Machine Learning in Orbit Estimation: a Survey (2207.08993v4)
Abstract: Since the late 1950s, when the first artificial satellite was launched, the number of Resident Space Objects has steadily increased. It is estimated that around one million objects larger than one cm are currently orbiting the Earth, with only thirty thousand larger than ten cm being tracked. To avert a chain reaction of collisions, known as Kessler Syndrome, it is essential to accurately track and predict debris and satellites' orbits. Current approximate physics-based methods have errors in the order of kilometers for seven-day predictions, which is insufficient when considering space debris, typically with less than one meter. This failure is usually due to uncertainty around the state of the space object at the beginning of the trajectory, forecasting errors in environmental conditions such as atmospheric drag, and unknown characteristics such as the mass or geometry of the space object. Operators can enhance Orbit Prediction accuracy by deriving unmeasured objects' characteristics and improving non-conservative forces' effects by leveraging data-driven techniques, such as Machine Learning. In this survey, we provide an overview of the work in applying Machine Learning for Orbit Determination, Orbit Prediction, and atmospheric density modeling.
- H. D. Curtis, Preliminary orbit determination, in: Orbital Mechanics for Engineering Students (Third Edition), third edition ed., Butterworth-Heinemann, Boston, 2014, pp. 239–298.
- S. J. Julier, J. K. Uhlmann, New extension of the Kalman filter to nonlinear systems, Signal Processing, Sensor Fusion, and Target Recognition VI 3068 (1997) 182 – 193.
- G. A. Einicke, Nonlinear prediction, filtering and smoothing, in: Smoothing, Filtering and Prediction - Estimating The Past, Present and Future, 2nd ed., IntechOpen, Rijeka, 2012, pp. 245–275.
- Fundamentals of orbit determination, in: B. D. Tapley, B. E. Schutz, G. H. Born (Eds.), Statistical Orbit Determination, Academic Press, Burlington, 2004, pp. 159–284.
- C. Uphoff, Numerical Averaging in Orbit Prediction, in: Astrodynamics Conference, volume 11, AIAA, Palo Alto,CA, 1972, pp. 1512–1516.
- High accuracy satellite drag model (HASDM), Advances in Space Research 36 (2005) 2497–2505.
- Gaussian sum filters for space surveillance: Theory and simulations, Journal of Guidance, Control, and Dynamics 34 (2011) 1839–1851.
- The development and evaluation of the Earth Gravitational Model 2008 (EGM2008), Journal of Geophysical Research: Solid Earth 117 (2012).
- Revisiting spacetrack report #3, in: AIAA/AAS Astrodynamics Specialist Conference and Exhibit, volume 3, AIAA, 2006, pp. 1984–2071.
- Y. Zhong Luo, Z. Yang, A review of uncertainty propagation in orbital mechanics, Progress in Aerospace Sciences 89 (2017) 23–39.
- T. Mortlock, Z. M. Kassas, Assessing machine learning for LEO satellite orbit determination in simultaneous tracking and navigation, in: 2021 Institute of Electric and Electronics Engineers (IEEE) Aerospace Conference, 2021, pp. 1–8.
- A. J. Krener, The Convergence of the Extended Kalman Filter, Directions in Mathematical Systems Theory and Optimization (2007) 173–182.
- R. E. Kalman, A new approach to linear filtering and prediction problems, Journal of Basic Engineering 82 (1960) 35–45.
- M. Ribeiro, I. Ribeiro, Kalman and extended kalman filters: Concept, derivation and properties, Institute for Systems and Robotics 43 (2004) 46.
- Y. Kim, H. Bang, Introduction to Kalman Filter and Its Applications, in: F. Govaers (Ed.), Introduction and Implementations of the Kalman Filter, IntechOpen, Rijeka, 2018, p. 19.
- O. Payne, A. Marrs, An unscented particle filter for gmti tracking, in: 2004 Institute of Electric and Electronics Engineers (IEEE) Aerospace Conference Proceedings, volume 3, 2004, pp. 1869–1875.
- A Tutorial on Particle Filters for Online Nonlinear/Nongaussian Bayesian Tracking, Institute of Electric and Electronics Engineers (IEEE) Transactions on Signal Processing 50 (2002) 723–737.
- Analysis of filtering methods for satellite autonomous orbit determination using celestial and geomagnetic measurement, Mathematical Problems in Engineering 2012 (2012).
- State-Space Inference for Non-Linear Latent Force Models with Application to Satellite Orbit Prediction, in: Proceedings of the 29th International Conference on Machine Learning, ICML, Edinburgh, Scotland, 2012, pp. 903–910.
