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The service areas of the BeiDou Navigation Satellite System (BDS) are China, the Asia–Pacific, and the world via three stages of development. The BDS constellation is designed to maintain a geostationary Earth orbit (GEO), inclined geosynchronous orbit (IGSO), and medium Earth orbit (MEO). These orbital maneuvers yield certain difficulties for data processing, especially for the BeiDou satellites, such as a decrease in the real-time service performance, which causes a missing precise orbit product from the maneuvered satellites. The frequencies of the orbital maneuvers for the GEO and IGSO satellites are higher than those for the MEO satellites. The maneuvering time and strategy cannot be obtained by common users due to secrecy, which can yield a decline in the service performance of the BDS. Thus, in this study, we analyzed the variation in the orbital semimajor axis for the satellites. The long-term variation in the orbital semimajor axis changes linearly. The short-term variation in the orbital semimajor axis also has periodicity, which can be described by the sum of sine functions. According to the long-term variation in the orbital semimajor axis for the satellites, we propose a detection method for in-plane orbital maneuvering of the GEO, IGSO, and MEO satellites. We then propose a detection method for out-of-plane maneuvering of the GEO satellites. BDS and Global Positioning System (GPS) data from the broadcast ephemeris were analyzed to verify the proposed methods. The experimental results from 2013 to 2019 show that the frequency of orbital maneuvering is approximately once a month for the GEO satellites, once every six months for the IGSO satellites, and once every 1.4 years for the MEO satellites.

This article reports on the calculation of upset rates in low and medium earth orbits using a design-of-experiments and Monte-Carlo approach to the parameters available in the Cosmic-Ray Effects on Micro-Electronics (CREME96) code. Rate-calculation accuracy is checked using on-orbit data from the published literature. The implications for data collection are discussed.

BeiDou Navigation Satellite System (BDS) is composed of satellites in geostationary Earth orbit (GEO), medium Earth orbit (MEO) and inclined geosynchronous orbit (IGSO). However, the orbit determination of geostationary Earth orbits and of geosynchronous orbits (GSO) with small inclination angle and small eccentricity is a challenging task that is addressed in this paper using Extended Kalman Filter (EKF). The satellite positions were predicted in Earth-centred inertial (ECI) reference frame when propagated through Keplerian model and perturbation force model for different values of right ascension of ascending node (RAAN). Root mean square (RMS) errors of 9.61 cm, 6.73 cm and 11.46 cm were observed in ECI X, Y and Z satellite position coordinates of GSO respectively, whereas, the RMS errors for GEO satellite were 8.89 cm, 7.92 cm, and 0.93 cm respectively in ECI X, Y and Z coordinates; for perturbation force model with maximum value of RAAN when compared with dynamic orbit determination model. Kolmogorov-Smirnov test for EKF reported a p-value > 0.05, indicating a good fit of perturbation force model for orbit propagation. Orbit determination using EKF with perturbation force model were compared with that using EKF with Kepler's model. Wilcoxon Rank Sum test was used to compare the residuals from EKF algorithm through Kepler's model and perturbation force model. EKF with Perturbation force model showed improvement in predicting the satellite positions as compared to Kepler's model. EKF with Perturbation force model was further applied to International GNSS Service (IGS) station data and kilometre level accuracy was achieved. RMS errors of 0.75 km, 2.53 km and 1.91 km were observed in ECI X, Y and Z satellite position coordinates of GSO, respectively, whereas, the RMS errors for GEO satellite were 3.89 km, 4.20 km and 6.66 km respectively in ECI X, Y and Z coordinates for perturbation force model.

Energetic electron measurements and spacecraft charging are of great significance for theoretical research in space physics and space weather applications. In this paper, the energetic electron detection package (EEDP) deployed on three Chinese navigation satellites in medium Earth orbit (MEO) is reviewed. The instrument was developed by the space science payload team led by Peking University. The EEDP includes a pinhole medium-energy electron spectrometer (MES), a high-energy electron detector (HED) based on ΔE-E telescope technology, and a deep dielectric charging monitor (DDCM). The MES measures the energy spectra of 50−600 keV electrons from nine directions with a 180°×30° field of view (FOV). The HED measures the energy spectrum of 0.5−3.0 MeV electrons from one direction with a 30° cone-angle FOV. The ground test and calibration results indicate that these three sensors exhibit excellent performance. Preliminary observations show that the electron spectra measured by the MES and HED are in good agreement with the results from the magnetic electron-ion spectrometer (MagEIS) of the Van Allen Probes spacecraft, with an average relative deviation of 27.3% for the energy spectra. The charging currents and voltages measured by the DDCM during storms are consistent with the high-energy electron observations of the HED, demonstrating the effectiveness of the DDCM. The observations of the EEDP on board the three MEO satellites can provide important support for theoretical research on the radiation belts and the applications related to space weather.

Submillimeter interferometry has the potential to image supermassive black holes on event horizon scales, providing tests of the theory of general relativity and increasing our understanding of black hole accretion processes. The Event Horizon Telescope (EHT) performs these observations from the ground, and its main imaging targets are Sagittarius A* in the Galactic Center and the black hole at the center of the M87 galaxy. However, the EHT is fundamentally limited in its performance by atmospheric effects and sparse terrestrial $(u,v)$-coverage (Fourier sampling of the image). The scientific interest in quantitative studies of the horizon size and shape of these black holes has motivated studies into using space interferometry which is free of these limitations. Angular resolution considerations and interstellar scattering effects push the desired observing frequency to bands above 500 GHz. This paper presents the requirements for meeting these science goals, describes the concept of interferometry from Polar or Equatorial Medium Earth Orbits (PECMEO) which we dub the Event Horizon Imager (EHI), and utilizes suitable space technology heritage. In this concept, two or three satellites orbit at slightly different orbital radii, resulting in a dense and uniform spiral-shaped $(u,v)$-coverage over time. The local oscillator signals are shared via an inter-satellite link, and the data streams are correlated on-board before final processing on the ground. Inter-satellite metrology and satellite positioning are extensively employed to facilitate the knowledge of the instrument position vector, and its time derivative. The European space heritage usable for both the front ends and the antenna technology of such an instrument is investigated. Current and future sensors for the required inter-satellite metrology are listed. Intended performance estimates and simulation results are given., Comment: 23 pages, 10 figures

We use electron flux derived from the environment monitoring unit “(EMU)-SURF” current monitor on board a Galileo Global Navigation Satellite System (GNSS) constellation satellite to modify and update the model of outer belt electrons for dielectric internal charging (MOBE-DIC). We describe how this data set, together with data from similar current–measuring instruments on Van Allen Probes, Giove-A, and STRV1d, are used to improve and expand the model. We have extended the spatial range to include the inner belt, exploited EMU data to widen the energy range for the electron spectrum, updated the statistical analysis of flux variation using a data set double the size used for the original model, and established a new and independent latitude function that yields improved agreement in medium earth orbit compared to the original model. The model is entirely characterized by a set of equations and parameters that produce fluxes as a function of magnetic coordinates at three distinct statistical levels.

