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In all Global Navigation Satellite Systems (GNSS) applications, the determination of the satellite orbits is an important task. In this study, we present the equations given in the Interface Specification Document of GPS and the Runge-Kutta method in the computation of the position P, velocity V, and acceleration A of the GPS satellites using the broadcast ephemeris. The definition of the differential equation describing the GPS satellite's motion has enabled us to introduce the Runge-Kutta method in the GPS orbit computation; this method uses the initial conditions determined in this study from the Keplerian elements provided in the broadcast ephemeris files. The Lagrange interpolation method is used for comparison of the results, where the vectors P, V, and A are estimated using the precise ephemeris. The difference not exceeding 2.4 m was obtained in the X, Y, and Z axes during seven days on the position of the GPS satellite number 9 tested in this study. In velocity and acceleration, the difference is about a few mm/s and mm/s2, respectively. [ABSTRACT FROM AUTHOR]

GNSS station movements as an indicator of the movement of the Earth's crust are determined by many researchers with the use of various position and trend determination methods. One of such methods is PPP method which allows the determination of a trend for the station without a correlation (direct determination of the position of each station separately). To achieve accuracy comparable with relative positioning, there is the need to use external, high-precision data or models (e.g. precise satellite orbits and clocks, ionosphere and troposphere models, etc.) while the PPP method is applied. The main purpose of the presented research is preliminary analyses of the results of processing daily GPS observations from permanent stations with the use of the PPP method. Daily GPS observational data in RINEX format have been acquired from a total of nine selected GNSS permanent stations from the Polish ASG EUPOS and the Ukrainian UA-EUPOS/ZAKPOS systems. As external data for PPP solutions JPL products have been used. A seven-year time series was created for each station. [ABSTRACT FROM AUTHOR]

In satellite geodesy, the motion of artificial satellites has a crucial importance and the satellite's position is the core point in the geodetic network. The simplicity of the broadcast ephemeris model directly determines the rate and efficiency of real-time navigation and positioning. GNSS broadcast message is transmitted in ECEF system either (GLONASS) or are Keplerian-like orbital elements (GPS, BeiDou, Galileo). The main aim of this paper is to describe the magnitude of Keplerian elements and correction coefficients of the navigational satellite changes based on a GPS satellite. The author examines six Keplerian elements and six correction coefficients for three different intervals: 2-hour, 1-day and 5-day intervals for periods of 9 days, a year and 10 years respectively. The analysis shows the varying behaviour of the time-series of the analysed components on the basis of the on-board GPS message, both random-like and repetitive (seasonal) trajectory time series. [ABSTRACT FROM AUTHOR]

Abstract Classical planetary ephemeris construction comprises three major steps which are to be performed iteratively: numerical integration of coupled equations of motion of a multi-body system (propagator step), reduction of observations (reduction step), and optimization of model parameters (adjustment step). In future, this approach may become challenged by further refinements in force modeling (e.g. inclusion of much more significant minor bodies than in the past), an ever-growing number of planetary observations (e.g. the vast amount of spacecraft tracking data), and big data issues in general. In order to circumvent the need for both the inversion of normal equation matrices and the determination of partial derivatives, and to prepare the ephemeris for applications apart from stand-alone solar-system planetary orbit calculations, here we propose an alternative ephemeris construction method. The main idea is to solve it as an optimization problem by straightforward direct evaluation of the whole set of mathematical formulas, rather than to solve it as an inverse problem with all its tacit mathematical assumptions and potential numerical difficulties. The usual gradient search is replaced by a stochastic search, namely an evolution strategy, the latter of which is perfect for the exploitation of parallel computing capabilities. Furthermore, this new approach allows for multi-criteria optimization and time-varying optima. These issues will become important in future once ephemeris construction is just one part of even larger optimization problems, e.g. the combined and consistent determination of a generalized physical state (orbit, size, shape, rotation, gravity, ...) of celestial bodies (planets, satellites, asteroids, or comets), and/or if one seeks near real-time solutions. Here, we outline the general idea and exemplarily optimize high-correlated asteroidal ring model parameters (total mass and heliocentric radius), and individual asteroid masses, based on simulated observations. [ABSTRACT FROM AUTHOR]

This paper provides analyses of the accuracy and convergence time of the PPP method using GPS systems and different IGS products. The official IGS products: Final, Rapid and Ultra Rapid as well as MGEX products calculated by the CODE analysis centres were used. In addition, calculations with weighting function of the observations were carried out, depending on the elevation angle. The best results were obtained for CODE products, with a 5-minute interval precision ephemeris and precise corrections to satellite clocks with a 30-second interval. For these calculations the accuracy of position determination was at the level of 3 cm with a convergence time of 44 min. Final and Rapid products, which were orbit with a 15-minute interval and clock with a 5 minute interval, gave very similar results. The same level of accuracy was obtained for calculations with CODE products, for which both precise ephemeris and precise corrections to satellite clocks with the interval of 5 minutes. For these calculations, the accuracy was 4 cm with the convergence time of 70 min. The worst accuracy was obtained for calculations with Ultra-rapid products, with an interval of 15 minutes. For these calculations, the accuracy was 10 cm with a convergence time of 120 min. The use of the weighting function improved the accuracy of position determination in each case, except for calculations with Ultra-rapid products. The use of this function slightly increased the convergence time, in addition to the CODE calculation, which was reduced to 9 min. [ABSTRACT FROM AUTHOR]

