Medium Earth Orbit Research Articles

Improving BeiDou Global Navigation Satellite System (BDS-3)-Derived Station Coordinates Using Calibrated Satellite Antennas and Station Inter-System Translation Parameters

The BeiDou global navigation satellite system (BDS-3) has been widely applied in various geodetic applications since its full operation. However, the estimated station coordinates using BDS-3 are less precise compared to GPS results. It contains systematic errors caused by scale bias with respect to International GNSS Service (IGS) 2020 frame and Inter-System Translation Parameters (ISTPs). In order to improve the consistency of BDS-3-derived station coordinates with respect to IGS20 products, we firstly estimated the satellite antenna Phase Center Offsets (PCOs) for BDS-3 Medium Earth Orbit (MEO) constellation, and then estimated station-specific ISTPs from GPS to BDS-3 systems. The results indicate that the PCO-Z estimates show large differences among satellites from different manufacturers and orbit planes. The estimated BDS-3 satellite PCOs exhibit a systematic bias of −9.3 cm in the Z-direction compared to ground calibrations. The maximum mean station-specific ISTPs can reach up to 3 mm, highlighting significant variability and the need for refinement in positioning. When using the estimated PCOs instead of igs20.atx values, the estimated scale bias with respect to the IGS20 frame is reduced from 0.38 ppb to −0.12 ppb, indicating that the refined BDS-3 satellite PCOs are well compatible with IGS20. Regarding the Up component that is correlated with the scale factor, the station coordinate differences with respect to the IGS20 frame is reduced from 7.0 mm to 6.2 mm in terms of the root mean square (RMS), which is improved by 11.4%. Considering the additional ISTP corrections, a further improvement of 17% was obtained in station coordinates. The RMS of station coordinate differences with respect to the IGS20 frame is 2.3 mm, 2.7 mm, and 5.2 mm for the North, East, and Up components, respectively.

Design study of a camera system for Earth observation as a payload on the small satellite ROMEO

AbstractThe importance of a safe food supply has increased due to climate change and its consequences. The number and severity of floods, droughts and plant diseases are rising which causes massive crop failures. Early and precise detection of plant diseases can lower crop failures as it enables early containment. Moreover, it promotes the targeted use of pesticides to protect the biodiversity. Satellite sensors improve the detection of plant diseases by enabling frequent and extensive vegetation observation. Hence, we present the design of a camera system for Earth observation on small satellites with a focus on the detection of plant diseases. The disease detection of sugar beets was chosen as the primary objective due to their importance for the German agriculture. This work is divided into two parts. First, the spectra of sugar beets are analyzed to determine spectral channels for a camera system. Second, a camera system is defined to capture spectral information within the previously defined wavelength ranges. The spectra of healthy and diseased sugar beets were measured in fields for agricultural research in Central Germany using a portable spectroradiometer. The investigated diseases are Cercospora leaf spot and virus yellows, which are among the most important pathogens worldwide. Based on the measured data, the so-called Normalized Difference Sugar Beet Index (NDSBI) is defined, which is a custom index to detect these diseases. We can prove that this index enables more precise detection of these sugar beet diseases than existing indices like the Normalized Difference Vegetation Index (NDVI). The camera system is designed as a payload for the small satellite Research and Observation in Medium Earth Orbit (ROMEO), which is being developed at the University of Stuttgart’s (US) Institute of Space Systems (IRS). The proposed design fulfills the high radiation requirements as well as the system constraints of mass and volume. Three different options for the camera system are developed: two designs for the development at the US, one with lens optics and one with mirror optics, and an adjusted commercial camera system. All defined camera systems permit the measurement of the NDSBI to precisely detect sugar beet diseases.

