Global Navigation Satellite System Satellites Research Articles

Determination of global geodetic parameters using satellite laser ranging to Galileo, GLONASS, and BeiDou satellites

The new Global Navigation Satellite System (GNSS) satellites, including GLONASS, Galileo, and BeiDou system, are equipped with Laser Retroreflector Arrays (LRA) to support Satellite Laser Ranging (SLR) tracking, which contributes to the estimation of global geodetic parameters. In this study, we estimate the global geodetic parameters using the SLR observations to GNSS satellites and also investigate the effects of different data processing strategies on the estimated Earth Rotation Parameters (ERP), geocenter motion, and terrestrial scale. The results indicate that setting range bias parameters for each satellite-station pair can effectively account for the satellite-specific biases induced by LRAs, leading to smaller Root Mean Square Errors (RMSE) of the post-fit SLR residuals. Furthermore, estimating the range biases for each satellite-station pair improves the accuracy of the estimated station coordinates and ERP. We also examine the impact of different arc lengths on the estimates of ERP, geocenter motion, and terrestrial scale. The results show that extending arc length can significantly reduce the formal error of ERP. The 7-day strategy produces the smallest RMSEs of 473 microarcseconds and 495 microarcseconds for the estimated X- and Y-component of pole coordinates, and 52 microseconds for length-of-day, respectively. However, the estimated geocenter motion is less affected by the arc length, even the shortest 1-day arc strategy can capture the seasonal variations of geocenter motion in Z component. For scale estimation, extending the arc length notably improves the accuracy of the estimated station coordinates and scale, but this advantage becomes less noticeable in longer arcs. The 7-day solution also obtains the closet scale results compared to ITRF2014, with the RMSE of 2.10 × 10–9.

Demand and key technology for a LEO constellation as augmentation of satellite navigation systems

A Low Earth Orbit (LEO) constellation augmenting satellite navigation is important in the future development of Global Navigation Satellite System (GNSS). GNSS augmented by LEO constellations can improve not only the accuracy of Positioning, Navigation, and Timing (PNT), but also the consistency and reliability of secure PNT system. This paper mainly analyzes the diverse demands of different PNT users for LEO augmented GNSS, including the precision demand in real-time, the availability demand in special areas, the navigation signal enhancement demand in complex electromagnetic environments, and the integrity demand with high security. Correspondingly, the possible contributions of LEO constellations to PNT performance are analyzed from multiple aspects. A particular attention is paid to the special PNT user requirements that cannot be fulfilled with existing GNSS, such as the PNT service demand in the polar regions and the onboard GNSS orbit determination demand of some LEO satellites. The key technologies to be considered in the constellation design, function realization, and payload development of the LEO-augmented navigation system are summarized.

Earth Rotation Parameters Derived from BDS-3 New Signals B1C/B2a Dual-Frequency Combination Observations

The Earth rotation parameters (ERP) play a crucial role in defining the global reference frame and the Global Navigation Satellite System (GNSS) is one of the important tools used to obtain ERP, including polar motion (PM), its rates, and length of day (LOD). The latest IGS Repro3 ERP products, which provided the IGS contribution to the latest ITRF2020, were generated without consideration of the Beidou Navigation Satellite System (BDS) observations. The global BDS, namely the BDS-3 constellation, has been completely constructed from July 2020 and the observing stations are evenly distributed globally now. Two couple dual-frequency combinations, including the B1I/B3I and B1C/B2a combinations, are commonly used for BDS-3 ionosphere-free combination usage. With the goal of identifying the optimal dual-frequency combination for BDS-3 ERP estimates for the future ITRF definition with a consideration of BDS-3, this research evaluated the performance of ERP estimation using B1I/B3I and B1C/B2a combinations. Firstly, we conducted a comparison of the ambiguity resolutions. The mean percentage of successfully resolved ambiguities for the BDS-3 B1C/B2a combination is 86.5%, surpassing that of B1I/B3I. The GNSS satellite orbits and ERP were estimated simultaneously, thus the accuracy of orbits could also reflect the performance of the ERP estimates. Subsequently, we validated the orbits of 22 BDS-3 Medium Earth Orbit (MEO) satellites using Satellite Laser Ranging (SLR), and the root mean square error (RMS) of the SLR residuals for the 3-day arc orbit with B1C/B2a signals was 5.72 cm, indicating superior accuracy compared with the B1I/B3I combination. Finally, we compared the performance of ERP estimation, considering both internal and external accuracy. For the internal accuracy, B1C/B2a-based solutions demonstrated a reduction in mean formal errors of approximately 17% for PM, 22% for LOD, and 21% for PM rates compared with B1I/B3I-based solutions. In terms of external accuracy, we compared BDS-3-derived ERP estimates with the IERS 20C04 products. The B1C/B2a combination exhibited a slightly better standard deviation performance and a significant reduction in mean bias by 56%, 54%, 39%, 64%, and 23% for X, Y polar motion, X, Y polar motion rates, and LOD, respectively, compared with B1I/B3I solutions. In conclusion, the results highlight the excellent signal quality for BDS-3 B1C/B2a and its superiority in ERP estimation when compared with the B1I/B3I combination.

