In this work, we first study the influence of the number of satellites and the number of stations on the detection results. Based on these results, the influence of the satellite distribution on the detection rate is analyzed. Finally, the detection rates at different frequency bands of different GNSS systems are compared.
All the GNSS observation data used in the experiment are taken from the IGS data center. The sampling period is 30 s, and each sampling point is counted as an event. The solar radio emission power value at 1415 MHz provided by RSTN is compared with our detected samples. The emission power values of different magnitudes are separately counted. Accordingly, the detection rate, which is used to represent the detection performance, is defined as the ratio between the number of predicted SRB samples and the number of real samples (from RSTN) in each emission power interval. We define the minimum emission power corresponding to the detection rate of 80% as the detection threshold in the experiments.
4.1. Detection of a Single Satellite
The data from station NNOR on 13 December 2006 are used for the detection of a single station. The detection period is 00:00:00–10:00:00 (UTC), and the time of the peak solar radio emission power is approximately 03:30:00 (UTC), with a solar incident angle of 77.1°. All satellites observed at the peak time are detected separately using the method described in
Section 3.1. The valley period common to at least
satellites is judged as the detection result of a single station. In this section, different values of
are compared and analyzed.
Figure 5 presents the detection rates corresponding to different
for GPS. At both the L1 and L2 frequencies, the detection rate decreases with increasing
for any flux range due to the increasingly severe restriction. Moreover, regardless of the value of
, the detection rate at the L2 frequency is significantly higher than that at the L1 frequency. A possible reason for this is that flux or power density at different frequencies of GNSS may have a big difference even for the same L-band SRB event [
22].
In the case of = 5, only a few flux ranges have a detection rate of 80%. For GPS L1, only 8–9 kSFU and 9–10 kSFU reach 80%; for GPS L2, only 1–2 kSFU, 4–5 kSFU, 7–8 kSFU, 8–9 kSFU, and 9–10 kSFU reach 80%. Overall, the detection rate is quite low in the case of = 5.
Conversely, in the case of = 2, the detection rate at both frequencies reaches the highest for all the flux ranges due to the less severe restriction. However, the detection rates of GPS L1 and L2 in the range of 0–100 SFU reach 12.87% and 51.82%, respectively. Note that the flux density under normal circumstances is below 100 SFU, and thus, the detection rate of this range represents the false alarm rate. As mentioned above, the false alarm rate is much higher in the case of = 2.
Furthermore, in the case of = 3 or = 4, the detection rate in the range of 0–100 SFU is close to 0, with higher reliability. Regarding GPS L1, for the ranges of 5–6 kSFU, 7–8 kSFU, 8–9 kSFU, and 9–10 kSFU, the detection rate of = 3 is equivalent to that of = 4. However, the detection rate of = 3 is significantly higher than that of = 4 when the flux is lower. Regarding GPS L2, for the range of 0.1–1 kSFU, the detection rate of = 3 is slightly higher than that of = 4, with a difference of 6.15%, and the detection rates of the other ranges are equivalent. From the above discussion, we conclude that the optimal value of is 3 due to its obvious advantage of low flux.
4.2. Analysis of Multiple Stations
In this section, to expand data coverage, we analyze additional three typical intense L-band SRB events. For each event, seven stations close to the subsolar point are selected.
Table 5 lists the detailed information for each SRB event, including the period when the SRB occurred, the RSTN stations, the time of the peak of flux density, the IGS stations and the solar incident angle. Due to the incompleteness of the RSTN and IGS data, it is impossible to guarantee that the flux density data for different events are from the same RSTN station and that all seven stations are the stations closest to the subsolar point. For each SRB event, the valley period common to at least
stations is judged as the final detection result. In addition, for each station, we take the value
= 3 from the optimization in
Section 4.1.
