Алгоритмы обработки многоточечных измерений в распределенных космических системах тема диссертации и автореферата по ВАК РФ 00.00.00, кандидат наук Афанасьев Антон Андреевич

• Афанасьев Антон Андреевич
• кандидат наук
• 2023

Оглавление диссертации кандидат наук Афанасьев Антон Андреевич

Table of Contents

Introduction

Distributed space systems

Multipoint measurements processing

State-of-the-art techniques

Methodology

Chapter 1 Kriging

1.1 Swarm

1.2 Kriging interpolation

1.3 Simulations for single satellite in perturbed environment

1.4 Simulations for swarm in perturbed environment

Chapter 2 Relative Motion

2.1 Orbital configuration of satellites

2.2 ESV comparison

2.3 Simulations for swarm in relative orbit

Chapter 3 Space Debris

3.1 Mission design

3.2 Optical system dynamics

3.3 Simulations for different formations

Conclusion

Bibliography

Введение диссертации (часть автореферата) на тему «Алгоритмы обработки многоточечных измерений в распределенных космических системах»

Introduction

The relevance of research

The thesis explores the relevance and importance of distributed space systems, which utilize multi-spacecraft formations to replace large single-satellite architectures. These systems aim to enhance mission reliability, achievable outcomes, and cost-effectiveness. While single-satellite missions offer advantages in terms of precision and functionality, distributed architectures provide improved flexibility and adaptability to accommodate structural and functional changes.

Distributed measurements play a crucial role in these systems, offering a multitude of benefits. Firstly, they enable improved data accuracy by collecting measurements from multiple points in space, mitigating individual measurement errors and providing more reliable observations. Secondly, distributed measurements enhance spatial coverage, allowing for comprehensive analysis of phenomena occurring over larger areas of interest. This broader spatial perspective leads to a better understanding of spatial variations and patterns.

Furthermore, distributed measurements offer higher temporal resolution, facilitating the study of dynamic processes, rapid changes, and time-dependent phenomena. By continuously monitoring and collecting data from multiple spacecraft simultaneously, researchers can capture intricate details that would be challenging with single-point measurements alone.

Additionally, distributed systems provide redundancy and fault tolerance. In the event of a failure or malfunction of one spacecraft within a formation, the remaining satellites can continue to operate and provide valuable data. This redundancy increases the reliability and robustness of the measurements, ensuring that critical information is not lost due to single-point failures.

The applications of distributed measurements are versatile and far-reaching. They are instrumental in remote sensing, climate monitoring, space weather analysis, atmospheric studies, Earth observation, and planetary exploration. Leveraging

distributed measurements opens up new avenues for scientific research and advancements in our understanding of the universe. One of the principal issues addressed in the thesis is the collective processing and utilization of data in a swarm of Cube-Sats, with particular emphasis on the spacecraft's attitude determination and control subsystem. The study illustrates how the swarm can effectively retrieve the actual magnetic field in regions where the swarm satellites are present by processing the exchanged measurement data facilitated through inter satellite links.

The thesis underscores the importance of multipoint measurements processing by a cluster of CubeSats for various space applications. These applications encompass synthetic aperture radars (SAR), optical interferometry, on-orbit inspection and servicing of other spacecraft, and the measurement of spatial gradients in environmental data.

In summary, distributed measurements in space offer improved data accuracy, enhanced spatial coverage, higher temporal resolution, and fault tolerance. They enable comprehensive observations, provide valuable insights into complex phenomena, and contribute to scientific knowledge, technological development, and decision-making processes in space exploration and Earth's environment.

Goal of the research

A goal of the research is to develop a set of algorithms to enhance measurements of environmental phenomena and improve their estimates, using a distributed group of satellites, taking advantage of the multipoint measurements processing and its inference on a variety of space applications.

Objectives of the research

To achieve this goal, the following objectives had to be completed:

1. To research an ability to improve measurements of the geomagnetic field with

Kriging interpolation in a swarm of 4 CubeSats.

2. To research on how the ADCS of each CubeSat from a formation of 4 bodies, constituted with magnetometers and sun sensors, can be improved with

measurements exchange and formation structure variation.

3. To research the most effective formations of satellites to make space-based optical observation for on-request short-arc orbit determination of smaller (1 to 10 cm in size) space debris objects in highly-polluted sun-synchronous orbits.