Abstract In this paper, natural deep space satellite constellations designs in the Earth-Moon system are presented, where the underlying dynamics model is the Elliptic Restricted Three-Body Problem (ERTBP) model. The ERTBP has taken into account the eccentricity of the Earth-Moon system. Therefore, the generated motion will be more realistic than that in the Circular Restricted Three-Body Problem (CRTBP) due to the relatively large eccentricity of the Earth-Moon system (about 0.0554). First, a type of strictly periodic orbit, Multi-revolution Elliptic Halo (ME-Halo) orbit, around the L 2 libration point in the Earth-Moon ERTBP is presented, generated through the continuation method starting from the conventional Halo orbits in the CRTBP. It is discovered that there are only a limited number of ME-Halo orbits that are practically useful, which restricts the mission design of a natural satellite constellation. Next, four different types of constellations consisting of the ME-Halo orbit, which are the focus on this paper, are presented and discussed. These configurations exist in the ERTBP and are nonautonomous. At last, the nominal ME-Halo orbit is analyzed with respect to the high-fidelity ephemeris model, which preliminarily validates that the nominal ME-Halo orbit is suitable for deep space constellation design, as it approximates the real Earth-Moon system with good accuracy. The results in this paper provide new natural satellite constellation options in the Earth-Moon system, which have different features through combining various ME-Halo orbits. Highlights • We propose 4 natural satellite constellations configurations in Earth-Moon system. • The Elliptic Restricted Three-Body Problem (ERTBP) model is used. • Basic orbits are multi-revolution Elliptic Halo orbits in the Earth-Moon ERTBP. • Configurations with specific parameters can provide 100% coverage to lunar poles. • Particular features of the configuration remain in the high-accuracy ephemeris model. [ABSTRACT FROM AUTHOR]

The reduction of the spacecraft's (SC) asymptotic velocity and the radiation hazard are really main problems for low-Delta V cost Jovian moons missions: orbiters and landers. Algorithm to overcome the "obstruction of solo disturbances" for one-body flybys around some Jovian moon with using full ephemeris with two coupled CR3BP engaging has been implemented. The region where the total received radiation dose (TID) exceeds is skirted along the upper section of Tisserand-Poincare graph. Withal low-cost reduction of the SC asymptotic velocity is required for rendezvous with small body. It became possible to find such scenarios when restricted three body problem is transformed into the two-coupled CR3BP models and full ephemeris model. Advanced Multi-Tisserand coordinates has been exploit for parametric passage into this region. With their help it is shown that the "cross" gravity assists at the early stage of reduction of the orbital period are required. As a result, a reasonable increase in the duration of the mission can be exchanged on a sharp decline TID and found "comfortable" (in TID) rounds scenario in the system (less than 70 krad for standard SC protection 8-10 mm Al). This will provide significant gains in the payload for spacecraft missions in Jovian system and systems of other outer planets and improving the reliability of their scientific instruments. [ABSTRACT FROM AUTHOR]

Abstract In this paper, low-energy transfers of asteroids to long-term capture (LTC) in the Earth-Moon system (EMS) based on the concept of short-term capture (STC) are constructed and analyzed. Stable LTC orbits distributed in three regions are investigated via the finite-time Lyapunov exponent. Then, five types of low-energy transfers to different target LTC orbits are constructed and discussed. Two kinds of design strategies of low-energy transfers starting from STC orbits and LTC orbits are proposed, respectively. Numerical results indicate that fuel costs of low-energy transfers to stable LTC orbits in the EMS are less than 50 m/s; fuel costs of low-energy transfers to unstable libration point orbits are less than 5 m/s. Taking asteroid 2006 RH120 as an example, a low-energy transfer is constructed in the ephemeris model. The design methods of low-energy transfers we proposed in this paper can be applied to the asteroid redirect missions. Highlights • Long-term capture of asteroids in the Earth-Moon system is studied. • Low-energy transfers from short-term capture to long-term capture are designed. • Five types of low-energy transfers to different target LTC orbits are constructed. • Our results can be applied to the asteroid redirect missions in the future. [ABSTRACT FROM AUTHOR]

Finding one's geographical position (fix) without the use of a Global Navigation Satellite System (GNSS), which was common place before the establishment of the latter, could be tedious and/or inaccurate. Apart from sound knowledge of spherical trigonometry and navigational methods, it also requires the knowledge of the navigator's approximate or assumed position, the use of the current year's celestial bodies' ephemeris (Nautical Almanac), and graphical methods (Lines of Position – LOP) which sometimes can prove wanting in accuracy and/or challenging for the unaccustomed user. The method proposed here is based on sight reduction from two celestial bodies, and directly calculates the geographical position, both for stationary and moving observers ("running fix") using easily available modern programmable calculating devices, without the need of the assumed position, graphical methods (LOP) or the current year's ephemeris, hence the term "stand-alone". This self-contained method is implemented by the author in a software application, which can be easily used in a portable computer (for example, a smartphone). The results are considered satisfactorily accurate. [ABSTRACT FROM AUTHOR]

In this paper, the trajectory correction maneuver (TCM) problem of several lunar flyby transfers is investigated in the ephemeris model. The error analysis indicates that the state error of a transfer orbit will be enlarged by lunar flyby; hence, a TCM must be executed before lunar flyby. A TCM approach based on the shooting method is proposed in the ephemeris model. This method is then applied to design the TCM of two kinds of lunar flyby transfers: transfers between the sun-Earth/moon libration point orbits, and transfers from the Earth to the sun-Earth/moon libration point orbits. Some regions with abnormally large fuel costs are found and explained by the numerical method. Furthermore, several TCM strategies of lunar flyby transfers under practical constraints are presented and discussed. Finally, the effect of the navigation errors on the TCM problem is investigated. [ABSTRACT FROM AUTHOR]

Abstract: A catalogue of equatorial coordinates and magnitudes for 2162 asteroids and 11 comets was compiled based on the results of processing of digitized photographic observations of the northern sky performed in 1981-1985. The positions were compared with the JPL DE431 ephemeris. The mean (O - C)αδ values for all positions obtained in this comparison are -0.08″ and 0.04″, and their root-mean-square errors are 0.70″ and 0.64″ in α and δ, respectively. It was found that the observations of 54 asteroids predate their discoveries, and the observations of four of them are the earliest known for these asteroids. [ABSTRACT FROM AUTHOR]