Simulating VLBI observations to BeiDou and Galileo satellites in L-band for frame ties

Abstract Using the very long baseline interferometry (VLBI) technique to observe Earth-orbiting satellites is a topic of increasing interest for the establishment of frame ties. We present a simulation study on VLBI observations to BeiDou and Galileo satellites in L-band to investigate the accuracy of inter-technique frame ties between VLBI and global navigation satellite system (GNSS). We employ a global network of 16 antennas equipped with dedicated L-band receivers capable of observing BeiDou’s B1 and B3 navigation signals and Galileo’s E1 and E6 navigation signals. Through extensive Monte Carlo simulations, we simulate 24-h sessions to determine the optimal ratio of satellite to quasar scans. The optimal schedule uses about 80–90% satellite sources. We find that the 10–20% observations of quasar sources improve the estimation of the troposphere and, consequently, the estimation of the antenna position. Combining the normal equations from seven 24-h sessions, we derive a 7-day solution. The average antenna position repeatability is 7.3 mm. We identify the limitations of the results as the tropospheric turbulence, inaccuracies in the satellite orbit determination, and the lack of a more homogeneously distributed global network. This simulation study supports the understanding in the topic of building a frame tie using VLBI observations to GNSS satellites.

Evaluation of The Effect of Spoofing on Dual-Frequency Global Navigation Satellite System (GNSS)

This paper aims to assess the impact of Global Navigation Satellite System (GNSS) spoofing on the performance of a Garmin GPSMAP 66sr dual-frequency GNSS receiver. The evaluation is conducted through field assessments under three conditions: 1) single-frequency GPS L1 coarse acquisition (C/A) only, 2) single-frequency GPS L1 C/A and Galileo E1 open service (OS), and 3) dual-frequency GPS L1 C/A and L5, as well as Galileo E1 OS and E5a. The results emphasise the critical role of multifrequency GNSS in mitigating spoofing. In the dual-frequency multi-GNSS mode, spoofing does not occur as the GPS L5 and Galileo E5a signals remain unaffected by spoofing signals in the L1 / E1 band. In the single-frequency multi-GNSS mode, the higher number of observed GNSS satellites contributes to higher minimum spoofing power levels and longer durations between position fix loss and spoofing as compared to the GPS only mode.

