Satellite closest approach calculation through Chebyshev Proxy Polynomials

Abstract

Calculating the Time of Closest Approach (TCA) and the minimal distance between two orbiting objects is a vital step in space debris collision risk assessment and avoidance maneuver computation. Currently, two methods are commonly used to compute the TCA and the corresponding minimal distance: propagating both objects with a small time-step and approximating the derivative of a distance function using cubic polynomials. Lately using the Surrogate-based Optimization (SBO) search was also suggested. Propagating is too slow; estimating is usually not accurate enough, and the SBO is considered a good compromise. This paper proposes a novel method based on Chebyshev Proxy Polynomials for the TCA computation problem. This method is designed to allow fast computation and high accuracy; this is demonstrated in several examples, and shown to be slightly slower than the approximation method and have accuracy competitive to those of the SBO method.