In this work, two dynamical models are formulated to describe the secular dynamics of navigation satellites moving in the medium Earth orbit (MEO) and geosynchronous orbit (GSO) regions. In the dynamical models, the leading terms of the Earth’s oblateness and the luni-solar gravitational perturbations are considered. For convenience, the orbits of the Sun and the Moon are described in the geocentric ecliptic reference frame, where the regression of nodal line and precession of apsidal line of the lunar orbit can be approximated as linear functions of time. The disturbing function acting on navigation satellites is analytically averaged over the mean motions of both the satellite and the third body (the Sun or the Moon). Explicit expressions of the averaged disturbing function are provided in the geocentric ecliptic and equatorial reference frames, corresponding to averaged model 1 and averaged model 2, respectively. It is found that there are seven resonant arguments in averaged model 1, while there are thirty-two resonant arguments in averaged model 2. The associated resonance curves corresponding to these resonant arguments in each model form the dynamical backbone in the phase space, organizing secular behavior of navigation satellites. At last, the averaged models are numerically compared to the associated non-averaged model, and simulation results indicate that (a) the averaged models formulated in the geocentric ecliptic and equatorial reference frames are identical, and (b) both of these two averaged models are applicable in predicting secular behavior of navigation satellites.

A growing number of satellites are operating on inclined geosynchronous orbits (IGSOs) with inclination typically much higher than that of traditional geosynchronous orbits (GEOs). Several recent studies have considered the long-term evolution of IGSOs. Unlike traditional GEO disposal orbits, IGSO disposal orbits can undergo large excursions in eccentricity due to the effect of luni-solar gravity perturbations. For specific ranges of initial orbital elements, perigee can reach the Earth's atmosphere, resulting in vehicle reentry. A previously published study by the authors on Tundra orbits, a specific class of IGSO with critical inclination and moderate eccentricity, demonstrated that orbital lifetime can be reduced below 200 years (in some cases below 25 years) and that the corresponding collision probability with background objects can be significantly reduced below that for traditional GEO disposal orbits. This paper presents a study of a broad range of IGSO disposal orbits. Three cases of IGSO disposal orbit were considered: (1) near circular orbits (motivated by the BeiDou and IRNSS constellations); (2) orbits with intermediate eccentricity (motivated by the QZS constellation); and (3) orbits with larger eccentricity (motivated by the Sirius Tundra constellation). For each case, a large number of long-term propagations using the high-precision code TRACE were performed. Disposal orbit initial inclination and right ascension of ascending node (RAAN) were parametrically varied. The Aerospace Debris Environment Projection Tool (ADEPT) suite was used to determine collision probability with inactive background objects and with operational satellites in GEO, medium Earth orbit (MEO), and low Earth orbit (LEO). Study results show that orbital lifetime of IGSOs can be reduced to less than 200 years for all three IGSO cases considered if initial inclination is high enough. The minimum required inclination depends on initial RAAN. An orbital lifetime less than 200 years offers effective reduction of probability of collision with inactive background objects (by 0.7–1.8 orders of magnitude) and can be achieved in a wider disposal orbit design space than would be needed to reduce orbital lifetime to less than 25 years. For near circular IGSOs, collision probability with operational satellites will be higher at high inclinations than at low inclinations, but there are options for mitigation. When inclination is not high enough to achieve reentry, a high eccentricity storage disposal orbit may be a consideration if collision probability is lower than for other options.

This paper presents a novel approach to test surface material charging under electron flux representative of space conditions below 400 keV. The experimental protocol used to test space material electrical properties consists in adapting the electron flux distribution to mimic worst case spectra met in space. Input environments are taken from Kp > 5 specifications at geosynchronous orbit (GEO) and from the analysis of both RBSP and LANL spacecraft data at middle Earth orbit (MEO) and GEO. Experimental results using GEO specifications show that the surface potential strongly depends on the energetic particle flux. Above a given > 100-keV electron flux, the radiation-induced conductivity tends to govern the charging dynamics. A numerical analysis based on the environments selected in this paper shows that charging levels could be larger at MEO than at GEO.

Continuous observation of polar regions from space remains an important unsolved technical challenge of great interest for the international meteorological community. This capacity would allow achieving global continuous coverage once combined with the geostationary (GEO) satellite network. From a practical point of view, continuous coverage of polar regions with a small number of spacecraft can be obtained from a constellation of satellites either in highly elliptical orbits (HEO) or in medium Earth orbits (MEO). The study compares HEO and MEO satellite constellations for their capacity to provide continuous imaging of polar regions as function of the viewing zenith angle (VZA) and evaluates the corresponding latitude limits that ensure sufficient overlap with GEO imagery. Earlier studies assumed the latitude boundary of 60° and the VZA range 70°–85° depending on the space mission focus: meteorological purposes or communications. From the detailed analysis of meteorological retrieval requirements, this study suggests that the overlap of the GEO and polar observing systems (HEO or MEO) should occur down to the latitude band 45°–50° with a maximum VZA ranging between 60° and 64°. This coverage requirement can be met with two sets of three-satellite HEO constellations (one for each polar area) or a six-satellite MEO constellation. The 12-h Molniya and 14-, 15-, and 16-h HEO systems have been analyzed and determined to meet these revised requirements. The study demonstrates that the six-satellite 24-h MEO system can provide a suitable solution, which is also beneficial from the point of view of ionizing radiation and image acquisition geometry. Among the HEO systems, the 16-h HEO has some advantages relative to other HEO systems from the point of view of spatial coverage and space radiation.

