Session B4b: Future of Space, Lunar, and Extraterrestrial Navigation 2

Assessment of a Deeply Coupled Orbital Dynamics Model-Integrated GNSS Vector Tracking Receiver for LEO Satellites Using a Single-Frequency Approach
Hsin-Cheng Liao and Shau-Shiun Jan, National Cheng Kung University
Location: Holiday 4-5 (Second Floor)
Date/Time: Thursday, Sep. 11, 2:35 p.m.

A spaceborne Global Navigation Satellite System (GNSS) receiver faces significant challenges in Low Earth Orbit (LEO) due to extreme dynamics and signal degradation. The high orbital velocity of LEO satellites induces Doppler frequency variations of up to ±60 kHz, creating challenges for signal acquisition and tracking. Additionally, the short orbital period (60–90 minutes) leads to frequent GNSS satellite obstructions by Earth. Rapid receiver motion causes frequent changes in satellite visibility and loss of signal lock, further reducing navigation availability. To address these challenges, this research deeply integrates a single-frequency vector tracking (VT) GNSS receiver with an orbital dynamics model to enhance signal tracking robustness and navigation accuracy for LEO applications.
Vector tracking employs a centralized navigation filter to control local signal tracking loops. By predicting the line-of-sight (LOS) dynamics between the receiver and GNSS satellites, the carrier and code frequencies are estimated and fed back to each channel for improved signal tracking. The VT receiver aggregates signal power across all channels by leveraging vector processing, enhancing tracking performance and sensitivity in weak-signal environments [1, 2]. Furthermore, by compensating for LOS dynamics, the navigation filter enhances the robustness of the signal tracking loop compared to conventional scalar tracking (ST) receivers in high-dynamic scenarios [1]. A preliminary study on a GPS L1 VT receiver for LEO satellite applications was presented in [3]. However, further improvements in navigation accuracy and signal tracking robustness can be achieved through two key enhancements: incorporating carrier phase measurements and integrating an orbital dynamics model. In the first enhancement, carrier phase measurements enable ionosphere-free combination and reduce pseudorange measurement noise [4]. A traditional Vector Delay Frequency Locked Loop (VDFLL) cannot track the carrier phase accurately for high-precision positioning [2]. Therefore, a Kalman filter based cascaded VDFLL architecture is implemented to improve the carrier phase accuracy. A local Kalman filter estimates the carrier phase, frequency, and rate to maintain accurate carrier phase tracking while mitigating the fast-changing noise. Meanwhile, the navigation filter predicts carrier and code frequencies at a slower rate to compensate for the LOS dynamics in the tracking loop. After integrating carrier phase measurements, the Group and Phase Ionosphere Correction (GRAPHIC) method can be implemented to eliminate first-order ionospheric effects [4]. For single-frequency GNSS receivers, the GRAPHIC method is effective and widely used in LEO satellites for real-time and offline orbit determination [5, 6]. By combining pseudorange measurements from both the carrier phase and code phase, the GRAPHIC method produces an ionosphere-free combination with fixed ambiguity. The combined pseudorange measurement reduces noise by half compared to standard pseudorange measurements. With the GRAPHIC ionosphere-free combination, a 1-to-1.5-meter 3D position accuracy can be achieved in the LEO mission using pure kinematic positioning, as demonstrated in [5].
The second enhancement integrates an orbital dynamics model to improve navigation accuracy. The model-aided VT receiver has been proven to enhance signal tracking accuracy by constraining receiver motion using a dynamics model [7]. For LEO satellites, orbital motion is governed by Keplerian dynamics, with additional perturbations from gravitational forces (e.g., geopotential variations, third-body effects) and nongravitational forces (e.g., atmospheric drag, solar radiation pressure). By integrating an orbital dynamics model, an accurate satellite orbit can be determined [8]. A Real-Time Orbit Determination (RTOD) framework based on the Extended Kalman Filter (EKF) is implemented, with satellite states propagated using fourth-order Runge-Kutta numerical integration at a fixed time step that matches the desired output sampling interval [10]. The integrated system leverages VT architecture's ability to handle high-dynamic, weak signal environments by deeply integrating the orbital dynamics model with the VT GNSS receiver. Also, the ionosphere-free pseudorange and Doppler frequency measurements from the GNSS receiver compensate for the dynamics modeling error, effectively mitigating long-term drift during dynamics model propagation. The orbital dynamics model constrains receiver motion, enhancing predicted frequencies' accuracy and maintaining reliable orbit estimation during GNSS outages.
An orbit simulation is conducted using the Ansys System Tool Kit (STK) to assess the performance, enabling preliminary analysis of GNSS satellite visibility, Doppler frequency shifts, and access time. A Spirent GNSS simulator, configured to generate GPS L1 C/A and Galileo E1 signals, produces the GNSS signals along a specific satellite orbit modeled in STK. Experiments are performed using the Ettus USRP X300 platform, with ground truth data from the simulator—including GNSS observation data, receiver position/velocity/time (PVT) information, and ionospheric delays—as the reference. This research will comprehensively analyze signal tracking performance and navigation accuracy.
In conclusion, this research develops a novel GNSS receiver architecture that combines an orbital dynamics model with a VT technique. The integrated approach improves navigation accuracy in radial, along-track, and cross-track directions and significantly reduces errors in predicted frequencies. The resulting system demonstrates enhanced robustness and precise real-time orbit determination for LEO satellite missions, outperforming conventional VT architectures.

Contributions
1. Development of a novel deeply coupled VT GNSS receiver with orbital dynamics model.
2. Evaluation of GRAPHIC technique and orbital dynamics integration to enhance navigation and predicted frequency accuracy.
3. Comparative analysis shows the better performance of the proposed architecture over conventional VT under an LEO scenario.

Reference
[1] Lashley, M., Bevly, D. M., & Hung, J. Y. (2009). Performance analysis of vector tracking algorithms for weak GPS signals in high dynamics. IEEE Journal of selected topics in signal processing, 3(4), 661-673.
[2] Lashley, M. V., Martin, S., & Sennott, J. (2020). Vector processing. Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications, 1, 377-418.
[3] Liao, H. C., & Jan, S. S. (2024). Vector Tracking Based GPS Software-Defined Receiver for LEO Satellite. In Proceedings of the 2024 International Technical Meeting of The Institute of Navigation (pp. 799-806).
[4] Yunck, T. P. (1993). Coping with the atmosphere and ionosphere in precise satellite and ground positioning. Geophysical Monograph Series, 73, 1-16.
[5] Montenbruck, O. (2003). Kinematic GPS positioning of LEO satellites using ionosphere-free single frequency measurements. Aerospace Science and Technology, 7(5), 396-405.
[6] Conrad, A. V., Axelrad, P., Haines, B., Zuffada, C., & O'brien, A. (2023). Improved GPS-based single-frequency orbit determination for the CYGNSS spacecraft using GipsyX. NAVIGATION: Journal of the Institute of Navigation, 70(1).
[7] Gómez, M. A., Solera-Rico, A., Valero, E., Lázaro, J. A., & Fernández-Prades, C. (2023). Enhancing GNSS receiver performance with software-defined vector carrier tracking for rocket launching. Results in Engineering, 19, 101310.
[8] Montenbruck, O., Gill, E., & Lutze, F. H. (2002). Satellite orbits: models, methods, and applications. Appl. Mech. Rev., 55(2), B27-B28.
[9] Montenbruck, O., & Ramos-Bosch, P. (2008). Precision real-time navigation of LEO satellites using global positioning system measurements. GPS Solutions, 12, 187-198.