Global Navigation Satellite System (GNSS) Monitoring and Assessment System (iGMAS) Wuhan Innovation Application Center (IAC) dedicated to exploring the potential of multi-GNSS signals and providing a set of products and services. This contribution summarizes the strategies, achievements, and innovations of multi-GNSS orbit/clock/bias determination in iGMAS Wuhan IAC. Both the precise products and Real-Time Services (RTS) are evaluated and discussed. The precise orbit and clock products have comparable accuracy with the precise products of the International GNSS Service (IGS) and iGMAS. The multi-frequency code and phase bias products for Global Positioning System (GPS), BeiDou Navigation Satellite System (BDS), Galileo navigation satellite system (Galileo), and GLObal NAvigation Satellite System (GLONASS) are provided to support multi-GNSS and multi-frequency Precise Point Positioning (PPP) Ambiguity Resolution (AR). Compared with dual-frequency PPP AR, the time to first fix of triple-frequency solution is improved by 30%. For RTS, the proposed orbit prediction strategy improves the three dimensional accuracy of predicted orbit by 1 cm. The multi-thread strategy and high-performance matrix library are employed to accelerate the real-time orbit and clock determination. The results with respect to the IGS precise products show the high accuracy of RTS orbits and clocks, 4–9 cm and 0.1–0.2 ns, respectively. Using real-time satellite corrections, real-time PPP solutions achieve satisfactory performance with horizontal and vertical positioning errors within 2 and 4 cm, respectively, and convergence time of 16.97 min.

Improve real-time GNSS orbit with epoch-independent undifferenced ambiguity resolution

AR (Ambiguity Resolution) is one of the critical issues in high-accuracy GNSS (Global Navigation Satellite System) applications. Commonly, the double-difference AR technique is employed in GNSS network data processing. With the demand of high-accuracy, low-latency and high-integrity GNSS orbit, the orbit estimation in sequential mode becomes a candidate of that in batch mode. Unlike orbit estimation with double-difference AR in either batch or sequential mode, researches on real-time orbit estimation with undifferenced AR in sequential mode is still limited. In this study, real-time orbit determination with epoch-independent undifferenced AR in sequential mode is assessed. With one-week observation data from about 100 global distributed IGS (International GNSS Service) network stations, simulated real-time Galileo orbit determination are conducted with GFZ post-processed solution as reference for validation. Numerical results indicate that, first, the 3D error RMS (Root Mean Square) of fixed orbit is about 30% smaller than that of float orbit; second, the Galileo orbit error RMS reach 3.66, 3.60 and 3.09 cm for the radial, tangential and normal directions respectively for the fixed solution; third, small jumps exist in the real-time orbit and may be attributed to the temporal variations of UPD (Uncalibrated Phase Delay) and wrongly fixed ambiguities. In summary, the orbit quality is comparable to that of IGS real-time solutions, and further improvements may be achieved with improved AR constraint strategy and background orbit model.

Performance assessment of GNSS-based real-time navigation for the Sentinel-6 spacecraft

The feasibility of precise real-time orbit determination of low earth orbit satellites using onboard GNSS observations is assessed using six months of flight data from the Sentinel-6A mission. Based on offline processing of dual-constellation pseudorange and carrier phase measurements as well as broadcast ephemerides in a sequential filter with a reduced dynamic force model, navigation solutions with a representative position error of 10 cm (3D RMS) are achieved. The overall performance is largely enabled by the superior quality of the Galileo broadcast ephemerides, which exhibits a two- to three-times smaller signal-in-space-range error than GPS and allows for geodetic-grade GNSS real-time orbit determination without a need for external correction services. Compared to GPS-only processing, a roughly two-times better navigation accuracy is achieved in a Galileo-only or mixed GPS/Galileo processing. On the other hand, GPS tracking offers a useful complement and additional robustness in view of a still incomplete Galileo constellation. Furthermore, it provides improved autonomy of the navigation process through the availability of earth orientation parameters in the new civil navigation message of the L2C signal. Overall, GNSS-based onboard orbit determination can now reach a similar performance as the DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite) navigation system. It lends itself as a viable alternative for future remote sensing missions.