- Latent force models, in: D. van Dyk, M. Welling (Eds.), Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics, volume 5 of Proceedings of Machine Learning Research, PMLR, Hilton Clearwater Beach Resort, Clearwater Beach, Florida USA, 2009, pp. 9–16.
- Gaussian process latent force models for learning and stochastic control of physical systems, IEEE Transactions on Automatic Control 64 (2019) 2953–2960.
- Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, Journal of Computational Physics 378 (2019) 686–707.
- Orbit determination with maneuver estimation in cislunar environment va physics informed neural networks, in: 2022 AAS/AIAA Astrodynamics Specialist Conference, Charlotte, USA, 2022, p. 13.
- Physics-informed orbit determination for cislunar space applications, in: Proceedings of the Advanced Maui Optical and Space Surveillance (AMOS) Technologies Conference, Wailea, HI, 2023, p. 10.
- Learning theory for distribution regression, The Journal of Machine Learning Research 17 (2016) 5272–5311.
- C. Jiang, An orbit determination method of spacecraft based on distribution regression, Open Astronomy 30 (2021) 159–167.
- Uncertainty Propagation for Nonlinear Dynamic Systems using Gaussian Mixture Models, Journal of Guidance, Control, and Dynamics 31 (2008) 1623–1633.
- Entropy-based approach for uncertainty propagation of nonlinear dynamical systems, Journal of Guidance, Control, and Dynamics 36 (2013) 1047–1057.
- D. L. Alspach, H. W. Sorenson, Nonlinear Bayesian Estimation using Gaussian Sum Approximations, Institute of Electric and Electronics Engineers (IEEE) Transactions on Automatic Control 17 (1972) 439–448.
- Nonlinear Uncertainty Propagation for Perturbed Two-body Orbits, Journal of Guidance, Control, and Dynamics 37 (2014) 1415–1425.
- Adaptive Gaussian Sum Filter for Nonlinear Bayesian Estimation, Institute of Electric and Electronics Engineers (IEEE) Transactions on Automatic Control 56 (2011) 2151–2156.
- V. Vittaldev, R. P. Russell, Space object collision probability using multidirectional gaussian mixture models, Journal of Guidance, Control, and Dynamics 39 (2016) 2163–2169.
- J. T. Horwood, A. B. Poore, Orbital State Uncertainty Realism, in: Advanced Maui Optical and Space Surveillance Technologies Conference, Wailea, HI, 2012, p. 48.
- A comparative study of new non-linear uncertainty propagation methods for space surveillance, in: Signal and Data Processing of Small Targets 2014, volume 9092, Baltimore, MD, 2014, p. 12.
- J. T. Horwood, A. B. Poore, Gauss von mises distribution for improved uncertainty realism in space situational awareness, SIAM/ASA Journal on Uncertainty Quantification 2 (2014) 276–304.
- A. H. Jazwinski, Stochastic differential equations, in: Stochastic Processes and Filtering Theory, volume 64 of Mathematics in Science and Engineering, Elsevier, 1970, pp. 93–141.
- B. Jones, R. Anderson, A survey of symplectic and collocation methods for orbit propagation, in: 22nd AAS/AIAA Space Flight Mechanics Meeting, Charleston, SC, 2012, p. 20.
- A new numerical integration technique in astrodynamics, in: Proceedings of the 22nd Annual AAS/AIAA Spaceflight Mechanics Meeting, Charleston, SC, 2012, pp. 1–20.
- X. Bai, J. L. Junkins, Modified chebyshev-picard iteration methods for orbit propagation, The Journal of the Astronautical Sciences 58 (2011) 583–613.
- Orbit and uncertainty propagation: A comparison of Gauss-Legendre-, Dormand-Prince-, and Chebyshev-Picard-based approaches, Celestial Mechanics and Dynamical Astronomy 118 (2014) 13–28.
- R. K. Sharma, M. X. James Raj, Long-term orbit computations with ks uniformly regular canonical elements with oblateness, Earth, Moon, and Planets 42 (1988) 163–178.
- Perturbation theory of kepler motion based on spinor regularization., Journal für die reine und angewandte Mathematik 1965 (1965) 204–219.
- H. Sperling, Computation of keplerian conic sections, American Rocket Society journal 31 (1961) 660–661.
- C. A. Burdet, Regularization of the two body problem, Zeitschrift für angewandte Mathematik und Physik ZAMP 18 (1967) 434–438.