An optical tracking network, the Optical Wide-field patroL Network (OWL-Net), has been developed to maintain the orbital ephemeris of 11 domestic low Earth orbit satellites. The schedule overlapped events were occurred in the scheduling of the OWL-Net with reduction of the optical observation chances. A short-arc observation strategy for the OWL-Net was tested to reduce schedule overlapped events with the optical observation simulation and the orbit determination. In the full-scale optical observation simulation from January 2014 to December 2016, the most frequent overlapped events were occurred 127, 132, and 116 times in the 4th, 34th, and 18th weeks of 2014, 2015, and 2016, respectively. The average number of overlapped event for three years was over 10% for the whole observation chances of five stations. Consequently, the short-arc observation strategy reduced the schedule overlapped events for every observation target of the OWL-Net. In case of the 5 s and 10 s cases, the most schedule overlapped events were removed. The test results of the orbit determination results show that the most maximum orbit prediction errors after seven days are maintained at <10 km in the in-track direction for the short-arc observation simulations. The results demonstrate that the short-arc optical observation strategy is more optimal to maintaining the accuracy of orbital ephemeris with more observation chances. [ABSTRACT FROM AUTHOR]

The Chinese Mars exploration mission is planned to be launched in 2020, which includes an orbiter, a lander, and a rover. High precision Martian ephemeris is very important in Mars exploration, especially for the Martian orbit insertion and the Martian lander/rover landing. In this paper, we used simulation data to analyze the short-term prediction accuracy of the Martian ephemeris. The simulation results show that the accuracy of Mars position is expected to be better than 50 m for 180-day prediction, when 90-150 days’ range measurements are used to estimate the orbit of the Mars. Range bias affects the prediction accuracy and the arc length for estimation is limited. The prediction accuracy will improve with higher orbit, and the orbit error of probes has an obvious effect on the prediction accuracy of the Martian ephemeris. [ABSTRACT FROM AUTHOR]

Although Earth’s surface parameters obtained from satellite data have become more and more precise, it is still difficult to guarantee temporal consistency and spatial continuity for large-scale geoscience phenomena. Developing new Earth observation platforms is a feasible way to improve the consistency and continuity of such data. As the planet’s only natural satellite, the Moon has special advantages as a platform for observing Earth, including long lifetime, whole disk view, tectonic stability and unique perspective. After presenting the observation geometry constructed by using the ephemeris, this paper mainly discusses the characteristics of a lunar platform and the proper Moon-based sensors, as well as the scientific objectives of Moon-based Earth observation. Solid Earth dynamics, the energy budget of Earth, Earth’s environmental elements and the Earth-space environment are four potential applications analysed in this paper. [ABSTRACT FROM AUTHOR]

To meet the requirements of different applications, the International Global Navigation Satellite System (GNSS) Service (IGS) has provided Global Positioning System (GPS) satellite ephemerides and clock products with different accuracy levels (final, rapid and ultra-rapid products). Comparison of Precise Point Positioning/Inertial Navigation System/Ultra Wideband (PPP/INS/UWB) tightly coupled positioning with different precise satellite ephemeris and clock products is made and corresponding data analysis is provided. Final, rapid and ultra-rapid products are applied in a PPP/INS/UWB integrated system. The field trajectories, position and velocity errors of the integrated system with different products are compared. The results indicate that PPP/INS/UWB tightly coupled positioning with final and rapid products achieves an accurate performance. Compared with the position resolution using final products, the position accuracy with the ultra-rapid products (observed half) is slightly reduced and the position accuracy with the ultra-rapid products (predicted half) has a 0·1–0·2 m reduction. The influence of precise satellite ephemeris and clock products is very minor for non-real-time positioning, relative to the accuracy of PPP/INS/UWB tightly coupled positioning. [ABSTRACT FROM AUTHOR]

Lunar IceCube is a 6U CubeSat that is designed to detect and observe lunar volatiles from a highly inclined orbit. This spacecraft, equipped with a low-thrust engine, is expected to be deployed from the upcoming Exploration Mission-1 vehicle. However, significant uncertainty in the deployment conditions for secondary payloads impacts both the availability and geometry of transfers that deliver the spacecraft to the lunar vicinity. A framework that leverages dynamical systems techniques is applied to a recently updated set of deployment conditions and spacecraft parameter values for the Lunar IceCube mission, demonstrating the capability for rapid trajectory design. [ABSTRACT FROM AUTHOR]

The maintenance of the nominal multirevolution elliptic halo orbit, whose special features can benefit mercurial explorations, is first investigated through Monte–Carlo simulations in the elliptic Sun–Mercury model, and then validated in the high-fidelity ephemeris model. The receding horizon control strategy solved by the indirect Radau pseudospectral method demonstrates that the orbit can be maintained robustly with respect to very large initial deviations. Moreover, the result proves that the elliptic Sun–Mercury model is an accurate approximation. [ABSTRACT FROM AUTHOR]

Receivers able to track satellites belonging to different GNSSs (Global Navigation Satellite Systems) are available on the market. To compute coordinates and velocities it is necessary to identify all the elements that contribute to interoperability of the different GNSSs. For example the timescales kept by different GNSSs have to be aligned. Receiver-specific biases, or firmware-dependent biases, need to be calibrated. The reference frame used in the representation of the orbits must be unique. In this paper we address the interoperability issues from the standpoint of a Single Point Positioning (SPP) user, i.e., using pseudoranges and broadcast ephemeris. The biases between GNSSs timescales and receiver-dependent biases are analyzed for a set of 31 MGEX (Multi-GNSS Experiment) stations over a time span of more than three years. Time series of biases between timescales of GPS (Global Positioning System), GLONASS (Global Navigation Satellite System), Galileo, BeiDou, QZSS (Quasi-Zenith Satellite System), SBAS (Satellite Based Augmentation System) andNAVIC (Navigation with Indian Constellation) are investigated, in addition to the identification of events like discontinuity of receiver-dependent biases due to firmware updating. The GPS broadcast reference frame is shown to be aligned to the one (IGS14) realized by the precise ephemeris of CODE (Center for Orbit Determination in Europe) to within 0.1 m and 2 milliarcsec, with values dependent on whether IIR-A, IIR-B/M or IIF satellite blocks are considered. Larger offsets are observed for GLONASS, up to 1 m for GLONASS K satellites. For Galileo the alignment of the broadcast orbit to IGS14/CODE is again at the 0.1 m and several milliarcsec level, with the FOC (Full Operational Capability) satellites slightly better than IOV (In Orbit Validation). For BeiDou an alignment of the broadcast frame to IGS14/CODE comparable to GLONASS is observed, regardless of whether IGSO (Inclined Geosynchronous Orbit) or MEO (Medium Earth Orbit) satellites are considered. For all satellites, position differences according to the broadcast ephemeris relative to IGS14/CODE orbits are projected to the radial, along-track and crosstrack triad, with the largest periodic differences affecting mostly the along track component. Sudden discontinuities at the level of up to 1 m and 2-3 ns are observed for the along-track component and the satellite clock, respectively. The time scales of GLONASS, Galileo, QZSS, SBAS and NAVIC are very closely aligned to GPS, with constant offsets depending on receiver type. The offset of the BeiDou time scale to GPS has an oscillatory pattern with peak-to-peak values up to 100 ns. To characterize receiver-dependent biases the average of six Septentrio receivers is taken as reference, and relative offsets of the other receiver types are investigated. These receiver-dependent biases may depend on the individual station, or for the same station on the update of the firmware. A detailed calibration history is presented for each multiGNSS station studied. [ABSTRACT FROM AUTHOR]

