Inter-satellite Distance Research Articles

Inter-satellite tracking methods and applications: A comprehensive survey

The accurate measurement of inter-satellite distances is fundamental to the successful operation of distributed spacecraft missions, facilitating diverse applications ranging from scientific exploration to navigation and communication. This study comprehensively overviews applications requiring inter-satellite tracking by analyzing 44 multi-spacecraft missions. These missions are divided into seven categories based on their use of inter-satellite distance measurements. Each category necessitates varying levels of accuracy, prompting the utilization of distinct tracking methods. The analysis reveals that missions near Earth typically rely on Global Navigation Satellite Systems measurements, achieving millimeter-level accuracy, while lunar missions opt for radio ranging for centimeter-level accuracy. Inter-satellite Laser Ranging Interferometry emerges as the preferred method for missions demanding exceptionally high accuracy (nanometer to picometer range), such as those dedicated to gravitational wave detection and gravimetry. Notably, the analysis identifies a burgeoning trend towards the adoption of Inter-satellite Laser Transponder Ranging, capable of achieving sub-millimeter accuracy. Furthermore, this work proposes a novel concept: integrating inter-satellite ranging with Laser Communication Terminal (LCTs), either to substitute for existing tracking methods or to enhance measurement accuracy within established frameworks. However, its full potential rests upon the successful adaptation of existing LCTs for ranging functionality without compromising data rates. Future research will play a critical role in quantifying achievable ranging performance by characterizing systematic errors within LCTs.

Assessment of Callisto Gravity-field Determination Using the Inter-satellite Range-rate Link

China will launch the “Tianwen-IV” mission around 2030, focusing on the orbiting exploration of Jupiter and Callisto, a moon of Jupiter. As part of this ambitious mission, a main satellite will carry another satellite that will be released in the Jupiter system to continue its journey toward Uranus. Considering the current mission planning, we propose an inter-satellite radio-observation mode that differs from the conventional observation mode of tracking from Earth to precisely determine the orbit of the satellites. Given the significance of the Callisto gravity field model in both science objectives and satellite navigation, we have conducted a series of simulation experiments to evaluate the potential of this inter-satellite range-rate data for accurately estimating the Callisto gravity field. The results obtained from the analysis demonstrate that by utilizing 40 days of ground station observations, it is possible to estimate the gravity field model of Callisto up to a degree of 70. Remarkably, when combining these ground station observations with inter-satellite observations, a comparable level of accuracy can be achieved with just 10 days of observations. Furthermore, with reduced inter-satellite observation noise, accuracy improves, enabling estimation up to 80 degrees or higher. Initial inter-satellite distance selection impacts estimation accuracy. These findings serve as a valuable test bed for the future “Tianwen-IV” mission to perform precise orbit determination and gravity field model estimation to reduce reliance on deep space stations.

Robust attitude coordinated control for gravitational-wave detection spacecraft formation with large-scale communication delays

This paper concentrates on robust attitude control issues for spacecraft formation in gravitational-wave detection missions. Notably, with the large-scale communication delays brought by the million kilometers-scale inter-satellite distance, the exponential convergence of the closed-loop delayed system is firstly achieved via a new delay-dependent nominal attitude coordinated control scheme. Then, a finite-time disturbance observer is deployed to reconstruct the unknown lumped disturbance from internal uncertainties and the external environment. Meanwhile, an integral sliding manifold is embedded in the delay-dependent attitude controller for superior systems’ robustness. Finally, two simulation examples illustrate the feasibility and effectiveness of the proposed attitude control strategy for in-orbit gravitational-wave detection spacecraft systems.

Absolute Ranging with Time Delay Interferometry for Space-Borne Gravitational Wave Detection.

