High Precision Orbit Determination Research Articles

Method and Application of High-Precision Open-Loop Velocity Measurement of Tianwen-1 Probe

In view of the requirements of Tianwen-1 missions on precision orbit determination and scientific application, this paper proposes a high-precision open-loop velocity measurement method based on ground-based radio. At first, relying on space–ground TT&C resources of the Tianwen-1 probe, the paper designs an open-loop velocity measurement strategy based on China’s deep-space network. Then, it proposes a core algorithm of open-loop velocity measurement based on local cross-correlation reconstruction to obtain instantaneous Doppler frequency observables. This algorithm is characterized by a high ability to avoid phase lock loss, convenient and efficient implementation, and flexible parameter configuration and is suitable for high-precision velocity measurement in the case of high dynamics and low signal-to-noise ratios. On this basis, the similarity and difference of velocity observables between open-loop and baseband velocity measurements are analyzed comparatively. Finally, on the basis of the open-loop velocity measurement method, the paper carries out tests on high precision orbit determination with independent support of velocity measurement, as well as on Mars radio occultation. According to the research results, the accuracy of open-loop velocity measurement can reach 0.05 mm/s (in 1-s integration time), which is 2 to 3 times better than that of baseband velocity measurement. Open-loop velocity measurement can independently support orbit determination accuracy of 50 m of the Tianwen-1 probe and effectively support autonomous retrieval of Martian ionospheric electron density profiles. Thus, this method can be effectively applied to future missions of deep-space exploration and research of planetary radio science.

High-Precision Orbit Determination of the Small TJU-1 Satellite Using GPS, GLONASS, and BDS

Tianjin University-1 (TJU-1) is a small low-Earth-orbiting (LEO) meteorological satellite equipped with a multi-GNSS receiver that provides the dual-frequency pseudorange and carrier-phase measurements from GPS, GLONASS, and BDS, including BDS-2 and BDS-3. In this contribution, the quality of GNSS data during the period of 2022/31~2022/37 is assessed, and the precise orbit determination (POD) based on the onboard GNSS data is conducted. Assessing the pseudorange measurement accuracy, it reveals that the GPS and BDS-3 are comparable, followed by BDS-2, and GLONASS the worst. The POD experiments demonstrate that, the orbit precision of all single-GNSS solutions is almost at an equivalent level of 2.2~3.4 cm, in terms of the overlapped orbit consistency, and the GPS-based solution is slightly worse than the BDS-based one and the GLONASS-based one is worse than other two. According to the orbit differences between different solutions, the orbit accuracy of single-GNSS solutions is inferred to be at the level of about 4.7~6.2 cm. With the multi-GNSS fusion, the precision and inferred accuracy of orbits could be improved significantly to 1.7~2.1 cm and about 1.7~3.7 cm, respectively. Furthermore, the root mean square (RMS) of posteriori carrier-phase residuals for all the IGSO/MEO satellites is at the level of 7~15 mm in different single-GNSS and multi-GNSS fusion solutions. These performances have fully demonstrated that, the centimeter-level POD is easily achievable for small LEO satellites by using the multi-GNSS receiver.

A Staring Tracking Measurement Method of Resident Space Objects Based on the Star Tacker

Measuring resident space objects (RSOs) by star trackers has become a research hotspot in space situational awareness. However, the arc length measured by star trackers is too short to complete the high-precision orbit determination of the RSO. In this paper, a staring–tracking measurement (STM) method is proposed to obtain a sufficiently long arc. Firstly, the three-axis attitude calculation model of the satellite is established for tracking RSOs during the staring process. Secondly, an observation method of the RSO location is proposed based on the principle of the angular distance invariance and the imaging mapping function of the star tracker. Finally, the numerical simulations and the ground experiment were conducted to verify the proposed algorithm. Simulation results show that the acquisition time of the measurable arcs is longer than 6 min, and the accuracy of the declination and the ascension can meet the standard for RSO orbit determination. The physical experiment shows that the acquisition time is consistent with that in the simulation. Our work provides a new idea for the realization of high-precision space-based optical measurement.