Millimetre-precise GNSS measurements may only be achieved by static relative (differential) positioning using a double-frequency receiver. This accuracy level is needed to address certain surveying and civil engineering issues. Relative measurements are performed using a single- or multi-network reference station, whose accuracy depends on a number of factors, such as the distance to the reference station, the session duration, the number of visible satellites, or ephemeris and clock errors. In this work, the author analyses the accuracy of static GNSS measurements according to the number of visible satellites, based on different minimal elevation cut-off angles. Each session was divided into three modes: GPS, GLONASS and hybrid GNSS (GPS+GLONASS). The final results were compared with the corresponding daily EPN solution at the observational epoch in order to determine their accuracy. [ABSTRACT FROM AUTHOR]

In the capture period of deep space exploration, three traditional celestial navigation methods including the direction, velocity, and distance measurements cannot completely meet the requirement of navigation accuracy due to ephemeris errors. To solve this problem, considering the fact that some impulses exist in solar light irradiance profile due to solar flares, we propose the solar flare time difference of arrival (TDOA) measurement method, which exploits these impulses to measure the position of the spacecraft. As the time of arrival (TOA) of solar flare cannot be predicted, we cannot use the solar flare TOA directly. The Mars light irradiance variation is related to the solar one, as the Mars light is the solar light filtered by the Martian atmosphere absorption filter. Based on this theory, the solar flare TDOA measurement method using direct and reflected light is developed. In this method, two solar flare TOAs are obtained by the spacecraft. One is from the sun directly. The other is the corresponding TOA reflected by Mars. Their difference is the TDOA measurement. In addition, we also propose two alternative schemes. One uses the solar light instead of flare if solar flares do not occur in the capture period, and the other adopts Phobos as the reflected point instead of Mars to solve the Martian atmospheric absorption. The traditional direction measurement-based navigation method can provide highly accurate navigation information at the tangential direction in the capture period. However, its accuracy at the radial direction is very low. Fortunately, the solar flare TDOA measurement method offsets this problem. To get highly accurate navigation information, the solar flare TDOA measurement and the Mars direction measurement are coupled into the solar flare TDOA/Mars direction integrated navigation system. We present simulation results that demonstrate the feasibility and effectiveness of the solar flare TDOA measurement method. Compared to the traditional direction measurement-based navigation method, the solar flare TDOA/Mars direction integrated navigation can provide higher positioning accuracy, especially the radial component. [ABSTRACT FROM PUBLISHER]

In this paper an algorithm is developed that combines the capabilities and advantages of several different astrodynamical models of increasing complexity. Splitting these models in a strict hierarchical order yields a clearer grasp on what is available. With the effort of developing a comprehensive model overhead, the equations for the spacecraft motion in simpler models can be readily obtained as particular cases. The proposed algorithm embeds the circular and elliptic restricted three-body problems, the four-body bicircular and concentric models, an averaged n -body model, and, at the top hierarchic ladder, the full ephemeris SPICE-based restricted n -body problem. The equations of motion are reduced to the assignment of 13 time-varying coefficients, which multiply the states and the gravitational potential to reproduce the proper vector field. This approach yields an efficient and quick way to check solutions for different dynamics and parameters. We show that in bottom-up applications, a gradual increase of model complexity benefits accuracy, the chances of success and the convergence rate of a continuation algorithm. Case studies are simple periodic orbits and low-energy transfers. [ABSTRACT FROM AUTHOR]

The BeiDou Navigation Satellite System (BDS) space constellation is composed of geostationary earth orbit (GEO), medium earth orbit (MEO), and inclined geosynchronous satellite orbit (IGSO) satellites, all of which adopt the Global Positioning System (GPS) broadcast ephemeris model of the United States of America (U.S.A). However, in the case of small eccentricity and small orbit inclination angle, the coefficient matrix is non-positive when fitting the broadcast ephemeris parameters due to the fuzzy definition of a few Keplerian orbit elements, thereby resulting in low precision or even failure. This study proposed a novel broadcast ephemeris model based on the second class of non-singular orbit elements. The proposed model can address the unsuitability of the classical broadcast ephemeris model in the condition of small eccentricity and small orbit inclination angle, and unify the broadcast ephemeris parameters user algorithm models of GEO, MEO, and IGSO. The proposed model is a 14-parameters broadcast ephemeris model constructed with the second class of non-singular orbit elements and the corresponding broadcast ephemeris parameters perturbation over time. Lastly, the proposed model was verified by precision orbit data generated by the Satellite Tool Kit (STK). Results show that the 14-parameters broadcast ephemeris model is suitable for the GEO, MEO, and IGSO satellites and has high fitting precision to fully meet the requirements of the BDS. Moreover, compared with the existing 16-parameters broadcast ephemeris model, two ephemeris parameters are decreased without reducing precision, thereby possibly saving communication resources. The proposed method provides a good prospect to optimize the design of the BDS broadcast ephemeris model. [ABSTRACT FROM AUTHOR]