Enhanced detection and identification of satellites using an all-sky multi-frequency survey with prototype SKA-Low stations

Abstract With the low Earth orbit environment becoming increasingly populated with artificial satellites, rockets, and debris, it is important to understand the effects they have on radio astronomy. In this work, we undertake a multi-frequency, multi-epoch survey with two SKA-Low station prototypes located at the SKA-Low site, to identify and characterise radio frequency emission from orbiting objects and consider their impact on radio astronomy observations. We identified 152 unique satellites across multiple passes in low and medium Earth orbits from 1.6 million full-sky images across 13 selected ≈ 1 MHz frequency bands in the SKA-Low frequency range, acquired over almost 20 days of data collection. Our algorithms significantly reduce the rate of satellite misidentification, compared to previous work, validated through simulations to be < 1%. Notably, multiple satellites were detected transmitting unintended electromagnetic radiation, as well as several decommissioned satellites likely transmitting when the Sun illuminates their solar panels. We test alternative methods of processing data, which will be deployed for a larger, more systematic survey at SKA-Low frequencies in the near future. The current work establishes a baseline for monitoring satellite transmissions, which will be repeated in future years to assess their evolving impact on radio astronomy observations.

A High-Resolution Spotlight Imaging Algorithm via Modified Second-Order Space-Variant Wavefront Curvature Correction for MEO/HM-BiSAR

A bistatic synthetic aperture radar (BiSAR) system with a Medium-Earth-Orbit (MEO) SAR transmitter and high-maneuvering receiver (MEO/HM-BiSAR) can achieve a wide swath and high resolution. However, due to the complex orbit characteristics and the nonlinear trajectory of the receiver, MEO/HM-BiSAR high-resolution imaging faces two major challenges. First, the complex geometric configuration of the BiSAR platforms is difficult to model accurately, and the ‘non-stop-go’ effects should also be considered. Second, non-negligible wavefront curvature caused by the nonlinear trajectories introduces residual phase errors. The existing spaceborne BiSAR imaging algorithms often suffer from image defocusing if applied to MEO/HM-BiSAR. To address these problems, a novel high-resolution imaging algorithm named MSSWCC (Modified Second-Order Space-Variant Wavefront Curvature Correction) is proposed. First, a high-precision range model is established based on an analysis of MEO SAR’s orbital characteristics and the receiver’s curved trajectory. Based on the echo model, the wavefront curvature error is then addressed by two-dimensional Taylor expansion to obtain the analytical expressions for the high-order phase errors. By analyzing the phase errors in the wavenumber domain, the compensation functions can be designed. The MSSWCC algorithm not only corrects the geometric distortion through reverse projection, but it also compensates for the second-order residual spatial-variant phase errors by the analytical expressions for the two-dimensional phase errors. It can achieve high-resolution imaging ability in large imaging scenes with low computational load. Simulations and real experiments validate the high-resolution imaging capabilities of the proposed MSSWCC algorithm in MEO/HM-BiSAR.

Performance of GNSS space service for geostationary autonomous operations

Abstract The geostationary orbit (GEO) belt hosts a substantial number of high-value satellites, making the study of autonomous navigation within this area significant. Features of autonomous operations such as patrolling the GEO belt and frequent manoeuvres at a certain location make real-time positioning using the Global Navigation Satellite System (GNSS) valuable. This paper studies the performance of positioning with GNSS considering main lobe and side lobe signals at different longitudes in the GEO belt. The research delves into the visibility and Position Dilution of Precision (PDOP) across the GEO belt, analysing the performance of the Global Positioning System (GPS), GLObalnaya NAvigatsionnaya Sputnikovaya Sistema (GLONASS) in Russian, BeiDou Navigation Satellite System (BDS), Galileo Navigation Satellite System (Galileo) and multi-systems. In particular, this paper investigates the impact of asymmetric constellations of mixed GEO, Inclined Geosynchronous Orbit (IGSO) and Medium Earth Orbit (MEO) satellites. The study reveals that BDS hybrid constellation provides long-term stable signal coverage over the GEO space above North America and Atlantic Ocean, where GEO signals are more sustainable while IGSO signals have wider coverage. This advantage positions BDS favourably in terms of performance in these regions.

