Navigation Satellite Research Articles

Time synchronization between satellites via inter-satellite link observations of BDS-3 Constellation: Method, experiment and analysis

Time synchronization through inter-satellite link (ISL) observations is crucial for enabling autonomous navigation in global navigation satellite systems. This study investigates the time synchronization performance within China's BeiDou Navigation Satellite System (BDS) using ISL measurements from 29 BDS-3 constellation satellites. A dedicated two-way time synchronization method is detailed, emphasizing its uniqueness and precision in ensuring accurate time synchronization. The study also delves into the application of various error corrections, encompassing time delay induced by motion, relativistic effects, and hardware delays. Ranging results show accuracies around 7 cm for one-way ISLs. The impact of error corrections is quantified, with the time delay error caused by motion exhibiting the most significant influence on synchronization accuracy. Using one month of BDS-3 ISL data, time synchronization accuracies better than 0.4 ns are consistently achieved between all satellites after implementing comprehensive error mitigation. The results indicate the robust performance of the BDS-3 ISL system for high-precision timekeeping, supporting autonomous orbit determination and navigation without relying on ground monitoring. These findings demonstrate the effectiveness of using ISLs for GNSS satellites and provide valuable insights for advancing satellite navigation capabilities.

Retrieval of high-precision precipitable water vapour maps using Sentinel-1A and Beidou satellite data

ABSTRACTPrecipitable water vapour (PWV) is a primary factor that affects climate and weather. The accurate retrieval of PWV is crucial for weather prediction and meteorological research. Interferometric Synthetic Aperture Radar (InSAR) has been rapidly developed in recent years and proven effective in PWV retrieval in the regions of good coherence. However, there are large areas of natural terrain where signals decoherence that limit the precision of PWV retrieval. Besides, due to the differential interference processing of InSAR data, the results of its retrieval are differential PWV (ΔPWV). In this study, the StaMPS-InSAR was used to overcome the problem of weak detection ability in low coherence regions. A series of 11 Sentinel-1A images were selected to retrieve space-continuous ΔPWV. Beidou Satellite Navigation System (BDS) can retrieve high-precision PWV. Hence, the BDS data was utilized to convert the InSAR-derived ΔPWV to PWV. Compared with the BDS-derived PWV, the root mean square error (RMSE) of the experimental results is 1.3 mm with a spatial resolution as fine as 20 m. The correlation coefficient between the deviations and Liquid Cloud Water is 0.65, indicating a positive correlation. We demonstrate the advantage of the proposed method for retrieving PWV in computational efficiency by comparing it with the SBAS-InSAR. With the increasing stack size of the SAR images, our method can reduce the taking time for processing. The proportion can reach 12.6% when the stack size of SAR images is 20. By the spatio-temporal analysis of the results, we found some characteristics of PWV in mountain areas especially. The results have certain reference value for the space-continuous PWV retrieval and the study of PWV spatio-temporal characteristics.

Research on an Active Hydrogen Maser Digital Circuit Control System Based on FPGA.

A hydrogen maser is a high-precision time measurement instrument with high frequency stability and low frequency drift, which is widely used in satellite navigation, ground time keeping, frequency measurement, and other fields. An active hydrogen maser (AHM) is better than the current space passive hydrogen maser (PHM) in orbit in terms of its frequency stability and drift rate, but it has the disadvantages of large volume and weight. To further reduce the volume and weight of the circuit, this paper demonstrates a digital circuit control system based on a field-programmable gate array (FPGA). It uses digital temperature control, digital detectors, digital down-conversion, digital phase-locked loops, and other digital methods for temperature control, cavity auto-tuning, and crystal phase locking, which improve the integration and flexibility of the circuit system. Meanwhile, a tuning method based on hydrogen flow is proposed, which effectively solves the problem of fluctuations in hydrogen maser resonance frequency with changes in the external environment. Our experimental results show that the designed digital circuit control system meets the requirements of an oven-controlled crystal oscillator (OCXO) loop and a cavity loop. Its frequency stability can reach 2.6×10-13/1 s and 1.4×10-15/10,000 s, which is close to the stability index of ground active hydrogen maser. This scheme has certain practical engineering value, and can be used in the design of hydrogen masers for next-generation space navigation satellites, deep space exploration, and space stations.