Robust ambiguity datum for real-time GNSS satellite integer clock estimation

With the capability for single-receiver AR (Ambiguity Resolution), real-time GNSS (Global Navigation Satellite System) satellite integer clock has been the research hotspot of GNSS community in the past decade. Robust ambiguity datum is one prerequisite for high-quality integer clock. In this paper, with undifferenced AR model derived, a robust ambiguity datum definition method is proposed to isolate the signal biases from the integer ambiguity. Firstly, based on the ambiguity graph, the ambiguity datum is selected with the minimum spanning tree algorithm. Secondly, the ambiguity datum is transferred to the subsequent epochs through signal bias connection. Moreover, additional datum ambiguities are introduced to accommodate the arising of receiver and satellite in real-time circumstance. With the combination of ambiguity graph and signal bias, the efficient definition and smooth transition of ambiguity datum are assured for the real-time processing. To validate the approach, simulated real-time integer clock estimation for GPS/Galileo/BDS-3 satellites are conducted with one-month (January 2022) data from about 100 global IGS (International GNSS Service) network stations. Experiments show that the proposed robust ambiguity datum can produce accurate real-time integer clock. The average WL (Wide-Lane) and NL (Narrow-Lane) fixed rates exceed 99 % and 95 %, respectively, for most of the GPS/Galileo satellites. While comparable WL fixed rate is achieved for the BDS-3 satellites, the NL fixed rate is about 5 % lower as a result of poor orbit quality and imperfect measurement model. With eclipsing satellites excluded, the standard deviations between real-time integer clock and post-processed reference clock reach 0.018 ns and 0.016 ns for the GPS and Galileo constellations, respectively, which are 28 % and 24 % smaller than those of corresponding float clocks. In contrast, the standard deviations of float and integer clocks are similar for the BDS-3 constellation. Further improvements on the background models, including unconservative force modeling, satellite attitude modeling and antenna calibration are required to achieve ultimate accuracy, especially for the BDS-3 satellites.

On the strength of E and F region irregularities for GNSS scintillation in the dayside polar ionosphere

We present results of the study conducted to quantify the relative contribution of different ionospheric regions to phase scintillation in Global Navigation Satellite Systems (GNSS) at the dayside high latitude ionosphere. By taking advantage of the scanning capability of the 32-m EISCAT radar in Svalbard (ESR) and its recurrent favourable location below the dayside auroral region, we developed a methodology to identify conjunctions between the radar and GNSS satellite signals in order to compare density irregularities identified by the radar with scintillation observed in GNSS signals. The analysis revealed that the dayside ionosphere contained irregularities predominantly in the F region with scintillation occurring 77% of the times. The likelihood of observing irregularities in the E region were comparatively less with a scintillation occurrence rate of 42%. The study therefore strongly suggests that the dayside F region is more structured than the E region and is the predominant source region for irregularities that cause scintillation at GNSS frequencies. The associated ionospheric conditions revealed enhanced F region electron and ion temperatures to be collocated with scintillation for majority of the times. This supports the fact that cusp/auroral dynamics play a crucial role in creating F region irregularities which can act as sources of scintillation in GNSS signals. The presented results provide a quantitative estimate of the effectiveness of irregularities and the associated ionospheric conditions in different regions of the dayside ionosphere during scintillation, which are relevant for high latitude modelling and instability studies as well as for space weather applications.

Improved LS+MAR hybrid method to UT1-UTC ultra-short-term prediction by using first-order-difference UT1-UTC

Accurate ultra-short-term prediction of the Earth rotation parameters (ERP) holds paramount importance for real-time applications, particularly in reference frame conversion. Among them, diurnal rotation (UT1-UTC) which cannot be directly estimated through Global Navigation Satellite System (GNSS) techniques, significantly affects the rapid and ultra-rapid orbit determination of GNSS satellites. Presently, the traditional LS (least squares) + AR (autoregressive) and LS + MAR (multivariate autoregressive) hybrid methods stand as primary approaches for UT1-UTC ultra-short-term predictions (1–10 days). The LS + MAR hybrid method relies on the UT1-UTC and LOD (length of day) series. However, the correlation between LOD and first-order-difference UT1-UTC is stronger than that between LOD and UT1-UTC. In light of this, and with the aid of the first-order-difference UT1-UTC, we propose an enhanced LS + MAR hybrid method to UT1-UTC ultra-short-term prediction. By using the UT1-UTC and LOD data series of the IERS (International Earth Rotation and Reference Systems Service) EOP 14 C04 product, we conducted a thorough analysis and evaluation of the improved method's prediction performance compared to the traditional LS + AR and LS + MAR hybrid methods. According to the numerical results over more than 210 days, they demonstrate that, when considering the correlation information between the LOD and the first-order-difference UT1-UTC, the mean absolute errors (MAEs) of the improved LS + MAR hybrid method range from 21 to 934 μs in 1–10 days predictions. In comparison to the traditional LS + AR hybrid method, the MAEs show a reduction of 7–53 μs in 1–10 days predictions, with corresponding improvement percentages ranging from 1 to 28%. Similarly, when compared to the traditional LS + MAR hybrid method, the MAEs have a reduction of 5–42 μs in 1–10 days predictions, with corresponding improvement percentages ranging from 4–20%. Additionally, when aided by GNSS-derived LOD data series, the MAEs of improved LS + MAR hybrid method experience further reduction.

