Autonomous Orbit Determination Research Articles

The communication and measurement architecture of BDS-3 global operations and services

This study introduces the third-generation BeiDou Navigation Satellite System (BDS-3) system’s creative global operation and service architecture based on regional stations and Ka-band inter-satellite links (ISLs). The architecture’s contributions to BDS-3 include not only combined orbit determination and time synchronization but also autonomous orbit determination and time synchronization, global operations and services. The BDS-3 on-orbit operation results are being presented in the paper to verify the designed capabilities. Compared with BDS-2, the orbit determination accuracy is improving from 0.6 m to 0.15 m, and the time synchronization accuracy is improving from 6.67 ns to 1.16 ns. Under autonomous orbit determination and time synchronization, the 30-day orbit maintenance accuracy reaches 16 m, and the time synchronization accuracy reaches 3.74 ns. The success rate of data transmission reaches 99%, and the delay is better than 12.9 s. In the future, laser ISLs will be used to enhance the system structure and further improve global operation and service capabilities.

Retracted: Autonomous Orbit Determination System of Navigation Satellite Based on Spaceborne GPS Technology

Retracted: Autonomous Orbit Determination System of Navigation Satellite Based on Spaceborne GPS Technology

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.

Analysis of Autonomous Orbit Determination in Various Near-Moon Periodic Orbits

Analysis of Autonomous Orbit Determination in Various Near-Moon Periodic Orbits

An improved robust filtering against observation and satellite state anomalies in centralized autonomous orbit determination for GNSS

Anomalies caused by the failure of ranging-related facilities and satellite orbit maneuvering will greatly affect the performance of Autonomous Orbit Determination (AOD) for Global Navigation Satellite System (GNSS). In view of that, we proposed an improved robust filtering named as Resisting Anomaly Robust Filtering (RARF) to improve the precision and enhance the reliability of AOD in situation of anomalies in observations and states of satellites (i.e. orbit maneuvering). We performed the centralized AOD with the RARF for a hybrid GNSS constellation using simulated observations, and analyzed its performance in cases of no anomaly, anomalies in observations only and anomalies in states of satellites only. The experimental results indicate that: (1) With anomalies in observations only, the RARF is much more robust than the extended Kalman filter (EKF), and results of AOD with the RARF are entirely free from abnormal observations; (2) In the situation of anomalies in states of satellites only, the precision of AOD with the RARF can reach to the order of 10 m after 1.5 h orbit recovery if an anchor is available. As the solving time extends, the precision of AOD can be up to dm level.

Feasibility Analysis of Autonomous Orbit Determination and Gravity-Field Recovery around Asteroids Using Inter-Satellite Range Data

Autonomous navigation and orbit determination are key problems of asteroid exploration missions. Inter-satellite range link is a type of measurement widely used in the orbit determination of Earth satellites, but not so widely used in missions around small bodies. In our study, we assume that highly accurate inter-satellite range data can be obtained around small bodies between the chief spacecraft and some low-cost deputies, and study the feasibility of simultaneous autonomous orbit determination of the spacecraft and the gravity-field recovery without the support from ground stations. After the feasibility analysis, two modified methods are proposed. Both methods demonstrate obvious improvements in both the convergence region and the accuracy. One remark is that the inter-satellite range data can be also used together with various observation data from ground stations to enhance the accuracy of the determined orbits and the gravity field.

Fully Autonomous Orbit Determination and Synchronization for Satellite Navigation and Communication Systems in Halo Orbits

This paper presents a solution for autonomous orbit determination and time synchronization of spacecraft in Halo orbits around Lagrange points using inter-satellite links. Lagrange points are stable positions in the gravitational field of two large bodies that allow for a sustained presence of a spacecraft in a specific region. However, a challenge in operating at these points is the lack of fixed landmarks for orbit determination. The proposed solution involves using inter-satellite links to perform range and range-rate measurements, allowing for accurate computation of the spacecraft’s orbit parameters without the need for any facilities on Earth. Simulations using a fleet of three satellites in Near Rectilinear Halo Orbits around the Earth–Moon Lagrange point, proposed for the Lunar Gateway stations, were conducted to demonstrate the feasibility of the approach. The results show that inter-satellite links can provide reliable and accurate solutions for orbit determination with a DRMS error lower than one meter (90th percentile) and synchronization errors of around one nanosecond. This solution paves the way for a fully autonomous fleet of spacecraft that can be used for observation, telecommunication, and navigation missions.

