Inter-satellite Link Measurements Research Articles

Simulation case study of precise orbit determination for IGSO satellites using onboard Ka/GNSS observations

Abstract Inter-satellite links (ISLs) can provide a more accurate spatial reference for inclined geosynchronous orbit satellite (IGSO) satellites than onboard global navigation satellite system (GNSS) side-lobe signals. In this study, precise orbit determination (POD) quality is analyzed based on onboard Ka/GNSS observations using a simulated IGSO satellite orbit. Considering the similar orbit altitude, we first select three IGSO satellites from BeiDou Navigation Satellite System (BDS-3) as target satellites, which have real Ka-band measurements available, along with other BDS-3 satellites and ground anchor stations, enabling us to evaluate POD performance. For the POD results using real Ka-band measurements, the root mean square of the residuals can reach 10.9 cm, and the orbit consistency in the 3D direction is better than 0.35 m. Additionally, simulations are conducted for onboard GNSS, ISL, and ground anchor-satellite link (GSL), considering the different constraints on the Ka-band resources. When only GNSS measurements are used, the 3D orbit accuracy estimated by the simulated theoretical orbit is approximately 1.5 m, and when only ISL measurements are used, the 3D orbit accuracy can reach approximately 0.35 m. However, when additional ISL and GSL measurements are included, the POD accuracy can exceed 0.28 m. These results demonstrate that incorporating Ka-band measurements can effectively enhance the POD accuracy for high-orbit satellites.

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.

Contribution of intersatellite link measurements to ECOM solar radiation pressure estimation on the BDS-3 MEO satellite

Contribution of intersatellite link measurements to ECOM solar radiation pressure estimation on the BDS-3 MEO satellite

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

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

Centimeter-level clock synchronization and space-borne timescale generation for BDS-3 using inter-satellite link measurements

Centimeter-level clock synchronization and space-borne timescale generation for BDS-3 using inter-satellite link measurements

Emerging errors in the orientation of the constellation in GNSS autonomous orbit determination based on inter-satellite link measurements

The emergence of inter-satellite link (ISL) technology, which realizes the high-precision measurement of the inter-satellite distances and forms a spatial geometric constraint within the constellation, enables the high-precision autonomous orbit determination of the GNSS satellites. Firstly, according to the fact that ISL adjustment is singular to the satellite orbit state vector, a distributed autonomous orbit determination algorithm employing the long-term forecast ephemeris to constrain the constellation orientation is designed in this paper. Then, the autonomous orbit determination using 60-day onboard ISL observations of the whole constellation is carried out. Then, the resulting orbits accuracy is evaluated by comparing them with a precise orbit determination using a global reference network with an accuracy of 0.10 m. The results show that the mean root mean square (RMS) of the user range error (URE) over a 60-day period of the 24 BDS-3 satellites in the constellation is 3.22 m. The characteristics of orbit errors for individual satellite are very similar, which is mainly caused by the overall orientation errors of the constellation. After eliminating these orientation errors, the corresponding mean RMS of URE is reduced to 0.68 m. The prediction errors of the Earth rotation parameters and the determination errors of the parameters of the state vectors, which compose the orientation errors, are further investigated. The Earth rotation parameter prediction errors mainly cause errors in the estimates of the longitude of ascending node, of which the 60-day error can reach 2.5e-5°. The determination errors of the parameters of the state vectors -- the inclination and the right ascension of ascending node, can reach 2.4e-5° and 5.1e-5° rad, respectively.

Analysis of BDS-3 distributed autonomous navigation based on BeiDou system simulation platform

Abstract Satellite autonomous navigation is an important function of the BeiDou-3 navigation System (BDS-3). Satellite autonomous navigation means that the navigation satellite uses long-term forecast ephemeris and Inter-Satellite Link (ISL) measurements to determinate its own spatial position and time reference without the support of the ground Operation and Control System (OCS) for a long time to ensure that the navigation system can normally maintain the time and space reference. This paper aims to analyze the feasibility of distributed autonomous navigation algorithms. For the first time, a ground parallel autonomous navigation test system (GPANTS) is built. The performance of distributed autonomous navigation is then analyzed using the two-way ISL ranging of BDS-3 satellites. First, the BDS simulation platform and the GPANTS are introduced. Then, the basic principles of distributed satellite autonomous orbit determination and time synchronization based on ISL measurements are summarized. Preliminary evaluation of the performance of the BDS-3 constellation autonomous navigation service under ideal conditions through simulation data. Then the performance of autonomous navigation for 22 BeiDou-3 satellites using ISL measurements is evaluated. The results show that when satellites operate autonomously for 50 days without the support of any ground station, the User Range Error (URE) of autonomous orbit determination is better than 3 m, and the time synchronization accuracy is better than 4 ns.