Flatness constraints in the estimation of GNSS satellite antenna phase center offsets and variations

Accurate information on satellite antenna phase center offsets (PCOs) and phase variations (PVs) is indispensable for high-precision geodetic applications. In the absence of consistent pre-flight calibrations, satellite antenna PCOs and PVs of global navigation satellite systems are commonly estimated based on observations from a global network, constraining the scale to a given reference frame. As part of this estimation, flatness and zero-mean conditions need to be applied to unambiguously separate PCOs, PVs, and constant phase ambiguities. Within this study, we analytically investigate the impact of different boresight-angle-dependent weighting functions for PV minimization, and we compare antenna models generated with different observation-based weighting schemes with those based on uniform weighting. For the case of the GPS IIR/-M and III satellites, systematic differences of 10 mm in the PVs and 65 cm in the corresponding PCOs are identified. In addition, new antenna models for the different blocks of BeiDou-3 satellites in medium Earth orbit are derived using different processing schemes. As a drawback of traditional approaches estimating PCOs and PVs consecutively in distinct steps, it is shown that different, albeit self-consistent, PCO/PV pairs may result depending on whether PCOs or PVs are estimated first. This apparent discrepancy can be attributed to potentially inconsistent weighting functions in the individual processing steps. Use of a single-step process is therefore proposed, in which a dedicated constraint for PCO-PV separation is applied in the solution of the normal equations. Finally, the impact of neglecting phase patterns in precise point positioning applications is investigated. In addition to an overall increase of the position scatter, the occurrence of systematic height biases is illustrated. While observation-based weighting in the pattern estimation can help to avoid such biases, the possible benefit depends critically on the specific elevation-dependent weighting applied in the user’s positioning model. As such, the practical advantage of such antenna models would remain limited, and uniform weighting is recommended as a lean and transparent approach for the pattern estimation of satellite antenna models from observations.

Derivation of the Sagnac (Earth-rotation) correction and analysis of its accuracy for GNSS applications

Global Navigation Satellite Systems (GNSS) applications require computation of the geometric range between the satellite vehicle at the time-of-signal transmission and the receiver antenna location at the time-of-signal reception. This computation requires attention to the frames of reference due to the rotation of the Earth-Centered Earth-Fixed (ECEF) frame during the time-of-signal propagation. Three range computation approaches are commonplace and will be discussed herein. The first is the Global Positioning System Interface Control Document recommendation to rotate the ECEF frames to a common reference time. The other two are forms of the Sagnac correction. The Sagnac derivations already in the literature are either limited to stationary receivers or lack the connection between the Earth-centered inertial (ECI) and ECEF frames. Neither form of the Sagnac correction exactly reproduces the geometric range. They are approximations. The literature does not currently contain an analysis of the error involved in using either form of the Sagnac correction. This article makes two contributions: (1) it presents derivations for both forms of the Sagnac correction that are valid for moving receivers and that maintain the connection between the ECI and ECEF frames; and (2) it analyzes the error of the Sagnac correction for orbits of different radius. The analysis shows that Sagnac corrections introduce range errors less than 7.57×10-4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$7.57\ imes 10^{-4}$$\\end{document} meters for GNSS satellites at medium Earth orbit.

Modeling of Solar Radiation Pressure for BDS-3 MEO Satellites with Inter-Satellite Link Measurements

As the largest non-gravitational force, solar radiation pressure (SRP) causes significant errors in precise orbit determination (POD) of the BeiDou global navigation satellite system (BDS-3) medium Earth orbit (MEO) satellite. This is mainly due to the imperfect modeling of the satellite’s cuboid body. Since the BDS-3’s inter-satellite link (ISL) can enhance the orbit estimation of BDS-3 satellites, the aim of this study is to establish an a priori SRP model for the satellite body using 281-day ISL observations to reduce the systematic errors in the final orbits. The adjustable box wind (ABW) model is employed to refine the optical parameters for the satellite buses. The self-shadow effect caused by the search and rescue (SAR) antenna is considered. Satellite laser ranging (SLR), day-boundary discontinuity (DBD), and overlapping Allan deviation (OADEV) are utilized as indicators to assess the performance of the a priori model. With the a priori model developed by both ISL and ground observation, the slopes of SLR residual for the China Academy of Space Technology (CAST) and Shanghai Engineering Center for Microsatellites (SECM) satellites decrease from −0.097 cm/deg and 0.067 cm/deg to −0.004 cm/deg and −0.009 cm/deg, respectively. The standard deviation decreased by 21.8% and 26.6%, respectively. There are slight enhancements in the average values of DBD and OADEV, and a reduced β-dependent variation is observed in the OADEV of the corresponding clock offset. We also found that considering the SAR antenna only slightly improves the orbit accuracy. These results demonstrate that an a priori model established for the BDS-3 MEO satellite body can reduce the systematic errors in orbits, and the parameters estimated using both ISL and ground observation are superior to those estimated using only ground observation.

