Session A4: PNT Solutions for Space Applications

Enhanced Real-Time Orbit Determination Based on Dynamic Model Assisted Vector Tracking for Spaceborne GNSS Receivers
Zihong Zhou and Bing Xu, Department of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University
Location: Beacon A

Compared to the conventional Scalar Tracking Loop (STL), the Vector Tracking Loop (VTL) technique has demonstrated superior performance in signal tracking and navigation processing in low Signal-to-Noise Ratio (SNR) environments and high-dynamic scenarios [1]-[3]. This makes VTL well-suited to address the challenges faced by spaceborne Global Navigation Satellite System (GNSS) receivers on small satellites operating in Low Earth Orbit (LEO). Given the increasing popularity of LEO-based Positioning, Navigation, and Timing (PNT) systems as an augmentation to GNSS, there is significant motivation to develop a VTL-based GNSS receiver algorithm optimised for the spaceborne scenario. This research deeply integrates VTL with dynamic force models to enable real-time Precise Orbit Determination (POD) for CubeSats in LEO-PNT applications.
LEO-PNT systems offer numerous advantages over GNSS, including improved satellite visibility, high signal strength, diverse frequency bands, multipath mitigation, and resilience against spoofing and interference [4]. In consideration of the small satellite footprint and cost constraints, constellations of miniaturised satellites, particularly CubeSats, present a viable solution for the implementation of dedicated LEO-PNT [5], in which real-time onboard POD becomes essential in this context. CubeSats typically rely on GNSS only for kinematic orbit determination due to the lack of other sensors, such as DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite), SLR (Satellite Laser Ranging), and high-quality IMUs (Inertial Measurement Units) [6]. However, the severe limitations on size and power consumption, as well as the suboptimal quality of Commercial Off-The-Shelf (COTS) components, hinder the use of high-performance clocks and antennas, which are the dominant power consumers [5], [7]. The reliance on low-quality clocks raises demands for frequent navigation updates, while antennas struggle with intermittent low SNR and poor satellite visibility, often leading to the use of outdated orbit and clock corrections [6].
In the LEO spaceborne environment, because of the satellite’s high velocity, the received GNSS signals are characterised by up to ± 60,000 Hz of severe Doppler shift, which reduces the obtained Carrier-to-Noise Density (C/N0) ratio after correlation and makes the Frequency Locked Loop (FLL) in the conventional STL receivers difficult to maintain locked onto signals [1]. Furthermore, the rapid change in position causes the GNSS satellites in view to switch frequently, which also contributes to fluctuating satellite visibility. This scenario places heavy stress on the acquisition and tracking algorithms, in which the sudden changes and drops in channels can lead to significant navigation state errors. Additionally, the strengths of the received signals in LEO can vary dramatically in which the C/N0 ratios range from 10 to 55 dB-Hz [8], [9]. The architecture of STL weighs the code phase and carrier frequency errors from all channels equally for the Numerically Controlled Oscillator (NCO) corrections, which yields sub-optimal results in such scenarios [3].
Given the conditions, VTL emerges as a promising method for real-time continuous POD. By aggregating power levels of all acquired channels and employing a Kalman filter for state estimation, stronger signals are weighted over the weaker signals, optimising the entire receiver. The coupling of information also allows better signals (in terms of SNR) to aid the weaker ones by feeding back navigation solutions for code phase and carrier frequency predictions [1], [10]. The feasibility of using VTL for LEO spaceborne receivers has been preliminarily demonstrated by [11], in which the study showed that in post-mission POD mode, VTL exhibited strong tracking capability in a simulated LEO environment. However, currently there are no studies exploring the use of VTL for real-time POD, which can be attributed to two main factors: First, historically there has been little demand for real-time POD in CubeSats, as most CubeSat applications have only required post-mission POD. However, the emergence of LEO-PNT has introduced new requirements. Second, VTL has the drawback that a single faulty channel can adversely affect all other healthy channels due to the nature of information fusion [2]. Therefore, this research aims to address this inherent issue of VTL by integrating it with orbital dynamic models and exploiting the respective advantages. The short-term accuracy of the dynamic model can rectify occasional false estimations in VTL caused by ill measurements, while VTL can restrain the long-term drift of the dynamic model.