The objective of this paper is to validate and evaluate the orbit accuracy of the BeiDou Navigation System (BDS) using satellite laser ranging (SLR) data over a 5-year time series. The microwave-based precise orbits of BDS derived from four Analysis Centers (ACs) are validated from 2013 to 2018, including three Multi-GNSS EXperiment (MGEX) ACs from WHU, CODE and GFZ, as well as a fourth AC, known as ISC in China, with the corresponding products designated as WUM, COM, GBM and ISC. The validated orbits of BDS include the Geostationary Earth Orbit (GEO) satellite of C01, the Inclined Geo-Synchronous Orbit (ISGO) satellites of C08, C10, and C13, as well as the Medium Earth Orbit (MEO) satellite of C11. In addition, the performances of the BDS orbits during noneclipse, eclipse and Yaw Maneuver (YM) period are evaluated. Finally, the dependencies of SLR residuals on the satellite nadir angle and on the Sun elevation angle β are analyzed in detail. The results demonstrated that (1) the optimal orbit accuracies of C01, C08, C10, C11 and C13 are 522.8 mm from WUM, 53.3 mm from ISC, 54.3 mm from ISC, 38.2 mm from ISC and 51.5 mm from COM, respectively. And the orbits derived from ISC have more stable and excellent accuracy than the other ACs due to the advantages of its orbit combination algorithm. (2) Due to the deficiencies of the Solar Radiation Pressure and the YM modeling for BDS satellites from four ACs, the microwave-based orbit accuracy of BDS IGSO and MEO satellites is significantly deteriorated during the eclipse period, especially in the YM period, while the accuracy of GEO C01 during the eclipse period is better than that during the noneclipse period. (3) The dependency of SLR residuals on the satellite nadir angle has been analyzed, but limited by the number and type of all the validated BDS satellites, the nadir-dependency offset of the SLR residuals cannot be well assigned from the characteristics of the SLR detector system, or the Laser Retro-reflector Arrays. (4) By analyzing the dependency of SLR residuals on the Sun elevation angle β , some commonalities of the patterns derived from four ACs have been found for BDS IGSO and MEO satellites, and the patterns are similar to that of the GLONASS, rather than those of GPS and Galileo.

Eight new-generation BeiDou satellites (BeiDou-3) have been launched into Medium Earth Orbit (MEO), allowing for global coverage since March 2018, and they are equipped with new hydrogen atomic clocks and updated rubidium clocks. Firstly, we analyzed the signals for the carrier-to-noise-density ratio (C/N0) and pseudorange multipath (MP) by using international GNSS (Global Navigation Satellite System) Monitoring and Assessment System (iGMAS) station data, and found that B1C has a lower C/N0, and B2a has the same level of C/N0 as the B1I and B3I signals. For pseudorange multipath, compared with the BeiDou-2 satellites, the obvious systematic variation of MP scatters related to the elevation angle is greatly improved for the BeiDou-3 and BeiDou-3e satellites signals. For the signals of the BeiDou-3 satellites, the order of the Root Mean Square (RMS) values of multipath and noise is B3I

Design and analysis of quadrifilar helical antenna is presented in this paper. The proposed antenna is designed for cube-sats in the low earth and medium earth orbit applications. It is a combination of 4 helical antennas, each separated by 90o, with left-handedness and it is designed for operation at 4.5GHz. The proposed antenna has 11.11% impedance bandwidth. The antenna is designed in 2 steps to analyze its proper radiation pattern and input characteristics. The first step of designing is selection of a ground plane with perfect dimensions, which can operate at desired frequency. While the second step is to analyses the antenna performance for different helix angle using proper ground plane dimensions. The gain versus frequency curve has been obtained for desired frequency and it is showing more than 5 dB gain at resonant frequency 4.5 GHz. Thus, based on desired application proposed antenna has been designed.

The relationship between the proper time of a satellite clock and the geocentric coordinate time (TCG) is discussed in the framework of general relativity. The influences of Earth's shape and the tidal potentials of the Sun and Moon are analyzed for onboard satellite clocks in different orbits. The results show that the influence of the shape of the Earth on Middle Earth Orbit (MEO) satellite reaches the level of 4.0 × 10-15, and it may be the direct cause of the half orbital-period variation in the clock frequency. The influences of the tidal potentials of the Sun and the Moon are relatively smaller. These influences on the frequencies of the clocks in the BeiDou MEO and GEO/IGSO (Geosynchronous Earth Orbit/Inclined Geosynchronous Satellite Orbit) satellites are 5.9 × 10-16 and 1.2 × 10-15, respectively, and appear to be half-day periodic variations. Therefore, these effects need to be considered in the precise assessment and application of BeiDou satellite clocks.

Compared to the BeiDou regional navigation satellite system (BDS-2), the BeiDou global navigation satellite system (BDS-3) includes the newly designed B1C and B2a signals, which are compatible with the L1 and L5 frequencies of the global positioning system (GPS). Considering that the precise orbit determination (POD) of the BDS-3 constellation is currently restricted to the legacy B1I and B3I signals, we reported the POD performance of BDS-3 satellites using B1C and B2a dual-frequency measurements. Nine globally distributed Multi-GNSS Experiment (MGEX) stations were selected to determine the orbits of BDS-3 satellites during the period of July 2019. The results show that B1C/B2a-based POD enables an average three-dimensional root-mean-square error (3D RMS) of 24.2 cm, and the precision is better than 6 cm in the radial component in a comparison of two-day overlapping arcs. Satellite laser ranging (SLR) validation achieves an overall precision of 6.8 cm in RMS differences. Compared to the B1I/B3I-based POD results, the quality of B1C/B2a-based orbits is improved by approximately 9% across the whole BDS-3 constellation, indicating that the new B1C/B2a signals can be employed for the superior POD performance of BDS-3 satellites. Moreover, we investigated the behavior of the solar radiation pressure (SRP), which is generally considered one of the primary error sources in BDS-3 medium earth orbit (MEO) dynamic orbit determination. The ECOM7 SRP model has a better POD performance in continuous yaw steering (CYS) mode than the ECOM5 and ECOM9 SRP models. The results also show that there is no degradation in the orbit precision of BDS-3 MEO satellites when the elevation angle of the sun above the orbital plane (β angle) varies within the range of − 4° to + 4°.

An in-depth and comprehensive assessment of new observations from BDS-3 satellites is presented, with the main focus on the Carrier-to-Noise density ratio (C/N0), the quality of code and carrier phase observations for B1C and B2a signal. The signal characteristics of geosynchronous earth orbit (GEO), inclined geosynchronous satellite orbit (IGSO) and medium earth orbit (MEO) satellites of BDS-3 were grouped and compared, respectively. The evaluation results of the new B1C and B2a signals of BDS-3 were compared with the previously B1I/B2I/B3I signals and the interoperable signals of GPS, Galileo and quasi-zenith satellite system (QZSS) were compared simultaneously. As expected, the results clearly show that B1C and B2a have better signal strength and higher accuracy, including code and carrier phase observations. The C/N0 of the B2a signal is about 3 dB higher than other signals. One exception is the code observation accuracy of B3I, which value is less than 0.15 m. The carrier precision of B1C and B2a is better than that of B1I/B2I/B3I. Despite difference-in-difference (DD) observation quantity or zero-base line evaluation is adopted, while B1C is about 0.3 mm higher carrier precision than B2a. The BDS-3 MEO satellite and GPS, Galileo, and QZSS satellites have the same level of signal strength, code and phase observation accuracy at the interoperable frequency, namely 1575.42 MHz and 1176.45 MHz which are very suitable for the co-position application.