Orbit and clock analysis of BDS-3 satellites using inter-satellite link observations

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

Initial results of distributed autonomous orbit determination for Beidou BDS-3 satellites based on inter-satellite link measurements

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

LEO Precise Orbit Determination with Inter-satellite Links

Traditional precise orbit determination (POD) for low Earth orbit (LEO) satellites relies on observations from ground stations and onboard receivers. Although the accuracy can reach centimeter level, there are still problems such as insufficient autonomous operation capability. The inter-satellite link (ISL) is a link used for communication between satellites and has a function of dual-way ranging. Numerous studies have shown that observational data using ISLs can be adopted for POD of navigation satellites. In this contribution, we mainly focus on LEO satellites POD with ISLs. First, we design LEO constellations with different numbers of satellites and ISL measurements, based on which the constellations are simulated. Then rough tests of POD using different link topologies are carried out. The results show that in the 60-LEO constellation the average 3-dimensional (3D) orbital errors are 0.112 m using “4-connected” link topology with constant 4 links per satellite and 0.069 m using “all-connected” link topology with theoretically maximum numbers of links. After that, we carry out refined POD experiments with several sets of satellite numbers and different observation accuracy. The results show the higher link ranging accuracy and the more numbers of links bring higher POD precision. POD with ISLs gets bad performance in the case of center of gravity reference when link ranging accuracy is poor and numbers of links are small. When the link accuracy is 40 cm, average 3D orbital errors of 60-LEO constellation are 0.358 m, which can only meet the demand of autonomous navigation. With the constraint of the right ascension of the ascending node (RAAN), POD using ISLs reaches an extremely high precision when adopting a spatial reference provided by navigation satellites. For 120-LEO constellation, the average 3D orbital errors are 0.010 m; for 192-LEO constellation, the errors are 0.006 m.

Inter-Satellite Link Enhanced Orbit Determination for BeiDou-3

The third generation of the BeiDou navigation satellite system (BDS-3) is a global navigation system, and is expected to be in full operation by 2020. High-precision orbits are a precondition for BDS-3 to provide a highly accurate service, which needs a global tracking and monitoring capability for the operational satellites. However, it is difficult for BDS to construct global ground monitoring stations. Fortunately, Ka-band Inter-Satellite Link (ISL) antennae fitted to the BDS-3 satellites can be used to extend the visible arc of the Medium Earth Orbit (MEO) satellites and to enhance the ground stations for orbit determination. This paper analyses the ISL-enhanced orbit determination for eight BDS-3 satellites, using the data from ten Chinese domestic stations and 13 international Global Navigation Satellite System (GNSS) Monitoring and Assessment System (iGMAS) overseas stations. The results show that the Three-Dimensional (3D) position Root Mean Square (RMS) error of the Overlapping Orbit Differences (OODs) is approximately 1 m when only ten regional stations are used. When the ISL measurements are added, the 3D position RMS error is decreased to 0·5 m, and the accuracy of the 24-hour orbit prediction can also be improved from 2 m to 0·7 m, which is even better than that of the orbits determined using globally distributed stations. It can be expected that with the subsequent launch of BDS-3 satellites and the increasing number of ISLs, the advantage of the ISL enhanced orbit determination will become more significant.

Comparing satellite orbit determination by batch processing and extended Kalman filtering using inter-satellite link measurements of the next-generation BeiDou satellites

