Analytical Process Noise Covariance Modeling for Absolute and Relative Orbits

TL;DR

This paper introduces new analytical models for process noise covariance in absolute and relative spacecraft states, enhancing accuracy and computational efficiency in orbit determination and conjunction analysis.

Contribution

It develops the first rigorous analytical process noise covariance models for relative spacecraft states using relative dynamics, applicable to both small and large separations.

Findings

Models validated through numerical simulations.

Improved accuracy over existing methods.

Applicable to both Cartesian and orbital element states.

Abstract

This paper develops new analytical process noise covariance models for both absolute and relative spacecraft states. Process noise is always present when propagating a spacecraft state due to dynamics modeling deficiencies. Accurately modeling this noise is essential for sequential orbit determination and improves satellite conjunction analysis. A common approach called state noise compensation models process noise as zero-mean Gaussian white noise accelerations. The resulting process noise covariance can be evaluated numerically, which is computationally intensive, or through a widely used analytical model that is restricted to an absolute Cartesian state and small propagation intervals. Moreover, mathematically rigorous, analytical process noise covariance models for relative spacecraft states are not currently available. To address these limitations of the state of the art, new analytical process noise covariance models are developed for state noise compensation for both Cartesian and orbital element absolute state representations by leveraging spacecraft relative dynamics models. Two frameworks are then presented for modeling the process noise covariance of relative spacecraft states by assuming either small or large interspacecraft separation. The presented techniques are validated through numerical simulations.