The recent decades have seen an increasing interest in Medium Earth Orbit and Low Earth Orbit satellite constellations. However, there is little information on the delay variation characteristics of these systems and the resulting impact on high layer protocols. To fill this gap, this paper simulates a constellation that exhibits the same delay characteristics as the already deployed Iridium but considers closer bandwidths to constellation projects’. We identify five major sources of delay variation in polar satellite constellations with different occurrence rates: elevation, intra-orbital handover, inter-orbital handover, orbital seam handover and Inter-Satellite Link changes. We simulate file transfers of different sizes to assess the impact of each of these delay variations on the file transfer. We conclude that the orbital seam is the less frequent source of delay and induces a larger impact on a small file transfers: the orbital seam, which occurs at most three times during 24 h, induces a 66% increase of the time needed to transmit a small file. Inter-orbital and intra-orbital handovers occur less often and reduce the throughput by approximately ∼ 8% for both low and high throughput configurations. The other sources of delay variations have a negligible impact on small file transfers, and long file transfers are not impacted much by the delay variations.

An autonomous spacecraft navigation scheme based on the stellar aberration and the starlight gravitational deflection is presented in the paper. The stellar aberration provides spacecraft velocity information in the plane perpendicular to the star line-of-sight unit vector, while the starlight gravitational deflection is sensitive to the spacecraft position relative to celestial bodies. For autonomous spacecraft navigation, a practical approach to collect measurements is to observe the change of inter-star angles caused by the stellar aberration and the starlight gravitational deflection through an optical interferometer. A measurement equation is established to describe the relation between the state vector and the observations. Then it is used together with the dynamical model for the design of an extended Kalman filter that provides spacecraft kinematic state estimation. To improve the navigation performance, an optical path delay bias estimation and compensation are implemented in the extended Kalman filter. It is shown via simulation that, for a medium Earth orbit (MEO) satellite, the position and velocity errors of the presented scheme are on the order of 150 m and 0.02 m/s with the inter-star angle measurement accuracy of about 1 mas.

China is currently focusing on the establishment of its BDS-3 system, and a BDS-3 constellation with 18 satellites in medium Earth orbit (MEO) and one satellite in geostationary Earth orbit (GEO) has been able to provide preliminary global services since the end of 2018. These BDS-3 satellites feature the inter-satellite link (ISL) and new high-quality onboard clocks. In this study, we present the analysis of BDS-3 orbits and clocks determined by Ka-band ISL measurements from 18 MEO satellites and one GEO satellite. The ISL data of 43 days from 1 January to 12 February 2019 are used. The BDS-3 ISL measurement is described by a dual one-way ranging model. After converting bidirectional observations to the same epoch, Ka-band clock-free and geometry-free observables are obtained by the addition and subtraction of dual one-way observations, respectively. One anchor station with Ka-band bidirectional observations is introduced into the orbit determination to provide the orientation constraints. Using Ka-band clock-free observables, BDS-3 satellite orbits are determined. The ISL hardware delays are estimated together with orbits, and the resulting hardware delay estimates are quite stable with STD of about 0.03 ns. The Ka-band orbits are evaluated by orbit overlap differences, comparison with L-band precise orbits, and satellite laser ranging validation. The results indicate that the radial orbit errors are on the 2–4 cm level for MEO satellites and 8–10 cm for the GEO satellite. In addition, we investigate the ground anchoring capability by adding one anchor station and reducing the amount of data of the anchor station. Using Ka-band geometry-free observables, BDS-3 satellite clocks are estimated and the RMS of post-fit ISL residuals is about 5 cm. The Ka-band clock offsets are analyzed and compared with L-band precise clocks. Independent of orbit errors, the Allan deviation of Ka-band clocks for averaging interval longer than 5000 s is superior to that of L-band clocks. Furthermore, a pronounced bump, which appears in the Allan deviation of L-band clocks, almost vanishes in Ka-band clocks. Finally, the periodic variations are detected for L-band and Ka-band clocks.

Autonomous orbit determination (AOD) is the ability of navigation satellites to estimate with accurate satellite orbit parameters using onboard using inter-satellite link (ISL) measurements. To overcome the unobservability of the constellation rotation error in AOD when using only the ISL measurements, the properties that the orbit inclination $$ i $$ and the longitude of the ascending node $$ \varOmega $$ of the medium earth orbit (MEO) navigation satellites, which can be predicted with high accuracy over a long time, are explored. This leads to an onboard extended Kalman filter (EKF) where $$ \left( {i,\varOmega } \right) $$ are subjected to constraints. Three experiments are carried out to assess the effectiveness of the proposed AOD EKF and analyze the causes of the constellation rotation error by processing 30-day ISL measurements of 18 MEO satellites of BDS-3 in a distributed mode. The results verify that the proposed EKF with $$ \left( {i,\varOmega } \right) $$ constraints can resolve the unobservable constellation rotation error issue effectively. When using precise EOP parameters, the 3D orbit errors of BDS-3 AOD in 30 days could be less than 2.30 m. The errors increase to 3.4 m when the predicted EOP parameters are used.

As of June 2019, 18 BDS-3 medium earth orbit (MEO) satellites have been launched into orbit. We perform precise orbit determination for these BDS-3 satellites with the rate-limited attitude models and the a priori box-wing solar radiation pressure model. The BDS-3 MEO satellites employ continuous yaw-steering attitude mode. By using proper yaw-attitude models during deep eclipse seasons, the orbit overlapping can be reduced by (0.6, 0.5, 0.4) cm for satellites developed by China Academy of Space Technology (CAST) and (0.5, 0.4, 0.3) cm for satellites developed by Shanghai Engineering Center for Microsatellites (SECM) in along-track, cross-track, and radial components, respectively. Compared to nominal attitudes, the attitude models also reduce the RMS of ionospheric-free carrier-phase residuals from 1.87 cm and 1.83 cm to 1.74 cm and 1.79 cm for CAST and SECM satellites in deep eclipse seasons, respectively. In addition, the satellite clock residuals become smoother by using the rate-limited yaw-attitude models. By applying the a priori box-wing SRP model along with a 5-parameter extended CODE orbit model (ECOM1), the orbit overlapping can be reduced to (6.9, 3.8, 1.9) cm for CAST satellites and (10.6, 5.8, 2.4) cm for SECM satellites, which are (0.6, 0.7, 0.6) cm and (0.7, 0.5, 0.7) cm smaller compared to those of the updated ECOM model (ECOM2). The BDS-3 orbits are then validated by satellite laser ranging (SLR), and the results demonstrate mean biases of 0–5 cm with standard derivations of 3–6 cm. The SLR validation also reveals that using an a priori box-wing model can reduce the SLR mean biases and standard deviations when compared to the ECOM2 model.