The next-generation BeiDou satellites are equipped with inter-satellite link (ISL) payloads to realize the ability of autonomous navigation (Auto-Nav). We focus on the application of batch processing and extended Kalman filtering (EKF) algorithm on Auto-Nav of BeiDou satellite system (BDS). The mathematical model of dual one-way measurements and principle of batch mode and EKF are introduced. Using real ISL measurements, Auto-Nav experiments are conducted with batch processing and EKF, respectively. For the sub-constellation, the EKF with a priori equipment delay constraints is proposed. The result shows that (1) with three ISLs and only one anchor station, the ISL measurements are sparsely distributed and the coverage of the whole arc is about 31%. The observations and dynamic models per epoch contribute more to satellite position and velocity parameters than to equipment delay parameters. (2) For batch processing, the overlap precision of precise orbit determination (POD) with ISLs and ground-satellite links (GSLs) is about 0.1 m in the radial direction and is better than 1 m three-dimensionally. The variation of the estimated equipment delays is within $$\pm \,0.6$$ ns. The observation residuals of ISLs behave such as a normal distribution, while the residual of GSLs show periodical variation due to uncorrected troposphere delay. (3) For the EKF, the ISL-only orbit determination is sensitive to the accuracy of the initial state. Compared with batch result, the precision of ISL-only orbit determination using EKF is better than 2 m given accurate initial states. The filtering does not show constellation drift or rotation within 8 days. However, with approximate initial states which position accuracy is 100 m, the precision of POD decreases to dozens of meters. (4) For the EKF, the accuracy of POD improves to 1.5 m in three dimensions with the support of an anchor station. The period for equipment delay parameters to converge is about 24 h. However, the convergence rate of equipment delay parameters is much slower than that of satellite state parameters. The possible reason is the unbalanced contribution of observation and dynamic model information on the estimated parameters. Thus, it is better to constrain the equipment delay parameters with a priori information while filtering.

Initial results of centralized autonomous orbit determination of the new-generation BDS satellites with inter-satellite link measurements

Autonomous orbit determination is the ability of navigation satellites to estimate the orbit parameters on-board using inter-satellite link (ISL) measurements. This study mainly focuses on data processing of the ISL measurements as a new measurement type and its application on the centralized autonomous orbit determination of the new-generation Beidou navigation satellite system satellites for the first time. The ISL measurements are dual one-way measurements that follow a time division multiple access (TDMA) structure. The ranging error of the ISL measurements is less than 0.25 ns. This paper proposes a derivation approach to the satellite clock offsets and the geometric distances from TDMA dual one-way measurements without a loss of accuracy. The derived clock offsets are used for time synchronization, and the derived geometry distances are used for autonomous orbit determination. The clock offsets from the ISL measurements are consistent with the L-band two-way satellite, and time–frequency transfer clock measurements and the detrended residuals vary within 0.5 ns. The centralized autonomous orbit determination is conducted in a batch mode on a ground-capable server for the feasibility study. Constant hardware delays are present in the geometric distances and become the largest source of error in the autonomous orbit determination. Therefore, the hardware delays are estimated simultaneously with the satellite orbits. To avoid uncertainties in the constellation orientation, a ground anchor station that “observes” the satellites with on-board ISL payloads is introduced into the orbit determination. The root-mean-square values of orbit determination residuals are within 10.0 cm, and the standard deviation of the estimated ISL hardware delays is within 0.2 ns. The accuracy of the autonomous orbits is evaluated by analysis of overlap comparison and the satellite laser ranging (SLR) residuals and is compared with the accuracy of the L-band orbits. The results indicate that the radial overlap differences between the autonomous orbits are less than 15.0 cm for the inclined geosynchronous orbit (IGSO) satellites and less than 10.0 cm for the MEO satellites. The SLR residuals are approximately 15.0 cm for the IGSO satellites and approximately 10.0 cm for the MEO satellites, representing an improvement over the L-band orbits.

Time synchronization of new-generation BDS satellites using inter-satellite link measurements

Abstract Autonomous satellite navigation is based on the ability of a Global Navigation Satellite System (GNSS), such as Beidou, to estimate orbits and clock parameters onboard satellites using Inter-Satellite Link (ISL) measurements instead of tracking data from a ground monitoring network. This paper focuses on the time synchronization of new-generation Beidou Navigation Satellite System (BDS) satellites equipped with an ISL payload. Two modes of Ka-band ISL measurements, Time Division Multiple Access (TDMA) mode and the continuous link mode, were used onboard these BDS satellites. Using a mathematical formulation for each measurement mode along with a derivation of the satellite clock offsets, geometric ranges from the dual one-way measurements were introduced. Then, pseudoranges and clock offsets were evaluated for the new-generation BDS satellites. The evaluation shows that the ranging accuracies of TDMA ISL and the continuous link are approximately 4 cm and 1 cm (root mean square, RMS), respectively. Both lead to ISL clock offset residuals of less than 0.3 ns (RMS). For further validation, time synchronization between these satellites to a ground control station keeping the systematic time in BDT was conducted using L-band Two-way Satellite Time Frequency Transfer (TWSTFT). System errors in the ISL measurements were calibrated by comparing the derived clock offsets with the TWSTFT. The standard deviations of the estimated ISL system errors are less than 0.3 ns, and the calibrated ISL clock parameters are consistent with that of the L-band TWSTFT. For the regional BDS network, the addition of ISL measurements for medium orbit (MEO) BDS satellites increased the clock tracking coverage by more than 40% for each orbital revolution. As a result, the clock predicting error for the satellite M1S was improved from 3.59 to 0.86 ns (RMS), and the predicting error of the satellite M2S was improved from 1.94 to 0.57 ns (RMS), which is a significant improvement by a factor of 3–4.