Integrated Navigation and Communication Service for LEO Satellites Based on BDS-3 Global Short Message Communication

Massive global Low Earth Orbit (LEO) constellations have been developed rapidly with the characteristics of larger number and shorter orbital periods of LEO satellites in recent years. The increasing requirements of real-time orbit determination and emergency data transfer in full arc can hardly meet the traditional strategies based on regional ground stations. An integrated communication and navigation service architecture based on the third phase of the BeiDou system (BDS-3) Global Short Message Communication (GSMC) is proposed, which enables global coverage and random access. The GSMC downlink single-frequency signal is used for real-time orbit determination, and is further combined with B1C navigation signal for real-time dual-frequency high-precision orbit determination. Considering fast moving of LEO satellites and short burst of uplink messages, the uplink BDS-3 satellite selection strategy based on carrier-to-noise ratio, and uplink high-precision compensation of frequency shift are adopted to increase the communication success rate. The service architecture proposed can improve the precision of the autonomous orbit determination and enhance the capability of real-time command transmission of LEO satellites even without the traditional ground stations involved. Integrated communication and navigation service has been validated by simulation and on-board BDS-3 GSMC test data. The precision of single-frequency real-time orbit determination can reach 2.86m, and the precision of dual-frequency can reach 0.26m. The average time delay of communication is about 11.45s, and the success rate is about 99.8%. The method may provide alternative means of real-time high-precision orbit determination and emergency data transfer of LEO satellites.

Performance analysis of crosslink radiometric measurement based autonomous orbit determination for cislunar small satellite formations

Recent advances in space technology provide an opportunity for small satellites to be launched in cislunar space. However, tracking these small satellites still depends on ground-based operations. Autonomous navigation could be a possible solution considering the challenges presented by costly ground operations and limited onboard power available for small satellites. There have been various studies on autonomous navigation methods for cislunar missions. One of them, LiAISON, provides an autonomous orbit determination solution solely using inter-satellite measurements. This study aims at providing a detailed performance analysis of crosslink radiometric measurements based on autonomous orbit determination for cislunar small satellite formations considering the effects of measurement type, measurement accuracy, bias, formation geometry, and network topology. This study shows that range observations provide better state estimation performance than range-rate observations for the autonomous navigation system in cislunar space. Line-of-sight angle measurements derived from radiometric measurements do not improve the overall system performance. In addition, less precise crosslink measurement methods could be an option for formations in highly observable orbital configurations. It was found that measurement biases and measurements with high intervals reduce the overall system performance. In case there are more than two spacecraft in the formation, the navigation system in the mesh topology provides a better overall state estimation than the centralized topology.

Autonomous orbit determination for satellite formations using relative sensing: Observability analysis and optimization

Orbit determination of spacecraft in orbit has been mostly dependent on either GNSS satellite signals or ground station telemetry. Both methods present their limitations, however: GNSS signals can only be used effectively in earth orbit, and ground-based orbit determination presents an inherent latency that increases with the Earth–spacecraft distance. For spacecraft flying formations, an alternative method of orbit determination, independent of external signals, consists in the observation of the spacecraft’s position with respect to the central body through the relative positioning history of the spacecraft within the formation. In this paper, the potential of the relative positioning method is demonstrated in the context of the SunRISE mission, and compared with the mission’s previously proposed orbit determination methods. An optimization study is then made to find the optimal placement of a new spacecraft in the formation so as to maximize the positioning accuracy of the system. Finally, the possibility of removing part of the system’s relative bearing measurements while maintaining its observability is also studied. The resulting system is found to be observable, but ill-conditioned.