In order to obtain high-precision CCD positions of Himalia, the sixth Jovian satellite, a total of 598 CCD observations have been obtained during the years 2015-2016. The observations were made by using the 2.4 and 1 m telescopes administered by Yunnan Observatories over 27 nights. Several factors that would influence the positional precision of Himalia were analysed, including the reference star catalogue used, the geometric distortion and the phase effect. By taking advantage of its unprecedented positional precision, the recently released catalogue Gaia Data Release 1 was chosen to match reference stars in the CCD frames of both Himalia and open clusters, whichwere observed for deriving the geometric distortion. The latest version of SOFA library was used to calculate the positions of reference stars. The theoretical positions of Himalia were retrieved from the Jet Propulsion Laboratory Horizons System that includes the satellite ephemeris JUP300, while the positions of Jupiter were based on the planetary ephemeris DE431. Our results showed that the means of observed minus computed (O-C) residuals are 0.071 and -0.001 arcsec in right ascension and declination, respectively. Their standard deviations are estimated at about 0.03 arcsec in each direction. [ABSTRACT FROM AUTHOR]

A Celestial Navigation System (CNS) is a feasible and economical autonomous navigation system for deep-space probes. Ephemeris errors have a great influence on the performance of CNSs during the Mars approach phase, but there are few research studies on this problem. In this paper, the analysis shows that the ephemeris error of Mars is slowly-varying, while the ephemeris error of Phobos and Deimos is periodical. The influence of the ephemeris errors of Mars and its satellites is analysed in relation to both the Sun-centred frame and the Mars-centred frame. The simulations show that the position error of a probe relative to the Sun caused by the Mars ephemeris error is almost equal to the ephemeris error itself, that the velocity error is affected slightly, and that the position and velocity relative to Mars are hardly affected. The navigation result of a Mars probe is also greatly affected by the quantities and periodicities of the ephemeris errors of Phobos and Deimos, especially that of Deimos. [ABSTRACT FROM AUTHOR]

We report on the spectral and timing properties of the accreting millisecond X-ray pulsar IGR J00291+5934 observed by XMM-Newton and NuSTAR during its 2015 outburst. The source is in a hard state dominated at high energies by a Comptonization of soft photons (~0.9 keV) by an electron population with kTe ~30 keV, and at lower energies by a blackbody component with kT ~0.5 keV. A moderately broad, neutral Fe emission line and four narrow absorption lines are also found. By investigating the pulse phase evolution, we derived the best-fitting orbital solution for the 2015 outburst. Comparing the updated ephemeris with those of the previous outbursts, we set a 3σ confidence level interval -6.6 × 10-13 s s-1 < Porb < 6.5 × 10-13 s s-1 on the orbital period derivative. Moreover, we investigated the pulse profile dependence on energy finding a peculiar behaviour of the pulse fractional amplitude and lags as a function of energy. We performed a phase-resolved spectroscopy showing that the blackbody component tracks remarkably well the pulse profile, indicating that this component resides at the neutron star surface (hotspot). [ABSTRACT FROM AUTHOR]

Timing analysis is a powerful tool used to determine periodic features of physical phenomena. Here we review two applications of timing analysis to gravitational microlensing events. The first one, in particular cases, allows the estimation of the orbital period of binary lenses, which in turn enables the breaking of degeneracies. The second one is a method to measure the rotation period of the lensed star by observing signatures due to stellar spots on its surface. [ABSTRACT FROM AUTHOR]

LX Ser is a deeply eclipsing cataclysmic variable with an orbital period of 0.1584325 d. 62 new eclipse times were determined by our observations and the AAVSO International Data base. Combining all available eclipse times, we analyzed the O - C behavior of LX Ser. We found that the O - C diagram of LXSer shows a sinusoidal oscillation with a period of 22.8 yr and an amplitude of 0.00035 d. Two mechanisms (i.e., the Applegate mechanism and the light-travel time effect) are applied to explain the cyclic modulation. We found that it is difficult to apply the Applegate mechanism to explain the cyclic oscillation in the orbital period. Therefore, the cyclic period change is most likely to be caused by the light-travel time effect due to the presence of a third body. The mass of the tertiary component was determined to be M3 ∼ 7.5MJup. We supposed that the tertiary companion is plausibly a giant planet. The stability of the giant planet was checked, and we found that the multiple system is stable. [ABSTRACT FROM AUTHOR]

Multi-color photometric light curves of NO Camelopardalis in V, RC, and IC bands are obtained and analyzed simultaneously using the Wilson-Devinney program. The solutions suggest that NO Cam is an A-subtype overcontact binary with a mass ratio of q = 0.439 and a contact degree of f = 55.5%. The small temperature difference (ΔT = 44 K) between its two components indicates that the system is under thermal contact. The high orbital inclination (i = 84.° 5) strengthens our confidence in the parameters determined from the light curves. All available times of minimum light are collected and period variations are analyzed for the first time. The O - C curve reveals that its period is increasing continuously at a rate of dP/dt = +1.46 × 10-9, which can be explained by mass transfer from the less massive component to the more massive one. After the upward parabolic variation is subtracted, the residuals suggest that there may be a cyclic variation with a period of 2.23 yr and an amplitude of A3 = 0.00153 d, which may due to the light-traveltime effect arising from the gravitational influence of a close-in tertiary component. The close-in companion reveals that early dynamic interaction among a triple system may have played a very important role in the formation of the WUMa-type binaries. [ABSTRACT FROM AUTHOR]