Analysis of BDS/GPS Signals’ Characteristics and Navigation Accuracy for a Geostationary Satellite

The utilization of Global Navigation Satellite System (GNSS) is becoming an attractive navigation approach for geostationary orbit (GEO) satellites. A high-sensitivity receiver compatible with Global Position System (GPS) developed by the United States and BeiDou Navigation Satellite System (BDS) developed by China has been used in a GEO satellite named TJS-5 to demonstrate feasibility of real-time navigation. According to inflight data, the GNSS signal characteristics including availability, position dilution of precision (PDOP), carrier-to-noise ratio (C/N0), observations quantity and accuracy are analyzed. The mean number of GPS and GPS + BDS satellites tracked are 7.4 and 11.7 and the mean PDOP of GPS and GPS + BDS are 10.24 and 3.91, respectively. The use of BDS significantly increases the number of available navigation satellites and improves the PDOP. The number of observations with respect to C/N0 is illustrated in detail. The standard deviation of the pseudorange noises are less than 4 m, and the corresponding carrier phase noises are mostly less than 8 mm. We present the navigation performance using only GPS observations and GPS + BDS observations combination at different weights through comparisons with the precision reference orbits. When GPS combined with BDS observations, the root mean square (RMS) of the single-epoch least square position accuracy can improve from 32.1 m to 16.5 m and the corresponding velocity accuracy can improve from 0.238 m/s to 0.165 m/s. The RMS of real-time orbit determination position accuracy is 5.55 m and the corresponding velocity accuracy is 0.697 mm/s when using GPS and BDS combinations. Especially, the position accuracy in x-axis direction reduced from 7.24 m to 4.09 m when combined GPS with BDS observations.

Precise real‐time navigation of LEO satellites using GNSS broadcast ephemerides

The availability of orbit information with high precision and low latency is a key requirement for many Earth-observation missions, predominantly in the field of radio occultation. Traditionally, precise orbit determination solutions of low-Earth orbit (LEO) satellites are obtained offline on ground after downloading GNSS measurements and auxiliary spacecraft data to the processing center. The latency of this processing depends on the frequency of LEO downlink contacts and the availability of precise GNSS orbit and clock products required for the orbit determination process. These dependencies can be removed by computing the precise orbit determination solution on board the satellite using GNSS broadcast ephemerides. In this study, both real data and simulated measurements from a representative LEO satellite are processed in a flight-proven Kalman-filter algorithm. The paper studies the use of GPS, Galileo and BeiDou-3 for real-time orbit determination in different combinations with simulated measurements. Results show that use of dual-frequency observations and broadcast ephemerides of Galileo and BeiDou-3 leads to a significant reduction of 3D rms orbit errors compared to GPS-only processing. An onboard navigation accuracy of about one decimeter can be achieved without external augmentation data, which opens up new prospects for conducting relevant parts of the science data processing in future space missions directly on board a LEO satellite.

Application of adaptive EKF in real-time orbit determination

High-precision orbits are essential for low Earth orbit (LEO) satellite applications. Instead of determinating orbit by the ground monitoring stations, LEO missions are trending to incorporate spaceborne global positioning system receivers for autonomous navigation. Focusing on this issue, we propose a method of real-time orbit determination based on ionosphere combination observation of dual-frequency data using adaptive extended Kalman filter (AEKF). The traditional Kalman filter heavily relies on the initial values of measurement and process noise covariance matrix. However, the environment of the satellite is time-variant, and it is hard to keep the error covariance matrix in the optimal condition all the time. To overcome this disadvantage, the Sage–Husa Kalman filter is introduced. The performance of the proposed algorithm is compared with the conventional EKF, and the results show that the proposed method can guarantee the precision and stability of orbit determination. With the proposed algorithms, we developed a software to solve the orbit suitable for one-day Gravity Recovery and Climate Experiment (GRACE) observations. The obtained results show that the accuracy of orbit determination error is improved with unknown Kalman process noise compared with traditional method. Additionally, the performances of AEKF for different gravity field models are analyzed and compared.

