Orbit Accuracy Research Articles

A Noninteracting Galactic Black Hole Candidate in a Binary System with a Main-sequence Star

We describe the discovery of a solar neighborhood (d = 468 pc) binary system with a main-sequence sunlike star and a massive noninteracting black hole candidate. The spectral energy distribution of the visible star is described by a single stellar model. We derive stellar parameters from a high signal-to-noise Magellan/MIKE spectrum, classifying the star as a main-sequence star with T eff = 5972 K, , and M = 0.91 M ⊙. The spectrum shows no indication of a second luminous component. To determine the spectroscopic orbit of the binary, we measured the radial velocities of this system with the Automated Planet Finder, Magellan, and Keck over four months. We show that the velocity data are consistent with the Gaia astrometric orbit and provide independent evidence for a massive dark companion. From a combined fit of our spectroscopic data and the astrometry, we derive a companion mass of M ⊙. We conclude that this binary system harbors a massive black hole on an eccentric (e = 0.46 ± 0.02), 185.4 ± 0.1 day orbit. These conclusions are independent of El-Badry et al., who recently reported the discovery of the same system. A joint fit to all available data yields a comparable period solution but a lower companion mass of . Radial velocity fits to all available data produce a unimodal solution for the period that is not possible with either data set alone. The combination of both data sets yields the most accurate orbit currently available.

Toward a Geodesy and Time Reference in Space (GETRIS): A Study of Apparent Satellite Clocks of a Future GNSS Satellite Constellation

Today, concepts within the Global Geodetic Observing System (GGOS) aim a Terrestrial Reference System (TRS) with 1 mm accuracy and long-term stability of 0.1 mm/year. GETRIS (Geodesy and Time Reference In Space) is a concept that aims to realize a relativistic reference system based on satellites as an extension to the TRS. This helps with another goal of the GGOS, namely, the connection of different satellite layers with the TRS. For a valuable contribution to the GGOS’s goals, we would expect to achieve precise determined satellite orbits at the level of 1–3 mm and satellite clocks with a picosecond accuracy. The use of increasingly precise links helps to improve the satellite precise orbit determination (POD) and is necessary to synchronize the clocks in the satellite/station network. We analyze a complementary use of high-precision optical dual one-way links at the level of 1 mm precision together with the L-band. In previous studies, we analyzed the benefit for satellite POD, achieving Medium Earth Orbit (MEO) as well as geosynchronous orbit (GSO) accuracies at the low-millimeter level. In this work, we analyze the capabilities for clock synchronization. We compare two different clock types for estimation and prediction. We analyze different satellite constellations and different combinations of measurement links.

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.

Research on Enhanced Orbit Prediction Techniques Utilizing Multiple Sets of Two-Line Element

Acquiring accurate space object orbits is crucial for many applications such as satellite tracking, space debris detection, and collision avoidance. The widely used two-line element (TLE) method estimates the position and velocity of objects in space, but its accuracy can be limited by various factors. A combination of multiple TLEs and advanced modeling techniques such as batch least squares differential correction and high-precision numerical propagators can significantly improve TLE accuracy and reliability, ensuring better space object surveillance. Previous studies analyzed additional factors that may influence TLE accuracy and evaluated the accuracy of Starlink TLE using precise ephemeris data from SpaceX. The results indicate that utilizing multiple TLEs for precise orbit determination can significantly enhance the performance of orbit prediction methods, particularly when compared to SGP4. By leveraging 10-day Starlink TLEs, the accuracy of 5-day predictions can be improved by approximately twofold. Additionally, producing two pseudo-observations within an orbital period near the TLE epoch yields the greatest effect on prediction accuracy, with this distribution of pseudo-observations increasing accuracy by approximately 10% compared to a uniform distribution. Further research can explore more data fusion and machine learning approaches to optimize operations in space.