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.

Topology Design for GNSSs Under Polling Mechanism Considering Both Inter-Satellite Links and Ground-Satellite Links

Inter-satellite links (ISLs) are adopted in global navigation satellite systems (GNSSs) for high-precision orbit determination and space-based end-to-end telemetry telecommand control and communications. Due to limited onboard ISL terminals, the polling time division duplex (PTDD) mechanism is usually proposed for space link layer networking. By extending the polling mechanism to ground-satellite links (GSLs), a unified management system of the space segment and the ground segment can be realized. However, under the polling system how to jointly design the topology of ISLs and GSLs that are both time-slotted to improve data interaction has not been studied. In this paper, we formulate the topology design problem as an integer linear programming problem, aiming at minimizing the average delay of data delivery from satellites to ground stations while satisfying the ranging requirement for orbit determination. To tackle the computational complexity problem, we first present a novel modeling method of delay to reduce the number of decision variables. Furthermore, we propose a more efficient heuristic based on maximum weight matching algorithms. Simulation results demonstrate the feasibility of the proposed methods for practical operation in GNSSs with time-slotted GSLs. Comparing the two methods, the heuristic can achieve similar performance with respect to average delay but with significantly less complexity.

VLBI technique for the orbit determination of Tianwen-1

<p indent="0mm">Since the launch of the Tianwen-1 probe on July 23, 2020, the orbit of this probe has been determined using very long baseline interferometry (VLBI) together with Doppler and ranging, and the Zhurong Mars rover has been located. More than 40 software and hardware sets have been developed, tested, and installed for VLBI to meet the Tianwen-1 high-precision orbit determination requirements. Until June 18, 2021, 198 VLBI observations have been performed. The measurement errors in VLBI time delay and time delay rate are <sc>0.11 ns</sc> and <sc>0.33 ps/s,</sc> respectively. The orbit error of Tianwen-1 during the interplanetary cruise is <sc>~2 km,</sc> and it is <sc>~1 km</sc> around Mars. Additionally, the positioning accuracy of the Mars rover is several km. VLBI has made important contributions to trajectory correction, deep-space, near Mars capture, and far Mars maneuvers, Mars landing, etc. It has laid a good foundation for future deep-space probe precision orbit determination. Therefore, this paper introduces the technical upgrade of the VLBI network and presents the analysis and implementation of VLBI measurement and orbit determination.

Effect of PCV and attitude on the precise orbit determination of Jason-3 satellite

Abstract Satellite attitude modes and antenna phase center variations have a great influence on the Precise Orbit Determination (POD) of Low Earth Orbit satellites (LEOs). Inaccurate information about spacecraft attitude, phase center offsets and variations in the POD leads to orbital error. The Jason-3 satellite experienced complex attitude modes which are fixed, sinusoidal, ramp-up/down and yaw-flip. Therefore, it is necessary to properly construct the attitude model in the process of POD especially when there is no external attitude data. For the antenna phase center correction, the PCO which is the deviation between Antenna Reference Point (ARP) and Mean Antenna Phase Center (MAPC) usually can be calibrated on the ground accurately, but the PCV which is the deviation between Instantaneous Antenna Phase Center (IAPC) and Mean Antenna Phase Center (MAPC) will change greatly with the change of space environment. Residual approach can be used to estimate the receiver PCV map. In this paper, we collected the on-board GPS data of Jason-3 satellite from January 2019 and analyzed the impacts of PCV and spacecraft attitude on the orbit accuracy by performing the reduced-dynamic POD. Compared with the reference orbit released by the Centre National d’Études Spatiales (CNES), using the PCV map can reduce the Root Mean Square (RMS) of orbit differences in the Radial (R), Along-track (T), Cross-track (N) and 3D direction about 0.3, 1.0, 0.9, and 1.4 mm. Based on the estimated PCV map, the orbit accuracy in R, T, N and 3D direction is 1.24, 2.81, 1.17, and 3.29 cm respectively by using the measured attitude data. When using the attitude model, the orbit accuracy in R, T, N and 3D directions is 1.60, 3.54, 1.33, and 4.13 cm, respectively. The results showed that the combination of measured attitude data and modeled PCV map can obtain the better orbit solution. It is essential to build a corresponding model in high-precision orbit determination, when there is no attitude data and PCV map.