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.

Performance Analysis of BDS-3 SAIM and Enhancement Research on Autonomous Satellite Ephemeris Monitoring

Integrity is one of the key indicators used to characterize the performance of the global navigation satellite systems (GNSSs) and is closely related to user safety. In order to realize real-time global integrity monitoring, the BeiDou Global Navigation Satellite System (BDS-3) has realized the “satellite autonomous integrity monitoring” (SAIM) function in its satellites for the first time. BDS-3 SAIM has the monitoring functions of signal power, pseudo-range, satellite clock frequency and phase, but not the monitoring function of broadcast ephemeris. In this study, the long-term stability and distribution characteristics of BDS-3 SAIM monitoring data were analyzed by using the actual telemetry data for the first time. The results show that the SAIM monitoring data have good long-term stability and basically follow a normal distribution, which meets the design expectations. Meanwhile, in view of the fact that BDS-3 SAIM does not have the ability to independently monitor broadcast ephemerides, which may lead to the over-tolerance of BDS-3 to the probability risk of risks of integrity in the active space environment, a SAIM enhancement design for ephemeris monitoring is proposed, which integrates three relatively independent methods, with the ephemeris extrapolated from the previous cycle, and the ephemeris generated by autonomous orbit determination, inter-satellite link distance measurement data as reference data, respectively. The three methods are analyzed and verified. The results show that each of the three methods has advantages and disadvantages in terms of monitoring accuracy and resource dependence. The integration of the three methods can combine their complementary advantages and can also provide valuable as an important reference for engineering applications.

Research on the Rotational Correction of Distributed Autonomous Orbit Determination in the Satellite Navigation Constellation

The autonomous orbit determination of the navigation constellation uses only bidirectional ranging data of the inter-satellite link for data processing. The lack of space-time benchmark information related to the Earth inevitably causes overall rotational uncertainty in the constellation, leading to a decrease in orbit accuracy and affecting user positioning accuracy. This study (1) introduces a method for rotation correction in distributed autonomous orbit determination based on inter-satellite bidirectional ranging; (2) conducts constellation autonomous orbit determination and time synchronization processing experiments based on inter-satellite ranging data for the 24 medium Earth orbit (MEO) satellites in the Beidou-3 global satellite navigation system (BDS-3); and (3) makes comparative analyses on the accuracy of autonomous orbit determination based on three rotation correction cases, including a no-rotation-correction case, independent satellite constraints case, and global satellite constraints case. The experimental results are described as follows. For the no-rotation-correction case, the prediction error of the orbital inclination angle (iot, i) for the entire constellation on the 30th day was 2.11 × 10−7/rad, the prediction error of the right ascension of the ascending point (Omega, Ω) was 2.25 × 10−7/rad, and the average root mean square (RMS) of the user range error (URE) for the entire constellation orbit was 1.41 m. In the autonomous orbit determination experiment with independent constraints on satellites, the prediction error of i for the entire constellation on the 30th day was 5.43 × 10−7/rad, the prediction error of Ω was 2.03 × 10−7/rad, and the average RMS of the orbital URE for the entire constellation was 1.09 m. In the autonomous orbit determination experiment with global satellite constraints, the prediction error of i for the entire constellation on the 30th day was 5.31 × 10−7/rad, the prediction error of Ω was 1.95 × 10−7/rad, and the RMS of the orbital URE for the entire constellation was 0.94 m. According to the analysis of the above experimental results, compared with the autonomous orbit determination under the no-rotation-correction case, the adoption of an algorithm for independent satellite constraints to correct the overall constellation rotation weakens the constellation rotation influence; however, it may destroy the overall constellation configuration, which affects the stability of autonomous orbit determination. Finally, the algorithm based on global satellite constraints both impairs the influence of constellation rotation and maintains the overall constellation configuration.