In future space-borne gravitational wave (GW) detectors, time delay interferometry (TDI) will be utilized to reduce the overwhelming noise, including the laser frequency noise and the clock noise etc., by time shifting and recombining the data streams in post-processing. The successful operation of TDI relies on absolute inter-satellite ranging with meter-level precision. In this work, we numerically and experimentally demonstrate a strategy for inter-satellite distance measurement. The distances can be coarsely determined using the technique of arm-locking ranging with a large non-ambiguity range, and subsequently TDI can be used for precise distance measurement (TDI ranging) by finding the minimum value of the power of the residual noises. The measurement principle is introduced. We carry out the numerical simulations, and the results show millimeter-level precision. Further, we perform the experimental verifications based on the fiber link, and the distances can be measured with better than 0.05 m uncertainty, which can well satisfy the requirement of time delay interferometry.

Signals of opportunity for space navigation: An application-oriented review

Space navigation using X-Ray pulsars is known as opportunistic navigation, where we rely on signals of opportunity from natural phenomena to determine navigation solutions for spacecraft. However, this definition becomes too small or shallow, as it doesn't include other forms of navigation using natural beacons reported over the last two decades. Since a classification or review of all opportunistic techniques is still missing, this article presents the first survey on the field of signals of opportunity (SOOP), and introduces a framework for this scientific area, where natural beacons could be associated to stars, distant planets or natural phenomena, and signals could come with distinct characteristics and wavelengths. The new classification groups dozens of existing technologies of navigation using natural beacons, making easier for newcomers to interpret quickly a variety of works and mathematical formalisms. In addition, we deepen into an engineering perspective on the ongoing status of SOOP-based navigation, highlighting what is required to achieve the level of readiness on the methods that still on theory. We also give answer to a number of open questions, such as e.g. what criterion defines if a signal from a given natural beacon could be used or not for navigational purposes, as well as what is the minimum intersatellite distance that we can detect using an opportunistic signal, what type of signal characteristics we need from natural phenomena to generate navigation solutions or how far apart natural beacons preferentially need to be. These results enrich the field and become fundamental with an increasing interest of the space industry to bring novel forms of navigation into low-cost spacecraft of limited hardware capabilities (such as Cubesats).Furthermore, using results from past remote sensing missions, we preliminary found that Earth's lightning is a natural resource available in large scale and in sufficient variability that can be potentially used for relative opportunistic navigation. The physics of the problem is introduced, where at least theoretically, multiple lightning events can be used to map the arrival times to cooperating spacecraft, fixing their positions relative to each other independently from ground.

Estimation of the possibility of matching the relative motion of nanosatellites under active aerodynamic control

The article discusses the prospects of utilization of aerodynamic control to maintain the formation of nanosatellites of the CubeSat class. The purpose of this work is to estimate the limits of the application of active aerodynamic control to stabilize the relative motion of two CubeSat 3U satellites in a sun-synchronous orbit with a height of 570 km. A review of theoretical information about aerodynamic forces acting on artificial Earth satellites is carried out, within the framework of which models of the Earth's upper atmosphere are considered. Aspects of creating a differential drag force for nanosatellites as an active control actuating mechanism are considered. To study the orbital motion of satellites under the action of aerodynamic control using the General Mission Analysis Tool program, a group flight of two spacecraft was simulated taking into account the factors causing orbital disturbances. Based on the results of experiments, the dynamics of the inter-satellite distance was studied, and a conclusion was made about the possibility of using an aerodynamic differential force to achieve a stable relative motion.

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

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

Combined optical line-of-sight and crosslink radiometric navigation for distributed deep-space systems

This manuscript aims to present and evaluate the applicability of combining optical line-of-sight (LoS) navigation with crosslink radiometric navigation for deep-space cruising distributed space systems. To do so, a set of four distributed space systems architectures is presented, and for each of those, the applicability of the combination is evaluated, comparing it to the baseline solutions, which are based on only optical navigation. The comparison is done by studying the performance in a circular heliocentric orbit in seven different time intervals (ranging from 2024 to 2032) and exploiting the observation of all the pairs of planets from Mercury to Saturn. The distance between spacecraft is kept around 200 km. Later, a NEA mission test case is generated in order to explore the applicability to a more realistic case. This analysis shows that the technique can also cope with a variable inter-satellite distance, and the best performance is obtained when the spacecraft get closer to each other.