Based on the motion of nearly parabolic comets, we have improved the position of planet X in its orbit obtained by Batygin and Brown (2016). By assuming that some of the comets discovered to date could have close encounters with this planet, we have determined the comets with a small minimum orbit intersection distance with the planet. Five comets having hyperbolic orbits before their entry into the inner Solar system have been separated out from the general list. By assuming that at least one of them had a close encounter with the planet, we have determined the planet's possible position. The planet's probable ephemeris positions at the present epoch have been obtained by assuming the planet to have prograde and retrograde motions. In the case of a prograde motion, the planet is currently at a distance Δ whose value belongs to the interval Δ ∈ (1110, 1120) AU and has a right ascension α and declination δ within the intervals α ∈ (83◦, 90◦) and δ ∈ (8◦, 10◦); the true anomaly υ belongs to the interval υ ∈ (176◦, 184◦). In the case of a retrograde motion: α ∈ (48◦, 58◦), δ ∈ (−12◦, −6◦), Δ ∈ (790, 910) AU, and υ ∈ (212◦, 223◦). It should be noted that in the case of a retrograde motion of the planet, its ephemeris position obtained from the motion of comets agrees with the planet's position obtained byHolman and Payne (2016) from highly accurate Cassini observations and is consistent with the results of Fienga et al. (2016). [ABSTRACT FROM AUTHOR]

The thermospheric mass density variations and the thermosphere-ionosphere coupling during geomagnetic storms are not clear due to lack of observables and large uncertainty in the models. Although accelerometers on-board Low-Orbit-Earth (LEO) satellites can measure non-gravitational accelerations and derive thermospheric mass density variations with unprecedented details, their measurements are not always available (e.g., for the March 2013 geomagnetic storm). In order to cover accelerometer data gaps of Gravity Recovery and Climate Experiment (GRACE), we estimate thermospheric mass densities from numerical derivation of GRACE determined precise orbit ephemeris (POE) for the period 2011–2016. Our results show good correlation with accelerometer-based mass densities, and a better estimation than the NRLMSISE00 empirical model. Furthermore, we statistically analyze the differences to accelerometer-based densities, and study the March 2013 geomagnetic storm response. The thermospheric density enhancements at the polar regions on 17 March 2013 are clearly represented by POE-based measurements. Although our results show density variations better correlate with Dst and k-derived geomagnetic indices, the auroral electroject activity index AE as well as the merging electric field E m picture better agreement at high latitude for the March 2013 geomagnetic storm. On the other side, low-latitude variations are better represented with the Dst index. With the increasing resolution and accuracy of Precise Orbit Determination (POD) products and LEO satellites, the straightforward technique of determining non-gravitational accelerations and thermospheric mass densities through numerical differentiation of POE promises potentially good applications for the upper atmosphere research community. [ABSTRACT FROM AUTHOR]

The Poseidon-3 altimeter on board Jason-2 includes a significant new capability with respect to its predecessors, an open-loop [Détermination Immédiate d'Orbite par Doris Embarqué (DIODE)/digital elevation model (DEM)] tracker mode. This innovative mode is capable of successfully tracking the backscatter signal over rapidly varying terrains, and thus it overcomes one of the limitations of the closed-loop Poseidon-2 tracker on board Jason-1. DIODE/DEM achieves this improvement thanks to a predetermined DEM on board that, when combined with DIODE orbit ephemeris, provides improved acquisition timing and reduced data loss in the coastal zone. As a further enhancement, Jason-3 and the Sentinel-3 programs will be capable of autonomously switching to this innovative mode in selected regions. To help recommend how these missions should utilize DIODE/DEM, the authors studied the impact of the tracker mode on the accuracy and precision of wave heights and wind speed, the continuity of the sea level climate data record, and the coverage in coastal regions. The results show close agreement between the open- and closed-loop tracker modes over the open ocean with the exception of some differences at high-tidal variability areas, the coastal zone, and sea ice regions. The DIODE/DEM tracker shows better performance than the closed-loop tracker mode at the coast and in the presence of sea ice. Jason-2, when operating in open-loop mode, allows for an approximately 5% increase of successful acquisitions at the ocean-to-land transition. However, open-loop tracking exhibits more variability in regions of high tides than closed-loop. [ABSTRACT FROM AUTHOR]

Gomes-Júnior et al. published 3613 positions for the eight largest irregular satellites of Jupiter and 1787 positions for the largest irregular satellite of Saturn, Phoebe. These observations were made between 1995 and 2014 and have an estimated error of about 60-80 mas. Based on this set of positions, we derived new orbits for the eight largest irregular satellites of Jupiter: Himalia, Elara, Pasiphae, Carme, Lysithea, Sinope, Ananke and Leda. For Phoebe we updated the ephemeris from Desmars et al. using 75 per cent more positions than the previous one. Because of their orbital characteristics, it is common belief that the irregular satellites were captured by the giant planets in the early Solar system, but there is no consensus for a single model explaining where they were formed. Size, shape, albedo and composition would help to trace back their true origin, but these physical parameters are yet poorly known for irregular satellites. The observation of stellar occultations would allow for the determination of such parameters. Indeed Jupiter will cross the galactic plane in 2019-2020 and Saturn in 2018, improving a lot the chances of observing such events in the near future. Using the derived ephemerides and the UCAC4 catalogue we managed to identify 5442 candidate stellar occultations between 2016 January and 2020 December for the nine satellites studied here. We discussed how the successful observation of a stellar occultation by these objects is possible and present some potential occultations. [ABSTRACT FROM AUTHOR]

We obtained the first VRI CCD light curves of the short-period contact eclipsing binary AQ Boo, which was observed on March 22 and April 19 in 2014 at Xinglong station of National Astronomical Observatories, and on January 20, 21 and February 28 in 2015 at Kunming station of Yunnan Observatories of Chinese Academy of Sciences, China. Using our six newly obtained minima and the minima that other authors obtained previously, we revised the ephemeris of AQ Boo. By fitting the O-C (observed minus calculated) values of the minima, the orbital period of AQ Boo shows a decreasing tendency P ˙ = − 1.47 ( 0.17 ) × 10 − 7 days/year. We interpret the phenomenon by mass transfer from the secondary (more massive) component to the primary (less massive) one. By using the updated Wilson & Devinney program, we also derived the photometric orbital parameters of AQ Boo for the first time. We conclude that AQ Boo is a near contact binary with a low contact factor of 14.43%, and will become an over-contact system as the mass transfer continues. [ABSTRACT FROM AUTHOR]