Autonomous Crosslink Radionavigation for a Lunar CubeSat Mission

This study presents an autonomous orbit determination system based on crosslink radiometric measurements applied to a future lunar CubeSat mission to clearly highlight its advantages with respect to existing ground-based navigation strategies. This work is based on the Linked Autonomous Interplanetary Satellite Orbit Navigation (LiAISON) method which provides an autonomous navigation solution solely using satellite-to-satellite measurements, such as range and/or range-rate, to estimate absolute spacecraft states when at least one of the involved spacecraft has an orbit with a unique size, shape, and orientation. The lunar vicinity is a perfect candidate for this type of application due to the asymmetrical gravity field: the selected lunar mission, an Earth-Moon L2(EML2) Halo orbiter, has an inter-satellite link between a lunar elliptical frozen orbiter. Simulation results show that, even in case of high-measurement errors (in the order of 100 m, 1σ), the navigation filter estimates the true states of spacecraft at EML2 with an error in the order of 500 m for position, and 2 mm/s for velocity, respectively and the elliptical lunar frozen orbiter states can be estimated in the order of 100 m for position and 1 cm/s for velocity, respectively. This study shows that range-only measurements provide better state estimation than range-rate-only measurements for this specific situation. Different bias handling strategies are also investigated. It has been found that even a less accurate ranging method, such as data-aided ranging, provides a sufficient orbit determination solution. This would simplify the communication system design for the selected CubeSat mission. The most observable states are found to be position states of the lunar orbiter via the observability analysis. In addition, the best tracking windows are also investigated for the selected mission scenario.

Mothership-Cubesat Radioscience for Phobos Geodesy and Autonomous Navigation

The knowledge of the interior structure (e.g., homogeneous, porous, or fractured) of Martian moons will lead to a better understanding of their formation as well as the early solar system. One approach to inferring the interior structure is via geodetic characteristics, such as gravity field and libration. Geodetic parameters can be derived from radiometric tracking measurements. A feasible mothership-CubeSat mission is proposed in this study with following purposes, (1) performing inter-sat Doppler measurements, (2) improving the understanding of Phobos as well as the dynamic model, (3) securing the mothership as well as the primary mission, and (4) supporting autonomous navigation, given the long distance between the Earth and Mars. This study analyzes budgets of volume, mass, power, deployment Δv, and link, and the Doppler measurement noise of the system, and gives a feasible design for the CubeSat. The accuracy of orbit determination and geodesy is revealed via the Monte-Carlo simulation of estimation considering all uncertainties. Under an ephemeris error of the Mars-Phobos system ranging from 0 to 2 km, the autonomous orbit determination delivers an accuracy ranging from 0.2 m to 21 m and 0.05 mm/s to 0.4 cm/s. The geodesy can return 2nd-degree gravity coefficients at an accuracy of 1‰, even in the presence of an ephemeris error of 2 km. The achieved covariance of gravity coefficients and libration amplitude indicates an excellent possibility to distinguish families of interior structures.

Autonomous navigation for Mars probes using only satellite-to-satellite tracking measurements by singularity-avoiding orbit elements

AbstractThis paper proposes a novel autonomous navigation method for Mars-orbiting probes. Satellite-to-satellite tracking (SST) between two probes is generally deemed to involve autonomous measurements with no dependence on any external observation sites on the Earth. For the conventional two-body dynamic model, it is well known that the orbit states cannot be estimated by merely using such SST measurements. Considering the effects of third-body gravitation perturbation and the weak Mars tesseral harmonics perturbation, autonomous navigation with SST measurements alone becomes weakly observable and may be achieved by some nonlinear filtering techniques. Two significant improvements are made to mitigate the nonlinearity brought by the dynamic models. First, singularity-avoiding orbit elements are selected to represent the dynamic models in order to reduce the intensity of the nonlinearity which cannot be overcome by the traditional position–velocity state expression. Second, the unscented Kalman filter method is effectively utilised to avoid the linearised errors calculated by its extended Kalman filter counterpart which may exceed the tesseral harmonics perturbation. A constellation, consisting of one low-orbit probe and one high-orbit probe, is designed to realise the autonomous orbit determination of both participating Mars probes. A reliable navigation solution is successfully obtained by Monte Carlo simulation runs. It shows that the errors of the semimajor axes of the two Mars probes are less than 10 m and the position errors are less than 1 km.