A method of using back propagation neural network to estimate orbital lifetime of LEO satellites

The “IADC space debris mitigation guidelines” requires that the post-mission orbit lifetime of low Earth orbiting (LEO) satellites should not be longer than 25 years, which is the key to debris mitigation. To analyze the degree of global compliance to this 25-year guideline, a fast and relatively accurate orbit life estimation algorithm is required. The traditional method uses numerical orbit propagation to accomplish the task, although its accuracy is high when a high-precision force model is used, the calculation is time-consuming. This paper proposes a new method for orbit lifetime estimation without relying on orbit propagation. A back propagation (BP) neural network is used to directly fit the relationship from the satellite parameters to the orbit lifetime. The space objects that have reentered the Earth’s atmosphere are selected from the catalog database of the US Space Surveillance Network (SSN), and are used to generate samples for network training. The genetic algorithm is combined with the traditional back propagation algorithm for the training of the neural network. The results show that for the specific application background of identifying whether a satellite complies with the 25-year guideline, the orbit lifetime estimation accuracy of the BP network meets the demand to some extent. Moreover, because it does not involve orbit propagation, the BP network has a high computational efficiency in estimating orbit lifetime, showing a good application prospect.

Reference clock impact on GNSS clock outliers

Abstract With the advent of the Global Navigation Satellite System (GNSS), the need for precise and highly accurate orbit and clock products becomes crucial in processing GNSS data. Clocks in GNSS observations form the basis of positioning. Their high quality and stability enable high accuracy and the reliability of the obtained results. The clock modelling algorithms are continuously improved; thus, the accuracy of the clock products is evolving. At present, 8 Analysis Centers (ACs) contribute to the International GNSS Service final clock products. These products are based on GNSS observations on a network of reference stations, where for a given day one of the reference station clocks is the reference clock. In this paper, the authors determined the impact of the reference clock on the quality of clock product, especially outliers, for the first time. For this purpose, the multi-GNSS final clock products provided by the Center for Orbit Determination in Europe (CODE) for the period 2014–2021 (1773–2190 GPS week, 2921 days) were analysed. Analysis shows that by applying the Median Absolute Deviation (MAD) algorithm for outlier detection, the Passive Hydrogen Maser (PHM) clock installed on board the GALILEO satellites have the lowest level of noise, whereas the Block IIR GPS satellite launched in 1999 appears to have the highest levels of noise. Furthermore, the GNSS station OHIE3, when used as a reference clock, generates an increase in the level of noise, especially noticeable on the G09 and E03 satellites.

Real‐time precise orbit determination for FY‐3C and FY‐3D based on BDS and GPS onboard observation

AbstractThe code multipath error associated with elevation in BDS‐2 is one of the main factors whose impact on the precision of real‐time reduced‐dynamic precise orbit determination (POD) using spaceborne multi‐global navigation satellite systems (GNSS) observation data for FengYun‐3C (FY‐3C) and FengYun‐3D (FY‐3D) satellites. The aim is to construct a code multipath piece‐wise linear error model and analyse the contribution of BDS‐2 to the performance of low earth orbit POD. Conclusions are drawn out from the experimental results: (1) the real‐time POD average precision of FY‐3C and FY‐3D is improved by about 11% and 12% after the correction of BDS‐2 code multipath error; (2) Due to the small number of available BDS‐2 satellites and the limited accuracy of geostationary earth orbit (GEO) satellite real‐time orbit products, the precision of the real‐time overlapping comparison for FY‐3C/FY‐3D by using the BDS‐2 onboard observation data can only reach the decimetre level. However, with the BDS‐2 signal capture capability of the FY‐3D onboard GNSS Occultation Sounder upgraded, the average precision of the BDS‐2‐based POD for FY‐3D is better than that of FY‐3C in each direction and with 10% improvement in the average 3 dimensional‐root mean square (3D‐RMS); (3) Cases of onboard global positioning system (GPS), GPS + BDS‐2 (with GEO), and GPS + BDS‐2 (without GEO) for real‐time POD can meet 5–8 cm precision requirement. The average 3D‐RMS of the real‐time POD for FY‐3C/FY‐3D, which utilises onboard GPS + BDS‐2 data is inferior only to GPS data, owing to the influence of the orbit accuracy of GEO satellites. However, after excluding the influence of GEO satellites, the average result (3D‐RMS) of the real‐time POD for FY‐3C (6.11 cm) and FY‐3D (5.95 cm) is better than those of other cases.