In the realm of increasing demand for stable and excellent connectivity around the world, researches are done heavily to boost up the connectivity and transmission distance. Therefore, in this research work, we have made the realization of an inter-satellite optical wireless channel, wavelength division multiplexed system implemented with polarization interleaving technique in order to realize an 8-channel system capable of transmitting data rate of 20 Gbps per channel for the transmission distance of LEO, MEO, and GEO satellite orbits. The designed system is capable of data transmission with mitigated channel non linearities and acceptable SNR, BER, and Q-factor for the transmission distance of 40,000 km, 10,000 km, and 5000 km covered under the geostationary equatorial orbit, medium earth orbit, and low earth orbit, respectively. The system realized here is also considered to work efficiently under 1 µ radian to 3 µ radian transmitter and receiver pointing error losses. Optimal results can be observed on the basis of transmitted and received optical power spectrum, SNR values, total power received, eye-opening diagrams, BER, and Q-factor.

Special features of orbital evolution of near-earth objects under conditions of superposition of the 1:2 orbital resonance with rotation velocity of the Earth and secular apsidal-nodal resonances associated with the Moon and the Sun are considered. The special features are considered on the example of dynamics of objects moving in the medium Earth orbit (МЕО) zone in the range of semimajor axes from 26550 to 26570 km and in the range of orbit inclinations from 50 to 70°. It is demonstrated that joint action of stable orbital and secular resonances does not lead to chaoticity in object motion; at the same time, the chaoticity arises in all cases when one of the jointly acting resonances, orbital or secular, is unstable.

This paper aims to investigate the effects of lunar node resonance on the circular medium Earth orbits (MEO). The dynamical model is established in classical Hamiltonian systems with the application of Lie transform to remove the non-resonant terms. Resonant condition, stability and phase structures are studied. The lunar node resonance occurs when the secular changing rates of the orbital node (with respect to the equator) and the lunar node (with respect to the ecliptic) form a simple integer ratio. The resonant conditions are satisfied for both inclined and equatorial orbits. The orbital plane would have long period (with typical timescales of several centuries) fluctuation due to the resonance.

Internal charging is an important hazard for navigation satellites, which operate in outer electron radiation belt and experience a very variable radiation environment because of the inclination of orbits. A rapid analysis method of internal charging is introduced, including physical model, conductivity model, shielding and electron transportation algorithm, and charging calculation method. Using this method, we calculate the charging processes of dielectric in medium earth orbit (MEO), geostationary earth orbit (GEO), and inclined geosynchronous orbit (IGSO). The results show that charging field fluctuates a lot in orbit and variation rate of field is proportional to electron flux. The saturated charging field in MEO is higher than that in GEO, and the field in GEO is higher than that in IGSO. So, the internal electrostatic discharging risk in MEO, GEO, and IGSO decreases in turn. If conductivity of dielectric is smaller, saturated field is larger and the difference of field in MEO, GEO, and IGSO is smaller. The dark and radiation-induced conductivity (RIC) of dielectric are important parameters in simulation, so we study the impact of conductivity in charging processes. In IGSO and MEO, when dark conductivity-induced time constant of charging is greater than orbital period and RIC is not large, the deposited electrons between different orbits accumulate and the charging field increase constantly. In this situation, the dark conductivity has a big influence on internal charging and it is important to measure it accurately.

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).

When full-electric orbit raising trajectories begin in a classic geostationary transfer orbit with low initial perigee altitude, the need for deployed solar arrays to power the propulsion system significantly increases the aerodynamic and gravity gradient torques. In fact, the torque magnitudes in the first few perigee passages may become a challenging requirement for the attitude control system. Apart from oversizing ac- tuators, other solutions may include the need for a backup thruster system or raising the perigee altitude, implying mass penalties and cost. This paper presents the design of an optimal attitude maneuver at the perigee that can be undertaken using nomi- nal reaction wheels. Attitude paths avoiding saturation of the wheels while dumping accumulated momentum are obtained performing a physically consistent modelling of aerodynamic torques and using Pseudospectal methods to solve the trajectory opti- mization problem. The optimization of solar array positions is also explored to further constrain the problem or improve the maneuver performance. Resulting mass and cost savings can be significant, which could be used for additional payload or to significantly extend the operational life of the satellite.

Areostationary satellites are considered a high interest group of satellites to satisfy the telecommunications needs of the foreseen missions to Mars. An areostationary satellite, in an areoequatorial circular orbit with a period of 1 Martian sidereal day, would orbit Mars remaining at a fixed location over the Martian surface, analogous to a geostationary satellite around the Earth. This work addresses an analysis of the perturbed orbital motion of an areostationary satellite as well as a preliminary analysis of the aerostationary orbit estimation accuracy based on Earth tracking observations. First, the models for the perturbations due to the Mars gravitational field, the gravitational attraction of the Sun and the Martian moons, Phobos and Deimos, and solar radiation pressure are described. Then, the observability from Earth including possible occultations by Mars of an areostationary satellite in a perturbed areosynchronous motion is analyzed. The results show that continuous Earth-based tracking is achievable using observations from the three NASA Deep Space Network Complexes in Madrid, Goldstone and Canberra in an occultation-free scenario. Finally, an analysis of the orbit determination accuracy is addressed considering several scenarios including discontinuous tracking schedules for different epochs and different areoestationary satellites. Simulations also allow to quantify the aerostationary orbit estimation accuracy for various tracking series durations and observed orbit arc-lengths.

A novel approach for minimum-time reconfiguration of satellite formations is proposed considering the perturbation forces as control variables. Planning appropriate attitude maneuvers for each sate...