Real-Time On-Orbit Estimation Method for Microthruster Thrust Based on High-Precision Orbit Determination

In order to enable the micro-nanosatellites equipped with microthrusters to better complete various space applications, it is necessary to estimate the thrust performance of the microthrusters in real-time on orbit. This paper proposes a real-time on-orbit estimation method for microthrust based on high-precision orbit determination. By establishing a high-precision orbit dynamic model, the microthrust generated by a microthruster is modeled as a first-order Markov model, combined with a high-precision GNSS measuring device, and the satellite position is obtained through the cubature Kalman filter algorithm, velocity, and thrust real-time on-orbit estimates. For a thrust of 100 μN, the error accuracy of the on-orbit estimation is 3.98%; for a thrust of 500 μN, the error accuracy is 1.79%; for a thrust of 5 mN, the error accuracy can be reduced to 1.43%; and when the thrust is 500 μN, the accuracy of orbit determination is 16 cm. This method solves the problem that the traditional on-orbit thrust estimation method cannot perform real-time on-orbit estimation of microthrust on the order of hundreds of μN. The real-time on-orbit estimation of microthrust of micro-nanosatellites equipped with microthrusters of the order of hundreds of micronewtons or even several mN to tens of mN has certain reference value.

High Precision Orbit Determination Method Based on GPS Flight Data for ALE-1

High Precision Orbit Determination Method Based on GPS Flight Data for ALE-1

Improving integrated precise orbit determination of GPS, GLONASS, BDS and Galileo through integer ambiguity resolution

The China Satellite Navigation Office announced on December 27, 2018 that the BDS-3 preliminary system had been completed to provide global services. Before this, GPS and GLONASS were the only two global navigation satellite systems (GNSS) supporting global positioning service, and have totally more than 50 satellites in normal operation. Furthermore, Galileo is intending to reach its full constellation around 2020. By that time, the number of available GNSS satellites will increase to more than 100, which brings both opportunities and challenges for high-precision positioning and orbit determination. The precision of orbits could be significantly improved through integer ambiguity resolution (AR), while AR is particularly difficult to achieve especially for GLONASS and BDS due to inter-frequency biases and satellite-induced code biases. Therefore, to address this limitation and further enhance the precision of multi-GNSS orbit determination, we try to fix the double-differenced intra-system ambiguities to integers and propose an integer AR method for multi-GNSS POD. To verify the contribution of AR, an experiment of 141 sites with global coverage is conducted. The results imply that the approach realizes an average fixing rate of 98.1%, 96.4%, 84.6% and 92.6% for GPS, GLONASS, BDS and Galileo over a whole year. The GNSS orbits are further improved with AR in terms of the precision compared with the International GNSS Service (IGS) final orbits, the discontinuity at overlapping day boundaries, and satellite laser ranging residuals. Thus, the integer AR improves the precision of multi-GNSS precise orbit determination, which can enhance integrated data processing of multi-GNSS and their applications in the future.