Investigation of Ionospheric Small‐Scale Plasma Structures Associated With Particle Precipitation

AbstractWe investigate the role of auroral particle precipitation in small‐scale (below hundreds of meters) plasma structuring in the auroral ionosphere over the Arctic. In this scope, we analyze together data recorded by an Ionospheric Scintillation Monitor Receiver (ISMR) of Global Navigation Satellite System (GNSS) signals and by an All‐Sky Imager located in Longyearbyen, Svalbard (Norway). We leverage on the raw GNSS samples provided at 50 Hz by the ISMR to evaluate amplitude and phase scintillation indices at 1 s time resolution and the Ionosphere‐Free Linear Combination at 20 ms time resolution. The simultaneous use of the 1 s GNSS‐based scintillation indices allows identifying the scale size of the irregularities involved in plasma structuring in the range of small (up to few hundreds of meters) and medium‐scale size ranges (up to few kilometers) for GNSS frequencies and observational geometry. Additionally, they allow identifying the diffractive and refractive nature of fluctuations on the recorded GNSS signals. Six strong auroral events and their effects on plasma structuring are studied. Plasma structuring down to scales of hundreds of meters is seen when strong gradients in auroral emissions at 557.7 nm cross the line of sight between the GNSS satellite and receiver. Local magnetic field measurements confirm small‐scale structuring processes coinciding with intensification of ionospheric currents. Since 557.7 nm emissions primarily originate from the ionospheric E‐region, plasma instabilities from particle precipitation at E‐region altitudes are considered to be responsible for the signatures of small‐scale plasma structuring highlighted in the GNSS scintillation data.

Fused Low-Earth-Orbit GNSS

Traditional Global Navigation Satellite System (GNSS) immunity to interference may be approaching a practical performance ceiling. Greater gains are possible outside traditional GNSS orbits and spectrum. GNSS from low Earth orbit (LEO) has long been viewed as promising but expensive, requiring large constellations for rapid navigation solutions. The recent emergence of commercial broadband LEO mega-constellations invites study on dual-purposing these for both communications-their primary mission-and a secondary positioning, navigation, and timing (PNT) service. Operating at shorter wavelengths than traditional GNSS, these constellations would permit highly directive, relatively compact receiver antennas. PNT-specific on-orbit resources would not be required: the transmitters, antennas, clocks, and spectrum of the hosting broadband network would suffice for PNT. Non-cooperative use of LEO signals for PNT is an option, but cooperation with the constellation operator (“fusion” with its communications mission) eases the burden of tracking a dense, low-altitude constellation from the ground and enables a receiver to produce single-epoch stand-alone PNT solutions. This paper proposes such a cooperative concept, termed fused LEO GNSS. Viability hinges on opportunity cost, or the burden a secondary PNT mission imposes on the communications constellation operator. This is assessed in terms of time-space-bandwidth product and energy budget. It is shown that a near-instantaneous-fix PNT service over ±60° latitude (covering 99.8% of the world's population) with positioning performance superior to traditional GNSS pseudoranging would cost less than 1.6% of downlink capacity for the largest of the new constellations, SpaceX's Starlink. This allocation is comparable to adding one user consuming 5.7 Mbps of broadband service to each cell.

Quantum-secured time transfer between precise timing facilities: a field trial with simulated satellite links