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.

An Interferogram Re-Flattening Method for InSAR Based on Local Residual Fringe Removal and Adaptively Adjusted Windows

InSAR technology uses the geometry between antennas and targets to obtain DEM and deformation; therefore, accurate orbit information, which can provide reliable geometry, is the prerequisite for InSAR processing. However, the orbit information provided by some satellites may be inaccurate. Further, this inaccuracy will be reflected in the interferogram and will be difficult to remove, finally resulting in incorrect results. More importantly, it was found that the residual fringes caused by inaccurate orbit information vary unevenly throughout the whole image and cannot be completely removed by the existing refinement and re-flattening methods. Therefore, an interferogram re-flattening method based on local residual fringe removal and adaptively adjusted windows was proposed in this paper, with the aim being to remove the unevenly varying residual fringes. There are two innovative advantages of the proposed method. One advantage is that the method aims at the global inhomogeneity of residual fringes; the idea of combining local processing and residual fringe removal was proposed to ensure the residual fringes in the whole image can be removed. The other is that an adaptively adjusted local flattening window was designed to ensure that the residual fringes within the local window can be removed cleanly. Three sets of GaoFen-3 data and one pair of Sentinle-1A data were used for experiments. The re-flattening process shows that the local flattening and the adjustment of the local window are absolutely essential to the clean removal of time-varying and uneven residual fringes. The generated DEM and the estimated building heights are used to indirectly reflect the performance of re-flattening methods. The final results show that compared with mature refinement and re-flattening methods, the DEMs based on the proposed method are more accurate, which reflects that the proposed method has a better performance in the removal of time-varying and uneven residual fringes.

Impact of ambiguity resolution on phase center offsets and hardware delay estimation for BDS-3 inter-satellite links

The Chinese BeiDou navigation satellite system (BDS) has already completed its three phases and developed into a global navigation satellite system for open positioning, navigation, and timing services. The BDS-3 satellites feature the inter-satellite link (ISL). The ISL observation-related error model and ambiguity resolution for L-band observation are the crucial factors in precise data processing. In this study, we present for the first time the impact of ambiguity resolution on phase center offsets (PCOs) and hardware delay estimation of BDS-3 inter-satellite links. Two weeks’ L-band observations from 99 globally distributed ground stations and Ka-band ISL observations are collected for experimental validation and analysis. First, network solutions with and without ISL observations are conducted to investigate the role of ISL observation in ambiguity resolution. Afterward, ISL observation-related errors, mainly PCOs and hardware delays, are estimated by processing L-band with ISL observations with and without ambiguity resolution to analyze the impact of ambiguity resolution on these two factors. Finally, orbit accuracy in the network solution is assessed to further validate the effectiveness of the estimated PCOs and hardware delays in our experiment. The result indicates that introducing the ISL can slightly improve the fixing rate compared to only L-band observations from 83.7% to 84.3%. Furthermore, ambiguity resolution has a positive influence on the stability of estimated PCOs and hardware delays in turn, although the root mean square (RMS) values basically remain unchanged. The standard deviation (STD) of the x-offset is reduced from 0.021 m to 0.012 m, a significant improvement of about 43%, and 0.022 m–0.016 m, with an improvement of about 27%, for the y-offset. There is a slight improvement of about 8% for z-offset. Similarly, around 10% improvement in the STD for hardware delays can be achieved while the RMS values almost stay the same except for C40. Orbit determination from network solutions shows high accuracy compared to the public products for the satellite with good geometry configuration, which further validates our estimates for ISL PCOs and hardware delays.