Modal synthesis of observers of state variables of ship dynamical systems

The purpose of the work is to increase the information content of ship control systems through the use of dynamic observers, which are, in essence, mathematical information sensors and allow you to fully restore the vector of state variables of the object model with high accuracy by measuring the output vector of a smaller dimension. An algorithm for the synthesis of observers based on the modal method of parametric evaluation of their model is proposed. It provides obtaining the parameters of the regulator according to the given spectra of the matrices of the state of the observed system and the object by means of the Control Toolbox of the MATLAB computing environment. The use of the modal method (subject to the conditions of observability and controllability) guarantees the stability of observers, which allows them to be used for stable and unstable observed objects and systems. The algorithm of modal synthesis of observers is suitable for increasing the information content of a wide range of ship dynamic systems and, above all, control systems for ship energy complexes and their components. These include autopilots, control systems for ship power plants and their elements, dynamic complexes of satellite and inertial navigation systems and positioning of moving objects in remote control conditions, monitoring and safety tools, identifiers, etc. It has been shown that in the conditions of digital transformation, the use of observers dramatically improves the quality and reduces the time for modeling the dynamics of ship systems and energy complexes operated under conditions of external disturbances, which makes it possible to improve the algorithms for estimating state variables of a class of autonomous objects modeled by nonlinear equations that allow the transition in the working area to quasi linear models with time-invariant parameters. The proposed algorithm is demonstrated by the example of the synthesis of a three-dimensional observer for the control system of a supertanker with deadweight of 150 thousand tons. The simulation of the control object is performed with an input signal of triangular shape, which most fully corresponds to the real control signal, and it is implemented in the form of a program compiled in MATLAB codes. The obtained values of state variables and errors of their recovery correspond to the specified speed and the required stability of the control system.

Analysis of Multifrequency GNSS Signals and an Improved Single-Epoch RTK Method for Medium-Long Baseline

In recent years, the quantity of visible satellites has increased significantly due to multiple satellite systems that leaped forward. The BeiDou Navigation Satellite System (BDS) and Galileo satellite navigation system (Galileo) broadcast triple-frequency signals and above to users, thus enhancing the reliability, continuity, and availability of the single-epoch real-time kinematic (RTK) positioning. In this study, an improved single-epoch multifrequency multisystem RTK method is successfully developed for the medium-long baseline. First, the Galileo and BDS extra-wide-lane (EWL) ambiguities are fixed at a high success rate, and the Galileo and BDS wide-lane (WL) ambiguity is achieved via the transformation process. Second, the fixed WL ambiguities of Galileo and BDS are exploited to elevate the fixed rate of GPS WL ambiguity. Third, the parametric strategies for ionospheric delay are carried out to upregulate the narrow-lane (NL) ambiguity-fixed rate of GPS. Further, the real-time data are adopted for verifying the feasibility of the method developed in this study. The experimental results demonstrate the optimal carrier-to-noise density ratio (C/N0) of full operational capability (FOC) E5a/E5b at all frequencies, followed by IIR-M L1, and IIR-A/B L2 exhibits the worst performance. Generally, the multipath combination (MPC) of Galileo signals shows root mean square (RMS) values within 0.4 m, ordered as follows: E 1 > E 5 b > E 5 a . For the BDS-2, the B3 signal exhibits optimal performance, while the B1 signal is the worst. The RMS of MPC errors of L1 signals is smaller than the L2 signals for the GPS. Furthermore, under the 50 km baseline, the GPS NL ambiguity-fixed rate using the ionosphere-free (IF) combination reaches only 47.74% at the ratio threshold of 2. Finally, compared to the ionosphere-free combination method, the GPS NL ambiguity-fixed rate is increased by 45.52% with the presented method. The proposed approach broadens the future application of deformation monitoring in medium-long baseline scenarios.

A Long Time Span-Specific Emitter Identification Method Based on Unsupervised Domain Adaptation

Specific emitter identification (SEI) is a professional technology to recognize different emitters by measuring the unique features of received signals. It has been widely used in both civilian and military fields. Recently, many SEI methods based on deep learning have been proposed, most of which assume that the training set and testing set have the same data distribution. However, in reality, the testing set is generally used later than the training set and lacks labels. The long time span may change the signal transmission environment and fingerprint features. These changes result in considerable differences in data distribution between the training and testing sets, thereby affecting the recognition and prediction abilities of the model. Therefore, the existing works cannot achieve satisfactory results for a long time span SEI. To address this challenge and obtain stable fingerprints, we transform the long time span SEI problem into a domain adaptive problem and propose an unsupervised domain adaptive method called LTS-SEI. Noteworthily, LTS-SEI uses a multilayer convolutional feature extractor to learn feature knowledge and confronts a domain discriminator to generate domain-invariant shallow fingerprints. The classifier of LTS-SEI applies feature matching to source domain samples and target domain samples to achieve the domain alignment of deep fingerprints. The classifier further reduces the intraclass diversity of deep features to alleviate the misclassification problem of edge samples in the target domain. To confirm the effectiveness and reliability of LTS-SEI, we collect multiple sets of real satellite navigation signals using two antennas with 13 m- and 40 m-large apertures, respectively, and construct two available datasets. Numerous experiments demonstrate that LTS–SEI can considerably increase the recognition accuracy of the long time span SEI and is superior to the other existing methods.