Autonomous Orbit Determination System of Navigation Satellite Based on Spaceborne GPS Technology

In recent years, many low-orbit satellites have been widely used in the field of scientific research and national defense in China. In order to meet the demand of high-precision satellite orbit in China’s space, surveying and mapping, and other related fields, navigation satellites are of great significance. The UKF (unscented Kalman filter) method is applied to space targets’ spaceborne GPS autonomous orbit determination. In this paper, the UKF algorithm based on UT transformation is mainly introduced. In view of the situation that the system noise variance matrix is unknown or the dynamic model is not accurate, an adaptive UKF filtering algorithm is proposed. Simulation experiments are carried out with CHAMP satellite GPS data, and the results show that the filtering accuracy and stability are improved, which proves the algorithm’s effectiveness. The experimental results show that the Helmert variance component estimation considering the dynamics model can solve the problem of reasonable weight determination of BDS/GPS observations and effectively weaken the influence of coarse error and improve the accuracy of orbit determination. The accuracy of autonomous orbit determination by spaceborne BDS/GPS is 1.19 m and 2.35 mm/s, respectively.

Comparison of Autonomous Orbit Determination for Satellite Pairs in Lunar Halo and Distant Retrograde Orbits

<h3>Summary</h3> A comprehensive study on the autonomous orbit determination (AOD) performance of satellite pairs in halo orbits and distant retrograde orbits (DROs) is carried out. A factor called <i>dynamic and geometric dilution of precision</i> (DAGDOP) is proposed to simultaneously incorporate influences from the dynamics and geometry of satellite pairs. Based on the DAGDOP, the effect of different observation arcs on the AOD accuracy is investigated. Next, the AOD accuracy of three different types of satellite pairs—halo+halo, DRO+DRO, and halo+DRO—is systematically analyzed. The hybrid halo+DRO type shows the best overall accuracy. Finally, the AOD performance of the hybrid type is verified in a realistic model. Our studies find that the average AOD accuracy of the halo orbit is about 170 meters, and that of the DRO is about 190 meters. The relative time synchronization error of two satellites is less than 30 nanoseconds.

Autonomous orbit determination and timekeeping in lunar distant retrograde orbits by observing X‐ray pulsars

<h3>Abstract</h3> A server satellite that is parked in a stable distant retrograde orbit (DRO) in the vicinity of the Moon can provide navigation service for satellites in the Earth– Moon system. In this study, X-ray pulsar navigation (XPNAV) is investigated to determine the server’s orbital position and velocity, and maintain its onboard timing autonomously to ensure the autonomy of the server. First, the feasibility and potential advantages of XPNAV in DRO are analyzed qualitatively based on the unique properties of DRO: long-term orbital stability and short-term, nearly uniform-velocity rectilinear motion. Second, high-fidelity X-ray photon timestamps are simulated to serve as the original measurements for XPNAV. A classical extended Kalman filter is used to estimate the orbital states (i.e., position and velocity) and the clock timing of the satellite in DRO, wherein the pulse phase and Doppler frequency are estimated as intermediate measurements. Finally, Monte Carlo simulations are conducted to assess the variation in the XPNAV performance with the DRO orbital period, clock noise, and detector effective area. The simulation results show that XPNAV in DRO can achieve considerably improved position accuracy than that in low Earth orbit using the same hardware while maintaining the long-term stability of the satellite onboard clock, thus demonstrating the capability of XPNAV to be used in an operational spaceflight mission around or beyond the Moon.

Navigator Notes

Welcome to the Winter 2021 issue of NAVIGATION . In this issue, we feature articles on GNSS interference and monitoring, autonomous orbit determination and timekeeping using X-ray pulsars, and the improvement of GNSS clock corrections and phase biases. We are also featuring articles reporting new