Figure 6 presents the results corresponding to different values of
for GPS. In addition to the time when the SRB occurred, the period detected in this experiment includes normal conditions. We can effectively test the false alarm rate based on the 2589 samples in the range of 0–100 SFU. Generally, the number of samples gradually decreases with increasing solar radio flow. The range of ≥10 kSFU is not further divided, as a flux density of more than 10 kSFU is quite easy to be detected.
With increasing , the detection rates of both frequencies gradually decrease and reach approximately 0% in the range of 0.1–1 kSFU, proving that the proposed method has a low false alarm rate and high reliability. Furthermore, the low false alarm rate indicates that the proposed method can avoid the impact of multipath to some extent. In other words, if multipath interference is detected as SRB by mistake, the predicted samples are distributed in each flux range instead of most being in the ranges above 100 SFU.
The detection rate at GPS L2 is much higher than that at GPS L1, which is consistent with
Figure 5. For GPS L1, there are a small number of flux ranges with a detection rate of 80%. In the case of
= 2, only 3–4 kSFU, 7–8 kSFU, 8–9 kSFU, and 10 kSFU have detection rates
80%. However, for GPS L2, in cases of
= 2, 3, and 4, the detection thresholds that meet the detection rate of 80% are in the ranges of 1–2 kSFU, 1–2 kSFU, and 2–3 kSFU, respectively. There is a sudden and obvious drop in the range of 9–10 kSFU at both the L1 frequency and L2 frequency. A possible reason for this is that merely 7 samples are in the range of 9–10 kSFU.
Due to the detection rate at the L2 frequency being higher than that at the L1 frequency, we further divide the range of 0.1–1 kSFU at the L2 frequency for more in-depth analysis. As shown in
Figure 7, there is a trend of fewer samples and a higher detection rate with increasing solar radio emission power. In the case of
= 3, 4 or 5, there are no flux ranges with detection rates reaching 80%. However, in the case of
= 2, the flux density threshold for a detection rate of 80% is in the range of 800–900 SFU. Specifically, the detection rates of 500–600 SFU, 600–700 SFU, and 700–800 SFU reach 80%, 75.68%, 79.17%, and 76.19%, respectively. As mentioned above, we can conclude that the optimal value of
is 2.
4.3. Influence of Satellite Distribution on the Detection Rate
In this section, the GPS L1 L2 data of four typical SRB events in
Table 5 are used to analyze the significance of the satellite distribution on the detection rate. The satellites are divided with respect to the incident direction of the Sun into two categories: ‘‘near-satellites’’ and ‘‘distant-satellites’’.
Figure 8 shows a sky image of the KUNM station at 03:30:00 (UTC) on 13 December 2006. The star-marked point represents the position of the Sun. The near-satellites G11 and G27 are consistent with the direction of the elevation of the Sun, while the distant-satellites G08 and G28 are in opposite directions.
Table 6 lists the azimuth (
) and elevation (
) of the Sun and the satellites at 03:30:00 (UTC). Two near-satellites and two distant-satellites are selected for each station.
There are few satellites that meet the requirements of ‘‘near-satellites’’ or ‘‘distant-satellites’’, and thus, the values of
= 3 and
= 2 from the optimization in
Section 4.1 and
Section 4.2 cannot be used for this section. This part of the experiment includes the following two steps:
For a single station, the intersection of the valley periods of two near-satellites (distant-satellites) is taken.
For each SRB event, the valley period common to at least two stations is judged as the final detection result.
The detection results of each flux range for four typical intense L-band SRB events in
Table 5 are shown in
Figure 9. For GPS L1, the detection results of the near-satellites and distant-satellites are different in several flux ranges. The results for the two categories are generally equivalent. Specifically, the detection rate of the distant-satellites is higher in the ranges of 1–2 kSFU, 3–4 kSFU, and 7–8 kSFU but lower in the ranges of 4–5 kSFU, 6–7 kSFU, and 8–9 kSFU. For GPS L2, the differences between the detection rate of the near-satellites and that of the distant-satellites are −3.70%, 5.00%, −5.56%, and −6.25%, respectively, which are smaller than those at the L1 frequency. Moreover, the detection rate at the L2 frequency is much smoother than that at the L1 frequency. Consequently, the distribution of the satellites relative to the Sun has no effect on the overall detection rate.