A new window function for the spectral analysis of effect of celestial body on Taiji mission below 0.1 mHz

The Taiji project is a space gravitational wave detection mission consisting of three satellites that form a large equilateral triangle with a side length of approximately 3×109 m in heliocentric orbit. It may have the potential to detect gravitational waves below 0.1 mHz. Gravitational wave signals in the μHz range have a strain sensitivity as large as 2.9×10-14, or approximately 8.7×10-5 m variation in inter-satellite distance. However, inter-satellite distances are affected by the celestial bodies in the solar system, introducing changes that may reach magnitudes of 3×107 m; thus, the effect of celestial bodies on these distances may exceed the gravitational signals below 0.1 mHz. Therefore, it is necessary to accurately estimate the effect of the gravity of celestial bodies below 0.1 mHz. In this study, based on the inter-satellite distances in the Taiji mission, a window function design method is proposed and a six-term cosine window function is designed. It has a high decay rate of h-12 and a good peak sidelobe level of −88 dB. It improves the attenuation of spectral leakage while maintaining an acceptable minimum number of signal periods, which is beneficial for signals where it is difficult to obtain more periods, such as for the Taiji mission. Based on the analytical results of the states of satellites in cases when the satellites move only in the gravitational field of the Sun, the ability of the new window function is validated.

GNSS-based baseline vector determination for widely separated cooperative satellites using L1-only receivers

Real time estimation of the relative position and velocity vectors between two satellites in a formation is an integral part of the formation control loop. Relative positioning based on Global Navigation Satellite Systems (GNSS) has been a dominating technology for formation missions in LEO, where extremely precise estimates could be obtained for formations with small inter-satellite distances (1-10 km). Larger baselines between the satellites (>10 km) are more challenging as they pose the problem of huge differences in the ionospheric delays experienced by the signals received by each receiver. This problem could be mitigated by using precise ionospheric-free combinations that could only be obtained by dual-frequency receivers, which is not a cost-efficient option for the modern low-cost miniature missions. In this paper, the problem of GNSS-based relative navigation between two spacecraft with large inter-satellite distance which are equipped with single-frequency receivers is treated through adopting the space-proven Extended Kalman Filter (EKF). Although using an EKF for relative navigation is a common practice, there are many variants of the filter settings, which vary in terms of the state and measurement vectors to be adopted as well as the techniques to be used to handle the ionospheric delay. In this research, optimal settings of the filter are sought for the problem of relative baseline vector estimation between two spacecraft that have large separation and which are equipped with with single-frequency GNSS receivers.

Bi-directional PRN laser ranging and clock synchronization for TianQin mission

Laser frequency coupling noise due to unbalanced arm lengths is the dominant noise source for space-based gravitational wave detection. Time-delay interferometry is a proposed technique to eliminate the coupling noise by constructing a virtual equal-arm-length interferometer, where the real-time information of both absolute inter-satellite distance and clock synchronization is required. Inter-satellite laser ranging based on pseudo-random noise (PRN) sequence modulation has become the main technical means for extraction of the inter-satellite distance and clock difference information. This paper shows a bi-directional laser ranging scheme based on PRN code modulation and experimentally demonstrates its function by using an optical fiber of 10 km long. The measured results of the transmission time duration and the clock difference are compared with independent methods of pulse laser ranging and 1PPS signal measurement, respectively, both of which coincide well. It is also evaluated that the laser ranging accuracy is 1.2 m, and the clock synchronization accuracy reaches 6.7 ns, applicable to TianQin with the preliminarily determined requirement of 3 m and 10 ns. This laser ranging scheme can be applied to satellite navigation and space-based gravitational wave detection.

On-orbit demonstration of inter-satellite free-space optical stable communication enabled by integrated optical amplification of HPA and LNA.