- Edromo: An accurate propagator for elliptical orbits in the perturbed two-body problem, Advances in the Astronautical Sciences 152 (2014) 379–399.
- DROMO propagator revisited, Celestial Mechanics and Dynamical Astronomy 124 (2015) 1–31.
- Improved SSA Through Orbit Determination of Two-Line Element Sets, in: 6th European Conference on Space Debris, volume 6, ESA, 2013, pp. 22–25.
- Orbital prediction error propagation of space objects, in: Orbital Data Applications for Space Objects: Conjunction Assessment and Situation Analysis, 1st ed., Springer, Singapore, 2017, pp. 23–75.
- C. Levit, W. Marshall, Improved Orbit Predictions Using Two-Line Elements, Advances in Space Research 47 (2011) 1107–1115.
- Improving Low-Earth Orbit Predictions Using Two-line Element Data with Bias Correction, in: Advanced Maui Optical and Space Surveillance Technologies Conference, Wailea, HI, 2012, p. 46.
- Analytical representations of precise orbit predictions for Earth orbiting space objects, Advances in Space Research 59 (2017) 698–714.
- Hybrid SGP4 orbit propagator, Acta Astronautica 137 (2017) 254–260.
- H. Peng, X. Bai, Machine Learning Approach to Improve Satellite Orbit Prediction Accuracy Using Publicly Available Data, Journal of the Astronautical Sciences 67 (2020) 762–793.
- Improved Orbital Debris Trajectory Estimation Based on Sequential TLE Processing, in: 60th International Astronautical Congress 2009, volume 3, International Astronautical Federation (IAF), Daejeon, South Korea, 2009, pp. 1864–1869.
- Latent force models in autonomous GNSS satellite orbit prediction, in: 2017 International Conference on Localization and GNSS, ICL-GNSS 2017, Institute of Electric and Electronics Engineers (IEEE), Piscataway, New Jersey, 2018, pp. 1–6.
- H. Peng, X. Bai, Exploring Capability of Support Vector Machine for Improving Satellite Orbit Prediction Accuracy, Journal of Aerospace Information Systems 15 (2018) 366–381.
- H. Peng, X. Bai, Comparative Evaluation of Three Machine Learning Algorithms on Improving Orbit Prediction Accuracy, Astrodynamics 3 (2019a) 325–343.
- H. Peng, X. Bai, Gaussian Processes for improving orbit prediction accuracy, Acta Astronautica 161 (2019b) 44–56.
- H. Peng, X. Bai, Fusion of a machine learning approach and classical orbit predictions, Acta Astronautica 184 (2021) 222–240.
- Improved orbit predictions using two-line elements through error pattern mining and transferring, Acta Astronautica 188 (2021) 405–415.
- Improvement of GPS and BeiDou extended orbit predictions with CNNs, in: 2018 European Navigation Conference, ENC 2018, Institute of Electric and Electronics Engineers (IEEE), Gothenburg, Sweden, 2018, pp. 54–59.
- Hybrid SGP4 propagator based on machine-learning techniques applied to GALILEO-type orbits, in: 69th International Astronautical Congress (IAC-18), International Astronautical Federation (IAF), Bremen, Germany, 2018, pp. 1–5.
- Two-line-element propagation improvement and uncertainty estimation using recurrent neural networks, CEAS Space Journal 14 (2022) 197–204.
- An adaptation of deep learning technique in orbit propagation model using long short-term memory, in: 2021 International Conference on Electrical, Communication, and Computer Engineering (ICECCE), Institute of Electric and Electronics Engineers (IEEE), Kuala Lumpur, Malaysia, 2021, pp. 1–6.
- A Machine Learning-Based Approach for Improved Orbit Predictions of LEO Space Debris with Sparse Tracking Data from a Single Station, Institute of Electric and Electronics Engineers (IEEE) Transactions on Aerospace and Electronic Systems 56 (2020) 4253–4268.
- H. Peng, X. Bai, Improving orbit prediction accuracy through supervised machine learning, Advances in Space Research 61 (2018) 2628–2646.
- J. T. Emmert, Thermospheric mass density: a review, Advances in Space Research 56 (2015) 773–824.
- A new empirical thermospheric density model JB2008 using new solar and geomagnetic indices, in: AIAA/AAS Astrodynamics Specialist Conference and Exhibit, AIAA, Honolulu, HI, 2008, p. 19.
- S. Bruinsma, C. Boniface, The operational and research DTM-2020 thermosphere models, Journal of Space Weather and Space Climate 11 (2021) 15.