Global Navigation Satellite Systems (GNSSs), such as GPS and Galileo, provide precise time and space coordinates globally and constitute part of the critical infrastructure of modern society. To reliably operate GNSS, a highly accurate and stable system time is required, such as the one provided by several independent clocks hosted in Precise Timing Facilities (PTFs) around the world. The relative clock offset between PTFs is periodically measured to have a fallback system to synchronize the GNSS satellite clocks. The security and integrity of the communication between PTFs is of paramount importance: if compromised, it could lead to disruptions to the GNSS service. Therefore, securing the communication between PTFs is a compelling use-case for protection via Quantum Key Distribution (QKD), since this technology provides information-theoretic security. We have performed a field trial demonstration of such a use-case by sharing encrypted time synchronization information between two PTFs, one located in Oberpfaffenhofen (Germany) and one in Matera (Italy)—more than 900 km apart. To bridge this large distance, a satellite-QKD system is required, plus a “last-mile” terrestrial link to connect the optical ground station (OGS) to the actual location of the PTF. In our demonstration, we have deployed two full QKD systems to protect the last-mile connection at both locations and have shown via simulation that upcoming QKD satellites will be able to distribute keys between Oberpfaffenhofen and Matera, exploiting already existing OGSs.

5G Positioning: An Analysis of Early Datasets.

Global Navigation Satellite Systems (GNSSs) are nowadays the prevailing technology for positioning and navigation. However, with the roll-out of 5G technology, there is a shift towards 'hybrid positioning': indeed, 5G time-of-arrival (ToA) measurements can provide additional ranging for positioning, especially in environments where few GNSS satellites are visible. This work reports a preliminary analysis, the processing, and the results of field measurements collected as part of the GINTO5G project funded by ESA's EGEP programme. The data used in this project were shared by the European Space Agency (ESA) with the DICA of Politecnico di Milano as part of a collaboration within the ESALab@PoliMi research framework established in 2022 between the two organizations. The ToA data were collected during a real-world measurement campaign and they cover a wide range of user environments, such as indoor areas, outdoor open sky, and outdoor obstructed scenarios. Within the test area, eleven self-made replica 5G base stations were set up. A trolley, carrying a self-made 5G receiver and a data storage unit, was moved along predefined trajectories; the trolley's accurate trajectories were determined by a total station, which provided benchmark positions. In the present work, the 5G data are processed using the least squares method, testing and comparing different strategies. Therefore, the primary goal is to evaluate algorithms for position determination of a user based on 5G observations, and to empirically assess their accuracy. The results obtained are promising, with positional accuracy ranging from decimeters to a few meters in the worst cases.

Kinematic Precise Point Positioning Performance-Based Cost-Effective Robot Localization System

The use of high-precision positioning systems in modern navigation applications is crucial since location data is one of the most important pieces of information in Industry 4.0, especially for robots operating outdoors. In the modernization process of global navigation satellite system (GNSS) positioning, precise point positioning (PPP) has demonstrated its effectiveness in comparison to traditional differential positioning methods over the past thirty years. However, various challenges hinder the integration of PPP techniques into Internet of Things (IoT) systems for robot localization, with accuracy being a primary concern. This accuracy is impacted by factors such as satellite availability and signal disruptions in outdoor environments, resulting in less precise determination of satellite observations. Effectively addressing various GNSS errors is crucial when collecting PPP observations. The paper investigates the trade-off between kinematic PPP accuracy and cost effectiveness, through the examination of various influencing factors, including the choice of GNSS system (single or mixed), observation type (single or dual frequency), and satellite geometry. This research investigates kinematic PPP accuracy variation on a 10.4 km observed track based on different factors, using the GNSS system (single or mixed), and observation type (single or dual frequency). It can be concluded that mixed (GPS/GLONASS) dual frequency offers a 3D position accuracy of 9 cm, while mixed single frequency offers a 3D position accuracy of 13 cm. In industry, the results enable manufacturers to select suitable robot localization solutions according to the outdoor working environment (number of available satellites), economical constraint (single or dual frequency), and 3D position accuracy.

Dual-Frequency Signal Enhancement Method of Moving Target Echoes for GNSS-S Radar

