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<p>The typical angles-only orbit determination (OD) process first fits a Keplerian preliminary orbit to a set of topocentric right ascension and declination measurements and then refines it via a nonlinear least squares minimization procedure. Yet, modern sky surveys dedicated to near-Earth objects (NEOs) often produce tracklets comprising few observations in a relatively short time span, known as too short arcs, that cannot be handled properly by the classical methods for preliminary OD. In this work, we adapt Gauss method for solving the preliminary OD problem to leverage jet transport techniques, i.e., we exploit high-order polynomial expansions around nominal parameters based on automatic differentiation techniques. Next, we introduce a new method based on minimizing a target function over the manifold of variations, which allows naturally to incorporate more realistic dynamical models beyond the two-body approximation as well as observational uncertainties. The latter serves both as a refinement procedure for an <i>a priori</i> orbit and as an alternative, to established statistical and systematic ranging methods, to compute a preliminary orbit. Further, we extend the nonlinear least squares step for OD to the framework of jet transport. This approach allows us to use second-order least squares optimization methods, like Newton method, in addition to the standard differential corrections method. We present results for individual NEOs, as well as tests based on larger samples of NEOs, showing the efficiency of the algorithms. Finally, we discuss the importance of properly handling outlier observations.</p>

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Jet transport applications to the preliminary orbit determination problem

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月18日

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  • Luis Eduardo Ramírez-Montoya,
  • Jorge A. Pérez-Hernández,
  • Luis Benet

摘要

The typical angles-only orbit determination (OD) process first fits a Keplerian preliminary orbit to a set of topocentric right ascension and declination measurements and then refines it via a nonlinear least squares minimization procedure. Yet, modern sky surveys dedicated to near-Earth objects (NEOs) often produce tracklets comprising few observations in a relatively short time span, known as too short arcs, that cannot be handled properly by the classical methods for preliminary OD. In this work, we adapt Gauss method for solving the preliminary OD problem to leverage jet transport techniques, i.e., we exploit high-order polynomial expansions around nominal parameters based on automatic differentiation techniques. Next, we introduce a new method based on minimizing a target function over the manifold of variations, which allows naturally to incorporate more realistic dynamical models beyond the two-body approximation as well as observational uncertainties. The latter serves both as a refinement procedure for an a priori orbit and as an alternative, to established statistical and systematic ranging methods, to compute a preliminary orbit. Further, we extend the nonlinear least squares step for OD to the framework of jet transport. This approach allows us to use second-order least squares optimization methods, like Newton method, in addition to the standard differential corrections method. We present results for individual NEOs, as well as tests based on larger samples of NEOs, showing the efficiency of the algorithms. Finally, we discuss the importance of properly handling outlier observations.