GPS Relative Navigation for the CanX-4 and CanX-5 Formation-Flying Nanosatellites

In November 2014 the CanX-4 and CanX-5 spacecraft became the first nanosatellites to demonstrate autonomous formation control with error less than 1 m. This feat was accomplished both in along-track formations at 1000 and 500 m range and projected circular orbit formations at 100 and 50 m. This control performance was enabled through carrier-phase differential GPS navigation techniques, providing online relative state estimates typically accurate to better than 10 cm. It was an important milestone on the road to regular and fully operational formation-flying missions. This paper provides an overview of the relative positioning algorithm design, presents an independent assessment of the receiver performance, and assesses the absolute and relative navigation results. The mission’s on-orbit results are compared with an independently determined orbit solution computed using the GPS High Precision Orbit Determination Software Tools at the German Aerospace Centre.

Yarkovsky-Schach effect on space debris motion

The Yarkovsky-Schach effect is a small perturbation affecting Earth satellites and space debris illuminated by the Sun. It was first applied to the orbit of LAGEOS satellites as an explanation of the residuals in orbital elements. In this work, we carry out several numerical integration tests taking into consideration various orbit and rotation parameters, in order to analyse this effect in a broader context. The semi-major axis variations remain small and depend on the spin axis attitude with respect to the Sun. We show that the force amplitude is maximised for orbits inclined with i≈ 20–30°. We also observe the influence on other orbital elements, notably on the orbit inclination. However, these effects are clearly observed only on long timescales; in our simulations, we propagated the orbits for 200 y. The Yarkovsky-Schach effect is thus confirmed to have a minuscule magnitude. It should be taken into account in studies requiring high-precision orbit determination, or on expanded timescales.

THE FIRST HIGH-PHASE OBSERVATIONS OF A KBO: NEW HORIZONS IMAGING OF (15810) 1994 JR1 FROM THE KUIPER BELT

ABSTRACT NASA’s New Horizons spacecraft observed (15810) 1994 JR1, a 3:2 resonant Kuiper belt object (KBO), using the LOng Range Reconnaissance Imager (LORRI) on 2015 November 2 from a distance of 1.85 au and again on 2016 April 7 from a distance of 0.71 au. These were the first close observations of any KBO other than Pluto. Combining ground-based and Hubble Space Telescope (HST) observations at small phase angles and the LORRI observations at higher phase angles, we produced the first disk-integrated solar phase curve of a typical KBO from α = 0.°6–58°. Observations at these geometries, attainable only from a spacecraft in the outer solar system, constrain surface properties such as macroscopic roughness and the single particle phase function. 1994 JR1 has a rough surface with a 37° ± 5° mean topographic slope angle and has a relatively rapid rotation period of 5.47 ± 0.33 hr. 1994 JR1 is currently 2.7 au from Pluto; our astrometric points enable high-precision orbit determination and integrations that show that it comes this close to Pluto every 2.4 million years (104 heliocentric orbits), causing Pluto to perturb 1994 JR1. During the November spacecraft observation, the KBO was simultaneously observed using HST in two colors, confirming its very red spectral slope. These observations have laid the groundwork for numerous potential future distant KBO observations in the New Horizons–Kuiper belt extended mission.

Orbit determination and estimation of non-gravitational accelerations for the GOCE reentry phase

During its reentry phase from 21 October to 10 November 2013, the European Space Agency (ESA) Gravity field and steady-state Ocean Circulation Explorer (GOCE) continued to provide high-quality, dual-frequency observations by its Global Positioning System (GPS) receiver, star tracker and accelerometers. This resulted in a unique data set for testing high-precision orbit determination at altitudes down to as low as 137km. In addition, the accelerometers kept working down to this altitude as well, be it with growing periods during which they were saturated. This made it possible to test the capability of estimating non-gravitational accelerations in high drag environments by GPS.A reduced-dynamic orbit determination based on an extended Kalman filter approach was adopted to cope with the estimation of the orbit parameters, including the exponentially growing non-gravitational accelerations. The orbits were found to be consistent with Satellite Laser Ranging (SLR) observations at a level of just a few centimeters for a few passes collected up to 2 November 2013. Also orbit overlap comparisons and comparisons with external orbit solutions indicate a 3-dimensional orbit quality at the dm level or better. In addition, high correlations were found between the estimated non-gravitational accelerations and those from the accelerometers during all periods when they were not saturated: typically close to 0.99 for the X axis of the gradiometer reference frame (close to the flight direction), for which the non-gravitational acceleration signal is by far the largest. High correlations were found as well for the Y axis (0.68–0.96) and Z axis (0.61–0.93), predominantly aligned with respectively the cross-track and height direction. The highest correlations were found for the last days, as long as the accelerometers were not saturated.