Radio Frequency (RF) signals broadcast by Global Positioning System (GPS) satellites have become an indispensable part of military and civil applications, right from missile guidance and civil aviation to farming and surveying. But the critical services provided by the GPS demand millimeter level positional accuracy. Over the years, research has been conducted and it is realized that the positional inaccuracy is mainly due to error in the pseudorange. The pseudorange is derived from the signal emission time (SET) of the satellite (known location) and signal reception time at the receiver (unknown location). Hence the better receiver position accuracy can be achieved by precise estimation of SET and accurate satellite position. If these errors are not corrected, they lead to inaccurate satellite position, which will propagate directly in to the range measurements. In this paper, an algorithm is proposed to estimate the SET and correct the satellite position for sagnac effect. Here the error in SET is modeled by taking into account the satellite clock aging parameters and the elliptical trajectory of the satellite, similarly the sagnac effect is corrected considering the earth's rotation during the signal propagation time. The implementation of the proposed algorithm for the ephemeris data collected from the Dual Frequency (DF) GPS receiver located in Indian subcontinent proved better positional accuracy. The SET and sagnac impact are assessed for all the tracked satellites, but the impact analysis pertaining to only SV PRN07 (Space Vehicle Pseudorandom Noise) are presented in this paper. The proposed algorithm can be implemented to achieve higher accuracy for navigation applications like civil aviation, category I/II Precision Approach (PA) aircraft's landing and Real Time Kinematic (RTK) positioning. [ABSTRACT FROM AUTHOR]

To obtain accurate navigation results with respect to Earth simultaneously with those with respect to the target for an interplanetary probe to approach the target planet, this paper proposes a Radio/Optical integrated navigation method based on ephemeris correction, which deeply affects the fusion accuracy. In this paper, the model of the ephemeris error is established, and taking the analytical solution of the ephemeris uncertainty as measurement, the target ephemeris error and its covariance are estimated by Kalman filter and fed back to modify the force models. By correcting the target ephemeris and using information fusion, the Radio/Optical integrated navigation prevents the ephemeris uncertainty polluting the fusion accuracy, and efficiently combines the radio and optical navigation results. The results show the influence of the ephemeris error can be removed, and the Radio/Optical integrated navigation is capable of providing accurate navigation results with respect to Earth and the target. The results demonstrate the proposed method yields an accuracy superior to the conventional method, which proves its effectiveness. [ABSTRACT FROM AUTHOR]

The probability of failure (failure rate) is a key input parameter to integrity monitoring systems used for safety, liability or mission critical applications. A standard approach in the design of Global Positioning System (GPS) integrity monitoring is to utilise the service commitment on the probability of major service failure, often by applying a conservative factor. This paper addresses the question of what factor is appropriate by applying Bayesian inference to real and hypothetical fault histories.Global Navigation Satellite System (GNSS) anomalies include clock or signal transmission type faults which are punctual (may occur at any time) and incorrect ephemeris data which are broadcast for a nominal two hours. These two types of anomaly, classified as continuous and discrete respectively are addressed. Bounds on the total probability of failure are obtained with given confidence levels subject to well defined hypotheses relating past to future performance. Factors for the GPS service commitment of 10−5 per hour per satellite are obtained within the range two to five with high confidence (up to 1–10−9). [ABSTRACT FROM AUTHOR]

Transits in the WASP-57 planetary system have been found to occur half an hour earlier than expected. We present 10 transit light curves from amateur telescopes, on which this discovery was based, 13 transit light curves from professional facilities which confirm and refine this finding, and high-resolution imaging which show no evidence for nearby companions. We use these data to determine a new and precise orbital ephemeris, and measure the physical properties of the system. Our revised orbital period is 4.5 s shorter than found from the discovery data alone, which explains the early occurrence of the transits. We also find both the star and planet to be larger and less massive than previously thought. The measured mass and radius of the planet are now consistent with theoretical models of gas giants containing no heavy-element core, as expected for the subsolar metallicity of the host star. Two transits were observed simultaneously in four passbands. We use the resulting light curves to measure the planet's radius as a function of wavelength, finding that our data are sufficient in principle but not in practise to constrain its atmospheric properties. We conclude with a discussion of the current and future status of transmission photometry studies for probing the atmospheres of gas-giant transiting planets. [ABSTRACT FROM AUTHOR]

Modelling the motion of Triton, the main satellite of Neptune, is specific. Earlier researchers built Triton's ephemeris by numerical integration of the equations of its motion. However, these ephemeris can be accessed only by using online ephemeris server or by borrowing a special calculating program and huge data file from authors of the ephemeris. In addition, the interval of the earlier ephemeris is limited. In this paper, simple and easily programmable formulae are presented for computing Triton's ephemeris for any instant of time. The formulae are based on a new analytical theory of Triton's motion all necessary perturbing factors being taken into consideration. The parameters of the theory are fit to all published observations made from 1847 to 2012 (10 254 observations in total). After the parameters were fit to observations, the root-mean-square residuals were 0.228 arcsec, the weighted average residual being 0.036 arcsec. The new ephemeris of Triton slightly differs from those produced by other authors because of differences in the sets of used observations. The new ephemeris of Triton are put on our online ephemeris server. It is shown that the available observations do not allow to determine reliably the quadratic term in the orbital longitude of Triton. Such a term would be an additional indicator of the accuracy of the theory and observations. [ABSTRACT FROM AUTHOR]

In computational tasks of satellite geodesy there is a need for transformation of coordinates between reference frames ECEF - Earth Centered, Earth Fixed and ECI - Earth Centered, Inertial. Strict and simplified transformation models, which can be used in case of the position and velocity short-term predictions of GLONASS satellites, have been presented in this study. Comparison of the results of state vector components predictions of the GLONASS satellites, in dependence of the used transformation model, have also been presented. Accuracy of the prediction has been determined on the basis of the analyse of deviations of the predicted positions and velocities of GLONASS satellites from their values given in broadcast ephemeris. [ABSTRACT FROM AUTHOR]