Research on Design and Staged Deployment of LEO Navigation Constellation for MEO Navigation Satellite Failure

Low Earth orbit (LEO) satellites have unique advantages in navigation because of their high signal intensity and rapid geometric changes in a short period. In order to solve the problem of constellation performance degradation after a potential failure pertaining one or more medium Earth orbit (MEO) navigation satellites, this paper designs the LEO navigation constellation and considers the task requirements of different stages of constellation deployment. Firstly, the LEO navigation constellation is designed by a non-dominated sorting genetic algorithm II (NSGA-II). The average position dilution of precision (PDOP) is 1.676, which is an improvement compared to the average PDOP offered by the four traditional GNSS. Secondly, the staged deployment of constellation takes into account the degradation of constellation performance caused by the failure of MEO navigation satellites, and the Monte Carlo method is used to analyze the case of three simultaneous satellite failures. The results show that a single satellite failure within each orbital plane and adjacent satellites with close phase separation has a great impact on the performance of the MEO navigation constellation. On this basis, a staged deployment strategy was adopted in order to balance cost, risk, and performance. The three phases deploy 66, 156, and 288 satellites, respectively; as a make-up constellation under contingencies, a navigation enhancement constellation, and an independent navigation constellation, the deployment of the staged sub-constellations meets the mission requirements. The constellation design and staged deployment method proposed in this paper can provide reference for the future study of LEO navigation constellations.

Effect of WHU/GFZ/CODE satellite attitude quaternion products on the GNSS kinematic PPP during the eclipse season

To ensure high-precision Global Navigation Satellite System (GNSS) applications, many analysis centers (ACs) have begun to provide satellite attitude products, which affect the modeling of phase variations and phase wind-up. Despite several studies having demonstrated the importance of providing attitude products, particularly eclipsing products, the performance of satellite attitude models for different ACs has not been further investigated. This study compared the satellite attitude models provided by Wuhan university (WHU), German Research Centre of Geosciences (GFZ), and Center for Orbit Determination in Europe (CODE), and investigated the impact of satellite attitude products on high-rate GNSS data processing (i.e., 1HZ). The satellite attitudes of most satellite blocks were consistent well with each other, except for the BDS-2 inclined geostationary orbit (IGSO), BDS-3 medium earth orbit (MEO), GPS IIIA, and GLONASS-M satellites. The differences in the yaw angle between the different ACs ranged as 10–180°. Compared to the good consistency of the wum and com products, gbm exhibited significant differences from the former for most constellations. Following the application of the satellite attitude products, the average 3D RMS value of the single-kinematic PPP was improved by 11 % and 10 % for the 30-s and 1-s sampling rate observations, respectively. Thus, these eclipsing satellites with inaccurate attitude models can be deleted while integrating more satellites into the GNSS data processing.

Analysis of multipath effects on Low Earth Orbit navigation satellites

Abstract With the large-scale emergence of Low-Earth Orbit (LEO) internet constellations, the direct or indirect utilization of LEO communication constellations for navigation and positioning has become a hot topic of current research. However, the multipath effect remains a critical factor influencing positioning accuracy. Compared to traditional Medium-Earth Orbit (MEO) satellites, LEO satellites move swiftly, resulting in faster multipath variations, which renders traditional multipath envelope analysis methods inapplicable. This study proposes a novel analytical model tailored to the multipath effect characteristics of LEO satellites. Through this model, we have observed that the multipath variations of high-frequency signals in LEO rapidly fluctuate near zero, offering the potential to reduce errors through smoothing methods. Furthermore, the study reveals that the impact of the multipath effect is positively correlated with orbital altitude and inversely correlated with carrier frequency. This study provides a new perspective for understanding the multipath effect characteristics of LEO satellites and offers necessary theoretical support and practical guidance for improving the accuracy of navigation and positioning systems based on LEO satellites. Future research can further explore multipath suppression methods and promote the widespread application of LEO satellites in the field of navigation and positioning.