基于&amp;Delta;DOR信号的高精度VLBI技术

During the Chinese Lunar Project Chang'E-2 mission, a series of experiments on ΔDOR (delta differential one-way ranging) technology was carried out over a two week period starting on April 2, 2011. ΔDOR technology was first adopted in China deep space navigation, and the ΔDOR delay observables were obtained and used for orbit determination. In this paper, we introduce the ΔDOR observing technology, including the ΔDOR measurement principles. We also discuss the experiment design, the rules for selecting the calibration quasars, the switching time choice, the signal recording setup for the channels, the ΔDOR data processing method implemented in the software, and our analysis of the error sources of the ΔDOR delay and its contribution to orbit determination based on the characteristics of the Chinese VLBI network. Through these analyses and verification studies on the orbit determination from the satellite orbits in the CE-1 and CE-2 missions, we conclude that the accuracy of the ΔDOR delay is about 0.5 ns, an improvement of about one order of magnitude compared with that from S-band telemetry signals of less than 1 MHz. This study presents an important technique for high precision orbit determination of lunar and deep space explorations.

Multiple Shooting Method for Initial Satellite Orbit Determination

After a satellite has been launched, the determination of its initial orbit is one of the primary tasks to be accomplished by mission control: e.g., in order to prepare for high-precision orbit determination or orbital transfers. For this purpose, tracking measurements are acquired by ground stations, which are the basis for the determination of the unknown orbit parameters. In this paper, the orbit determination problem is formulated as a least-squares parameter estimation problem, and a newly developed multiple shooting method is presented for its solution. For the generation of initial guesses, the method incorporates a so-called analytical projection, which is specifically tailored to the available measurement data. Original tracking data of the launch and early orbit phases of the Artemis satellite and the second pair of Cluster-II satellites are used for tests of the method. Both scenarios constitute challenging benchmark problems, because the satellites were launched into orbits significantly different from the expected ones. A comparison to the widely employed single shooting method reveals that the newly developed method significantly improves the convergence behavior.

Antenna phase center calibration for precise positioning of LEO satellites

Phase center variations of the receiver and transmitter antenna constitute a remaining uncertainty in the high precision orbit determination (POD) of low Earth orbit (LEO) satellites using GPS measurements. Triggered by the adoption of absolute phase patterns in the IGS processing standards, a calibration of the Sensor Systems S67-1575-14 antenna with GFZ choke ring has been conducted that serves as POD antenna on various geodetic satellites such as CHAMP, GRACE and TerraSAR-X. Nominal phase patterns have been obtained with a robotic measurement system in a field campaign and the results were used to assess the impact of receiver antenna phase patterns on the achievable positioning accuracy. Along with this, phase center distortions in the actual spacecraft environment were characterized based on POD carrier phase residuals for the GRACE and TerraSAR-X missions. It is shown that the combined ground and in-flight calibration can improve the carrier phase modeling accuracy to a level of 4 mm which is close to the pure receiver noise. A 3.5 cm (3D rms) consistency of kinematic and reduced dynamic orbit determination solutions is achieved for TerraSAR-X, which presumably reflects the limitations of presently available GPS ephemeris products. The reduced dynamic solutions themselves match the observations of high grade satellite laser ranging stations to 1.5 cm but are potentially affected by cross-track biases at the cm-level. With respect to the GPS based relative navigation of TerraSAR-X/TanDEM-X formation, the in-flight calibration of the antenna phase patterns is considered essential for an accurate modeling of differential carrier phase measurements and a mm level baseline reconstruction.