We used recently produced Solar System ephemerides, which incorporate 2 years of ranging observations to the MESSENGER spacecraft, to extract the secular orbital elements for Mercury and associated uncertainties. As Mercury is in a stable 3:2 spin-orbit resonance, these values constitute an important reference for the planet's measured rotational parameters, which in turn strongly bear on physical interpretation of Mercury's interior structure. In particular, we derive a mean orbital period of $$(87.96934962 \pm 0.00000037)\,\hbox {days}$$ and (assuming a perfect resonance) a spin rate of $$(6.138506839\pm 0.000000028){}^{\circ }/\hbox {day}$$ . The difference between this rotation rate and the currently adopted rotation rate (Archinal et al. in Celest Mech Dyn Astron 109(2):101-135, . doi:), corresponds to a longitudinal displacement of approx. 67 m per year at the equator. Moreover, we present a basic approach for the calculation of the orientation of the instantaneous Laplace and Cassini planes of Mercury. The analysis allows us to assess the uncertainties in physical parameters of the planet, when derived from observations of Mercury's rotation. [ABSTRACT FROM AUTHOR]

This work investigates end-of-life trajectories for spacecraft in orbit about the sun-Earth L1 and L2 libration points. A decommission plan is often required during the mission design process. The spacecraft's natural departure dynamics are studied in both the circular restricted three-body problem and an ephemeris model. In particular, the roles of the unstable manifold and forbidden regions in determining disposal outcomes are considered. A close correspondence is observed between the models when computing the probabilities of return to the Earth neighborhood. A simple maneuver scheme, which uses regions partitioned by the zero-velocity surfaces to prevent returns to the Earth vicinity, is also analyzed. Disposal maneuver costs less than 50 m/s are possible for many initial libration point orbits during a decommissioning phase lasting less than one year. [ABSTRACT FROM AUTHOR]

Satellite orbit error and clock bias are the keys to precise point positioning (PPP). The traditional PPP algorithm requires precise satellite products based on worldwide permanent reference stations. Such an algorithm requires considerable work and hardly achieves real-time performance. However, real-time positioning service will be the dominant mode in the future. IGS is providing such an operational service (RTS) and there are also commercial systems like Trimble RTX in operation. On the basis of the regional Continuous Operational Reference System (CORS), a real-time PPP algorithm is proposed to apply the coupling estimation of clock bias and orbit error. The projection of orbit error onto the satellite-receiver range has the same effects on positioning accuracy with clock bias. Therefore, in satellite clock estimation, part of the orbit error can be absorbed by the clock bias and the effects of residual orbit error on positioning accuracy can be weakened by the evenly distributed satellite geometry. In consideration of the simple structure of pseudorange equations and the high precision of carrier-phase equations, the clock bias estimation method coupled with orbit error is also improved. Rovers obtain PPP results by receiving broadcast ephemeris and real-time satellite clock bias coupled with orbit error. By applying the proposed algorithm, the precise orbit products provided by GNSS analysis centers are rendered no longer necessary. On the basis of previous theoretical analysis, a real-time PPP system was developed. Some experiments were then designed to verify this algorithm. Experimental results show that the newly proposed approach performs better than the traditional PPP based on International GNSS Service (IGS) real-time products. The positioning accuracies of the rovers inside and outside the network are improved by 38.8% and 36.1%, respectively. The PPP convergence speeds are improved by up to 61.4% and 65.9%. The new approach can change the traditional PPP mode because of its advantages of independence, high positioning precision, and real-time performance. It could be an alternative solution for regional positioning service before global PPP service comes into operation. [ABSTRACT FROM AUTHOR]

The performance of a spaceborne atomic clock on a navigation satellite and the accuracy of the clock data in broadcast ephemeris are two critical factors for real-time high-accuracy global navigation satellite systems applications. A novel clock performance assessment method is proposed, which is indexed by the maximum clock error, clock rate, and clock drift rate, and the performance of the BeiDou-2 satellite-borne clock is assessed by this method compared to the GPS. To mitigate the negative effects of clock errors on pseudo-range measurements and positioning results, an integrated clock prediction method is also presented in this paper based on polynomial modeling, wavelet denoising, and autoregressive integrated moving average modeling. An example is shown to test and verify the effectiveness of the integrated clock prediction method. Real data clock assessment results demonstrate the equivalent quality of BeiDou-2 and GPS spaceborne clocks. The proposed clock prediction method can be used to detect and mitigate clock errors in broadcast ephemeris. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

Low-latency high-rate ( $$>$$ 1 Hz) precise real-time kinematic (RTK) can be applied in high-speed scenarios such as aircraft automatic landing, precise agriculture and intelligent vehicle. The classic synchronous RTK (SRTK) precise differential GNSS (DGNSS) positioning technology, however, is not able to obtain a low-latency high-rate output for the rover receiver because of long data link transmission time delays (DLTTD) from the reference receiver. To overcome the long DLTTD, this paper proposes an asynchronous real-time kinematic (ARTK) method using asynchronous observations from two receivers. The asynchronous observation model (AOM) is developed based on undifferenced carrier phase observation equations of the two receivers at different epochs with short baseline. The ephemeris error and atmosphere delay are the possible main error sources on positioning accuracy in this model, and they are analyzed theoretically. In a short DLTTD and during a period of quiet ionosphere activity, the main error sources decreasing positioning accuracy are satellite orbital errors: the 'inverted ephemeris error' and the integration of satellite velocity error which increase linearly along with DLTTD. The cycle slip of asynchronous double-differencing carrier phase is detected by TurboEdit method and repaired by the additional ambiguity parameter method. The AOM can deal with synchronous observation model (SOM) and achieve precise positioning solution with synchronous observations as well, since the SOM is only a specific case of AOM. The proposed method not only can reduce the cost of data collection and transmission, but can also support the mobile phone network data link transfer mode for the data of the reference receiver. This method can avoid data synchronizing process besides ambiguity initialization step, which is very convenient for real-time navigation of vehicles. The static and kinematic experiment results show that this method achieves 20 Hz or even higher rate output in real time. The ARTK positioning accuracy is better and more robust than the combination of phase difference over time (PDOT) and SRTK method at a high rate. The ARTK positioning accuracy is equivalent to SRTK solution when the DLTTD is 0.5 s, and centimeter level accuracy can be achieved even when DLTTD is 15 s. [ABSTRACT FROM AUTHOR]