Orbit determination of the Next-Generation Beidou satellites with Intersatellite link measurements and a priori orbit constraints

Abstract Intersatellite Link (ISL) technology helps to realize the auto update of broadcast ephemeris and clock error parameters for Global Navigation Satellite System (GNSS). ISL constitutes an important approach with which to both improve the observation geometry and extend the tracking coverage of China’s Beidou Navigation Satellite System (BDS). However, ISL-only orbit determination might lead to the constellation drift, rotation, and even lead to the divergence in orbit determination. Fortunately, predicted orbits with good precision can be used as a priori information with which to constrain the estimated satellite orbit parameters. Therefore, the precision of satellite autonomous orbit determination can be improved by consideration of a priori orbit information, and vice versa. However, the errors of rotation and translation in a priori orbit will remain in the ultimate result. This paper proposes a constrained precise orbit determination (POD) method for a sub-constellation of the new Beidou satellite constellation with only a few ISLs. The observation model of dual one-way measurements eliminating satellite clock errors is presented, and the orbit determination precision is analyzed with different data processing backgrounds. The conclusions are as follows. (1) With ISLs, the estimated parameters are strongly correlated, especially the positions and velocities of satellites. (2) The performance of determined BDS orbits will be improved by the constraints with more precise priori orbits. The POD precision is better than 45 m with a priori orbit constrain of 100 m precision (e.g., predicted orbits by telemetry tracking and control system), and is better than 6 m with precise priori orbit constraints of 10 m precision (e.g., predicted orbits by international GNSS monitoring & Assessment System (iGMAS)). (3) The POD precision is improved by additional ISLs. Constrained by a priori iGMAS orbits, the POD precision with two, three, and four ISLs is better than 6, 3, and 2 m, respectively. (4) The in-plane link and out-of-plane link have different contributions to observation configuration and system observability. The POD with weak observation configuration (e.g., one in-plane link and one out-of-plane link) should be tightly constrained with a priori orbits.

Centralized autonomous orbit determination of Beidou navigation satellites with inter-satellite link measurements: preliminary results

Autonomous orbit determination is the process by which the orbit parameters of navigation satellites are estimated onboard using Inter-Satellite Link (ISL) measurements. In this contribution, autonomous orbit determination experiments using ISL measurements in a centralized mode of the new-generation Beidou navigation satellites are conducted. The mathematical formulation and the processing method of the dual one-way measurements are addressed as well as the main feathers of the ISL measurements are introduced. It is concluded that the ISL ranging data are high-precision measurements. The centralized autonomous orbit determination is processed in a batch mode. The average value of ISL measurements residuals is within 1.0 cm, standard deviation of ISL measurements residuals is within 10.0 cm and the standard deviation of the estimated ISL hardware delays is within 0.2 ns. The orbital accuracy is assessed by overlap comparison, User Equivalent Ranging Error and Satellite Laser Ranging (SLR) residuals. The radial overlap differences of the autonomous orbits are less than 6.0 cm and 24 h predicted orbital radial overlap differences less than 10.0 cm. The User Equivalent Ranging Error of 24 h predicted autonomous orbits is about 0.43 m and is better than the 24 h predicted L-band orbits at the 0.76 m level. The SLR residuals for the autonomous orbits are less than 10.0 cm. The ground anchor station which observes the constellation with ISL is important to maintain the Earth-Fixed-Frame and avoid the uncertainties of the entire constellation orientation. The influence of the ground station observation time span on autonomous orbit accuracy is also discussed. Even if the cutoff elevation of the ground anchor station is less than 60°, the radial accuracy of the autonomous orbits and 24 h predicted orbits is still better than 10.0 cm and three-dimensional orbit accuracy better than 1.5 m.