The GNSS-S radar utilizes the signals of a global navigation satellite system (GNSS) to carry out target detection. Due to the very low power of GNSS signals, long-term accumulation is needed to improve the gain of the echo signals. However, when it is used for moving object detection, the random movement of the target will cause residual Doppler frequency after the echoes are correlated and compressed through the direct signal. The residual Doppler frequency will cause two problems: on the one hand, the signal coherence will deteriorate, affecting the coherent accumulation gain; on the other hand, the amplitude of the signal after compression will decrease due to the sensitivity of GNSS signals to Doppler frequency. Therefore, how to increase the signal amplitude and eliminate the phase fluctuation caused by the Doppler frequency shift in the GNSS echoes of moving targets is an important issue for GNSS-S radar to detect moving targets. This paper proposes a dual-frequency GNSS echo enhancement method that uses the dual-frequency signals transmitted by the GNSS satellites to enhance and regularize the target echo. First, the phase relationship model of the GNSS dual-frequency echo is constructed, and the phase difference is made to the compressed dual-frequency echo signal to obtain the differential phase without fluctuation; then, the amplitudes of the dual-frequency echo signals are added together; and finally, a new signal with enhanced amplitude and consistent phase is constructed by using the dual-frequency additive amplitude and differential phase, and the long-term coherent accumulation of the signal is carried out, which can improve the processing gain of the weak echo signal of the moving target. The simulation and field experiments show that this method makes full use of the energy of the GNSS dual-frequency signal and eliminates the phase fluctuation in the echo signal of the moving target so that the compressed signal energy remains consistent in the slow-time dimension. After long-term coherent accumulation, the echo SNR was greatly improved, which enabled the detection of two high-speed cars by GNSS-S radar in the experiment.

Improving the Pulse-Limited Footprint Resolution of GNSS-R Based on the Novel Joint Bandwidth Method

The bistatic global navigation satellite system’s (GNSS) signal reflection technology has become an effective means of space-based sea surface wind field retrieval and height retrieval. By adopting a wider signal bandwidth, a higher pulse-limited footprint resolution can be achieved. However, for the GNSS-Reflectometry (GNSS-R) system, its signal bandwidth is affected by the signal bandwidth of the GNSS satellite, which limits the further improvement of the pulse-limited footprint resolution. This article proposes a method based on the novel signal bandwidth joint principle to improve the resolution of GNSS-R pulse-limited footprints. Firstly, currently in-orbit GNSS-R satellites use the traditional single frequency band (TSFB) method, which is limited by the GNSS satellite’s signals and has a theoretical upper limit on its signal bandwidth. In response to this issue, this article proposes the novel joint bandwidth (NJBW) method (Galileo E5a and E5b signals) based on the auto-correlation function (ACF) signal ambiguity theory. The NJBW method reduces the main lobe width of the ACF of the GNSS-R signal by jointly processing the signals of E5a and E5b frequency bands, thus improving the pulse-limit footprint resolution of GNSS-R. Secondly, in order to verify the improvement effect of the novel joint bandwidth method on the pulse-limited footprint resolution of GNSS-R, this paper designs and fabricates an NJBW antenna verification prototype for the joint Galileo E5a and E5b frequency band and tests it in a microwave anechoic chamber. The test results indicate that the radio frequency (RF) bandwidth of the NJBW antenna validation prototype can cover both the frequency bands of E5a and E5b, making it suitable for use as the NJBW method for the GNSS-R receiving antenna. The bandwidth test values of the NJBW antenna validation prototype are consistent with the design values, which verifies the correctness of the NJBW antenna design model and further proves the feasibility of the NJBW method. Thirdly, based on the joint Galileo E5a and E5b frequency band signals, the NJBW method was applied to analyze the improvement effect of the pulse-limited footprint resolution. Compared to the TSFB method, the application of the NJBW method can increase the resolution of the GNSS-R pulse-limiting footprint by 1.73 times, which effectively improves the performance of the GNSS-R system. The NJBW method proposed in this article provides the theoretical method foundation and key technical support for sea surface wind field retrieval and height retrieval and the antenna design for the future high-precision and high pulse-limited footprint resolution GNSS-R sea surface wind field retrieval and height retrieval verification satellite.