Satellite free-space optical (FSO) communication is very promising in improving the bandwidth and capacity of space information networks in the future. However, the inter-satellite transmission distance of over 1000km leads to unstable optical beam pointing, acquisition, and tracking and then generates optical power jitter by a large margin before detection-demodulation. Therefore, it is difficult to realize high-stability and long-time FSO communication between satellites due to the generated bit error rate (BER) by jitter. In this paper, we report an autonomously self-designed and high-integration laser communication payload (LCP) and on-orbit-demonstrated inter-satellite 145min, zero-BER FSO stable communication with a line rate of 2.8Gbps. Moreover, based on the inter-satellite laser communication link, a video phone was clearly implemented for more than 10min, and authentic user data transmitted 459,149 packets, achieving results of zero-packet loss. Summarily, this on-orbit experiment demonstrated an excellent performance of the LCP owing to the distinctive design of integrating a high-power amplifier and low-noise amplifier optical amplification function. Our space mission was successfully completed, and the on-orbit demonstration results may offer a significant reference for the field of satellite laser communication and space information networks.

Assessment of gravity field recovery from a quantum satellite mission with atomic clocks and cold atom gradiometers

The aim of the MOCAST+ (MOnitoring mass variations by Cold Atom Sensors and Time measures) project, which was carried out during the years 2020–2022, was the investigation of the performance of a gravity field mission based on the integration of atomic clocks and cold atom interferometers. The idea was that the combined observations of the two sensors would be beneficial for the detection and monitoring of geophysical phenomena which have an impact on the time-variable part of the Earth gravity field models. Several different mission scenarios were simulated, considering different satellite configurations such as a Gravity Recovery and Climate Experiment (GRACE)-class formation and a Bender-class formation with either two or three in-line satellites along each orbit. Moreover, different atomic species (rubidium and strontium), different inter-satellite distances, different noise power spectral densities, and different observation rates were taken into account. For the gravity field estimation from the simulated data, the space-wise approach was exploited. The results showed that, as it could be expected, the Bender configuration provides significantly better monthly gravity field solutions, as compared to a ‘nominal’ configuration with two or three satellites in a GRACE-class formation. In this way, and pushing the quantum sensors technology to its limits, it is in fact possible to obtain results which are comparable with those from GRACE at low harmonic degrees, and are better at higher degrees with positive effects in the detectability of localized time variable phenomena, as well as in the determination of the static gravity field at a higher maximum spherical harmonic degree than the one achieved by Gravity Field and Steady-State Ocean Circulation Explorer (of course considering an equivalent mission life-time).

Effect of celestial body gravity on Taiji mission range and range acceleration noise

The Taiji project is a space gravitational-wave detection mission consisting of three satellites that form a giant equilateral triangle with a side length of approximately $3\ifmmode\times\else\texttimes\fi{}{10}^{6}\text{ }\text{ }\mathrm{km}$ in the heliocentric orbit. The target of the mission is to detect gravitational-wave signals in the 0.1 mHz to 1 Hz band. However, its intersatellite distances are affected by celestial bodies in the solar system, introducing changes that may reach levels of 30,000 km in magnitude. Thus, it is important to investigate whether the gravitational fields of celestial bodies in the detection frequency band will have an impact on the realization of ultrahigh-sensitivity intersatellite ranging measurements. In this study, a high-precision orbit propagator with an accuracy of 0.03 pm on the 1 AU scale is developed. Based on this orbit propagator, the impact of the major large celestial bodies in the solar system on the detection sensitivity in the intersatellite measurements are analyzed. Detailed numerical studies show that the linear spectral density of the range and range acceleration are approximately $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\text{ }\text{ }\mathrm{m}/\sqrt{\mathrm{Hz}}$ and $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}\text{ }\text{ }\mathrm{m}/{\mathrm{s}}^{2}/\sqrt{\mathrm{Hz}}$, respectively, at 0.1 mHz, indicating that the gravitational disturbance generated by the major celestial bodies in the solar system will not affect the aim of the Taiji mission to detect gravitational waves in the frequency band 0.1 mHz to 1 Hz.

