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Perturbed Initial Orbit Determination

Alberto Fossà, Matteo Losacco, Roberto Armellin

TL;DR

The paper tackles robust initial orbit determination under perturbed Earth-centric dynamics while quantifying uncertainty. It extends differential algebra-based map inversion with an automatic domain splitting strategy to produce a polynomial ensemble that represents the IOD solution and its confidence region for three ground-based sensor types: range radar, Doppler-only radar, and optical telescopes. The core contribution is the Perturbed IOD framework (DAIOD) that couples Taylor-map expansions with ADS to accommodate J2 perturbations, providing both a nominal orbit estimate and uncertainty bounds across short and long arcs. Numerical simulations on NORAD LEO objects demonstrate improved accuracy over Keplerian IOD, with the perturbation model offering advantages for longer observation windows and tighter, reliable uncertainty bounds, highlighting practical benefits for catalog maintenance and data association.

Abstract

An algorithm for robust initial orbit determination (IOD) under perturbed orbital dynamics is presented. By leveraging map inversion techniques defined in the algebra of Taylor polynomials, this tool returns a highly accurate solution to the IOD problem and estimates a range centered on the aforementioned solution in which the true orbit should lie. To meet the specified accuracy requirements, automatic domain splitting is used to wrap the IOD routines and ensure that the local truncation error, introduced by a polynomial representation of the state estimate, remains below a predefined threshold. The algorithm is presented for three types of ground-based sensors, namely range radars, Doppler-only radars, and optical telescopes, by considering their different constraints in terms of available measurements and sensor noise. Finally, the improvement in performance with respect to a Keplerian-based IOD solution is demonstrated using large-scale numerical simulations over a subset of tracked objects in low Earth orbit.

Perturbed Initial Orbit Determination

TL;DR

The paper tackles robust initial orbit determination under perturbed Earth-centric dynamics while quantifying uncertainty. It extends differential algebra-based map inversion with an automatic domain splitting strategy to produce a polynomial ensemble that represents the IOD solution and its confidence region for three ground-based sensor types: range radar, Doppler-only radar, and optical telescopes. The core contribution is the Perturbed IOD framework (DAIOD) that couples Taylor-map expansions with ADS to accommodate J2 perturbations, providing both a nominal orbit estimate and uncertainty bounds across short and long arcs. Numerical simulations on NORAD LEO objects demonstrate improved accuracy over Keplerian IOD, with the perturbation model offering advantages for longer observation windows and tighter, reliable uncertainty bounds, highlighting practical benefits for catalog maintenance and data association.

Abstract

An algorithm for robust initial orbit determination (IOD) under perturbed orbital dynamics is presented. By leveraging map inversion techniques defined in the algebra of Taylor polynomials, this tool returns a highly accurate solution to the IOD problem and estimates a range centered on the aforementioned solution in which the true orbit should lie. To meet the specified accuracy requirements, automatic domain splitting is used to wrap the IOD routines and ensure that the local truncation error, introduced by a polynomial representation of the state estimate, remains below a predefined threshold. The algorithm is presented for three types of ground-based sensors, namely range radars, Doppler-only radars, and optical telescopes, by considering their different constraints in terms of available measurements and sensor noise. Finally, the improvement in performance with respect to a Keplerian-based IOD solution is demonstrated using large-scale numerical simulations over a subset of tracked objects in low Earth orbit.
Paper Structure (20 sections, 99 equations, 1 figure, 12 tables)

This paper contains 20 sections, 99 equations, 1 figure, 12 tables.

Table of Contents

  1. Introduction
  2. Mathematical background
  3. Differential algebra
  4. Map inversion
  5. Automatic domain splitting
  6. Measurements regression
  7. Dynamical models
  8. Perturbed Initial orbit determination
  9. Range radars
  10. Initial orbit determination
  11. Doppler-only radars
  12. Initial orbit determination
  13. Range estimation
  14. State estimate expansion
  15. Optical telescopes
  16. ...and 5 more sections

Figures (1)

  • Figure 1: Geometry of bistatic radar sensor