Orbit Accuracy Research Articles

Sentinel-1A – First precise orbit determination results

Sentinel-1A is the first satellite of the European Copernicus programme. Equipped with a Synthetic Aperture Radar (SAR) instrument the satellite was launched on April 3, 2014. Operational since October 2014 the satellite delivers valuable data for more than two years. The orbit accuracy requirements are given as 5cm in 3D. In order to fulfill this stringent requirement the precise orbit determination (POD) is based on the dual-frequency GPS observations delivered by an eight-channel GPS receiver.The Copernicus POD (CPOD) Service is in charge of providing the orbital and auxiliary products required by the PDGS (Payload Data Ground Segment). External orbit validation is regularly performed by comparing the CPOD Service orbits to orbit solutions provided by POD expert members of the Copernicus POD Quality Working Group (QWG). The orbit comparisons revealed systematic orbit offsets mainly in radial direction (approx. 3cm). Although no independent observation technique (e.g. DORIS, SLR) is available to validate the GPS-derived orbit solutions, comparisons between the different antenna phase center variations and different reduced-dynamic orbit determination approaches used in the various software packages helped to detect the cause of the systematic offset. An error in the given geometry information about the satellite has been found. After correction of the geometry the orbit validation shows a significant reduction of the radial offset to below 5mm. The 5cm orbit accuracy requirement in 3D is fulfilled according to the results of the orbit comparisons between the different orbit solutions from the QWG.

Variation of Static-PPP Positioning Accuracy Using GPS-Single Frequency Observations (Aswan, Egypt)

Abstract Precise Point Positioning (PPP) is a technique used for position computation with a high accuracy using only one GNSS receiver. It depends on highly accurate satellite position and clock data rather than broadcast ephemeries. PPP precision varies based on positioning technique (static or kinematic), observations type (single or dual frequency) and the duration of collected observations. PPP-(dual frequency receivers) offers comparable accuracy to differential GPS. PPP-single frequency receivers has many applications such as infrastructure, hydrography and precision agriculture. PPP using low cost GPS single-frequency receivers is an area of great interest for millions of users in developing countries such as Egypt. This research presents a study for the variability of single frequency static GPS-PPP precision based on different observation durations.

Enhanced activity of the Southern Taurids in 2005 and 2015

The paper presents an analysis of Polish Fireball Network (PFN) observations of enhanced activity of the Southern Taurid meteor shower in 2005 and 2015. In 2005, between October 20 and November 10, seven stations of PFN determined 107 accurate orbits with 37 of them belonging to the Southern Taurid shower. In the same period of 2015, 25 stations of PFN recorded 719 accurate orbits with 215 orbits of the Southern Taurids. Both maxima were rich in fireballs which accounted to 17% of all observed Taurids. The whole sample of Taurid fireballs is quite uniform in the sense of starting and terminal heights of the trajectory. On the other hand a clear decreasing trend in geocentric velocity with increasing solar longitude was observed. Orbital parameters of observed Southern Taurids were compared to orbital elements of Near Earth Objects (NEO) from the NEODYS-2 database. Using the Drummond criterion $D'$ with threshold as low as 0.06, we found over 100 fireballs strikingly similar to the orbit of asteroid 2015 TX24. Several dozens of Southern Taurids have orbits similar to three other asteroids, namely: 2005 TF50, 2005 UR and 2010 TU149. All mentioned NEOs have orbital periods very close to the 7:2 resonance with Jupiter's orbit. It confirms a theory of a "resonant meteoroid swarm" within the Taurid complex that predicts that in specific years, the Earth is hit by a greater number of meteoroids capable of producing fireballs.