- NRLMSIS 2.0: A whole-atmosphere empirical model of temperature and neutral species densities, Earth and Space Science 8 (2021).
- A. E. Hedin, Neutral thermospheric composition and thermal structure, Reviews of Geophysics 17 (1979) 477–485.
- A. E. Hedin, A revised thermospheric model based on mass spectrometer and incoherent scatter data: MSIS-83, Journal of Geophysical Research: Space Physics 88 (1983) 10170–10188.
- A. E. Hedin, MSIS-86 Thermospheric Model, Journal of Geophysical Research: Space Physics 92 (1987) 4649–4662.
- A. E. Hedin, Extension of the msis thermosphere model into the middle and lower atmosphere, Journal of Geophysical Research: Space Physics 96 (1991) 1159–1172.
- NRLMSISE-00 empirical model of the atmosphere: Statistical comparisons and scientific issues, Journal of Geophysical Research: Space Physics 107 (2002).
- A thermospheric model based on satellite drag data., Annales de Geophysique 34 (1978) 9–24.
- Improvement of the empirical thermospheric model DTM: DTM94 – a comparative review of various temporal variations and prospects in space geodesy applications, Journal of Geodesy 72 (1998) 161–178.
- S. Bruinsma, R. Biancale, Total densities derived from accelerometer data, Journal of Spacecraft and Rockets 40 (2003) 230–236.
- Evaluation of the DTM-2009 thermosphere model for benchmarking purposes, Journal of Space Weather and Space Climate 2 (2012) 4.
- L. G. Jacchia, A working model for the upper atmosphere, Nature 192 (1961) 1147–1148.
- L. G. Jacchia, Static diffusion models of the upper atmosphere with empirical temperature profiles, Smithsonian Contributions to Astrophysics 8 (1965) 213–257.
- L. G. Jacchia, New Static Models of the Thermosphere and Exosphere with Empirical Temperature Profiles, SAO Special Report 313 (1970).
- L. G. Jacchia, Revised Static Models of the Thermosphere and Exosphere with Empirical Temperature Profiles, SAO Special Report 332 (1971).
- Earth global reference atmospheric model (gram-99) and trace constituents, Advances in Space Research 34 (2004) 1731–1735.
- The JB2006 empirical thermospheric density model, Journal of Atmospheric and Solar-Terrestrial Physics 70 (2008) 774–793.
- D. A. Vallado, D. Finkleman, A critical assessment of satellite drag and atmospheric density modeling, Acta Astronautica 95 (2014) 141–165.
- Review and comparison of empirical thermospheric mass density models, Progress in Aerospace Sciences 103 (2018) 31–51.
- Propagation of Forecast Errors from the Sun to LEO Trajectories: How Does Drag Uncertainty Affect Conjunction Frequency?, in: Advanced Maui Optical and Space Surveillance Technologies Conference, Wailea, HI, 2014, p. 8.
- K. E. Williams, Prediction of solar activity with a neural network and its effect on orbit prediction, Johns Hopkins APL Technical Digest (Applied Physics Laboratory) 12 (1991) 310–317.
- Predicting geomagnetic storms from solar-wind data using time-delay neural networks, Annales Geophysicae 14 (1996) 679–686.
- Forecast daily indices of solar activity, F10. 7, using support vector regression method, Research in Astronomy and Astrophysics 9 (2009) 694–702.
- Solar radio proxies for improved satellite orbit prediction, Journal of Space Weather and Space Climate 7 (2017) 17.
- The SOLAR2000 empirical solar irradiance model and forecast tool, Journal of Atmospheric and Solar-Terrestrial Physics 62 (2000) 1233–1250.
- Linear forecasting of the F10.7 proxy for solar activity, Space Weather 15 (2017) 1039–1051.
- A deep learning approach to solar radio flux forecasting, Acta Astronautica 193 (2022) 595–606.
- E. Camporeale, The Challenge of Machine Learning in Space Weather: Nowcasting and Forecasting, Space Weather 17 (2019) 1166–1207.
- Use of two-line element data for thermosphere neutral density model calibration, Advances in Space Research 41 (2008) 1115–1122.
- Calibrating the scale of the NRLMSISE00 model during solar maximum using the two line elements dataset, Advances in Space Research 56 (2015) 1–9.
- Modification of atmospheric mass density model coefficients using space tracking data–a simulation study for accurate debris orbit prediction, Advances in the Astronautical Sciences 140 (2011) 1479–1493.