Galileo real-time orbit determination with multi-frequency raw observations

Real-time GNSS-based applications require corresponding real-time orbit products. While traditional GNSS orbits are generated with the dual-frequency IF (Ionosphere-Free) model, the increase of multi-frequency signal satellites brings new challenges for the data processing. Therefore, real-time orbit determination with the multi-frequency UC (Uncombined) model is introduced in this study considering its flexibility. With the derived mathematical model conforming to IGS (International GNSS Service) dual-frequency clock definition and one-week triple-frequency Galileo observation data from 90 IGS network stations, the convergence and accuracy of real-time orbits is assessed and the characteristics of satellite IFCB (Inter-Frequency Clock Bias) are analyzed. Results indicate that the model differences, including dual-frequency IF model, dual-frequency UC model and triple-frequency UC model, contribute to only cm-level differences with CODE (Center for Orbit Determination in Europe) final orbits after a convergence time of around 12 h. The constellation-mean RMS (Root Mean Square) differences of the converged real-time orbits with the CODE final orbits reaches about 5.0 cm, 7.0 cm and 5.0 cm for the radial, tangential and normal directions. The convergence of satellite IFCB is much faster than that of satellite orbit, which reflects a loose correlation between these two parameters. While the Galileo satellite IFCB are temporally stable, the modeling of satellite IFCB may be unreliable when over constrained and becomes even more unstable with commonly encountered datum changes. In summary, real-time GNSS orbit determination with multi-frequency raw observations is feasible and extendable with proper treatment of IFCB.

LICIACube - The Light Italian Cubesat for Imaging of Asteroids In support of the NASA DART mission towards asteroid (65803) Didymos

“LICIACube – the Light Italian Cubesat for Imaging of Asteroids” is managed by the Italian Space Agency (ASI) and will be part of the NASA DART mission, with the aim of i) documenting the DART impact’s effects on the secondary member of the (65803) Didymos binary asteroid system, ii) characterizing the shape of the target, and iii) performing dedicated scientific investigations on it. DART probe will be launched at the end of 2021 and LICIACube will be hosted as piggyback during the interplanetary cruise, then released 10 days before the impact, and autonomously guided along its fly-by trajectory. The LICIACube payload is composed by LEIA, a narrow FoV camera, and LUKE, a wide FoV imager with an RGB Bayer pattern filter, that will collect and transmit to Earth several unique images of the effects of the DART impact on the asteroid, such as the formation and the development of the plume potentially determined by the impact.LICIACube will be the first deep space mission developed and autonomously managed by an Italian team: the design, integration and test of the CubeSat have been assigned by ASI to the aerospace company Argotec, while the LICIACube Ground Segment has a complex architecture based on the Argotec Mission Control Center, antennas of the NASA Deep Space Network and data archiving and processing, managed at the ASI Space Science Data Center. The LICIACube team includes a wide Italian scientific community, involved in the definition of all the aspects of the mission: trajectory design; mission definition (and real-time orbit determination during operations); impact, plume and imaging simulation and modelling, in preparation of a suitable framework for the analysis and interpretation of in-situ data. The major technological mission challenge, i.e. the autonomous targeting and imaging of such a small body during a fast fly-by, to be accomplished with the limited resources of a CubeSat, is affordable thanks to a strong synergy of all the mentioned teams in support of the engineering tasks.