External Measurement System for Aircraft Structural Parts Based on Digital Image Correlation in Signal-limited Spaces

An experimental study was performed on the application of the digital image correlation (DIC) technique to characterize aircraft components for which accurate time information is required. This study builds an aircraft external measurement system based on Stereo DIC. This system obtains real-time satellite time information from a GPS clock source and transmits it to a trigger unit. A camera acquires this information and displays it on the image. This solves the problem that some closed laboratories can use only computer time and cannot obtain accurate satellite time when using camera measurements. Moreover, we verify the reliability and accuracy of this approach, finding an average angular accuracy of better than 0.02 degrees and a relative error of less than 1%. Using the binocular Stereo DIC system, the accuracy of the measurements is clarified for specific conditions. Furthermore, we use this system to measure simulated aircraft landing gear, which moves at an angular velocity of 52.4 °/ s over a distance of 5 m with a wide field of view of 16.8°. The satellite time information acquired by the camera and the time information of the captured time targets are highly stable. The system’s reliability is demonstrated for use in practical engineering, contributing to the engineering application of Stereo DIC for external aircraft measurements.

The orbits of outer planetary satellites using theGaiadata

ABSTRACTLaunch of the Gaia space observatory started a new era in astrometry when the accuracy of star coordinates increased by thousands of times. Significant improvement in accuracy was also expected for the coordinates of the Solar system bodies. Gaia Data Release 3 (DR3) provided us with the data that could be used to test our expectations. In this work, we refine the orbits of a number of outer planetary satellites using both ground-based and Gaia observations. From 13 outer satellites observed by Gaia, we chose 6 to obtain their orbits. Some specific moments in using observations of outer satellites made by Gaia are demonstrated. These peculiarities stem from scanning motion of Gaia, in particular from the fact that the accuracy of observations is significantly different along and across the scanning direction. As expected, Gaia observations proved to be more precise than those made from Earth, which results in more accurate satellite ephemerides. We estimate accuracy of the ephemerides of considered satellites for the interval between 1996 and 2030. As astrometric positions published in Gaia DR3 were not corrected for the relativistic light deflection by the Sun, we took into account this effect, which slightly diminished the rms residuals. In addition, relativistic light deflection by the giant planets was estimated, which, as it turned out, can be neglected with the given accuracy of Gaia observations.

Precise Orbit Determination and Accuracy Analysis for BDS-3 Satellites Using SLR Observations

Satellite laser ranging (SLR) is the space geodetic technique with the highest degree of range, measuring precision and distances right down to the millimeter level. Thanks to the improvement of SLR station layouts and the advance of SLR technology, in recent years, more research has been conducted to determine Global Navigation Satellite System (GNSS) satellite orbits using SLR data. The primary goal of this contribution is to investigate the accuracy of BeiDou Navigation-3 (BDS-3) Satellite precise orbit determination (POD) using solely SLR data, as well as explore the impact of various factors on that accuracy. Firstly, we used actual SLR data to make the POD for BDS-3 satellites, and the POD accuracy was positively connected with the orbital arc lengths. The 9-day median root mean square (RMS) in radial (R), along-track (T), and cross-track (N) directions were estimated at 4.7–8.2, 22.1–35.2, and 27.4–43.8 cm, respectively, for comparison with WUM precise orbits. Then, we explored the impact of SLR observations and stations on POD accuracy. For 9-day orbital arc lengths, five station or 20 observation arcs may offer an orbit with a 1 m precision. Six to eight stations or 30–35 observation arcs allow an improved orbit accuracy up to approximately 0.5 m. Furthermore, we examined how measurement errors and orbit modeling errors affect the SLR-only POD accuracy using simulated SLR data. For orbital arc lengths of 9 days, each cm of random error leads to a 9.3–11.0 cm decrease in orbit accuracy. The accuracy of an orbit is reduced by 10.1–15.0 cm for every 1 cm of systematic error. Moreover, for solar radiation pressure (SRP) errors, the effect of POD accuracy is 20.5–45.1 cm, respectively.