The GNSS Occultation Sounder instrument onboard the Chinese meteorological satellite Fengyun-3C (FY-3C) tracks both GPS and BDS signals for orbit determination. One month’s worth of the onboard dual-frequency GPS and BDS data during March 2015 from the FY-3C satellite is analyzed in this study. The onboard BDS and GPS measurement quality is evaluated in terms of data quantity as well as code multipath error. Severe multipath errors for BDS code ranges are observed especially for high elevations for BDS medium earth orbit satellites (MEOs). The code multipath errors are estimated as piecewise linear model in $$2{^{\circ }}\times 2{^{\circ }}$$ grid and applied in precise orbit determination (POD) calculations. POD of FY-3C is firstly performed with GPS data, which shows orbit consistency of approximate 2.7 cm in 3D RMS (root mean square) by overlap comparisons; the estimated orbits are then used as reference orbits for evaluating the orbit precision of GPS and BDS combined POD as well as BDS-based POD. It is indicated that inclusion of BDS geosynchronous orbit satellites (GEOs) could degrade POD precision seriously. The precisions of orbit estimates by combined POD and BDS-based POD are 3.4 and 30.1 cm in 3D RMS when GEOs are involved, respectively. However, if BDS GEOs are excluded, the combined POD can reach similar precision with respect to GPS POD, showing orbit differences about 0.8 cm, while the orbit precision of BDS-based POD can be improved to 8.4 cm. These results indicate that the POD performance with onboard BDS data alone can reach precision better than 10 cm with only five BDS inclined geosynchronous satellite orbit satellites and three MEOs. As the GNOS receiver can only track six BDS satellites for orbit positioning at its maximum channel, it can be expected that the performance of POD with onboard BDS data can be further improved if more observations are generated without such restrictions.

The regional part of the current BeiDou navigation satellite system (BDS) consists of five Geostationary Earth Orbit (GEO) satellites, five Inclined Geosynchronous Satellite Orbit (IGSO) satellites and four Medium Earth Orbit (MEO) satellites. We examined three algorithms for BDS velocity estimation. In addition, the performance of velocity estimation using different BDS satellite combinations was analysed. Static tests demonstrated that velocity precision using Raw Doppler (RD) measurements was of the order of centimetres per second, whereas the carrier-phase-Derived Doppler (DD) measurements and Time-Differenced Carrier Phase (TDCP) method provided accuracies of the order of millimetres per second. Because of the irregularity of the satellites' distribution, three peaks exist on the north component in the 24-hour velocity series. Besides, the GEO satellites contribute significantly in velocity estimation and the satellites' geometry condition seriously declined when excluding GEO satellites. In kinematic tests, the root mean square of the velocity error derived by DD and TDCP both attained the centimetre per second level. Moreover, the precision of velocity determination with these three methods was degraded by the sudden acceleration of the vehicle.

In the mid-90s of the past century Arnon Spitzer offered a flight scheme comprising an elliptical synchronous equatorial orbit for the SC injection into geostationary orbit (GEO). The advantages of such scheme were related to the SC control simplicity during its transfer from the elliptical synchronous orbit into GEO. The main advantage of Spitzer's scheme is the possibility of observing spacecraft from Earth using a limited number of ground stations along the entire trajectory of the SC flight from an intermediate orbit into GEO. Some flight schemes, which preserve the main advantage of the Spitzer's scheme, are analyzed. The inclination and the eccentricity of the intermediate synchronous orbit are optimized. Several variants of the yaw angle control are analyzed. Numerical analysis was carried out for a space transportation system based on the launch vehicle “Angara-A5”, chemical upper stage “KVTK”, and electric propulsion system comprising four thrusters SPD-140 with the specific impulse of 1700 s.

The paper solves the problem of control over and insertion into geostationary orbit of a spacecraft with diffractive optical elements with the help of low torque electric propulsion (EP). Main features of a design layout of a spacecraft with diffractive optics and the requirements for inserting such spacecraft into geostationary orbit are discussed. The prototype of such system is the MOIRE project spacecraft. The paper suggests a three-stage ballistic insertion scheme: lifting to near Earth orbit by a launch vehicle, transfer to intermediate orbit with the help of acceleration module, and at the final stage the spacecraft is transferred from intermediate to geostationary orbit by low thrust electric propulsion system.

Сalibration spacecraft (CSC) is used to assess the energy potential of the radar channel of a ground-based complex for the motion control of space objects. A high precision spherical shell is one option for the geometric shape of such a CSC. The passive repeaters of signals and some types of reference reflectors have a shape of the same character. Along with the orbits close to the Arctic ones, said CSC may be in the circular and elliptical earth orbits, which have areas shaded by the Earth from the sun rays.We can assume that in the shaded area of the earth orbit the CSC shell is under temperature extremes only of the intrinsic radiation of the Earth surface, the intensity of which is substantially less than the intensity of the Sun heat radiation that reaches the near-Earth space. In this regard, one should expect a lower temperature of the shell in this area of the orbit as compared with its temperature in the sun-lit area. This will cause a significant change in CSC shell temperature within a period of its revolution around the Earth. Long-term cyclic change of the temperature condition of the CSC shell may restrict the resource efficiency of its material.As the shell material, is, usually, used a polymer film with several tens of microns in thickness, covered by a thin layer (a few nanometers of thickness) of deposited aluminum that is necessary to meet the CSC performance requirements. Following the CSC Earth orbital injection the shell takes a spherical shape due to the relatively low pressure produced by gas that fills it. In this case it is possible to obtain a spherical shell of a sufficiently large diameter, which is specific for the modern trends in deployment of large orbit transformable structures.To predict the health of the shell material resource is necessary to have information on the temperature distribution across its surface not only in the lit but also in the shaded area of the orbit. A quantitative analysis of the temperature condition of the CSC shell can be conducted through mathematical modeling, using its thermal model. The paper offers three stages to create such a model for a spherical shell as applied to the conditions in the shaded area of the orbit.At the first step for an arbitrary portion of the outer surface of the shell is determined a density of the incident-on-it intristic Earth's radiation on the premise that the angular distribution of intensity of this radiation according to directions obeys Lambert's law. Depending on the optical characteristics of the outer surface, part of this radiation is absorbed by the outer surface of the shell. The second stage builds a thermal model of a spherical shell, which establishes a pattern of redistribution of energy absorbed by radiation from its inner surface with regard a reradiation effect between the concave portions of the surface. Finally, the third stage uses the ratio of the local heat balance of a separate shell portion, which allows you to find the temperature of this portion, and then build the temperature distribution across the entire surface of the shell.

The presence of plasma in Low Earth Orbit and above can be the cause of electrostatic charging on space objects with a conductive surface, which then become subject to the Lorentz force induced by the magnetic field. This paper investigates it effects on the trajectory of orbital debris with a high area-to-mass ratio, as their course is particularly influenced by non-gravitational perturbations such as atmospheric drag or solar radiation pressure. Depending on the altitude (low or medium) and the available data, different charging models have been coupled with an orbit propagator, featuring a range of non-Keplerian accelerations and both three and six degrees-of-freedom dynamics. In particular, there has been a focus on long-term effects by simulating charged versus non-charged objects over the time span of years or decades.