LEO Onboard Real-Time Orbit Determination Using GPS/BDS Data with an Optimal Stochastic Model

The advancements of Earth observations, remote sensing, communications and navigation augmentation based on low Earth orbit (LEO) platforms present strong requirements for accurate, real-time and autonomous navigation of LEO satellites. Precise onboard real-time orbit determination (RTOD) using the space-borne data of multiple global navigation satellite systems (multi-GNSS) becomes practicable along with the availability of multi-GNSS. We study the onboard RTOD algorithm and experiments by using America’s Global Positioning System (GPS) and China’s regional BeiDou Navigation Satellite System (BDS-2) space-borne data of the FengYun-3C satellite. A new pseudo-ambiguity parameter, which combines the constant phase ambiguity, the orbit and clock offset error of the GPS/BDS broadcast ephemeris in the line-of-sight (LOS), is defined and estimated in order to reduce the negative effect of the LOS error on onboard RTOD. The analyses on the variation of the LOS error in the GPS/BDS broadcast ephemeris indicate that the pseudo-ambiguity parameter could be modeled as a random walk, and the setting of the power spectral density in the random walk model decides whether the pseudo-ambiguity can be estimated reasonably and the LOS error could be reduced or not. For different types of GPS/BDS satellites, the LOS errors show different variation characteristics, so the power spectral density should be set separately and differently. A numerical search approach is presented in this paper to find the optimal setting of the power spectral density for each type of GPS/BDS satellite by a series of tests. Based on the optimal stochastic model, a 3-dimensional (3D) real-time orbit accuracy of 0.7–2.0 m for position and 0.7–1.7 mm/s for velocity could be achieved only with dual-frequency BDS measurements and the broadcast ephemeris, while a notably superior orbit accuracy of 0.3–0.5 m for position and 0.3–0.5 mm/s for velocity is achievable using dual-frequency GPS/BDS measurements, due to the absorption effect of the estimated pseudo-ambiguity on the LOS error of the GPS/BDS broadcast ephemeris. Compared to using GPS-alone data, the GPS/BDS fusion only marginally improves the onboard RTOD orbit accuracy by about 1–3 cm, but the inclusion of BDS satellites increases the number of the tracked GNSS satellites and thus speeds up the convergence of the filter. Furthermore, the GPS/BDS fusion could help suppress the local orbit errors, ensure the orbit accuracy and improve the reliability and availability of the onboard RTOD when fewer GPS satellites are tracked in some anomalous arcs.

A Bistatic Analytical Approximation Model for Doppler Rate Estimation Error from Real-Time Spaceborne SAR Onboard Orbit Determination Data

Real-time spaceborne bistatic SAR imaging could significantly reduce the whole processing time and can enhance the spaceborne SAR mission availability. Onboard real-time SAR imaging relies on the Doppler parameters estimated from the real-time onboard orbit determination system (OODS) measurement, whose accuracy level is not comparable to the orbit ephemeris data in ground-based SAR processing. The investigation of the impact of error in real-time OODS measurements on bistatic SAR image quality is necessary, and it can help to clarify the key parameter limits of the real-time OODS. The monostatic analytical approximation model (MonoAAM) for spaceborne SAR reduces simulation complexity and processing time compared to the widely used numerical simulation method. However, due to the different configurations between spaceborne bistatic and monostatic SAR, simply applying the MonoAAM on spaceborne bistatic SAR cannot guarantee the desired result. A bistatic analytical approximation model (BiAAM) for Doppler rate estimation error from real-time OODS measurement in real-time spaceborne bistatic SAR imaging is proposed for characterizing the estimation error. Selecting quadratic phase error (QPE) as an evaluation variable, the proposed BiAAM model can provide QPE estimation results for each position of the satellite in its orbit and the maximum QPE estimation for the whole orbit, while revealing the different process of OODS measurement error transferring to QPE in spaceborne bistatic SAR. The correctness and reliability of BiAAM are evaluated by comparing the result with a Monte Carlo numerical simulation method. With the supporting result from BiAAM, the concept and early-stage development of a real-time onboard bistatic SAR imaging mission could be possibly benefited.