DORIS time bias estimated using Jason-1, TOPEX/Poseidon and ENVISAT orbits

DORIS is a globally distributed, all-weather satellite tracking system providing near-continuous precise Doppler coverage of the TOPEX/Poseidon (T/P), Jason-1, ENVISAT, and SPOT series of satellites. The DORIS system, which has been critical in establishing the high-precision orbit determination standards now enjoyed by these missions, continues to evolve and improve. There is a small, 5 to 10 μs, discrepancy between the DORIS time-tag computed by Centre National d’Etudes Spatiales (CNES) using the DORIS timing data, and a time-tag estimated using DORIS range-rate data with respect to orbits referred to Satellite Laser Ranging (SLR) or Global Positioning System (GPS) time. This discrepancy is evaluated using DORIS time biases estimated over T/P, Jason-1, and ENVISAT orbits, which are computed using SLR or GPS tracking and reference SLR or GPS time. Although DORIS is installed on other satellites, these are the only three where the DORIS time bias can be observed with the help of an alternate tracking system – SLR or GPS. For T/P, Jason-1 and ENVISAT, this DORIS time bias quantities to 5–10 μs. Over the span of the T/P mission following cycle 92, this time bias has ranged from +10 to − 10 μs. This paper addresses the precision and nature of the estimated time biases by evaluating such estimates over orbits computed with various gravity field models, computed using SLR + DORIS and GPS tracking, and computed by the Goddard Space Flight Center (GSFC), Jet Propulsion Laboratory (JPL), and CNES analysis centers. The paper includes descriptions of the DORIS measurement, time-tag processing, expected time-tag error, and time bias estimation. In describing the estimated DORIS time bias, the paper offers a new approach for evaluating the DORIS resolution capability.

Routine operational and high-precision orbit determination of envisat

ESA's Earth observation satellite Envisat was successfully launched on 1 March 2002 by an Ariane-5 launcher, and ESOC immediately took over the task of determining and predicting the orbit using S-band tracking data, and optimising the manoeuvre sequence to bring the spacecraft into an orbit accurately phased with ERS-2. On-board, Envisat carries, among others, a radar altimeter, a DORIS instrument and a laser retro-reflector array (SLR). Data from these instruments are being used at ESOC for high-precision orbit determination, for verification of the routine orbit determination and for cross-comparison with orbits computed on-board by the DORIS navigator and with those delivered with the Envisat products. This paper presents the first consolidated results obtained for Envisat routine and high-precision orbit determination. All orbit determination and control activities were performed with the software package NAPEOS, which was developed in-house.

CHAMP rapid orbit determination for GPS atmospheric limb sounding

In preparation of the CHAMP small satellite LEO (Low Earth Orbit) mission to be launched on July 15, 2000, the GeoForschungsZentrum Potsdam (GFZ) enhanced its high precision orbit determination capabilities in order to rapidly produce precise LEO and GPS (Global Positioning System) orbital products. These orbits shall be available at 3 hour intervals with a latency of 2 hours after the actual observation for the application of GPS atmospheric limb sounding. Rapid orbit determination will exploit spaceborne GPS high-low satellite-to-satellite tracking data, fast delivery GPS ground tracking data from a global network and on-board accelerometer data for surface force modelling. Rapidly available ground based laser ranges support the orbit determination task. Because of the timeliness requirements of the orbital products, the availability of input data in space and time for POD may be sub-optimal. It is planned to apply dynamic orbit integration and an either separate or combined adjustment for CHAMP and GPS satellites' routine rapid orbit determination. For quality control purposes and during the initial mission phase, when the available force models, in particular the gravity field model, are not accurate enough, the CHAMP orbit can also be computed in a purely kinematic/geometric approach not using any dynamical model.