The effect of DD ionospheric delays can be unexpectedly large in the range of the equatorial anomaly, that is, in mid-low-latitude regions near noon and/or afternoon, and the large delays cause instantaneous AR to fail even over short baselines. Ionospheric delays can be represented by a function of vertical total electron content values, which often have significant latitudinal gradients in mid-low-latitude regions near noon and/or afternoon. Therefore, a short separation between the pivot and secondary satellites in the latitudinal direction indicates smaller effects of DD ionosphere. In the BeiDou system (BDS), five geostationary earth orbit (GEO) satellites are nearly motionless over the equator. We can use adjacent GEO satellites to form a DD pair whose pivot and secondary satellites are close in latitude (

Statistical Orbit Determination techniques are used to find satellite positions for various navigation applications. The present paper reports the simulation study of the statistical orbit determination algorithm developed for geostationary and geosynchronous orbits for BeiDou constellation. BeiDou Navigation Satellite System (BDS) space constellation is composed of geostationary earth orbit (GEO), medium earth orbit (MEO) and inclined geosynchronous satellite orbit (IGSO). However, predicting the orbital parameters for geostationary earth orbits with zero inclination and for geosynchronous satellite orbits (GSO) with small inclination angle and small eccentricity is a challenging task [1]. Thus this paper is focused on mainly satellite orbit determination techniques for GEO and GSO orbits in the BDS.

Since November 2017, eight BeiDou global navigation system (BDS-3) satellites equipped with Ka-band inter-satellite link (ISL) payloads have been launched into medium earth orbit. We present the precise orbit determination (POD) for BDS-3 satellites using both L-band satellite-ground and Ka-band ISL observations. The satellite-ground tracking data are collected from the international GNSS Monitoring and Assessment System stations. The data period is DOY (day of year) 127---156, 2018. The BDS-3 ISL measurements are described by a dual one-way observation model. After transforming the dual one-way observations to the same epoch, clock-free and geometry-free observables can be obtained by the addition and subtraction of dual one-way observations. Using the geometry-free observables, the ISL measurement noise is analyzed and confirmed to be less than 10?cm. Using the clock-free observables and ground tracking data, the precise orbits are determined together with combined ISL hardware delays. For the estimates of hardware delays, the mean STD is 0.08?ns. For the satellite orbits, the ground-only POD solutions are also computed for comparison. When using 16 globally distributed ground stations, the addition of the ISLs improves the POD performance. For example, the 3D RMS of orbit overlap differences is reduced from 15.9?cm to 9.2?cm, yielding an improvement of 42% compared to ground-only POD. When only 6 stations in China are used for POD, the addition of ISLs enables the 3D RMS to be reduced from 85.4?cm to 14.8?cm with a greater improvement of 83%.

The multipath of BDS-2 medium earth orbit (MEO) satellites and BDS-3 satellites is analyzed. The multipath bias of BDS-2 satellites is corrected by second order polynomial fitting. By calculating Pearson correlation coefficient between multipath and elevation angle, it is found that the correlation coefficient between multipath and elevation angle of BDS-3 satellites is less than 0.1, and the correlation is not strong. Further, the fourth polynomial fitting model is used to verify that there is no code multipath bias for BDS-3 satellites. By comparing the Root Mean Square (RMS) of BDS-3 satellites code multipath, it is found that the multipath of B1C signal is the largest, approaching 0.5 m, while that of other signals is better than 0.3 m.

Real-time precise orbit/clock product is fundamental to BeiDou Navigation Satellite System (BDS) real-time precise point positioning (PPP). In order to explore achievable performance of BDS real-time orbit/clock products and thus offer usage recommendations for BDS real-time PPP users, this paper studies BDS real-time orbit/clock corrections provided by four International GNSS Service (IGS) Analysis Centers (ACs), i.e. Wuhan University (WHU), Deutsches Zentrum fur Luft- und Raumfahrt (DLR), GeoForschungsZentrum Potsdam (GFZ) and Centre National d’ Etudes Spatiales (CNE) for seven consecutive days staring from day of year (DOY) 324, 2019. Firstly, the availability of BDS-2 real-time orbit/clock corrections is studied. Larger than 85% availabilities are identified for all ACs. During the test period, DLR does not provide all Geosynchronous Earth Orbit (GEO) satellites’ corrections, whereas CNE does not provide C14/C16′s corrections. Secondly, the BDS real-time orbit accuracy is analyzed. Results indicate that the real-time orbit accuracy of GEO satellites is at meter level, and those of Inclined Geosynchronous Satellite Orbit (IGSO)/Medium Earth Orbit (MEO) satellites are at decimeter level. Among all ACs, the accuracy of CNE’s three-dimensional (3D) orbit correction is the best, which is 2.391/0.278/0.271 m for GEO/IGSO/MEO satellites, respectively. DLR has the largest orbit errors of 1.116/0.504 m for IGSO/MEO satellites. Thirdly, the BDS real-time clock offset precision is investigated. On the one hand, CNE’s real-time corrections still perform best with 1.19/0.28/0.32 ns clock offset precision for GEO/IGSO/MEO satellites, respectively. On the other hand, DLR’s real-time clock is the worst with 2.61/1.91 ns IGSO/MEO clock offset precision. Finally, all corrections are applied to estimate 47 Multi-GNSS Experiment (MGEX) station’s BDS-2 real-time PPP on DOY 330, 2019. Results show an average of 0.53–1.46 h convergence time and 8.8–10.9 cm positioning accuracy in the static mode. In the meantime, the average convergence time in the kinematic mode is 2.11–9.84 h, much longer than the static counterpart. The corresponding converged positioning accuracy is 30.7–68.0 cm. To sum up, WHU/GFZ/CNE’s real-time corrections are proven with satisfied orbit/clock performance, thus are recommended for BDS-2 real-time PPP.

This letter focuses on exploiting parameters, including peak power spectral density (PSD), integrated power, mean frequency, and spectrum width of reflected BeiDou signals in the frequency domain, to retrieve wind speed. The PSD of reflected signals is estimated after choosing proper parameters of the Welch method. Then, the features of PSD are illustrated, and a method is proposed based on fitting estimated PSD with a Gaussian function to evaluate the aforementioned PSD parameters. The estimated parameters of collected BeiDou medium earth orbit (MEO)/inclined geosynchronous satellite orbit (IGSO) and geostationary orbit (GEO) data are fitted with in situ wind speed using polynomial. Fitting results show that the peak PSD, mean frequency, and spectrum width of reflected signals from GEO have more evident dependence on wind speed, compared with MEO/IGSO. To obtain the most accurate results, the impact of delay used in lagging direct replica to align reflected signals is analyzed. Results show that regardless of delay locating within the interval of $[\tau_{0}-\tau_{c},\tau_{0}+\tau_{c}]$ , the better root-mean-square error (rmse) of less than 1.7 m/s and the larger coefficient of determination over 0.8 can be obtained by retrieving from the spectrum width, compared with peak PSD and mean frequency, whose optimal results, with rmse values of 2.03 and 1.70 m/s and coefficient of determination values of 0.73 and 0.81, are obtained as delay is $\tau_{0}-0.85\tau_{c}$ and $\tau_{0}+0.9\tau_{c}$ , respectively, where $\tau_{0}$ is the delay of specular reflection, and $\tau_{c}$ is the length of the B1 code.

