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Comparison of uncertainty propagation techniques in small-body environment

Niccolò Michelotti, Antonio Rizza, Carmine Giordano, Francesco Topputo

TL;DR

This study evaluates how three uncertainty propagation techniques—Linear Covariance Propagation, Unscented Transformation, and Polynomial Chaos Expansion—perform for spacecraft near small bodies, using Apophis and Eros as test environments. By simulating seven proximity scenarios, the authors compare method accuracy against Monte Carlo as a reference, revealing that PCE consistently captures non-Gaussian distributions and higher moments with markedly lower computational cost than MC. LinCov and UT offer faster alternatives but can misrepresent uncertainty under strong nonlinearities, with LinCov tending to underestimate dispersion and UT overestimating it in some cases. The findings provide practical guidance for selecting uncertainty propagation methods in autonomous proximity operations around asteroids and comets.

Abstract

Close-proximity exploration of small celestial bodies is crucial for the comprehensive and accurate characterization of their properties. However, the complex and uncertain dynamical environment around them contributes to a rapid dispersion of uncertainty and the emergence of non-Gaussian distributions. Therefore, to ensure safe operations, a precise understanding of uncertainty propagation becomes imperative. In this work, the dynamical environment is analyzed around two asteroids, Apophis, which will perform a close flyby to Earth in 2029, and Eros, which has been already explored by past missions. The performance of different uncertainty propagation methods (Linear Covariance Propagation, Unscented Transformation, and Polynomial Chaos Expansion) are compared in various scenarios of close-proximity operations around the two asteroids. Findings are discussed in terms of propagation accuracy and computational efficiency depending on the dynamical environment. By exploring these methodologies, this work contributes to the broader goal of ensuring the safety and effectiveness of spacecraft operations during close-proximity exploration of small celestial bodies.

Comparison of uncertainty propagation techniques in small-body environment

TL;DR

This study evaluates how three uncertainty propagation techniques—Linear Covariance Propagation, Unscented Transformation, and Polynomial Chaos Expansion—perform for spacecraft near small bodies, using Apophis and Eros as test environments. By simulating seven proximity scenarios, the authors compare method accuracy against Monte Carlo as a reference, revealing that PCE consistently captures non-Gaussian distributions and higher moments with markedly lower computational cost than MC. LinCov and UT offer faster alternatives but can misrepresent uncertainty under strong nonlinearities, with LinCov tending to underestimate dispersion and UT overestimating it in some cases. The findings provide practical guidance for selecting uncertainty propagation methods in autonomous proximity operations around asteroids and comets.

Abstract

Close-proximity exploration of small celestial bodies is crucial for the comprehensive and accurate characterization of their properties. However, the complex and uncertain dynamical environment around them contributes to a rapid dispersion of uncertainty and the emergence of non-Gaussian distributions. Therefore, to ensure safe operations, a precise understanding of uncertainty propagation becomes imperative. In this work, the dynamical environment is analyzed around two asteroids, Apophis, which will perform a close flyby to Earth in 2029, and Eros, which has been already explored by past missions. The performance of different uncertainty propagation methods (Linear Covariance Propagation, Unscented Transformation, and Polynomial Chaos Expansion) are compared in various scenarios of close-proximity operations around the two asteroids. Findings are discussed in terms of propagation accuracy and computational efficiency depending on the dynamical environment. By exploring these methodologies, this work contributes to the broader goal of ensuring the safety and effectiveness of spacecraft operations during close-proximity exploration of small celestial bodies.
Paper Structure (15 sections, 21 equations, 19 figures, 3 tables)

This paper contains 15 sections, 21 equations, 19 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Uncertainty propagation methods
  3. Spacecraft dynamics
  4. Case studies
  5. Scenarios and initial conditions
  6. Uncertainty propagation results
  7. Scenario 1: hovering arc around Apophis in deep-space
  8. Scenario 2: single revolution around Apophis in deep-space
  9. Scenario 3: hovering arc around Apophis during Earth's flyby
  10. Scenario 4: single revolution around Apophis during Earth's flyby
  11. Scenario 5: multiple revolutions around Eros
  12. Scenario 6: single revolution around Eros
  13. Scenario 7: low-altitude flyby to Eros
  14. Discussion on the performance of uncertainty propagation methods
  15. Conclusions

Figures (19)

  • Figure 1: Dynamical environment around Apophis. The $x$-axis is shown into two different scales: mean body radius and kilometres. The spherical harmonics model has been implemented up to the fourth order following the one presented in lang_apophis
  • Figure 2: Dynamical environment around Eros along its heliocentric orbit. The $x$-axis is shown into two different scales: mean body radius ($r_m = 7.311$ km) and kilometres. The spherical harmonics model NEAR15A is implemented up to the 15th order
  • Figure 3: Scenario 1. (a) nominal trajectory, (b) dynamical environment
  • Figure 4: Scenario 2. (a) nominal trajectory, (b) dynamical environment
  • Figure 5: Scenario 3. (a) nominal trajectory, (b) dynamical environment
  • ...and 14 more figures