Adapting empirical solar radiation pressure model for BDS-3 medium Earth orbit satellites

For the precise orbit determination (POD) of global navigation satellite systems (GNSS) constellation, it is very difficult to precisely model the solar radiation pressure (SRP) force acting on GNSS satellites. For GPS satellites, the ECOM model developed by the Center for Orbit Determination in Europe has been utilized by most of International GNSS Service (IGS) analysis centers. However, it should be adapted and optimized to the characteristics of satellites of each GNSS system or even individual satellites. It was extended to the ECOM2 model for GLONASS satellites and then for Galileo satellites by employing a box–wing model. Since November 2020, the third generation of the BeiDou satellite system (BDS-3) has been in its full operation and there are about 200 globally distributed IGS ground stations tracking BDS-3 signals, which creates a great potential to evaluate and optimize its SRP modeling. From the POD processing carried out in this study, we found significant fluctuations of up to 20 cm in overlapping orbit differences for satellites over eclipses in the radial direction and of about 20 and 50 cm in the cross and along directions for ECOM2 and ECOM models. Then, based on numerical analyses we demonstrate that the fourth- and sixth-order sine terms in the Sun direction can significantly reduce the overlapping orbit differences of ECOM. Therefore, an adapted SRP model by adding the fourth- and sixth-order sine periodical terms in the Sun direction to the ECOM model is presented. The adapted model is then validated for BDS-3 POD and orbit prediction. Results show that fluctuations in the amplitude of overlapping estimated orbits using ECOM models are reduced from 20 to < 10 cm in the radial-track component and satellite laser ranging residuals are reduced to half by the adapted SRP model. For the predicted BDS-3 satellite orbits, the RMS values over deep eclipses can be improved from about 7, 14 and 26 cm to about 3, 5 and 12 cm, in the radial, cross and along directions, respectively, compared to the ECOM model.

Evaluating Optical Clock Performance for GNSS Positioning.

Atomic clocks are highly precise timing devices used in numerous Positioning, Navigation, and Timing (PNT) applications on the ground and in outer space. In recent years, however, more precise timing solutions based on optical technology have been introduced as current technology capabilities advance. State-of-the-art optical clocks-predicted to be the next level of their predecessor atomic clocks-have achieved ultimate uncertainty of 1 × 10-18 and beyond, which exceeds the best atomic clock's performance by two orders of magnitude. Hence, the successful development of optical clocks has drawn significant attention in academia and industry to exploit many more opportunities. This paper first provides an overview of the emerging optical clock technology, its current development, and characteristics, followed by a clock stability analysis of some of the successfully developed optical clocks against current Global Navigation Satellite System (GNSS) satellite clocks to discuss the optical clock potentiality in GNSS positioning. The overlapping Allan Deviation (ADEV) method is applied to estimate the satellite clock stability from International GNSS Service (IGS) clock products, whereas the optical clock details are sourced from the existing literature. The findings are (a) the optical clocks are more stable than that of atomic clocks onboard GNSS satellites, though they may require further technological maturity to meet spacecraft payload requirements, and (b) in GNSS positioning, optical clocks could potentially offer less than a 1 mm range error (clock-related) in 30 s and at least 10 times better timing performance after 900 s in contrast to the Galileo satellite atomic clocks-which is determined in this study as the most stable GNSS atomic clock type used in satellite positioning.

Performance Evaluation of CentiSpace Navigation Augmentation Experiment Satellites

This paper presents the performance analysis of CentiSpace low earth orbit (LEO) experiment satellites. Distinguishing them from other LEO navigation augmentation systems, the co-time and co-frequency (CCST) self-interference suppression technique is employed in CentiSpace to mitigate significant self-interference caused by augmentation signals. Consequently, CentiSpace exhibits the capability of receiving navigation signals from the Global Navigation Satellite System (GNSS) while simultaneously broadcasting augmentation signals within the same frequency bands, thus ensuring excellent compatibility for GNSS receivers. CentiSpace is a pioneering LEO navigation system to successfully complete in-orbit verification of this technique. Leveraging the on-board experiment data, this study analyzes the performance of space-borne GNSS receivers equipped with self-interference suppression and evaluates the quality of navigation augmentation signals. The results show that CentiSpace space-borne GNSS receivers are capable of covering more than 90% visible GNSS satellites and the precision of self-orbit determination is at the centimeter level. Furthermore, the quality of augmentation signals meets the requirements outlined in the BDS interface control documents. These findings underscore the potential of the CentiSpace LEO augmentation system for the establishment of global integrity monitoring and GNSS signal augmentation. Moreover, these results contribute to subsequent research on LEO augmentation techniques.

