Session A3b: Next-Generation Satellite Navigation Technology

Accuracy Degradation Rate of LEO Satellite Predicted Orbits Using Different POD Methods
Jiawei Liu, National Time Service Center (NTSC), Chinese Academy of Sciences (CAS), Universily of Chinese Academy of Sciences (UCAS), Key Laboratory of Time Reference and Applications (CAS); Kan Wang, Beixi Chen, NTSC, CAS, UCAS, Key Laboratory of Time Reference and Applications (CAS); Ahmed El-Mowafy, Amir Allahvirdi-Zadeh, School of Earth and Planetary Sciences, Curtin University; Xuhai Yang, NTSC, CAS, UCAS, Key Laboratory of Time Reference and Applications (CAS)
Location: Beacon A

In the past decade, Low Earth Orbit (LEO) satellites have been increasingly considered as an essential complementation to the Global Navigation Satellite Systems (GNSSs) for future applications. Benefiting from the lower altitudes and higher speeds of LEO satellites, their augmentation of the GNSSs offers several advantages. These advantages include broadcasting signal strengths that are hundreds to thousands of times stronger than GNSS satellites, whitening multipath effects, and accelerating the convergence time of precise point positioning (PPP) and the PPP- Real-Time Kinematic (PPP-RTK) positioning due to the LEO rapid geometry change. In addition to these advantages, LEO satellites have also been used in the integrity monitoring of GNSS signals and products.
To achieve high-accuracy positioning and timing for ground applications using LEO navigation signals, the precision of the orbital and clock products is of high necessity. The post-processed Precise Orbit Determination (POD) for LEO satellites has been extensively studied and can now achieve a high precision of 1 cm (in 3D RMS) after the resolution of integer ambiguities. The challenge lies more in generating real-time LEO satellite orbital and clock products to fulfill the needs of the real-time LEO-augmented Positioning, Navigation, and Timing (PNT) service. Reduced-dynamic LEO satellite POD using Batch Least-Squares (BLS) adjustment of GNSS data collected onboard LEO satellites can nowadays provide near-real-time orbits with an accuracy of centimeters using high-precision GNSS real-time products. The real-time users can then rely on broadcast LEO satellite ephemeris based on short-term prediction of these near-real-time orbits. However, in the case of observation data problems collected onboard LEO satellite or satellite manoeuvers not performed as planned, large orbital errors or residuals could result due to the incorrect estimation of the dynamic parameters, which hampers the orbits from passing the self-check, and accordingly their availability to users. In such a case, the kinematic POD delivers a redundant option that delivers also high-precision near-real-time orbits, independent of dynamic models. Compared with the BLS kinematic POD, filter-based kinematic POD is less precise, with an accuracy of sub-dm to dm-level. However, it is more time efficient compared to both the BLS reduced-dynamic and kinematic POD processing, which implies a shorter prediction time needed for real-time applications.
In this study, all three solution methods, i.e., the BLS reduced-dynamic near-real-time POD, the BLS kinematic near-real-time POD, and the back-and-forward Sequential-Least-Squares-based (SLS-based) near-real-time POD are processed in parallel, each started at the planned time, e.g., every 5 min. Short-term prediction is performed directly after each round of the near-real-time POD. Then, an ephemeris fitting routine is applied, selecting the best-predicted orbits at the fitting time window. The predicted orbital accuracy of each orbital processing method varies with its prediction time, affecting the accuracy degradation rate when increasing the prediction time. As an example, although the accuracy of the predicted orbits based on BLS reduced-dynamic POD could degrade slower than the BLS kinematic POD, the corresponding prediction time could be higher when one round of processing fails, due to the reasons mentioned above. This could influence the selection of other types of predicted orbits in real time.
While the prediction time of different orbital results required for the ephemeris fitting can be obtained precisely in real time, the accuracy degradation rate with increasing the prediction time could vary for different POD methods and different orbital heights. Previous studies mostly concentrate on the reduced-dynamic methods, but paid less attention to the BLS and SLS kinematic processing options. As such, this study assesses and compares the rate of accuracy degradation of the predicted orbits using different processing strategies. This will support the selection of the best orbital type for real-time ephemeris fitting. In addition to the accuracy degradation rate, the degradation in the predicted orbital integrity is also of concern, as the reliability of real-time orbits is even more important than the accuracy in certain applications. This is also analyzed and discussed in this study.
In this contribution, using 6 days of GPS and GPS/Galileo-combined dual-frequency phase and code observations tracked onboard Sentinel-3B (about 800 km) and Satellite-6A satellites (about 1300 km), all three types of predicted orbits, named “RP” for BLS reduced-dynamic POD, “KP” for BLS kinematic POD, and “TP” for SLS kinematic POD, are assessed. The starting times of the POD processing are shifted by 5 min to produce 1728 sets of samples of predicted orbits for each type. The degradation rates of the Orbital User Range Errors (OUREs) are calculated for RP, KP, and TP connecting the prediction errors at prediction starts (minimal prediction errors) and the highest prediction errors within the first hour using a linear polynomial, amounting to 4.3, 8.3, and 3.1 cm/h, respectively, for Sentinel-3B, and 2.6, 4.3 and 4.0 cm/h, respectively, for Sentinel-6A. The TP prediction is based on a less precise POD option, but it does not exhibit the highest degradation rate. This is possibly caused by the fact that the TP prediction is not influenced by the border effects in the BLS POD results, which plays an important role in producing the prediction dynamic parameters using the last few hours of the POD results. In addition to the calculation strategy for the degradation rate mentioned above, named the best-case scenario in this study, other strategies were also tested, including the “worst-case” scenario, the “half-hour” scenario, and scenarios using quadratic polynomials for calculating different degradation rates. These scenarios will be discussed in detail in the paper.
Next, the integrity of the three types of predicted orbits is analyzed using the 68.3%, 95.5% and 99.9% confidence levels (CL). Within the 1 h prediction time, the RP option exhibits the smallest OUREs among the three types of predicted orbits, with maximum values of 6.7 cm (68.3% CL), 13.4 cm (95.5% CL), and 18.9 cm (99.9% CL), respectively, for Sentinel-3B, and 4.7, 10.1 and 15.6 cm, respectively, for Sentinel-6A. In contrast, the TP exhibits the largest OURE values, with maximums of 11.1, 15.9, and 27.4 cm, respectively, for Sentinel-3B, and 7.3, 14.7, and 44.1 cm for Sentinel-6A. Moreover, it was found that the RP and KP orbital errors follow the normal distributions rather well, while the TP values deviate largely from the normal distribution with heavy tails. Overall, compared to the other two types of predicted orbits, RP demonstrates superior precision and integrity.