PreMevE‐MEO: Predicting Ultra‐Relativistic Electrons Using Observations From GPS Satellites

AbstractUltra‐relativistic electrons with energies greater than or equal to two megaelectron‐volt (MeV) pose a major radiation threat to spaceborne electronics, and thus specifying those highly energetic electrons has a significant meaning to space weather communities. Here we report the latest progress in developing our predictive model for MeV electrons in the outer radiation belt. The new version, primarily driven by electron measurements made along medium‐Earth‐orbits (MEO), is called PREdictive MEV Electron (PreMevE)‐MEO model that nowcasts ultra‐relativistic electron flux distributions across the whole outer belt. Model inputs include >2 MeV electron fluxes observed in MEOs by a fleet of GPS satellites as well as electrons measured by one Los Alamos satellite in the geosynchronous orbit. We developed an innovative Sparse Multi‐Inputs Latent Ensemble NETwork (SmileNet) which combines convolutional neural networks with transformers, and we used long‐term in situ electron data from NASA's Van Allen Probes mission to train, validate, optimize, and test the model. It is shown that PreMevE‐MEO can provide hourly nowcasts with high model performance efficiency and high correlation with observations. This prototype PreMevE‐MEO model demonstrates the feasibility of making high‐fidelity predictions driven by observations from longstanding space infrastructure in MEO, thus has great potential of growing into an invaluable space weather operational warning tool.

Calibration Method for Relativistic Navigation System Using Parallel Q-Learning Extended Kalman Filter.

For the relativistic navigation system where the position and velocity of the spacecraft are determined through the observation of the relativistic perturbations including stellar aberration and starlight gravitational deflection, a novel parallel Q-learning extended Kalman filter (PQEKF) is presented to implement the measurement bias calibration. The relativistic perturbations are extracted from the inter-star angle measurement achieved with a group of high-accuracy star sensors on the spacecraft. Inter-star angle measurement bias caused by the misalignment of the star sensors is one of the main error sources in the relativistic navigation system. In order to suppress the unfavorable effect of measurement bias on navigation performance, the PQEKF is developed to estimate the position and velocity, together with the calibration parameters, where the Q-learning approach is adopted to fine tune the process noise covariance matrix of the filter automatically. The high performance of the presented method is illustrated via numerical simulations in the scenario of medium Earth orbit (MEO) satellite navigation. The simulation results show that, for the considered MEO satellite and the presented PQEKF algorithm, in the case that the inter-star angle measurement accuracy is about 1 mas, after calibration, the positioning accuracy of the relativistic navigation system is less than 300 m.

Severe Electron Environment for Surface Charging at Geostationary and Medium Earth Orbits

Electron radiation environment with keV energies on medium earth orbit (MEO) is investigated around the times when worst-case severe environments for surface charging were detected at Los Alamos National Laboratory (LANL) satellites on geostationary earth orbit (GEO). The Inner Magnetosphere Particle Transport and Acceleration Model (IMPTAM) is employed to model 1–100 keV electron fluxes in the inner Earth’s magnetosphere (inside 10RE) during four representative events selected out of 400 LANL worst-case severe environment events. Modeled fluxes are compared to the observed ones on GEO, and the peak electron fluxes are then extracted at L=4.6 which is considered as approximate MEO environment following the LANL events. IMPTAM generally reproduces the 10–50 keV electron fluxes on GEO but underestimates (of factor of 2 to 5) at energies above. It is found that the maximum electron flux on MEO is reached in about 1.5–2 h after the worst-case environment for surface charging was detected at GEO. Whereas the magnetic local time (MLT) location of the worst-case severe environments on GEO varies from 23 to 05, the maximum electron flux on MEO is located on 6–7.8 MLT. The maximum electron flux values on MEO can be 2 to 10 times higher than those observed on GEO and those estimated using European Cooperation for Space Standardization and National Aeronautics and Space Administration guidelines, which can be a significant increase of the risks in terms of surface charging.