Constructing a Regional Ionospheric TEC Model in China with Empirical Orthogonal Function and Dense GNSS Observation

Using Global Navigation Satellite Systems (GNSS) observation data for developing a high-precision ionospheric Total Electron Content (TEC) model is one of the essential subjects in ionospheric physics research and the application of satellite navigation correction. In this study, we integrate the Empirical Orthogonal Function (EOF) method with the TEC data provided by the Center for Orbit Determination in Europe (CODE), and observed by the dense GNSS receivers operated by the Crustal Movement Observation Network of China (CMONOC) to construct a regional ionospheric TEC model over China. The EOF analysis of CODE TEC in China from 1998 to 2010 shows that the first-order EOF component accounts for 90.3813% of the total variation of the ionospheric TEC in China. Meanwhile, the average value of CODE TEC is consistent with the spatial and temporal distribution characteristics of the first-order EOF base function, which mainly reflects the latitude and diurnal variations of TEC in China. The first-order coefficient after EOF decomposition shows an obvious 11-year period and semi-annual variations. The maximum amplitude of semi-annual variation mainly appears in March and October, which is closely associated with the variation in geographical longitude, the semi-annual change of the low-latitude electric field, and the ionospheric fountain effect. The second-order coefficient has an evident annual variation, the minimum amplitude mainly occurs in March, August, and September, and the amplitude values in the high solar activity years are more significant than those in the low solar activity years. The third-order coefficient mainly shows the characteristics of annual variation, and the fourth-order coefficient shows the noticeable semi-annual and annual variations. The third and fourth-order coefficients are both modulated by the solar activity index F10.7. The ionospheric TEC model in China, driven by CMONOC real-time GNSS observation data, can better reflect the latitude, local time and seasonal variation characteristics of ionospheric TEC over China. In particular, it can clearly show the spring and autumn asymmetry of ionospheric TEC in the low latitudes. The root mean square error of the absolute error between the model and the actual observation is mainly distributed around 2.45 TECU (1 TECU = 1016 electrons/m2). The values of the TEC model constructed in this study are closer to the actual observed values than those of the CODE TEC in China.

Terrestrial reference frames and their internal accuracy at coordinate system level

The accuracy assessment of terrestrial reference frames (TRFs) at coordinate system level is a key task to ensure their successful use in Earth studies, satellite navigation and other geodetic positioning applications. Currently, the TRF quality specifications for the most demanding users dictate that the origin, orientation and scale should be determined at an accuracy level of 1 mm, and they should remain stable over time at a rate of 0.1 mm/yr. To evaluate the conformity of the internal accuracy of modern TRFs to such requirements, an appropriate mapping is needed to convert frame coordinate errors (and their CV matrix) in a terrestrial network to matching errors (and their CV matrix) in the realized coordinate system. Several projection schemes may be considered for this mapping problem, all of which aim at extracting the correlated part of the estimation error in TRF coordinates that is describable by small random perturbations in their coordinate system. The goal of the present paper is to investigate the inference problem of frame accuracy at coordinate system level, and to discuss not only the theoretical aspects of the required covariance projectors, but also the practical impact on the results obtained by their implementation in space geodetic solutions. For this purpose, a relevant case study is performed to evaluate the accuracy of the realized origin, orientation and scale in the ITRF frame series based on the formal CV matrices for their estimated positions and velocities in the four technique subnetworks (DORIS, SLR, VLBI, GNSS).

