Segmented Reconstruction of Low-Acceleration Orbital Maneuvers

Abstract

This paper considers the problem of inferring the acceleration acting on a spacecraft in a near-circular orbit around a large planetary body when the acceleration is known to act in the along-track direction. A segmented approach is analyzed where the acceleration profile over a given period of time is approximated as a piecewise-constant profile. Noisy measurements of the spacecraft's position are collected throughout the acceleration profile, from which the constant acceleration for each segment of the piecewise-constant profile can be inferred. The primary contribution of this work is an analytical approximation for the sensitivity of each measurement with respect to the constant acceleration of each segment. The resulting analytically-approximated sensitivity matrix enables an analytical reconstruction of the acceleration profile given a numerically-simulated reference trajectory. Applications of the segmented approach for thrust inference for both discontinuous and continuous thrust profiles are demonstrated. In particular, the reconstruction of a simulated thruster degradation profile over the course of sixty hours is shown.