Laser Observations of GALILEO Satellites at the CBK PAN Astrogeodynamic Observatory in Borowiec

The laser station (BORL) owned by the Space Research Centre of the Polish Academy of Sciences and situated at the Astrogeodynamic Observatory in Borowiec near Poznań regularly observes more than 100 different objects in low Earth orbit (LEO) and medium Earth orbit (MEO). The BORL sensor’s laser observation range is from 400 km to 24,500 km. The laser measurements taken by the BORL sensor are utilized to create various products, including the geocentric positions and movements of ground stations, satellite orbits, the components of the Earth’s gravitational field and their changes over time, Earth’s orientation parameters (EOPs), and the validation of the precise Galileo orbits derived using microwave measurements, among others. These products are essential for supporting local and global geodetic and geophysics research related to time. They are crucial for the International Terrestrial Reference Frame (ITRF), which is managed by the International Earth Rotation and Reference Systems Service (IERS). In 2023, the BORL laser station expanded its list of tracked objects to include all satellites of the European satellite navigation system GALILEO, totaling 28 satellites. During that year, the BORL laser station recorded 77 successful passes of GALILEO satellites, covering a total of 21 objects. The measurements taken allowed for the registration of 7419 returns, resulting in 342 normal points. The average RMS for all successful GALILEO observations in 2023 was 13.5 mm.

Extension of the BDS IGSO and MEO satellite antenna patterns with FengYun-3C and LuTan-1 onboard data

The International Global Navigation Satellite System (GNSS) Service (IGS) has recommended calibrating the extended satellite antenna Phase Center Variation (PCV) model for all navigation satellites to support low-Earth-Orbit (LEO) satellite applications. Owing to the absence of ground-calibrated PCVs for the BeiDou Navigation Satellite System (BDS), tracking data from global ground stations were used for in-orbit estimations. However, limited by the observed maximum nadir angle, PCVs based on ground data cannot cover the entire range of nadir angles observed using by LEO satellites. In this study, the FengYun-3C and LuTan-1 missions were used to extend the PCVs of the BDS Inclined GeoSynchronous orbit (IGSO) and medium-Earth-orbit (MEO) satellites. The PCVs corresponding to the ionosphere-free linear combinations of B1I/B2I, B1I/B3I, and B1C/B2a were calibrated in-orbit by extending the maximum nadir angle from 9° to 10° for the IGSO and from 13° to 15° for the MEO. There was good consistency among the estimated PCVs of satellites of the same type. In addition, these estimated PCVs were close to the corresponding satellite block-specific values estimated based on ground tracking data. The impact of the extended PCVs of the BDS satellite antenna was investigated by comparing them with the unextended PCVs model in the receiver antenna PCVs pattern estimation and precise orbit determination of the FengYun-3C and LuTan-1 satellites. The results showed that the extended BDS satellite PCVs effectively reduced the unmodeled error of the unextended BDS satellite PCVs in the low-elevation region of the LEO receiver antenna PCV patterns. In addition, compared with the introduction of phase center offset alone, the introduction of ground-based PCVs can improve the overlapping orbit differences (OODs) of LEO satellites, and the extended BDS satellite PCVs can further improve the OODs. Taking B1C/B2a as an example, the improvement ratio of OODs in the 3D direction of Lutan-1A increased from 5.2 % to 8.0 %, and that of Lutan-1B can rise from 1.7 % to 4.2 %.