Methods for Parametric Identifi cation of Systematic Errors of Onboard Measurements of Aerodynamic Angles in Aircraft Flight Tests

Methods of the actual values of the angles of attack and slip determination in the technology of air data systems estimation using satellite navigation systems during aircraft flight tests of are stated. Also methods of parametric identification of mathematical models of on-board aerodynamic angles measurements errors are presented. The technology has been developed and implemented in the practice of flight tests at Flight Research Institute. The technology shows high efficiency of solving tasks of air data on-board systems, vertical separation systems, flight performance and takeoff and landing characteristics estimation in flight tests. The technology covers a wide range of issues of aerometric measurements, many of which have already been published. Here, attention is paid to measurements of aerodynamic angles. The features of determining the angles of attack and slip using data from air data systems, satellite and inertial navigation systems are shown. Equations for determining the angles of attack and slip during testing, factors of measurement errors, the structure of the mathematical model of the aerodynamic errors of the angle of attack on-board measurements are presented in a stationary approximation. Algorithms for solving problems in steady and unsteady modes of flight, takeoff and landing are considered. The completeness of the solution for the wind speed vector is noted. Estimates of methodological errors in determining aerodynamic angles using the technology are made. Compliance with modern requirements is showing. The effectiveness of the technology is confirmed by the materials of flight tests of a short-range aircraft. Typical examples of test materials presentation, features of measurements depending on the type of test mode, aerodynamic influence factors are shown.

A cutting width measurement method for the unmanned rice harvester based on RGB-D images

Currently, the unmanned rice harvester based on satellite navigation is affected by tracked chassis steering errors and navigation accuracy, which can result in harvesting omissions and undercutting. Therefore, we proposed a cutting width measurement method for unmanned rice harvesters based on RGB-D images. The proposed method can provide navigational aids for driving and may also provide a basis for feed quantity detection and adjustment. We designed a lightweight unharvested area segmentation model (UANet) with a mean pixel accuracy (mPA) and a mean intersection over union (mIoU) of 98.28% and 97.15%, respectively, which are both higher than the lightweight semantic segmentation models, such as DABNet, CFPNet-V2 and ENet. We implemented unharvested area segmentation and harvesting boundary points extraction on RGB images, combined with depth maps to convert the pixel coordinates of harvesting boundary points into 3D world coordinates for cutting width measurement. Through experiments on rice harvest field images under different working conditions, the results showed that the success rate of harvesting boundary points detection was 98.33%, the error of cutting width measurement was within 2.34%, and the speed of the algorithm was approximately 9.7 fps. The proposed method can be adapted to complex harvesting scenarios and has the advantages of low hardware cost, high measurement accuracy, and good robustness, which can be extended to wheat.

Adaptive Satellite Navigation Anti-Interference Algorithm Based on Inverse Cosine Function

Contrasting the dilemma that the traditional time-domain least mean square (LMS) algorithm in the existing satellite navigation receiver anti-interference system cannot satisfy the convergence time is short and maintain a low level of steady-state error at the same time, an inverse cosine variable step size LMS algorithm (ICVS-LMS) is proposed. To begin with, the LMS algorithm, with a fixed step size focuses on its effectiveness in attenuating and suppressing interference signals, is analyzed, and then the proposed ICVS-LMS algorithm is analyzed. In conclusion, both the ICVS-LMS algorithm and the traditional algorithm are simulated and compared in terms of their effectiveness in suppressing interference in satellite navigation signals. The experimental results demonstrate that the improved algorithm significantly reduces convergence time while maintaining a small steady-state error. The improved algorithm demonstrates high robustness and an obvious suppression effect on interference signals. The anti-interference performance is 8.41–12.22% higher than that of the proposed algorithm.

A novel integrated signal structure of satellite navigation and communication system with plug-and-play capability

An integrated navigation/communication signal is proposed in our previous work. It considered Cyclic Code Shift Keying (CCSK) as a communication signal combined with traditional Global Navigation Satellite System (GNSS) signal, further the optimized cyclic shift set for communication signal was designed. Based on the previous research, a fuzzy judging algorithm is proposed to acquire the integrated signal in this paper. This algorithm adopts segmenting correlation domain to improve the integrated signal transmission robustness. Moreover, in order to solve incompatibility problem between the integrated signal and binary communication system, a strategy for optimizing cyclic shift set basing on dual-thresholds is proposed, in which interleaving coding is used to resist interference. The fault-tolerant rate of proposed algorithm is improved by about 87% compared with traditional algorithms. Based on the compatibility, the Bit Error Rate (BER) of the integrated signal decreases obviously, and the reliability of the communication system is improved greatly, benefiting from that interleaving technology and error correction coding is applied.