Chlorophyll dynamics from Sentinel-3 using an optimized algorithm for enhanced ecological monitoring in complex urban estuarine waters

Urban estuaries are dynamic environments that hold high ecological and economic value. Yet, their optical complexity hinders accurate satellite retrievals of important biogeochemical variables, such as chlorophyll-a (Chl-a) biomass. Approaches based on a limited number of satellite spectral bands often fail to capture seasonal transitions and sharp spatial gradients in estuarine Chl-a concentrations, inhibiting integration of satellite data into water quality monitoring and conservation programs. We propose a novel approach that utilizes the wide range of spectral information captured by the Ocean and Land Color Instrument (OLCI) to retrieve estuarine Chl-a. To validate our approach, we used measurements in Long Island Sound (LIS), a highly urbanized estuary increasingly susceptible to anthropogenic stressors and climate change. Hyperspectral remote sensing reflectance (Rrs) and Chl-a data representing the spatiotemporal diversity of LIS were used to assess the ideal atmospheric correction approach for OLCI and develop a multi-spectral multiple linear regression (MS-MLR) Chl-a algorithm. POLYMER derived Rrs proved to be the preferred atmospheric correction approach. Evaluation of MS-MLR performance in retrieving Chl-a with in situ Rrs showed good agreement with field measurements. Application to OLCI-retrieved Rrs showed significant improvement (20%-30%) in common error metrics relative to other algorithms assessed. The MS-MLR approach successfully captured seasonal cycles and spatial gradients in Chl-a concentration. Application of this method to urban estuaries and coasts enables accurate, high resolution Chl-a observations at the ecosystem scale and across a range of conditions, as needed for conservation and ecosystem management efforts.

Signal-in-Space Range Error of the Global BeiDou Navigation Satellite System and Comparison with GPS, GLONASS, Galileo, and QZSS

Based on the standard of precise multisystem orbit and clock offset, the evaluation methods of satellite orbit, satellite clock offset and the signal-in-space range error (SISRE) from broadcast ephemeris were given in this study. The SISRE was used as a key performance index to compare the global BeiDou navigation satellite system (BDS-3) with the regional navigation satellite system (BDS-2), Global Positioning System (GPS), Galileo, Globalnaya Navigazionnaya Sputnikovaya Sistema (GLONASS), and Quasi-Zenith Satellite System (QZSS). Through the combination of domestic tracking stations and inter satellite links, the orbit determination accuracy of BDS-3 has been significantly improved. The radial (R), tangential (T) and normal (N) direction orbit accuracies of BDS-3 medium Earth orbit (MEO) satellites were 0.08, 0.37, and 0.34 m, respectively, which were considerably better than those of other satellite navigation systems. The R-, T-, and N-direction orbit accuracies of BDS-3 inclined geosynchronous orbit (IGSO) satellites were 0.17, 0.59, and 0.56 m, respectively, which were better than those of QZSS IGSO satellites. The R-, T-, and N-direction orbit accuracies of BDS-3 geostationary earth orbit (GEO) satellites were 0.27, 3.42, and 1.29 m, respectively, revealing considerable accuracy advantages in the R and N directions compared with QZSS GEO, although performance in the T direction was inferior. For the clock offset, the BDS-3 MEO satellites had an accuracy of 1.83 ns, which was noticeably superior, similar, slightly inferior, and superior to those of BDS-2, GPS, Galileo, and GLONASS. The clock offset accuracies of BDS-3 IGSO and GEO satellites were 3.13 and 3.17 ns, respectively, which were slightly better than those of QZSS IGSO and GEO satellites but did not have an obvious advantage over BDS-2. The primary reason could be that the launch time of the two types of BDS-3 satellites was close to the analysis period, and therefore, the clocks may be still in the aging process. Considering only orbit error, the average SISRE (orb) of BDS-3 MEO, Galileo, GPS, and GLONASS was 0.10, 0.28, 0.57, and 1.03 m, respectively. The SISRE (orb) of BDS-3 IGSO was 0.19 m, which was marginally greater than that of BDS-3 MEO but smaller than those of the other systems and considerably smaller than that (0.90 m) of QZSS IGSO. The SISRE (orb) of BDS-3 GEO was 0.60 m, which was comparable to that of GPS (0.59 m) and considerably smaller than that of QZSS GEO (0.91 m) satellites. Considering both orbit and clock offset error, the SISRE of BDS-3 MEO satellites was 0.52 m, which was slightly greater than that of Galileo (0.40 m), marginally smaller than that of GPS (0.59 m), and considerably smaller than that of GLONASS (2.33 m). The BDS-3 IGSO satellites had a SISRE of 0.90 m, which was greater than those of GPS and Galileo but comparable to that of QZSS IGSO (0.92 m). The average SISRE of BDS-3 GEO satellites was 1.15 m, which was greater than those of GPS and Galileo and slightly greater than that of QZSS0.95 m GEO satellites, but smaller than that of GLONASS.