Space interferometer orbit determination with multi-GNSS

Spacecraft positioning plays a crucial role in scientific space mission design, as well as in the further scheduling of scientific observations for such a mission. We examine the application of global navigation satellite systems (GNSS) to solve the orbit determination problem in a pure space very long baseline interferometer (VLBI) project. A network of GPS, GLONASS, Galileo and BeiDou navigation satellites may be a more efficient solution to determining the position and velocity of space radio telescopes and space interferometer baselines. For such a project, it is necessary to take into account the special conditions of GNSS observations, as well as the high accuracy of determining not only position but also velocity. In this paper, we estimate visibility of navigation satellite systems for Low and Medium orbits of a pure space-VLBI system and simulate GNSS code and phase measurements. Orbit determination was performed on smoothed code measurements. Phase measurements simulated with a step of 1 s and combined in Doppler measurements yield average position and velocity errors of 1.01 m and 8.8 mm/s in Medium Earth orbit. The results showed that GNSS observations are sufficient to solve the problems of orbit determination of a space-VLBI interferometer both in Low-Earth and Medium Earth orbits.

Navigation Resource Allocation Algorithm for LEO Constellations Based on Dynamic Programming

Navigation resource allocation for low-earth-orbit (LEO) constellations refers to the optimal allocation of navigational assets when the number and allocation of satellites in the LEO constellation have been determined. LEO constellations can not only transmit navigation enhancement signals but also enable space-based monitoring (SBM) for real-time assessment of GNSS signal quality. However, proximity in the frequencies of LEO navigation signals and SBM can lead to significant interference, necessitating isolated transmission and reception. This separation requires that SBM and navigation signal transmission be carried out by different satellites within the constellation, thus demanding a strategic allocation of satellite resources. Given the vast number of satellites and their rapid movement, the visibility among LEO, medium-earth-orbit (MEO), and geostationary orbit (GEO) satellites is highly dynamic, presenting substantial challenges in resource allocation due to the computational intensity involved. Therefore, this paper proposes an optimal allocation algorithm for LEO constellation navigation resources based on dynamic programming. In this algorithm, a network model for the allocation of navigation resources in LEO constellations is initially established. Under the constraints of visibility time windows and onboard transmission and reception isolation, the objective is set to minimize the number of LEO satellites used while achieving effective navigation signal transmission and SBM. The constraints of resource allocation and the mathematical expression of the optimization objective are derived. A dynamic programming approach is then employed to determine the optimal resource allocation scheme. Analytical results demonstrate that compared to Greedy and Divide-and-Conquer algorithms, this algorithm achieves the highest resource utilization rate and the lowest computational complexity, making it highly valuable for future resource allocation in LEO constellations.

SLR Validation and Evaluation of BDS-3 MEO Satellite Precise Orbits

Starting from February 2023, the International Laser Ranging Service (ILRS) began releasing satellite laser ranging (SLR) data for all BeiDou global navigation satellite system (BDS-3) medium earth orbit (MEO) satellites. SLR data serve as the best external reference for validating satellite orbits, providing a basis for comprehensive evaluation of the BDS-3 satellite orbit. We utilized the SLR data from February to May 2023 to comprehensively evaluate the orbits of BDS-3 MEO satellites from different analysis centers (ACs). The results show that, whether during the eclipse season or the yaw maneuver season, the accuracy was not significantly decreased in the BDS-3 MEO orbit products released from the Center for Orbit Determination in Europe (CODE), Wuhan University (WHU), and the Deutsches GeoForschungsZentrum (GFZ) ACs, and the STD (Standard Deviation) of SLR residuals of those three ACs are all less than 5 cm. Among these, CODE had the smallest SLR residuals, with 9% and 12% improvement over WHU and GFZ, respectively. Moreover, the WHU precise orbits exhibit the smallest systematic biases, whether during non-eclipse seasons, eclipse seasons, or satellite yaw maneuver seasons. Additionally, we found some BDS-3 satellites (C32, C33, C34, C35, C45, and C46) exhibit orbit errors related to the Sun elongation angle, which indicates that continued effort for the refinement of the non-conservative force model further to improve the orbit accuracy of BDS-3 MEO satellites are in need.

Imaging the event horizon of M87* from space on different timescales

Imaging the event horizon of M87* from space on different timescales