# Kernel Embedding Approaches to Orbit Determination of Spacecraft Clusters

## TL;DR

This paper introduces a machine learning-based approach for orbit determination of spacecraft clusters that works under broad, noisy, and non-linear conditions, enabling autonomous operations with limited ground station data.

## Contribution

It presents a novel formulation of orbit determination as a learning problem using domain generalization and distribution regression techniques, applicable to noisy and non-linear observations.

## Key findings

- Successfully estimated orbits of real spacecraft (GRIFEX and MCubed-2)
- Performed well with synthetic datasets of multiple spacecraft and lunar orbits
- Outperformed standard EKF techniques under high noise conditions

## Abstract

This paper presents a novel formulation and solution of orbit determination over finite time horizons as a learning problem. We present an approach to orbit determination under very broad conditions that are satisfied for n-body problems. These weak conditions allow us to perform orbit determination with noisy and highly non-linear observations such as those presented by range-rate only (Doppler only) observations. We show that domain generalization and distribution regression techniques can learn to estimate orbits of a group of satellites and identify individual satellites especially with prior understanding of correlations between orbits and provide asymptotic convergence conditions. The approach presented requires only visibility and observability of the underlying state from observations and is particularly useful for autonomous spacecraft operations using low-cost ground stations or sensors. We validate the orbit determination approach using observations of two spacecraft (GRIFEX and MCubed-2) along with synthetic datasets of multiple spacecraft deployments and lunar orbits. We also provide a comparison with the standard techniques (EKF) under highly noisy conditions.