Robust Angles-Only Initial Relative Orbit Determination Using Polynomial Optimization

TL;DR

This paper introduces a robust angles-only initial relative orbit determination method using polynomial optimization, improving accuracy and stability under noise and unfavorable geometries.

Contribution

It presents a novel polynomial optimization approach with a reduced-order weighting strategy and robustness enhancements for nonlinear orbit dynamics.

Findings

Improves IROD accuracy by about three orders of magnitude.

Reduces downstream orbit-refinement burden.

Enhanced stability and accuracy under high noise conditions.

Abstract

This paper develops a robust angles-only IROD method based on polynomial optimization for arbitrary nonlinear dynamics. First, the relative motion is approximated by high-order Taylor polynomials within the differential algebra framework, and the resulting cross-product-residual minimization problem is solved through a recursive polynomial optimization procedure. Second, a reduced-order weighting strategy is introduced by projecting the residual onto the two-dimensional tangent subspace of the line of sight, thereby structurally removing the intrinsic singularity of conventional three-dimensional weighting. Third, a zero-solution-avoidance constraint together with an adaptive threshold-selection mechanism is developed to improve robustness against poor initialization, strong measurement noise, and unfavorable observation geometries. Numerical simulations show that the proposed method improves IROD accuracy by about three orders of magnitude relative to the baseline methods, while also reducing the downstream orbit-refinement burden. The reduced-order weighting strategy further improves accuracy by about 43% in the nominal case and remains stable under large-noise conditions, outperforming the conventional three-dimensional weighting by about 81%.