Accurate orbit propagation in the presence of planetary close encounters

We present an efficient strategy for the numerical propagation of small Solar System objects undergoing close encounters with massive bodies. The trajectory is split in several phases, each of them being the solution of a perturbed two-body problem. Formulations regularized with respect to different primaries are employed in two subsequent phases. In particular, we consider the Kustaanheimo-Stiefel regularization and a novel set of non-singular orbital elements pertaining to the Dromo family. In order to test the proposed strategy, we perform ensemble propagations in the Earth-Sun CR3BP using a variable step-size and order multi-step integrator and an improved version of Everhart's RADAU solver of 15th order. By combining the trajectory splitting with regularized equations of motion in short-term propagations (one year), we gain up to six orders of magnitude in accuracy with respect to the classical Cowell's method for the same computational cost. Moreover, in the propagation of asteroid (99942) Apophis through its 2029 Earth encounter, the position error stays within 100 meters after 100 years. In general, as to improve the performance of regularized formulations, the trajectory must be split between 1.2 and 3 Hill radii from the Earth. We also devise a robust iterative algorithm to stop the integration of regularized equations of motion at a prescribed physical time. The results rigorously hold in the CR3BP, and similar considerations may apply when considering more complex models. The methods and algorithms are implemented in the NAPLES Fortran 2003 code, which is available online as a GitHub repository.

Rapid satellite capture by a space robot based on delay compensation

PurposeRapid satellite capture by a free-floating space robot is a challenge problem because of no-fixed base and time-delay issues. This paper aims to present a modified target capturing control scheme for improving the control performance.Design/methodology/approachFor handling such control problem including time delay, the modified scheme is achieved by adding a delay calibration algorithm into the visual servoing loop. To identify end-effector motions in real time, a motion predictor is developed by partly linearizing the space robot kinematics equation. By this approach, only ground-fixed robot kinematics are involved in the predicting computation excluding the complex space robot kinematics calculations. With the newly developed predictor, a delay compensator is designed to take error control into account. For determining the compensation parameters, the asymptotic stability condition of the proposed compensation algorithm is also presented.FindingsThe proposed method is conducted by a credible three-dimensional ground experimental system, and the experimental results illustrate the effectiveness of the proposed method.Practical implicationsBecause the delayed camera signals are compensated with only ground-fixed robot kinematics, this proposed satellite capturing scheme is particularly suitable for commercial on-orbit services with cheaper on-board computers.Originality/valueThis paper is original as an attempt trying to compensate the time delay by taking both space robot motion predictions and compensation error control into consideration and is valuable for rapid and accurate satellite capture tasks.

Benefits of satellite clock modeling in BDS and Galileo orbit determination

In the process of Global Navigation Satellite Systems (GNSS) satellite orbit determination, satellite clocks are typically estimated as epoch-wise white noise in addition to the satellite orbit parameters. This results in high correlation between the satellite clock estimates and the satellite orbits, especially the radial component. In this paper, an appropriate clock model is proposed to constrain the satellite clock estimates in order to improve the accuracy of satellite orbits. SLR residuals and Day Boundary Discontinuities (DBDs) were used to assess the orbit quality. The benefits of satellite clock modeling in BDS and Galileo orbit determination is validated by experimental data sets. The results show that for satellites equipped with highly stable clocks, employing an appropriate linear model constraint for the clock estimates in orbit determination can result in an improved orbit consistency as well as accuracy. In detail, for Medium Earth Orbit (MEO) satellites, C12, C14, E11, E12 and E19, the improvements of DBDs range from 10% to 20%. Furthermore, the Standard Deviation (STD) of Satellite Laser Ranging (SLR) residuals were improved up to 30% for the Galileo satellites (using a passive hydrogen maser clock).

HST Proper Motions of Distant Globular Clusters: Constraining the Formation & Mass of the Milky Way

AbstractProper motions (PMs) are required to calculate accurate orbits of globular clusters (GCs) in the Milky Way (MW) halo. We present our HST program to create a PM database for 20 GCs at distances of RGC = 10–100 kpc. Targets are discussed along with PM measurement methods. We also describe how our PM results can be used for Gaia as an external check, and discuss the synergy between HST and Gaia as astrometric instruments in the coming years.

Robust finite time second-order sliding mode stabilization control for floated inertial platform

High precision inertial navigation system is one of the main ways to improve the accuracy of the satellite orbit and to prolong life. In order to solve the suspension stabilization problem of the floated inertial navigation platform (or the floated platform), a robust finite time second-order sliding mode control scheme is proposed. This control method can guarantee the stability and rapidity of the system under the complex disturbances. Then, focusing on the design problem of the observer, the nonlinear extended state observer is designed to enhance the adaptability for random uncertainty and to improve the robust performance and the stabilization accuracy of the controller. Finally, the stability and convergence of the control system are proven by the homogeneous theory. The simulation results demonstrate that the proposed method can eliminate the input chattering of the sliding mode control efficiently and the high precision inertial stabilization of the floated inertial platform is realized with the accuracy higher than [Formula: see text].