Relativistic electrons can penetrate spacecraft shielding and can damage satellite components. Spacecraft in medium Earth orbit pass through the heart of the outer radiation belt and may be exposed to large fluxes of relativistic electrons, particularly during extreme space weather events. In this study we perform an extreme value analysis of the daily average internal charging currents at three different shielding depths in medium Earth orbit as a function of L∗ and along the orbit path. We use data from the SURF instrument on board the European Space Agency's Giove-A spacecraft from December 2005 to January 2016. The top, middle, and bottom plates of this instrument respond to electrons with energies >500 keV, >700 keV, and >1.1 MeV, respectively. The 1 in 10 year daily average top plate current decreases with increasing L∗ ranging from 1.0 pA cm−2 at L∗=4.75 to 0.03 pA cm−2 at L∗=7.0. The 1 in 100 year daily average top plate current is a factor of 1.2 to 1.8 larger than the corresponding 1 in 10 year current. The 1 in 10 year daily average middle and bottom plate currents also decrease with increasing L∗ ranging from 0.4 pA cm−2 at L∗=4.75 to 0.01 pA cm−2 at L∗=7.0. The 1 in 100 year daily average middle and bottom plate currents are a factor of 1.2 to 2.7 larger than the corresponding 1 in 10 year currents. Averaged along the orbit path the 1 in 10 year daily average top, middle, and bottom plate currents are 0.22, 0.094, and 0.094 pA cm−2, respectively.

In order to simplify the attitude control for inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) satellites of the BeiDou Navigation Satellite System (BDS) in eclipse seasons, two attitude modes, namely yaw-steering (YS) and orbit-normal (ON) mode are used. Significant accuracy degradation is observed for the orbits determined with the purely empirical CODE solar radiation pressure (SRP) model when these satellites switch to the ON mode. In addition, even though BDS IGSO satellites are in the YS mode, the orbits determined with the CODE SRP model show undesirable systematic errors that depend on the elevation angle β of the sun above the satellite orbit plane and on the argument angle μ of satellite with respect to the midnight point in the orbit plane as identified from satellite laser ranging residuals. We present the yaw attitude model used for the bus of BDS IGSO and MEO satellites, and constrain the mode-switch conditions by the β and μ angles. In order to overcome the deficiency of the purely empirical CODE SRP model for precise orbit determination (POD) of BDS IGSO and MEO satellites in the ON mode, an additional constant acceleration bias with tight constraint of 1.0 × 10ź10 m/s2 in the along-track direction has been introduced to the CODE SRP model, and it is denoted as the C5a model. Although the orbit accuracy of IGSO and MEO satellites is significantly improved in the ON mode, the β- and μ-dependent systematic orbit errors of BDS IGSO are not reduced. Hence, with the presented yaw attitude model of the satellite bus and two assumed orientations of solar panels, the adjustable box-wing (ABW) model has been modified. Two modified ABW models are compared with the purely empirical CODE and C5a model. Based on the analysis of real data of 2014, the C5a model shows the best performance in the ON mode among the four SRP models. Although two modified ABW models show a rather worse performance for POD in the ON mode, particularly in the cross-track and radial direction, the β- and μ-dependent systematic orbit errors of BDS IGSO satellites are reduced. This provides a new insight and a possible way to improve the orbits of BDS IGSO and MEO satellites.

The use of Global Positioning System (GPS) observables provides the primary and advantageous technique for satellite orbit determination in low earth orbit (LEO), in particular when onboard autonomy is required. A wide range of LEO spacecraft equipped with GPS receivers have been launched into space for different applications. Aiming at determining the position and velocity of the satellite in real-time, a consider Kalman filter (CKF)-based reduced-dynamic orbit determination (RDOD) is introduced in this paper. In the CKF, orbit dynamic model is simplified to meet the space-borne computational limitations. The atmospheric drag and solar radiation pressure coefficients are considered rather than estimated in the conventional RDOD strategy. Only a lower order and degree of an earth gravity model is used in the orbit model. However, the propagation of the covariance of the consider parameters is able to absorb the unmodeled and dismodeled perturbations. Therefore, the filter could become convergent with desirable orbit determination performance. The CKF-RDOD method is implemented with a set of the Gravity Recovery and Climate Experiment flight data. The solutions indicate that this proposed method could achieve satisfactory precision orbit determination with approximately 1.5 m level of three-dimensional root-mean-square error using GPS broadcast messages in real-time scenarios.

Two classic empirical solar radiation pressure (SRP) models, the Extended Center for Orbit Determination in Europe (CODE) Orbit Model ECOM 5 and ECOM 9 have been widely used for Global Positioning System (GPS) Medium Earth Orbit (MEO) satellites precise orbit determination (POD). However, these two models are not suitable for BeiDou Geostationary Earth Orbit (GEO) satellites due to their special attitude control mode. With the experimental design method this paper proposes a new empirical SRP model for BeiDou GEO satellites, which is featured by three constant terms in DYX directions, two sine terms in DX directions and one cosine term in the Y direction. It is the first time to reveal that the periodic terms in the D direction are more important than those in YX directions for BeiDou GEO satellites. Compared with ECOM 5 and ECOM 9, the BeiDou GEO satellite orbits are significantly stabilized with the new SRP force model. The average orbit overlapping root mean square (RMS) achieved by the proposed model is 7.5 cm in the radial component, which is evidently improved over those of 37.4 and 13.2 cm for ECOM 5 and ECOM 9, respectively. In addition, the correlation coefficients between GEO orbit overlaps precision and the elevation angle of the Sun have been decreased to −0.12, 0.21, and −0.03 in radial, along-track and cross-track components by using the proposed model, while they are −0.94, −0.79 and −0.29 for ECOM 5 and −0.70, 0.21 and 0.10 for ECOM 9. Moreover, the standard deviation (STD) of Satellite Laser Ranging (SLR) data residuals for the GEO satellite C01 is reduced by 37.4% and 16.1% compared with those of ECOM 5 and ECOM 9 SRP models.