Figure 10 presents the carrier-to-noise ratio observation data of GPS, GLONASS, and Galileo at the HARB station during 11:30:00–12:30:00 (UTC) on 6 September 2017, and the shaded area indicates the period when the SRB occurred. At the time of the peak flux density (12:02:30), the
values of GPS L2, GPS L5, GLONASS G2 and Galileo E5 drop sharply by approximately 5–7 dB-Hz. Additionally, there is a slight drop near 12:08:00 (UTC). In each subdiagram of
Figure 10, the decline degree of
at each satellite appears to be similar at the same frequency. However, the
values at various frequencies are affected by the SRB to different extents. The
values of the high frequencies of GNSS (GPS L1, GLONASS G1, and Galileo E1) show an inconspicuous decrease, which is consistent with the conclusions of the study in [
22]. They also pointed out that a possible reason for this is the different sensibilities of the GNSS frequencies and systems to SRB interference. Accordingly, this phenomenon leads to a difference in the detection rates at different GNSS frequencies in subsequent experiments.
Figure 11 shows the detection results at different frequencies for different systems. The detection performance at GPS L2 is the best of all systems. Specifically, the detection rates at GPS L2 of the flux ranges
1 kSFU are 100%, with a low false alarm rate. Moreover, the detection performance at GLONASS G2 is second only to that at GPS L2 and achieves 100% on the condition of flux ranges
3 kSFU.
Overall, a comparison of
Figure 10 and
Figure 11 shows that the more obvious the response to the SRB system is, the better the detection performance is. The detection thresholds of GPS L1 L5, GLONASS G1, and GALILEO E1 E5, under the condition of a detection rate above 80%, are 8–9 kSFU, 8–9 kSFU, 8–9 kSFU, 8–9 kSFU, and 7–8 kSFU, respectively, indicating worse performance than other frequencies and systems. However, the responses of the
values of GPS L5 and GALILEO E5 to SRB is still evident, which appears to contradict the above trend. Through ample analysis, we found that the data of GPS L5 and GALILEO E5 from the IGS contain few satellites that can be observed simultaneously (the values vary from 4 to 6 and 5 to 8, respectively). Hence, the values of
= 3 and
= 2 from the optimization in
Section 4.1 and
Section 4.2 are not suitable for GPS L5 and GALILEO E5. Through specific experiments, the optimal values for
and
for GPS L5 are 2 and 2, respectively. For GALILEO E5, the values are 1 and 4, respectively. Although we modified the optimal values for
and
for GPS L5 and GALILEO E5 to adapt to their smaller number of satellites and obtain better performance, the detection performance still appears to be unsatisfactory, as shown in
Figure 11. The reason is that the core step of the proposed method is the comparison of multiple satellites and multiple stations, and thus, a reduction in the number of satellites can have a great impact on the detection results.
Sato et al. [
21] determined the impacts of the SRB at the GPS L2 and L5 frequencies but not at the L1 frequency during the SRB event on 6 September 2017. Beyond their work, our analysis indicates that this SRB event may have an impact at the L1 frequency. The impact of this SRB event on the
at the L1 frequency is difficult to observe with the naked eye but can be reflected by the experimental results of the proposed method. As shown in
Figure 11, the detection rate is much higher in the ranges above 100 SFU than at 0–100 SFU. Although the number of samples for 6–7 kSFU, 8–9 kSFU, 9–10 kSFU, and ≥10 kSFU is merely 1, the number of samples in other ranges is sufficient. The detection rate of 0–100 SFU is close to 0%, while the number of samples in this range accounts for almost half of all samples. Most of the predicted samples are in flux density ranges above 100 SFU, and this phenomenon does not seem to be an accident.