Effect of the low-order coefficients of the Earth gravity model in calculating the satellite orbit

The Earth's gravity model is a crucial factor in determining satellite orbits. Scientific organizations such as GFZ Potsdam in Germany, GRGS Toulouse in France, and AIUB in Switzerland have established Earth gravity models with increasing precision of spherical harmonic coefficients. Low-order coefficients, including C ̅_21,( S) ̅_21, C ̅_10,C ̅_11,( S) ̅_11and C ̅_20, play a vital role in describing changes in the Earth's poles, geometric center, and flattening. To evaluate the impact of these coefficients and understand altimeter satellite orbital error, the Propagerror program was developed. This program calculates satellite orbital error from the differential components of Earth gravity model spherical harmonic coefficients (dC/Slm), which can be obtained from the difference between two gravity models or from seasonal and annual components of spherical harmonics. By separating appropriate low-order components in the Earth gravity models, the Propagerror program enables the estimation of satellite orbital error. In this study, we isolate C ̅_10,C ̅_11,( S) ̅_11, and C ̅_21,( S) ̅_21 coefficients in the EIGEN-GRGS.RL02bis.MF and EIGEN-6S gravity models to assess the geophysical impact on satellite orbits. The influence of the geometry center elements results in a 2 cm error in the Jason-2 satellite, while the rotational axis elements have no effect. The C ̅_31,( S) ̅_31 coefficient has a 6-7 mm impact on the accuracy of the Jason-2 satellite, as demonstrated by the satellite error map in two situations with and without the C ̅_31,( S) ̅_31 harmonic coefficient. This study highlights the significance of regulating function coefficients in satellite orbit determination, particularly the low-level harmonic parameters. The Propagerror program provides insights into the impact of each spherical harmonic parameter on satellite orbits, contributing to the improvement of orbit accuracy and the understanding of the Earth's gravity model.

Micro-Thrust, Low-Fuel Consumption, and High-Precision East/West Station Keeping Control for GEO Satellites Based on Synovial Variable Structure Control

Aiming at the shortcomings of non-optimal fuel consumption and low accuracy of Geosynchronous orbit (GEO) satellites in the east/west station keeping (EWSK) at the current stage, a micro-thrust EWSK algorithm for GEO satellites based on a single-synovial surface is proposed. This algorithm has the characteristics of low fuel consumption and high control precision. However, when this algorithm performs GEO station switching under the condition of limited velocity increment, the mean longitude capture path may not be optimal, the capture time of the mean longitude is too long, and the engineering applicability is not good. In view of the above problems, a micro-thrust EWSK for GEO satellites based on dual synovial surfaces is proposed. Through the advance planning of the mean longitude, the control lag caused by the limited velocity increment is eliminated, the optimal path-planning problem of the mean longitude is solved, and the capture time of the mean longitude is greatly shortened. The two EWSK algorithms proposed in this paper have the advantages of small calculation amount, optimal fuel consumption, high precision and strong stability, which have good engineering application value.

Comprehensive Assessment of BDS-2 and BDS-3 Precise Orbits Based on B1I/B3I and B1C/B2a Frequencies from iGMAS

