Real-Time Joint Tracking and Polarization Alignment for Satellite Quantum Key Distribution Using an Artificial-Angle Auxiliary System

Polarization-encoded satellite quantum key distribution (QKD) demands simultaneous, high-precision alignment of both spatial pointing and polarization reference frames. However, classical tracking systems ignore polarization, and existing QKD solutions treat it via slow, separate calibration, leaving a critical gap for real-time joint stabilization in dynamic inter-satellite links. This work introduces a novel dual-wavelength auxiliary system that, through a new artificial-angle diversity scheme, renders the transmitter tracking error observable after single-mode fiber coupling in a practical sense, thereby enabling joint estimation. We propose a family of estimators: a three-dimensional maximum-likelihood (3D-ML) benchmark, a new decoupled two-stage 2D-ML method, and a novel log-linear approximate ML (Log-Lin) estimator. The Log-Lin method decouples polarization estimation and solves the tracking error via a fast, deterministic weighted least-squares procedure, offering a closed-form solution. Furthermore, we provide a comprehensive design analysis that characterizes the critical trade-offs between tracking and polarization accuracy with respect to tunable parameters, most notably the artificial-angle radius. Extensive Monte Carlo simulations for a 1000-km inter-satellite link demonstrate that the Log-Lin estimator achieves micro-radian tracking and sub-degree polarization accuracy while completing in only 30 mu s , over two orders of magnitude faster than iterative searches. These results establish a practical pathway toward real-time joint stabilization of quantum satellite links.