Real-time orbit determination of Low Earth orbit satellite based on RINEX/DORIS 3.0 phase data and spaceborne GPS data

High-precision of Low Earth orbit (LEO) satellite orbit is essential for some applications having real-time requirements, such as LEO navigation enhancement, real time scientific satellite research, and so on. Currently, more mature means for real-time orbit determination of LEO satellites rely on spaceborne GPS data and RINEX/DORIS 3.0 data. However, most researchers conduct experiments using spaceborne GPS data or RINEX/DORIS 3.0 data separately, and the experiment results from combining the two types of data simultaneously have not been obtained. Therefore, we evaluate simulated real-time orbit determination capability of using the RINEX/DORIS 3.0 phase observations and spaceborne GPS pseudo-range observations from the HY2A satellite in this paper. Since the 1-km precision of the RINEX/DORIS 3.0 pseudo-range observations are unfavorable for the initial orbit, the GPS pseudo-range areused for this computation. But, the RINEX/DORIS 3.0 phase observations are used to solve the real-time orbit of HY2A satellite. Our analysis results are: (1) the three-dimensional (3D) position accuracy of HY2A satellite calculated by the spaceborne GPS pseudo-range is 6.803 m, which meets the initial orbit positional accuracy requirement. The initial orbit velocity requirement can be met when the 5–7th-order Lagrangian interpolation method is used to solve the satellite velocity. The 3D-RMS values of the HY2A satellite velocity is smaller than 0.500 m/s, indicating the initial velocity accuracy requirement is satisfied. (2) After Kalman filter convergence, the agreement of the comparison with the CNES precise orbit shows better than 0.100 m in radial position, an RMS of 0.373 m in 3D total position, and an RMS of 0.374 mm/s in 3D total velocity. The results suggest that the radial position accuracy is better than 0.100 m, and could meet some HY2A altimetry applications. In the course of this study, a Fortran-based prototype real-time orbit determination system RTODLEO (Real-Time Orbit Determination Software for Low Earth Orbit Satellite) was developed and used for the analysis. The results from thirteen-day of real-time orbit determination also validate the RTODLEO software, and show it is reliable.

Impact of ECOM Solar Radiation Pressure Models on Multi-GNSS Ultra-Rapid Orbit Determination

The Global Navigation Satellite System (GNSS) ultra-rapid precise orbits are crucial for global and wide-area real-time high-precision applications. The solar radiation pressure (SRP) model is an important factor in precise orbit determination. The real-time orbit determination is generally less accurate than the post-processed one and may amplify the instability and mismodeling of SRP models. Also, the impact of different SRP models on multi-GNSS real-time predicted orbits demands investigations. We analyzed the impact of the ECOM 1 and ECOM 2 models on multi-GNSS ultra-rapid orbit determination in terms of ambiguity resolution performance, real-time predicted orbit overlap precision, and satellite laser ranging (SLR) validation. The multi-GNSS observed orbital arc and predicted orbital arcs of 1, 3, 6, and 24 h are compared. The simulated real-time experiment shows that for GLONASS and Galileo ultra-rapid orbits, compared to ECOM 1, ECOM 2 increased the ambiguity fixing rate to 89.3% and 83.1%, respectively, and improves the predicted orbit accuracy by 9.2% and 27.7%, respectively. For GPS ultra-rapid orbits, ECOM 2 obtains a similar ambiguity fixing rate as ECOM 1 but slightly better orbit overlap precision. For BDS GEO ultra-rapid orbits, ECOM 2 obtains better overlap precision and SLR residuals, while for BDS IGSO and MEO ultra-rapid orbits, ECOM 1 obtains better orbit overlap precision and SLR residuals.

