Comparative evaluation of three machine learning algorithms on improving orbit prediction accuracy

Abstract

In this paper, the recently developed machine learning (ML) approach to improve orbit prediction accuracy is systematically investigated using three ML algorithms, including support vector machine (SVM), artificial neural network (ANN), and Gaussian processes (GPs). In a simulation environment consisting of orbit propagation, measurement, estimation, and prediction processes, totally 12 resident space objects (RSOs) in solar-synchronous orbit (SSO), low Earth orbit (LEO), and medium Earth orbit (MEO) are simulated to compare the performance of three ML algorithms. The results in this paper show that ANN usually has the best approximation capability but is easiest to overfit data; SVM is the least likely to overfit but the performance usually cannot surpass ANN and GPs. Additionally, the ML approach with all the three algorithms is observed to be robust with respect to the measurement noise.

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Abbreviations

RSO(s):

resident space object(s)

SSO:

solar-synchronous orbit

LEO:

low Earth orbit

MEO:

medium Earth orbit

SVM:

support vector machine

ANN:

artificial neural network

GPs:

Gaussian processes

RSW:

local orbital frame (orthogonal axes along radial/along-track/cross-track directions respectively)

e :

orbit prediction errors in RSW frame

ex, ey, ez :

position components of e (km)

evx, evy, evz :

velocity components of e (m/s)

eζ :

a general reference to one of six components of e above

eT :

vector of true prediction error

eres :

vector of residual error

êML :

vector of ML-predicted orbit prediction error

P ML(eζ):

performance of the ML model on the component eζ

m :

number of learning variables for ML models

n :

number of data points in the training data

k :

number of basis functions of GP models

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Acknowledgements

The authors would acknowledge the research support from the Air Force Office of Scientific Research (AFOSR) FA9550-16-1-0184 and the Office of Naval Research (ONR) N00014-16-1-2729. Large amount of simulations of RSOs have been supported by the HPC cluster in School of Engineering, Rutgers University.

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Correspondence to Xiaoli Bai.

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Hao Peng has been a postdoctoral associate at Rutgers University since August 2016. He received his Ph.D. degree of engineering in 2016 from Beihang University. His current study focuses on introducing machine learning, data mining, and artificial intelligence techniques into the aerospace field to solve previously seemingly impossible tasks. His research interests also include dynamical system theory, restricted three-body problem, space trajectory design, orbit control, and optimal control problems. Dr. Peng's academic activities are actively updated at https://SpaceResearch.top, Google Scholar, and Research Gate.

Xiaoli Bai has been an assistant professor in the Department of Mechanical and Aerospace Engineering at Rutgers University since July 2014. She obtained her Ph.D. degree of aerospace engineering in 2010 from Texas A&M University. One consequence of her dissertation is a set of methods which significantly enhances and accelerates the fundamental processes underlying the creation and maintenance of space debris catalogs. Her current research interests include astrodynamics and space situational awareness with a focus on the unstable and inactive space debris that are out of control and have uncertain origins; spacecraft guidance, control, and space robotics; and Unmanned Aerial Vehicle navigation and control. Dr. Bai was a recipient of Outstanding Young Aerospace Engineer Award from Texas A&M University in 2018, A. Water Tyson Assistant Professor Award from Rutgers in 2018, the 2016 Air Force Office of Scientific Research Young Investigator Research Program Award the American Institute of Aeronautics and Astronautics Foundation John Leland Atwood Graduate Award, and Amelia Earhart Fellowship. E-mail: xiadi.bai@rutgers.edu.

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Peng, H., Bai, X. Comparative evaluation of three machine learning algorithms on improving orbit prediction accuracy. Astrodyn 3, 325–343 (2019). https://doi.org/10.1007/s42064-018-0055-4

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Keywords

  • resident space objects (RSOs)
  • orbit prediction
  • machine learning (ML)
  • support vector regression
  • artificial neural network (ANN)
  • Gaussian processes (GPs)