- Improved orbit prediction of LEO objects with calibrated atmospheric mass density model, Journal of Spatial Science 64 (2019) 97–110.
- Improved forecasting of thermospheric densities using multi-model ensembles, Geoscientific Model Development 9 (2016) 2279–2292.
- D. Pérez, R. Bevilacqua, Neural Network based calibration of atmospheric density models, Acta Astronautica 110 (2015) 58–76.
- Storm-time atmospheric density modeling using neural networks and its application in orbit propagation, Advances in Space Research 53 (2014) 558–567.
- An empirical atmospheric density calibration model based on long short-term memory neural network, Atmosphere 12 (2021).
- Calibration of atmospheric density model based on gaussian processes, Acta Astronautica 168 (2020) 273–281.
- P. M. Mehta, R. Linares, Data-Driven Framework for Real-time Thermospheric Density Estimation, in: Advances in the Astronautical Sciences Conference 2019, volume 167, Portland, ME, 2019, pp. 191–207.
- P. M. Mehta, R. Linares, A new transformative framework for data assimilation and calibration of physical ionosphere-thermosphere models, Space Weather 16 (2018) 1086–1100.
- D. J. Gondelach, R. Linares, Real-time thermospheric density estimation via two-line element data assimilation, Space Weather 18 (2020) 20.
- D. J. Gondelach, R. Linares, Real-Time Thermospheric Density Estimation Via Radar and GPS Tracking Data Assimilation, Space Weather 19 (2021) 18.
- Machine learning algorithms for improved thermospheric density modeling, in: Dynamic Data Driven Applications Systems, Springer International Publishing, Cham, 2020, pp. 143–151.
- Autoencoder-Based Thermospheric Density Estimation Using GPS Tracking Data, in: 72nd International Astronautical Congress, IAF, Dubai, United Arab Emirates, 2021, p. 10.
- New density estimates derived using accelerometers on board the CHAMP and GRACE satellites, Space Weather 15 (2017) 558–576.
- T. R. George, C. A. McLaughlin, The Use of Long Short-Term Memory Artificial Neural Networks for the Global Prediction of Atmospheric Density, Advances in the Astronautical Sciences 175 (2021) 1815–1832.
- Dropout and Ensemble Networks for Thermospheric Density Uncertainty Estimation, in: Bayesian Deep Learning Workshop, Dec., NeurIPS, 2021, pp. 1–7.
- Deep super learner: A deep ensemble for classification problems, in: Advances in Artificial Intelligence, Springer International Publishing, Cham, 2018, pp. 84–95.
- Simultaneous Multivariate Forecast of Space Weather Indices using Deep Neural Network Ensembles, in: Fourth Workshop on Machine Learning and the Physical Sciences, NeurIPS, 2021, pp. 1–6.
- The SET HASDM Density Database, Space Weather 19 (2021) 1–4.
- Machine‐Learned HASDM Thermospheric Mass Density Model With Uncertainty Quantification, Space Weather 20 (2022) 1–18.
- R. J. Licata, P. M. Mehta, Uncertainty Quantification Techniques for Space Weather Modeling: Thermospheric Density Application, Scientific Reports 12 (2022) 1–17.
- E. Goan, C. Fookes, Bayesian neural networks: An introduction and survey, in: Case Studies in Applied Bayesian Data Science, Springer International Publishing, Cham, 2020, pp. 45–87.
- D. T. Hall, Expected collision rates for tracked satellites, Journal of Spacecraft and Rockets 58 (2021) 715–728.
- Image-based attitude determination of co-orbiting satellites using deep learning technologies, Aerospace Science and Technology 120 (2022) 14.
- S. Sharma, S. D’Amico, Neural network-based pose estimation for noncooperative spacecraft rendezvous, Institute of Electric and Electronics Engineers (IEEE) Transactions on Aerospace and Electronic Systems 56 (2020) 4638–4658.
- Satellite pose estimation with deep landmark regression and nonlinear pose refinement, in: 2019 IEEE/CVF International Conference on Computer Vision Workshop (ICCVW), IEEE Computer Society, Los Alamitos, CA, USA, 2019, pp. 2816–2824.
- Space objects classification via light-curve measurements using deep convolutional neural networks, The Journal of the Astronautical Sciences 67 (2020) 1063–1091.
- Space Debris Identification and Characterization via Deep Meta-Learning, in: First International Orbital Debris Conference, volume 2109 of LPI Contributions, Sugar Land,TX, 2019, p. 9.