An improved approach for rapid filter convergence of GNSS satellite real-time orbit determination

Introduction: The real-time precise satellite orbit of Global Navigation Satellite System (GNSS) usually takes a long time to converge to a stable state using the filter method. The ultra-rapid orbit products are helpful to improve convergence speed by introducing them as external constraints. Reasonably determination of stochastic model of the constraint equation from the ultra-rapid products is the key for a better performance of convergence whereas it has not been well solved.Methods: We propose to establish the stochastic model of the orbit constraint equation by analyzing the differences between the predicted part of the ultra-rapid orbit and the filter orbit after convergence. To improve the orbit accuracy during the convergence, the constant stochastic model of the constraint equation is first determined for each system by averaging the root mean square (RMS) time-series of the differences between predicted orbit from the ultra-rapid products and the SRIF orbit after convergence in different time ranges. Besides, a time-dependent stochastic model of the constraint equation is then determined by analyzing the variation of the RMS time-series. To validate the proposed method, a month of multi-constellation data collected from 80 globally distributed stations is processed using the Square Root Information Filter (SRIF) algorithm.Results: Orbit results without introducing external orbit constraints show that the convergence time in the radial direction is 13.75, 15.25 and 17.75 h for GPS, Galileo and BDS-3 satellite, respectively. For the scheme of constant stochastic model using the average RMS over 6 h, results show that there is no significant convergence phenomenon for each system in all directions. The one-dimensional (1D) RMS during the constraint period is improved by 86.5%, 84.8%, 96.8% for GPS, Galileo and BDS-3 satellites when compared to the results without introducing external orbit constraints. As for the scheme of time-dependent stochastic model, results show that the quadratic function is suitable for modeling the RMS time-series for each system, and the accuracy of results during the constraint period has a further improvement of 1.3%, 3.7% in 1D direction for GPS, BDS-3 satellites when compared to the constant stochastic model using the average RMS over 6 h. In addition, the orbit accuracy with external orbit constraint is slightly better than those without external orbit constraint after the constraint period.Discussion: The above results show that when introducing the ultra-rapid product as the external constraint, there is basically no convergence phenomenon for GNSS satellite, while the orbit accuracy for time-dependent stochastic model has further improvement than constant stochastic model. These results indicate that the proposed method can significantly improve the convergence performance without damaging the orbit accuracy after convergence, and time-dependent stochastic model is better than constant stochastic model.

Absolute and relative POD of LEO satellites in formation flying: Undifferenced and uncombined approach

Absolute or relative precise orbit determination (POD) is an essential prerequisite for many low earth orbit (LEO) missions. The POD of LEO satellites typically relays on processing the onboard global navigation satellite system (GNSS) measurements. The absolute POD is usually based on an ionosphere-free (IF) combination, and currently, integer ambiguity resolution (IAR) can be achieved only when external GNSS satellite phase bias (SPB) products are used. The use of these products is not flexible in multi-frequency/multi-constellation scenarios and is difficult to achieve in real-time missions. For relative POD, the double-differenced (DD) with IAR is the most general method. However, the differencing process amplifies observation noise and loses the opportunity to impose dynamic constraints on some eliminated parameters. In this contribution, based on the use of undifferenced and uncombined (UDUC) observations, a new model for both absolute and relative POD is proposed. In this model, the ambiguities of common-view satellites are constructed into DD form, thus IAR can be achieved without any external SPB products. Working with the UDUC observations, multi-frequency scenarios can be easily applied, and residuals can be separated for each frequency. In addition, with precise GNSS satellite clock/orbit products, both the absolute and relative orbits can be derived, which supports absolute and relative LEO POD. Based on onboard GPS observations of T-A and T-B satellites in formation flying, the performance of the UDUC POD model with DD ambiguity was evaluated. With the UDUC algorithm and IAR, the proposed model presented a consistency of 2.8–3.8 cm in 3D with the reference orbits, and the orbit difference was reduced by 16.3% and 10.6% for T-A and T-B compared with the IF-based POD, respectively. In addition, the relative orbit of the two satellites derived from the proposed model showed a consistency of 1.1–1.5 mm, which proved the feasibility of the UDUC POD model with DD ambiguity for formation flying missions.