Analytical Approximation Model for Quadratic Phase Error Introduced by Orbit Determination Errors in Real-Time Spaceborne SAR Imaging

Research on real-time spaceborne synthetic aperture radar (SAR) imaging has emerged as satellite computation capability has increased and applications of SAR imaging products have expanded. The orbit determination data of a spaceborne SAR platform are essential for the SAR imaging procedure. In real-time SAR imaging, onboard orbit determination data cannot achieve a level of accuracy that is equivalent to the orbit ephemeris in ground-based SAR processing, which requires a long processing time using common ground-based SAR imaging procedures. It is important to study the influence of errors in onboard real-time orbit determination data on SAR image quality. Instead of the widely used numerical simulation method, an analytical approximation model of the quadratic phase error (QPE) introduced by orbit determination errors is proposed. The proposed model can provide approximation results at two granularities: approximations with a satellite’s true anomaly as the independent variable and approximations for all positions in the satellite’s entire orbit. The proposed analytical approximation model reduces simulation complexity, extent of calculations, and the processing time. In addition, the model reveals the core of the process by which errors are transferred to QPE calculations. A detailed comparison between the proposed method and a numerical simulation method proves the correctness and reliability of the analytical approximation model. With the help of this analytical approximation model, the technical parameter iteration procedure during the early-stage development of an onboard real-time SAR imaging mission will likely be accelerated.

Sensitivity of the Gravity Model and Orbital Frame for On-board Real-Time Orbit Determination: Operational Results of GPS-12 GPS Receiver

This paper describes the sensitivity of both the orbital frame domain selection and the gravity model on the performance of on-board real-time orbit determination. Practical error sources, which affect the navigation solution of spaceborne global positioning system (GPS) receivers, are analyzed first. Then, a reasonable orbital frame (radial, in-track, cross-track (RIC)) is proposed to clearly represent the characteristics of the error in order to improve the performance of the orbit determination (OD) logic. In addition, the sensitivity of the gravity model affecting the orbit determination logic is analyzed by comparison with the precise orbit ephemeris (POE) of the Challenging Minisatellite Payload (CHAMP) satellite, and it is confirmed that the Gravity Recovery And Climate Experiment (GRACE) Gravity Model 03 (GGM03) outperforms the Earth Gravity Model 1996 (EGM96). The effects of both proposed orbit frames and the gravity model on the orbit determination logic are verified using a GPS simulator and observation data from the CHAMP satellite. Moreover, the practical performance of on-board real-time orbit determination logic is verified by updating the software of the spaceborne GPS receiver, GPS-12, on DubaiSat-2 operating at low Earth orbit (LEO). The results show that the position accuracy of on-board real-time orbit determination logic in GPS-12 is improved by 59%, from 12.6 m (1 σ) to 5.1 m (1 σ), after applying the proposed methods. The velocity accuracy is also improved by 57%, from 13.7 mm/s (1 σ) to 5.9 mm/s (1 σ).

Impact of ambiguity resolution with sequential constraints on real-time precise GPS satellite orbit determination

The real-time precise orbit is an essential prerequisite for a real-time precise point positioning service. Focusing on the impact of ambiguity resolution on real-time orbital precision, we propose an efficient approach for real-time ambiguity resolution, which consists of two modules. The first module resolves the double-differenced ambiguities according to their proximity to the nearest integer. The second module sequentially adds the resolved integer ambiguity constraints to the square-root information filter process, after confirming that the same constraints have not been imposed before the current epoch. To validate our method, GPS data collected from 100 globally distributed stations are used to simulate a real-time precise orbit determination. The convergence performance is analyzed, and the accuracy of the orbit is evaluated. The results show that: (1) Almost 90% of the double-differenced ambiguities are fixed correctly in real time for baselines shorter than 1000 km. (2) After application of the proposed approach, the root-mean-square errors of all the satellite orbits are reduced from (5.9, 3.4, 2.3) cm to (4.7, 2.6, 2.2) cm for the along-track, cross-track and radial directions, respectively, with improvements of about 22% for the along-track and cross-track directions, and 6% for the radial direction. (3) Simulated real-time orbits determined with this method can obtain almost the same accuracy as some ultra-rapid products and, particularly, better accuracy can be achieved for eclipsing satellites.

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

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