Precise Orbit Solution for Swarm Using Space-Borne GPS Data and Optimized Pseudo-Stochastic Pulses

Swarm is a European Space Agency (ESA) project that was launched on 22 November 2013, which consists of three Swarm satellites. Swarm precise orbits are essential to the success of the above project. This study investigates how well Swarm zero-differenced (ZD) reduced-dynamic orbit solutions can be determined using space-borne GPS data and optimized pseudo-stochastic pulses under high ionospheric activity. We choose Swarm space-borne GPS data from 1–25 October 2014, and Swarm reduced-dynamic orbits are obtained. Orbit quality is assessed by GPS phase observation residuals and compared with Precise Science Orbits (PSOs) released by ESA. Results show that pseudo-stochastic pulses with a time interval of 6 min and a priori standard deviation (STD) of 10−2 mm/s in radial (R), along-track (T) and cross-track (N) directions are optimized to Swarm ZD reduced-dynamic precise orbit determination (POD). During high ionospheric activity, the mean Root Mean Square (RMS) of Swarm GPS phase residuals is at 9–11 mm, Swarm orbit solutions are also compared with Swarm PSOs released by ESA and the accuracy of Swarm orbits can reach 2–4 cm in R, T and N directions. Independent Satellite Laser Ranging (SLR) validation indicates that Swarm reduced-dynamic orbits have an accuracy of 2–4 cm. Swarm-B orbit quality is better than those of Swarm-A and Swarm-C. The Swarm orbits can be applied to the geomagnetic, geoelectric and gravity field recovery.

Improving BDS integer ambiguity resolution using satellite-induced code bias correction for precise orbit determination

Successful resolution of integer ambiguity over long baselines is a key to improve the accuracy of precise orbit determination for global navigation satellite system satellites. The satellite-induced code bias (SCB) found in BDS signals severely prevents the BDS integer ambiguity resolution (AR) of long baselines. We present BDS AR using satellite-induced code bias correction for precise orbit determination. The impacts of the BDS SCB on double-difference AR for different baseline length and satellite type are first assessed. About one month of BDS tracking data collected from the MGEX and Fugro network are processed for precise orbit determination using independent single-system method. The results of orbit overlap comparison and satellite laser ranging (SLR) validation suggest that the SCB has no obvious impacts on BDS float solutions; however, it shows significant implications on ambiguity-fixed solutions, especially for MEO satellites and long baselines. When applying the SCB correction model to BDS AR, the 3D mean RMS of overlapping orbit are reduced from 14.02 to 10.46 cm for IGSO and from 10.97 to 6.89 cm for MEO satellite, with the improvement of 25.4 and 37.2%. The contribution of AR with SCB correction on orbit accuracy of BDS could reach the level close to that of GPS. SLR residuals also confirm the improvement.

Versatile time-dependent spatial distribution model of sun glint for satellite-based ocean imaging

We propose a versatile model to describe the time-dependent spatial distribution of sun glint areas in satellite-based wave water imaging. This model can be used to identify whether the imaging is affected by sun glint and how strong the glint is. The observing geometry is calculated using an accurate orbit prediction method. The Cox-Munk model is used to analyze the bidirectional reflectance of wave water surface under various conditions. The effects of whitecaps and the reflectance emerging from the sea water have been considered. Using the moderate resolution atmospheric transmission radiative transfer model, we are able to effectively calculate the sun glint distribution at the top of the atmosphere. By comparing the modeled data with the medium resolution imaging spectrometer image and Feng Yun 2E (FY-2E) image, we have proven that the time-dependent spatial distribution of sun glint areas can be effectively predicted. In addition, the main factors in determining sun glint distribution and the temporal variation rules of sun glint have been discussed. Our model can be used to design satellite orbits and should also be valuable in either eliminating sun glint or making use of it.