Four years of multimodal odometry and mapping on the rail vehicles

AbstractPrecise, seamless, and efficient train localization as well as long‐term railway environment monitoring is the essential property towards reliability, availability, maintainability, and safety engineering for railroad systems. Simultaneous localization and mapping is right at the core of solving the two problems concurrently. To this end, we propose a high‐performance and versatile multimodal framework in this paper, targeted for the odometry and mapping task for various rail vehicles. Our system is built atop an inertial‐centric state estimator that tightly couples light detection and ranging (LiDAR), visual, optionally satellite navigation, and map‐based localization information with the convenience and extendibility of loosely coupled methods. The inertial sensors inertial measurement unit and wheel encoder are treated as the primary sensor, which achieves the observations from subsystems to constrain the accelerometer and gyroscope biases. Compared with point‐only LiDAR‐inertial methods, our approach leverages more geometry information by introducing both track plane and electric power pillars into state estimation. The visual‐inertial subsystem also utilizes the environmental structure information by employing both lines and points. Besides, the method is capable of handling sensor failures by automatic reconfiguration bypassing failure modules. Our proposed method has been extensively tested in the long‐during railway environments over 4 years, including general‐speed, high‐speed, and metro, where both passenger and freight traffic are investigated. Further, we aim to share, in an open way, the experiences, problems, and successes of our group with the robotics community so that those who work in such environments can avoid these errors. In this view, we open source some of the data sets to benefit the research community.

FilterformerPose: Satellite Pose Estimation Using Filterformer.

Satellite pose estimation plays a crucial role within the aerospace field, impacting satellite positioning, navigation, control, orbit design, on-orbit maintenance (OOM), and collision avoidance. However, the accuracy of vision-based pose estimation is severely constrained by the complex spatial environment, including variable solar illumination and the diffuse reflection of the Earth's background. To overcome these problems, we introduce a novel satellite pose estimation network, FilterformerPose, which uses a convolutional neural network (CNN) backbone for feature learning and extracts feature maps at various CNN layers. Subsequently, these maps are fed into distinct translation and orientation regression networks, effectively decoupling object translation and orientation information. Within the pose regression network, we have devised a filter-based transformer encoder model, named filterformer, and constructed a hypernetwork-like design based on the filter self-attention mechanism to effectively remove noise and generate adaptive weight information. The related experiments were conducted using the Unreal Rendered Spacecraft On-Orbit (URSO) dataset, yielding superior results compared to alternative methods. We also achieved better results in the camera pose localization task, indicating that FilterformerPose can be adapted to other computer vision downstream tasks.

Improved path following for autonomous marine vehicles with low-cost heading/course sensors: comparative experiments

By overcoming constraints of low-cost sensors equipped on the autonomous marine vehicle (AMV), the classic path following approaches based on heading autopilot and course autopilot are improved to enhance the following accuracy of AMV, respectively. For the heading autopilot, adaptive line-of-sight (ALOS) is proposed to compensate for the generalized sideslip including the actual sideslip angle and the magnetic compass bias. For the course autopilot, extended Kalman filter (EKF) is employed to fusion the position and yaw angular rate to obtain the more precise and stable course, so as to substitute the unreliable course feedback from the satellite navigation receiver in cases of low speed and non ideal positioning. The performance and characteristics of both improved schemes are summarized through comparative experiments conducted on a low-cost AMV. Compared with the classic path following method, the straight line path following accuracy of the heading autopilot with generalized sideslip compensation and the course autopilot with EKF feedback are improved by 78.3% and 85.8% respectively. The circular path following accuracy are improved by 61.8% and 66.7% respectively. Engineers can choose the path following methods flexibly based on the hardware configuration, working environment and path type of the AMV to improve the following accuracy.

PRECISION EVALUATION FOR DIFFERENT GNSS RINEX 3 USING ONLINE SERVICES AND OPEN-SOURCE SOFTWARE PPP-MANS

It is critical to evaluate the reliability of using free online processing software for Global Navigation Satellite System post-processing since the advancement of GNSS gives satellite navigation customers all over the world great benefits. AUSPOS, IBGE, Magic GNSS, CSRS-PPP, and open-source software are some of the online processing solutions being evaluated for accuracy in this study. GNSS observations from IGS were used to conduct field observations using RINEX 3 data from three stations, with an observation duration of 30 seconds. After data acquisition, it was processed with online and free software that made use of GPS, GPS, and GLONASS. When compared to coordinates obtained from reference stations, the relative differences and correctness of the coordinates generated by each piece of software were then evaluated. coordinates in the ITRF14 reference for the X, Y, and Z directions. Online GNSS processing services may be used with greater accuracy for engineering and geodetic applications and are simple to use without the need for GNSS data processing expertise.