Scientific novelty

1. The Kriging interpolation is proposed for the first time to use as a technique for space-based multipoint measurements processing, increasing accuracy of measured and dependent parameters estimations.

The powered exponential model function was proposed as the best fit for an empirical semivariogram of geomagnetic field.

It is suggested to use a measurement history to enhance the accuracy of interpolation.

2. Law of motion for tetrahedral satellites formation is researched for near-circular orbits and the best possible structure was found to perform multipoint measurements with Kriging interpolation.

3. The best configuration of satellites was discovered for a short-arc space debris orbit determination with optical sensors and up to 4 spacecraft.

The highlights of the thesis are:

1. The Kriging interpolation model is suggested to enhance the accuracy of estimation of geomagnetic field, which compares favorable to other interpolators, like inverse distance weighing and splines, since it tales into account variational properties of the considered region.

The best fit of powered exponential model function is found for an empirical semivariogram of the geomagnetic field.

The Kriging solution for interpolation of geomagnetic field is proven to be robust to the presence of strong model noise, making it possible to use theoretically found semivariograms in real-life missions.

Mean-squared errors of measurements and Kriging interpolation estimates are compared and the latter is found to be more effective, especially for satellite formations with low characteristic size.

Measurements history were used to increase the number of interpolation points, thus increasing the accuracy of geomagnetic field estimation.

2. Mean-squared errors of attitude determination with Extended Kalman Filter and Lyapunov-based controller on magnetometers were compared for scenarios with singular CubeSat and with a swarm of 4 CubeSats, performing measurements exchange and Kriging interpolation. The latter is found to be more effective.

The rigid body structure with measurements extrapolation and relative motion on a near-circular orbits were used to simulate the work of ADCS for a swarm of 4 CubeSats.

The tetrahedral formation with relative motion on a near-polar circular orbit was implemented to simulate an ionospheric mission. The relative motion was based on a Hill-Clohessy-Wiltshire equations, maintain the best possible tetrahedron quality and preserve distances between satellites as long as possible. Laws of motion for such formation were derived.

3. Space-based optical observations of small debris to determine their orbit were conducted on a train, general circular orbit and tetrahedron satellites configurations with various number of satellites and various triangulation bases on a sun-synchronous orbits.

The Extended Information filter was used to produce estimates of radius-vector and linear velocity of a debris, based on measurements of elevation and

azimuth angles. Information filter was chosen instead of Kalman filter due to small processing time of short-arc orbit determination.

All configurations were compared in terms of mean-squared errors of state-space vector estimation, and the best one was recommended to be used in real-life missions.

Practical significance

Results of the work can be used in real-life space missions to increase the accuracy of any sorts of measurements, such as ionospheric missions, distributed SAR missions, debris short-arc orbit determination. Also, the formation of 4 satellites can be used as a generator of accurate geomagnetic field measurements and broadcast the data to neighbouring spacecraft with noisy magnetometers.

Practical significance is confirmed by a participation in a grant of the RFBR 19-38-90278 "Algorithms of Decentralized Coordinated Control for Satellites' Swarms Dynamics".

Approbation of the work

The main results of the work were reported at the following conferences: 5th IAA Conference on University Satellite Missions and CubeSat Workshop (2020), 71st International Astronautical Congress, The CyberSpace Edition (2020). Publications

The main results on the topic of the dissertation are presented in 4 printed works in peer-reviewed journals included in the international citation systems Web of Science and Scopus.

1. Anton Afanasev, Shamil Biktimirov. CubeSats formation architecture for small space debris surveillance and orbit determination // Informatsionno-upravli-aiushchie sistemy [Information and Control Systems], 2021, no. 4, P. 37-46, DOI: 10.31799/1684-8853-2021-4-37-46.

2. Anton Afanasev, Mikhail Shavin, Anton Ivanov, Dmitry Pritykin. Tetrahedral satellite formation: Geomagnetic measurements exchange and interpolation//

Advances in Space Research, 2021, Vol. 67, no. 10, P. 3294 3307, DOI: 10.1016/j.asr.2021.02.012 (Scopus Q2).

3. Anton Afanasev, Anton Ivanov. Attitude control algorithms aided by multipoint statistics and distributed measurements processing in a swarm of cube-Sats // Proceedings of the International Astronautical Congress, IAC-20. 2020.

