Noncooperative Spacecraft Pose Estimation Under Low Sampling Frequency: A Variational Integrator-Aided Factor Graph Optimization Approach

Visual navigation is the prerequisite for proximity operations. However, for defunct spacecraft removal and repurposing, insufficient onboard computational resources and high visual processing overhead lead to low-frequency measurements, thereby reducing navigation accuracy and reliability. This article proposes a factor graph optimization (FGO) framework incorporating a dual quaternion variational integrator (DQVI) for relative pose estimation. This framework leverages the kinetic energy conservation characteristics of a tumbling spacecraft, maintaining high estimation accuracy with minimal computational cost even at low sampling rates. Specifically, a pose increment constraint equation between adjacent timestamps using dual quaternion variational integration is constructed, based on which a binary constraint factor is further established. To fuse visual data, two pseudo-measurement factors are designed for both cameras and LiDAR. Pose increments, along with the complete pose (including relative attitude and position) are then embedded into optimization variables. A full-state factor graph model is developed, allowing the visual navigation to be handled. Finally, semi-physical experimental validations demonstrate a 63.58% attitude accuracy improvement and a 64.48% enhancement in position estimation under 4 Hz sampling rates. It is shown that the proposed method enhances reliability under low sampling frequency conditions.