Classification of Meteorological Satellite Ground System Applications

Meteorological satellite ground application system carries a large number of applications. These applications deal with a variety of tasks. In order to classify these applications according to the resource consumption and improve the rational allocation of system resources, this paper introduces several application analysis algorithms. Firstly, the requirements are abstractly described, and then analyzed by hierarchical clustering algorithm. Finally, the benchmark analysis of resource consumption is given. Through the benchmark analysis of resource consumption, we will give a more accurate meteorological satellite ground application system.

Evolution of the Selenopotential Model and Its Effects on the Propagation Accuracy of Orbits around the Moon

The current work analyzes the effect of applying different selenopotential models to the propagation of a lunar orbiting spacecraft. A brief evolution history of the selenopotential model is first presented; then, four representative selenopotential models are selected for force modeling. Expected propagation errors are presented with respect to three different circular polar orbits around the Moon. As a result, an expected but rather significant number of orbit propagation errors are discovered. Compared to the solutions obtained using the GRAIL1500E model, the overall 3D propagation errors for a 4-day period could reach up to several tens of kilometers (50 km altitude case with the GLGM2 model) and up to several hundreds of meters (50, 100, and 200 km altitude cases even with the GRAIL660B model). For each different orbiter’s altitude, the appropriate ranges of the degree and order of the gravitational harmonic coefficients are also suggested to yield the best propagation performances with respect to the performance obtained with the full harmonic coefficients using the GRAIL1500E model. The results of the current work are expected to serve as practical guidelines for the field of system budget analysis, mission design, mission operations, and the analysis of scientific results.

Centralized autonomous orbit determination of Beidou navigation satellites with inter-satellite link measurements: preliminary results

Autonomous orbit determination is the process by which the orbit parameters of navigation satellites are estimated onboard using Inter-Satellite Link (ISL) measurements. In this contribution, autonomous orbit determination experiments using ISL measurements in a centralized mode of the new-generation Beidou navigation satellites are conducted. The mathematical formulation and the processing method of the dual one-way measurements are addressed as well as the main feathers of the ISL measurements are introduced. It is concluded that the ISL ranging data are high-precision measurements. The centralized autonomous orbit determination is processed in a batch mode. The average value of ISL measurements residuals is within 1.0 cm, standard deviation of ISL measurements residuals is within 10.0 cm and the standard deviation of the estimated ISL hardware delays is within 0.2 ns. The orbital accuracy is assessed by overlap comparison, User Equivalent Ranging Error and Satellite Laser Ranging (SLR) residuals. The radial overlap differences of the autonomous orbits are less than 6.0 cm and 24 h predicted orbital radial overlap differences less than 10.0 cm. The User Equivalent Ranging Error of 24 h predicted autonomous orbits is about 0.43 m and is better than the 24 h predicted L-band orbits at the 0.76 m level. The SLR residuals for the autonomous orbits are less than 10.0 cm. The ground anchor station which observes the constellation with ISL is important to maintain the Earth-Fixed-Frame and avoid the uncertainties of the entire constellation orientation. The influence of the ground station observation time span on autonomous orbit accuracy is also discussed. Even if the cutoff elevation of the ground anchor station is less than 60°, the radial accuracy of the autonomous orbits and 24 h predicted orbits is still better than 10.0 cm and three-dimensional orbit accuracy better than 1.5 m.