To fully understand and analyse the spaceborne scenario for LEO-PNT CubeSats, a comprehensive system-level orbit simulation was first developed using Ansys System Tool Kit (STK) and MATLAB, as no publicly available simulations meet the requirements. The objectives are to obtain key factors for receiver design, such as GNSS satellite visibility, single-satellite access time, link budget, range, Doppler shift, and Doppler shift rate. Parameters with a strong correlation are set as the input variables, which include orbit altitude, orbit inclination, GNSS constellation, signal frequency, antenna performance, and receiver C/N0 threshold. The simulation assumes a single-frequency, single-antenna receiver configuration for the low-cost CubeSats. While dual-frequency and multi-antenna POD techniques have been studied in the literature [12], [13], these are generally unsuitable for real-time mode or unfeasible for the CubeSat platform. That said, the simulation can be easily expanded to accommodate additional configurations and variables. The LEO-PNT transmission framework and the ground-based user segment are jointly modelled, providing a one-stop simulation for the entire LEO-PNT system to facilitate design optimisation. Preliminary results show that, for most CubeSats in LEO, the absolute Doppler shift of the GPS L1 C/A signal falls between 40,000 to 60,000 Hz, 48.1% of the time. The GNSS visibility and received C/N0 value align well with actual data and existing literature [8], [9]. Upon completion, the full simulation will be made open-source, accompanied by detailed tutorials.
Unlike the widely used reduced-dynamic POD technique, in which the dynamic model is primarily responsible for orbit propagation and GNSS observations serve as auxiliary corrections to long-term drifts [6], [14], this research places the GNSS-based VTL in the dominant role, with the dynamic model providing assistance. The rationale for this approach is that in LEO-PNT applications, the CubeSat’s timing accuracy is equally as critical as position and velocity for delivering PNT services to ground users. VTL is better suited for the frequent clock bias and drift estimations required for correcting the code and carrier NCOs.
Before integration, the VTL algorithm originally designed for ground-based applications is modified for the LEO spaceborne environment. Three-dimensional acceleration is incorporated into the navigation state estimations. The dynamic process noise covariances are adjusted based on the expected noise power spectral density in LEO, while the clock process noise covariances are set relatively high at the noise levels of TCXO (Temperature-Compensated Crystal Oscillator) and CSAC (Chip-Scale Atomic Clock), which are the low-quality oscillators commonly used on CubeSats. The process and measurement noise covariances can be updated adaptively [15], although the decision to implement this measure will depend on the computational load. For the dynamic force model, a lower-precision model is adopted to balance the computational cost. An EMG96 model, truncated to degree 10, is employed as the Earth gravity model. Atmospheric drag, solar radiation pressure coefficients, and empirical accelerations are also modelled instead of estimated as state variables [16], [17]. The models of other perturbations are provided by [17]. Encke’s method and the 4th-order Runge-Kutta method will be evaluated as potential orbit integrators, with an interpolant employed to output intermediate results between propagation steps [14].
The deep integration of the two techniques is implemented such that the navigation solution of the dynamic model is referenced during the Extended Kalman Filter (EKF) update in the VTL algorithm. The dynamic model first propagates the orbit to determine the position, velocity, and acceleration vectors using the estimated states from the previous iteration (including clock bias and drift). It then predicts a set of GNSS pseudorange and Doppler measurements together with the ephemeris. In the VTL’s EKF, after the a priori state propagation, during the innovation phase, the residual is calculated as the difference between the observed measurements and a weighted average of the predicted measurements of both the EKF and dynamic model. Hence, the following a posteriori state estimate is effectively updated by the product of the Kalman gain and the measurement pre-fit residuals from both methods. The weighting coefficients used in the innovation phase are updated at each iteration and determined by the post-fit measurement residuals. The final state estimates are ultimately fed back into the dynamic model and navigation filter, completing the loop. As a result, for the state outputs, the long-term drift of the model propagator is suppressed by the VTL, while the GNSS measurements with stochastic noise are enhanced in accuracy by the dynamic model. In the event of a fault in one channel affecting all of VTL’s navigation estimates and tracking loops, the dynamic model can correct it within a single propagation step.
The effectiveness of the developed algorithm will be evaluated under the levels of dynamics, signal strength, and GNSS visibility in the simulated LEO spaceborne scenario. A comprehensive investigation of suitable step size will be conducted to optimise computational efficiency for CubeSats. As the satellite motion in LEO is sufficiently smooth for interpolation [14], the step size for the dynamic model is expected to exceed 60 s, significantly larger than that for the EKF, which sits at around 20 ms. At similar signal power levels and computational loads, results are anticipated to outperform STL-based real-time kinematic (RTK) POD in terms of accuracy.
In conclusion, this research addresses the emerging trend of LEO-PNT on CubeSats by comprehensively analysing the LEO spaceborne environment and proposing a novel integration framework combining VTL and dynamic models. This approach is designed to overcome the challenges of achieving real-time POD on CubeSat platforms using spaceborne GNSS receivers. The developed algorithm is expected to be efficient within the constraints of power and hardware quality, and to outperform existing STL POD methods under similar conditions. The system-level orbit simulation developed will be made open-source, contributing to further research in LEO-PNT technology.
References
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