Close-range leader–follower flight control technology for near-circular low-orbit satellites

Abstract Based on the characteristics of near-circular orbits and close-range leader–follower flights, the relative dynamics equations of the eccentricity/inclination ( e/i ) vector method are introduced herein. Additionally, the constraint terms in the design of the leader–follower flight formation are found to satisfy the conditions of the line-of-sight angle and inter-satellite distance. The control box algorithm is proposed under the flying task’s constraints, such as the line-of-sight angle and distance between the satellites according to the e/i vector and Gauss perturbation equations. The algorithm comprehensively takes into account the relationship between the relative motion variations in the satellite formation in near-circular orbits as well as their relationship with the velocity increment applied to the satellites. The example simulated in this study not only illustrates the existence of a coupling relationship between the flight-following distance and flight-following line-of-sight angle but also verifies the influence of the relative eccentricity of the two satellites on the leader–follower flight stability. The simulation results show that when the control box algorithm was used to maintain the leader–follower flight, this method was simple, intuitive, and may be feasibly introduced as a flight-following control strategy.

Design of Novel Laser Crosslink Systems Using Nanosatellites in Formation Flying: The VISION

With growth in data volume from space missions, interest in laser communications has increased, owing to their importance for high-speed data transfer in the commercial and defense fields, spaceborne remote sensing, and surveillance. Here, we propose a novel system for space-to-space laser communication, a very high-speed inter-satellite link system using an infrared optical terminal and nanosatellite (VISION), which is aimed at establishing and validating miniaturized laser crosslink systems and several space technologies using two 6U nanosatellites in formation flying. An optical link budget analysis is conducted to derive the signal-to-noise ratio requirements and allocate the system budget; the optical link margin should be greater than 10 dB to guarantee communication with practical limitations. The payload is a laser transceiver with a deployable space telescope to enhance the gain of the beam transmission and reception. Nanosatellites, including precise formation flying GNC systems, are designed and analyzed. The attitude control system ensures pointing and tracking errors within tens of arcsec, and they are equipped with a propulsion system that can change the inter-satellite distance rapidly and accurately. This novel concept of laser crosslink systems is expected to make a significant contribution to the future design and construction of high-speed space-to-space networks.

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.

Application and Analysis of Mode Expansion Method in Simulation of Intersatellite Ultra-Long Distance Diffraction Propagation

Application and Analysis of Mode Expansion Method in Simulation of Intersatellite Ultra-Long Distance Diffraction Propagation

Differential Tropospheric Delay Estimation by Simultaneous Multi-Angle Repeat-Pass InSAR

Tropospheric delays are one of the main contributors to the interferometric phase in synthetic aperture radar (SAR) interferometry. When the phase contributions from surface deformation, topography, and ionospheric delays are negligible or known, the interferogram can be used to estimate the differential tropospheric delay (DTD), which can help to improve tropospheric delay predictions from weather models and in situ measurements. In conventional repeat-pass interferometric SAR (InSAR), however, the estimation of the DTD can still be significantly hindered by baseline errors. In addition, a single interferogram provides only relative DTDs, as the delays can be retrieved up to an unknown offset. To address such issues, this article presents a method for the estimation of DTDs on large scales by using repeat-pass simultaneous multi-angle SAR systems. Complementary simultaneous observations of the correlated troposphere from multiple angles are used to retrieve estimates of the absolute DTD and, at the same time, to mitigate the effect of baseline knowledge errors. Finally, a performance evaluation is presented for the Harmony Earth Explorer 10 candidate mission. A centimeter-level absolute accuracy and a submillimeter-level relative accuracy of the DTD estimation are achieved under the multistatic Harmony case when at least one companion satellite has an inter-satellite distance longer than 300 km to provide enough sensitivity.