Model improvements and validation of TerraSAR-X precise orbit determination

The radar imaging satellite mission TerraSAR-X requires precisely determined satellite orbits for validating geodetic remote sensing techniques. Since the achieved quality of the operationally derived, reduced-dynamic (RD) orbit solutions limits the capabilities of the synthetic aperture radar (SAR) validation, an effort is made to improve the estimated orbit solutions. This paper discusses the benefits of refined dynamical models on orbit accuracy as well as estimated empirical accelerations and compares different dynamic models in a RD orbit determination. Modeling aspects discussed in the paper include the use of a macro-model for drag and radiation pressure computation, the use of high-quality atmospheric density and wind models as well as the benefit of high-fidelity gravity and ocean tide models. The Sun-synchronous dusk–dawn orbit geometry of TerraSAR-X results in a particular high correlation of solar radiation pressure modeling and estimated normal-direction positions. Furthermore, this mission offers a unique suite of independent sensors for orbit validation. Several parameters serve as quality indicators for the estimated satellite orbit solutions. These include the magnitude of the estimated empirical accelerations, satellite laser ranging (SLR) residuals, and SLR-based orbit corrections. Moreover, the radargrammetric distance measurements of the SAR instrument are selected for assessing the quality of the orbit solutions and compared to the SLR analysis. The use of high-fidelity satellite dynamics models in the RD approach is shown to clearly improve the orbit quality compared to simplified models and loosely constrained empirical accelerations. The estimated empirical accelerations are substantially reduced by 30% in tangential direction when working with the refined dynamical models. Likewise the SLR residuals are reduced from $$-3\,\pm \,17$$ to $$2\,\pm \,13$$ mm, and the SLR-derived normal-direction position corrections are reduced from 15 to 6 mm, obtained from the 2012–2014 period. The radar range bias is reduced from $$-10.3$$ to $$-6.1$$ mm with the updated orbit solutions, which coincides with the reduced standard deviation of the SLR residuals. The improvements are mainly driven by the satellite macro-model for the purpose of solar radiation pressure modeling, improved atmospheric density models, and the use of state-of-the-art gravity field models.

Pre-DECIGO can get the smoking gun to decide the astrophysical or cosmological origin of GW150914-like binary black holes

Pre-DECIGO consists of three spacecraft arranged in an equilateral triangle with 100km arm lengths orbiting 2000km above the surface of the earth. It is hoped that the launch date will be in the late 2020s. Pre-DECIGO has one clear target: binary black holes (BBHs) like GW150914 and GW151226. Pre-DECIGO can detect $\sim 30M_\odot-30M_\odot$ BBH mergers up to redshift $z\sim 30$. The cumulative event rate is $\sim 1.8\times 10^{5}\,{\rm events~yr^{-1}}$ in the Pop III origin model of BBHs like GW150914, and it saturates at $z\sim 10$, while in the primordial BBH (PBBH) model, the cumulative event rate is $ \sim 3\times 10^{4}\,{\rm events~ yr^{-1}}$ at $z=30$ even if only $0.1\%$ of the dark matter consists of PBHs, and it is still increasing at $z=30$. In the Pop I/II model of BBHs, the cumulative event rate is $(3-10)\times10^{5}\,{\rm events~ yr^{-1}}$ and it saturates at $z \sim 6$. We present the requirements on orbit accuracy, drag free techniques, laser power, frequency stability, and interferometer test mass. For BBHs like GW150914 at 1Gpc, SNR$\sim 90$ is achieved with the definition of Pre-DECIGO in the $0.01-100$Hz band. Pre-DECIGO can measure the mass spectrum and the $z$-dependence of the merger rate to distinguish various models of BBHs like GW150914. Pre-DECIGO can also predict the direction of BBHs at $z=0.1$ with an accuracy of $\sim 0.3\,{\rm deg}^2$ and a merging time accuracy of $\sim 1$s at about a day before the merger so that ground-based GW detectors further developed at that time as well as electromagnetic follow-up observations can prepare for the detection of merger in advance. For intermediate mass BBHs at a large redshift $z > 10$, the QNM frequency after the merger can be within the Pre-DECIGO band so that the ringing tail can also be detectable to confirm the Einstein theory of general relativity with SNR$\sim 35$. [abridged]

Status and perspectives of the VEPP-2000

The electron-positron collider VEPP-2000 operates at BINP from 2010 year. The application of round colliding beams concept along with the accurate orbit and lattice correction yielded the high peak luminosity of 1.2 × 1031 cm−2 s−1 at 500MeV. The peak luminosity limited only by beam-beam effects, while average luminosity–by present lack of positrons in whole energy range of 160–1000 MeV. To perform high luminosity at high energies the top-up injection is needed. At present new electron and positron injection complex at BINP is commissioned and ready to feed VEPP-2000 collider with intensive beams with energy of 450MeV.