Multi-agent reinforcement learning satellite guidance for triangulation of a moving object in a relative orbit frame

Multi-agent systems are of ever-increasing importance in a contested space environment—use of multiple, cooperative satellites potentially increases positive mission outcomes on orbit, while autonomy becomes an ever-increasing requirement to increase reaction time to dynamic situations and lower the burden on space operators. This research explores multi-agent satellite swarm Guidance, Navigation, and Control (GNC) using deep reinforcement learning (DRL). DRL policies are trained to provide guidance inputs to agents in multi-agent swarm environments for completing complex, teamwork-focused objectives in geosynchronous orbit. An example scenario is explored for a group of satellite agents maneuvering to triangulate an object that is non-stationary in the relative orbit frame. Reward shaping is used to encourage learning guidance that positions swarm members to maximize triangulation accuracy, using angles-only observations for navigation relative to the target. Results show the policies successfully learn guidance through reward shaping to improve triangulation accuracy by a significant factor.

EFFECTIVENESS OF PRECISION AGRICULTURE ELEMENTS IN POTATO PRODUCTION IN THE WESTERN SIBERIAN FOREST-STEPPE

Theresultsofcomprehensiveresearchconductedin 2020-2022 usinggeoinformationtechnologies in potato cultivation at ZAO Plemzavod "Irmens" in the Ordynsky District of the Novosibirsk Region, located in the forest-steppe zone of Western Siberia, are presented. Potatoes require specific environmental factors to achieve high yields with good product quality. Using satellite navigation systems ensures an increase in potato yield and product quality. The research aims to develop elements of potato cultivation technology using innovative satellite navigation systems. The experiments were conducted in the soil and climate zone of drained forest-steppe in the northern forest-steppe area of the Priobye foothills. The soil of the experimental plots is alkaline black soil with a humus content of 6.32%, total nitrogen content of 0.28%, phosphorus content of 0.23%, and potassium content of 1.19%. The concentration of quickly hydrolysable nitrogen was 10.3, exchangeable phosphorus was 20.7, and exchangeable potassium was 14.4 mg/100 g of soil, with a pH of Early potato varieties Gala and Riviera were cultivated in the experiments. During the research period, aggregated data were obtained, and regression equations between yield indicators, the sum of productive soil moisture reserves, and precipitation in interphase periods of potato varieties were calculated. Correlation coefficients were determined for specific interphase periods. The dependence of potato yield on precipitation indicators in interphase periods was established. The significance of precision agriculture elements in ensuring early potato varieties' high product and quality was noted.

A High-Temperature Superconducting Wideband Bandpass Filter at the L Band for Radio Astronomy

In order to ensure the normal operation of radio astronomy observations, an extremely sensitive receiver system needs to be equipped in front of the large radio telescope. An 8-pole wideband high-temperature superconducting (HTS) filter using a Coplanar Spiral Resonator Structure with a passband of 1160∼1670 MHz is developed to suppress strong radio interference. The filter is fabricated on a 36 mm × 14 mm YBCO HTS film, which is deposited on a 0.5 mm thick MgO substrate. The minimum insertion loss measured in the liquid nitrogen temperature region is 0.03 dB, and the first parasitic passband appears at 2600 MHz. The measured results are in good agreement with the simulations. The filter can be used in radio telescope receivers for the observation of neutral hydrogen and pulsars, as well as in high-sensitivity satellite navigation instruments.

Precise Relative Navigation in Medium Earth Orbits with Global Navigation Satellite Systems and Intersatellite Links for Black Hole Imaging

The Event Horizon Telescope (EHT) is a ground-based array of Very Long Baseline Interferometry (VLBI) telescopes designed to image the event horizon of black holes. To overcome its limitations, this study explores a mission concept involving a two-satellite constellation of VLBI telescopes deployed in Medium Earth Orbit (MEO). Achieving high-resolution black hole images requires precise baseline determination at the millimetre level. To address this challenge, each satellite in the constellation is equipped with two Global Navigation Satellite System (GNSS) receivers and an optical Intersatellite Link (ISL) to enhance orbit determination. The results highlight the importance of integer ambiguity resolution and reveal that the ISL primarily improves baseline estimation along the link direction, with minimal impact along the black hole direction. Large intersatellite distances lead to sub-optimal relative orbit accuracy, challenging the attainment of the 3.5 mm relative position accuracy goal along the black hole direction.