The BeiDou Global Navigation Satellite System (BDS), including the second generation (BDS-2) and the third generation (BDS-3), has been widely used in areas of positioning, navigation, and timing (PNT). One of the essential prerequisites for accurate PNT service is the precise satellite orbits of multi-frequency and multi-constellation BDS-2 and BDS-3 satellites. As usual, the precise orbit products can be obtained from analysis centers (ACs) of the international GNSS Service (IGS). The precise orbits can also be downloaded from the international GNSS Monitoring and Assessment System (iGMAS). Compared with the IGS ACs, the iGMAS can provide featured services such as satellite orbits based on the new B1C/B2a BDS signals. Considering the indispensability of the new signals, the performance of all BDS precise orbits from iGMAS needs to be known. However, there is no comprehensive assessment of BDS-2 and BDS-3 precise orbits based on B1I/B3II and B1C/B2a frequencies from iGMAS, especially for the period after the BDS entered the stable operation stage. In this paper, BDS-2/BDS-3 final (ISC), rapid (ISR), and ultra-rapid (ISU) products based on B1I/B3I and B1C/B2a frequencies from iGMAS are all assessed comprehensively. Specifically, at first, the precise orbits from iGMAS are compared with the ones from the IGS ACs. Based on this, the satellite laser ranging inspects the precise orbits from iGMAS. Finally, the orbit errors are discussed systematically by considering the beta and elongation angles. Using one year of data, the orbit accuracy of geostationary orbit, inclined geosynchronous orbit, and medium earth orbit (MEO) satellites can almost reach meter to decimeter level, decimeter to sub-decimeter level, and centimeter level, respectively, where the ISC products are the best. The ISC, ISR, and ISU products based on B1I/B3I frequencies are generally better than the ones based on B1C/B2a frequencies. Additionally, according to the SLR data, the results show that the accuracy of precise orbits of BDS-3 is better than that of BDS-2. The mean values of orbit biases of BDS-3 MEO satellites are approximately 2.88 cm. In addition, the orbit errors are related to the beta angle and elongation angle to some extent, and the manufacturers may also have an influence on the orbit errors.

Refinement of GRACE‐FO Kinematic Orbit by Combining Least Squares Method and Orbital Dynamic Model

Gravity Recovery and Climate Experiment Follow‐On (GRACE‐FO) satellites are used to map the gravity field of the Earth. The orbit accuracy of GRACE‐FO depends on the quality of on‐board GPS data, which is key factor affecting GRACE‐FO mission execution. To improve the orbit accuracy of GRACE‐FO, a dynamical method was developed to reprocess kinematic orbits. First, with known kinematic orbits, the least squares method was used to estimate the initial state and dynamical parameters of GRACE‐FO orbits. Second, during data processing, orbit coordinates containing outliers were deleted. Finally, GRACE‐FO dynamical orbits with high accuracy were determined by combining initial state and dynamical parameters. To assess the orbit accuracy, dynamical and kinematic orbits were compared with Jet Propulsion Laboratory (JPL) orbits. Three‐dimensional root‐mean‐square (3D‐RMS) results show dynamical and kinematic orbit accuracy of 6.3 and 9.5 cm for GRACE‐FO‐C and 6.6 and 9.7 cm for GRACE‐FO‐D, achieving improvements of 33.68% and 31.96%, respectively. The RMS of satellite laser range (SLR) residuals was about 4.1 and 5.1 cm for GRACE‐FO‐C dynamical and kinematic orbit accuracy, and about 4.2 and 5.4 cm for GRACE‐FO‐D.

Improved GPS-Based Single-Frequency Orbit Determination for the CYGNSS Spacecraft Using GipsyX

<h3>Summary</h3> This paper presents methods for the precise orbit determination (POD) of a satellite in the CYGNSS constellation based on available single-frequency GPS code and carrier measurements. The contributions include the development and evaluation of procedures for single-frequency POD with GipsyX, improvement of CYGNSS orbit knowledge, and an assessment of its final accuracy. Ionospheric effects are mitigated using the GRAPHIC processing method, and spacecraft multipath effects are calibrated with an azimuth/elevation-dependent antenna calibration map. The method is demonstrated using comparable data from the GRACE mission, from which we infer the expected accuracy of the CYGNSS results. Processing more than 170 days of data from each mission, a 1<i>σ</i> CYGNSS orbit accuracy of 2.8 cm radial, 2.4 cm cross-track, and 6 cm in-track is demonstrated. We expect that achieving this level of performance will expand the set of future scientific investigations that can be undertaken using satellites equipped with single-frequency GNSS.