Real-time kinematic positioning of LEO satellites using a single-frequency GPS receiver

Due to their low cost and low power consumption, single-frequency GPS receivers are considered suitable for low-cost space applications such as small satellite missions. Recently, requirements have emerged for real-time accurate orbit determination at sub-meter level in order to carry out onboard geocoding of high-resolution imagery, open-loop operation of altimeters and radio occultation. This study proposes an improved real-time kinematic positioning method for LEO satellites using single-frequency receivers. The C/A code and L1 phase are combined to eliminate ionospheric effects. The epoch-differenced carrier phase measurements are utilized to acquire receiver position changes which are further used to smooth the absolute positions. A kinematic Kalman filter is developed to implement kinematic orbit determination. Actual flight data from China small satellite SJ-9A are used to test the navigation performance. Results show that the proposed method outperforms traditional kinematic positioning method in terms of accuracy. A 3D position accuracy of 0.72 m and 0.79 m has been achieved using the predicted portion of IGS ultra-rapid products and broadcast ephemerides, respectively.

Analytical representations of precise orbit predictions for Earth orbiting space objects

Accurate orbits of Earth orbiting space objects are usually generated from an orbit determination/prediction process using numerical integrators, and presented to users in a tabulated form or a state vector including force model parameters. When dealing with hundreds of thousands of space objects such as in the space conjunction assessment, the memory required for the tabulated orbits or the computing time for propagating orbits using the state vector are both confronting to users. This paper presents two methods of analytically representing numerical orbits considering the accuracy, computing efficiency and memory. The first one is a two-step TLE-based method in which the numerical orbits are first fitted into a TLE set and then correction functions are applied to improve the position accuracy. In the second method, the orbit states are represented in equinoctial elements first, and then again correction functions are applied to reduce the position errors. Experiments using six satellite laser ranging (SLR) satellites and 12 debris objects with accurate orbits show that both methods can represent the accurate orbits over 5days in an accuracy of a few dozens of meters for the circular orbits and several hundred meters for the eccentric orbits. The computing time is similar to that using the NORAD TLE/SGP4 algorithm, and storage for the orbit elements and function coefficients is about 3–5KB. These features could make the two methods beneficial for the maintenance of orbit catalog of large numbers of space objects.

Pre-DECIGO can get the smoking gun to decide the astrophysical or cosmological origin of GW150914-like binary black holes

Pre-DECIGO consists of three spacecraft arranged in an equilateral triangle with 100km arm lengths orbiting 2000km above the surface of the earth. It is hoped that the launch date will be in the late 2020s. Pre-DECIGO has one clear target: binary black holes (BBHs) like GW150914 and GW151226. Pre-DECIGO can detect $\sim 30M_\odot-30M_\odot$ BBH mergers up to redshift $z\sim 30$. The cumulative event rate is $\sim 1.8\times 10^{5}\,{\rm events~yr^{-1}}$ in the Pop III origin model of BBHs like GW150914, and it saturates at $z\sim 10$, while in the primordial BBH (PBBH) model, the cumulative event rate is $ \sim 3\times 10^{4}\,{\rm events~ yr^{-1}}$ at $z=30$ even if only $0.1\%$ of the dark matter consists of PBHs, and it is still increasing at $z=30$. In the Pop I/II model of BBHs, the cumulative event rate is $(3-10)\times10^{5}\,{\rm events~ yr^{-1}}$ and it saturates at $z \sim 6$. We present the requirements on orbit accuracy, drag free techniques, laser power, frequency stability, and interferometer test mass. For BBHs like GW150914 at 1Gpc, SNR$\sim 90$ is achieved with the definition of Pre-DECIGO in the $0.01-100$Hz band. Pre-DECIGO can measure the mass spectrum and the $z$-dependence of the merger rate to distinguish various models of BBHs like GW150914. Pre-DECIGO can also predict the direction of BBHs at $z=0.1$ with an accuracy of $\sim 0.3\,{\rm deg}^2$ and a merging time accuracy of $\sim 1$s at about a day before the merger so that ground-based GW detectors further developed at that time as well as electromagnetic follow-up observations can prepare for the detection of merger in advance. For intermediate mass BBHs at a large redshift $z > 10$, the QNM frequency after the merger can be within the Pre-DECIGO band so that the ringing tail can also be detectable to confirm the Einstein theory of general relativity with SNR$\sim 35$. [abridged]