4. Anton Afanasev, Anton Ivanov, Ahmed Mahfouz, Dmitry Pritykin. Attitude control algorithms in a swarm of cubesats: Kriging interpolation and coordinated data exchange // Advances in the Astronautical Sciences, 2020, Vol. 173.

Personal contribution of the author

The main finding of the thesis was obtained either by the applicant in person, or in collaboration with co-authors where the role of the applicant was dominant. The numerical implementations of all the algorithms and other computer programs were fulfilled by the applicant personally.

Заключение диссертации по теме «Другие cпециальности», Афанасьев Антон Андреевич

Conclusion

Our preliminary study [62] has shown that even the simplest interpolation algorithm IDW enhances the on-board magnetic field model, thus making the attitude determination algorithms more robust and more immune, for instance, to magnetic storms. Another problem, arising when dealing with controllers, based on magnetic phenomena, is a presence of residual magnetization, which creates a bias in the process noise. We discussed methods to deal with such problem in the paper [63], but since they do not use multipoint measurements, respective results were not transferred into this work.

Our study [64] delineates a method to enhance attitude determination algorithms in a satellite swarm by exchanging and processing distributed measurements of the geomagnetic field. Kriging interpolator has been implemented to simulate the communication between the swarm nodes and enhance the attitude control on the basis of optimized magnetic field measurements. To analyze the spatial correlation in the interpolation region, an empirical semivariogram, based on the direct dipole of the geomagnetic field, is acquired and fit into the powered exponential mathematical model, which was used in the communication algorithm. Based on the proposed determination algorithm, a complete set of solely magnetic attitude control algorithms is developed, implemented and tested by numerical experiments. Filtration of CubeSat's magnetic ADCS is performed and compared with the filtration in the swarm. It appears that the the system which uses the interpolator has on average 1.5° better accuracy. However, the disturbances used in simulations are rather small and the in-orbit resulting MSEs are expected to be different, with greater standard deviations and non-zero means.

In paper [65] we studied different semivariogram models and separated them into the atlas, depending on the current sector of the orbit. We acquired empirical semivariograms for the IGRF-13 model of the geomagnetic field and fitted into them best possible model function, which was proven empirically. We found that usage

of interpolated estimates in the formation of CubeSats can enhance the accuracy of the attitude control up to 2° in comparison with singleton ADCS and direct measurements.

The paper [66] considers an extra function, a satellite formation can carry out, namely, data exchange and interpolation. We studied a mission, whose orbital configuration is similar to tentative ionospheric mission for distributed spatial plasma measurements in a polar orbit. As an example of the distributed measurements geomagnetic field was considered.

We showed that even for a four-satellite formation, distributed measurements and appropriate interpolation methods can produce comparatively precise instantaneous maps of the measured quantity. We established the size of the 3d local map that can be constructed with the four available satellites and discussed how the quality of this map can be improved by using measurements history. We quantified how the enhanced geomagnetic field data can be used to improve the attitude determination routine quality for any satellite, which happens to be within the coverage of the servicing formation. It appears that even for such simplistic attitude determination routine as TRIAD the result can be improved by 1-3°, which is quite significant for university ionospheric missions, that rely on the low-cost components-off-the-shelf and require pointing accuracy of a few degrees.

In study [67] we managed to construct viable configurations for satellites formations with optical sensors and compare the effectiveness in scenarios with different number of points of view (satellites) and measurement times. We implemented the EIF to make the simulations of the measurement of the target position by several optical sensors and calculated respective MSEs. The error diminishes when the number of sensors increases and also when the time of continuous measurement grows. The most important part is actually that the GCO configuration outstrips the train one in cases of 2 and 3 observation points, which means that the tetrahe-dral configuration, which is natural extension of GCO onto the case of 4 satellites, is the best use-case for determining the target debris orbit using short-arc optical

measurements.

On completion of this work, we believe that the Kriging interpolation algorithms are worthy of close attention of the researchers involved with distributed space measurements. One other thing, that we should like to point out is that with the advent of megaconstellations, when networking satellites will occupy large regions of space, such service as we showed through the example of four-satellite formation, may actually become as universal as that of GPS.

Список литературы диссертационного исследования кандидат наук Афанасьев Антон Андреевич, 2023 год

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