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Hyperspectral Lightcurve Inversion for Attitude Determination

Simão da Graça Marto, Massimiliano Vasile, Andrew Campbell, Paul Murray, Stephen Marshall, Vasili Savitski

TL;DR

This work investigates attitude determination from hyperspectral lightcurves without prior knowledge of inertia or attitude dynamics, using a Lambertian facet model that yields intrinsic symmetries. It develops two complementary approaches: a regularised least-squares framework with differential dynamic programming for trajectory optimization, and a neural-network–based estimator that leverages inertial-frame conditioning to mitigate symmetry effects. Through synthetic datasets and laboratory tests, the study reveals the crucial role of symmetry handling and reference-frame conditioning in achieving accurate estimates, with ML showing strong gains when inputs are framed to reduce viewpoint variation. The findings underscore both the feasibility and the fundamental ambiguities of attitude inference from spectral lightcurves, guiding future improvements in initialization, symmetry-aware learning, and physics-based regularisation for inertia-free scenarios.

Abstract

Spectral lightcurves consisting of time series single-pixel spectral measurements of spacecraft are used to infer the spacecraft's attitude and rotation. Two methods are used. One based on numerical optimisation of a regularised least squares cost function, and another based on machine learning with a neural network model. The aim is to work with minimal information, thus no prior is available on the attitude nor on the inertia tensor. The theoretical and practical aspects of this task are investigated, and the methodology is tested on synthetic data. Results are shown based on synthetic data.

Hyperspectral Lightcurve Inversion for Attitude Determination

TL;DR

This work investigates attitude determination from hyperspectral lightcurves without prior knowledge of inertia or attitude dynamics, using a Lambertian facet model that yields intrinsic symmetries. It develops two complementary approaches: a regularised least-squares framework with differential dynamic programming for trajectory optimization, and a neural-network–based estimator that leverages inertial-frame conditioning to mitigate symmetry effects. Through synthetic datasets and laboratory tests, the study reveals the crucial role of symmetry handling and reference-frame conditioning in achieving accurate estimates, with ML showing strong gains when inputs are framed to reduce viewpoint variation. The findings underscore both the feasibility and the fundamental ambiguities of attitude inference from spectral lightcurves, guiding future improvements in initialization, symmetry-aware learning, and physics-based regularisation for inertia-free scenarios.

Abstract

Spectral lightcurves consisting of time series single-pixel spectral measurements of spacecraft are used to infer the spacecraft's attitude and rotation. Two methods are used. One based on numerical optimisation of a regularised least squares cost function, and another based on machine learning with a neural network model. The aim is to work with minimal information, thus no prior is available on the attitude nor on the inertia tensor. The theoretical and practical aspects of this task are investigated, and the methodology is tested on synthetic data. Results are shown based on synthetic data.
Paper Structure (21 sections, 26 equations, 14 figures, 3 tables)

This paper contains 21 sections, 26 equations, 14 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Attitude from spectral lightcurve
  3. Regularised least squares
  4. Initial guess
  5. Spectral Light Curve Symmetries
  6. Solution Search with Differential Dynamic Programming
  7. Best first search
  8. Attitude Estimation with Machine Learning
  9. Network Architecture
  10. Results
  11. Dataset 1
  12. Dataset 2
  13. Illustration of Symmetries in Light Curve Inversion
  14. Phase dispersion minimisation
  15. Regularised Least Squares
  16. ...and 6 more sections

Figures (14)

  • Figure 1: Diagram showing the symmetry planes and the axes of the H frame $\left(\hat{\bf h} \hat{\bf i} \hat{\bf j} \right)$
  • Figure 2: Diagram illustrating the various inertial reference frames
  • Figure 3: Diagram illustrating the overall ML approach.
  • Figure 4: Model used to simulate the spectral observations for dataset 2.
  • Figure 5: Appearance of cube object for attitudes in $\mathcal{R}$ at $t=140s$. Faces colours are illustrative only, and do not correspond to the spectral reflectance of these faces, but the brightness of the faces is accurate to the viewing conditions
  • ...and 9 more figures