Ionospheric TEC and ROT Analysis with Signal Combinations of QZSS Satellites in the Korean Peninsula

Abstract

This study investigates the performance of three different signal combinations (L1-L2, L1-L5, and L2-L5) for estimating ionospheric total electron content (TEC) and the rate of TEC (ROT) using Quasi-Zenith Satellite System (QZSS) observations over the Korean Peninsula. GNSS data collected from nine stations across the Korean Peninsula were analyzed for the period from Day of Year (DOY) 1 to 182 in 2024. Differential Code Bias (DCB) was estimated for QZSS satellites, showing high temporal stability with daily variations within ±0.3 ns. The TEC values derived from three different signal combinations were compared with the CODE Global Ionospheric Map (GIM). Compared to other combinations, the L1-L5 pair shows the closest agreement with the CODE GIM, yielding a mean bias of +0.25 TEC units (TECU) with a root mean square (RMS) of 3.59 TECU. In addition, the ROT analysis over the consecutive six days revealed that the L1-L5 combination consistently exhibited the lowest RMS values of about 0.027 TECU compared to other signal pairs. As a result, we suggest that the L1-L5 combination can provide better performance for QZSS-based ionospheric monitoring and TEC studies.

1. Introduction

The Global Navigation Satellite System (GNSS) has proven to be a highly effective tool for estimating and continuously monitoring the total electron content (TEC) in the Earth’s ionosphere [1]. TEC can be accurately estimated using global GNSS measurements [2,3] or empirical models such as the International Reference Ionosphere (IRI) [4]. In addition, various methods have been proposed to enhance the accuracy of regional ionospheric TEC estimation [5,6,7,8,9]. Moreover, an approach to enhance the forecasting accuracy of regional ionospheric TEC has also been introduced [10]. Recent studies have focused on improving the accuracy and reliability of ionospheric TEC modeling [11,12,13]. The modeled TEC is primarily evaluated through comparative analysis with observations from the Global Ionosphere Map (GIM) [14,15,16].

Currently, modern GNSS constellations, such as the United States’ Global Positioning System (GPS), Russia’s GLObal NAvigation Satellite System (GLONASS), China’s BeiDou Navigation Satellite System (BDS), the European Union’s Galileo, India’s Navigation with Indian Constellation (NavIC), and Japan’s Quasi-Zenith Satellite System (QZSS), are capable of transmitting signals on dual or triple frequencies, which enhances positioning and ionospheric correction. While signals are functionally similar with different GNSSs, they may differ in their center frequencies.

The GPS dual frequencies, L1 (1575.42 MHz) and L2 (1227.60 MHz), have been predominantly used for accurate ionospheric TEC estimation [17,18,19,20]. With the increasing availability of ground-based GNSS receivers capable of tracking BDS and Galileo signals, the integration of multi-GNSS constellations has enabled more precise and reliable estimations of ionospheric TEC. Hu et al. [21] employed data collected from 30 GNSS reference stations distributed across China to estimate TEC based on BDS GEO satellite signals. Their results demonstrated that TEC derived from BDS GEO satellites can deliver continuous and reliable ionospheric observations even during storm conditions.

Satellites in Medium Earth Orbit (MEO), such as those comprising the GPS constellation, ensure extensive spatial coverage, while those in Geosynchronous Earth Orbit (GEO) and Inclined Geosynchronous Satellite Orbit (IGSO) enable sustained observation over specific locations or constrained regional areas [22]. Moreover, Yang et al. [23] showed that newer BDS signals, specifically B1C (1575.42 MHz) and B2a (1176.45 MHz), provide enhanced precision for ionospheric studies compared to the legacy B1I and B3I signals. Similarly, the Galileo system transmits signals at E1 (1575.42 MHz), E5a (1176.45 MHz), and E5b (1207.140 MHz), with the E1-E5a pair commonly used for ionospheric applications.

The QZSS is a Japanese regional navigation satellite system composed of three IGSO satellites and one GEO satellite. With the launch of three additional satellites, the system is scheduled to reach Full Operational Capability (FOC) by 2025 [24]. Despite the growing availability of GNSS stations capable of receiving multi-GNSS signals, those equipped to track QZSS signals remain predominantly concentrated in the East Asia and Oceania regions, reflecting the system’s regional operational design. Therefore, the sparse spatial distribution of QZSS-tracking stations constrains the feasibility of the simultaneous modeling of ionospheric TEC and Differential Code Bias (DCB) [25]. As a result, studies employing QZSS observations for TEC estimation remain limited.

A recent study [26] reported significant findings on ionospheric behavior based on QZSS observations, analyzing the ionospheric disturbances induced by the Fukutoku-Okanoba volcano using QZSS data collected in Japan. In addition, Choi et al. [27] estimated ionospheric TEC over the Korean Peninsula using QZSS L1 and L2 signals, reporting a high level of consistency with the TEC values derived by the GIM products from the Center for Orbit Determination Europe (CODE).

QZS-6, a geostationary satellite, was successfully launched in Japan on 2 February 2025. This satellite will be located at a longitude of 90.5°E. One remarkable feature of the QZS-6 satellite is that it no longer transmits the L1 C/A and L2C signals [28]. Therefore, efforts to achieve high-precision TEC estimation with the QZSS can be dependent on the availability of L1C and L5 signals.

An increasing number of studies have recently employed QZSS for ionospheric TEC research. However, few previous studies have explored the mid-term behavior of QZSS TEC as influenced by different signal combinations. Moreover, deriving stable QZSS DCB and TEC values is challenging not only due to the limited observations from QZSS satellites but also because of the narrow coverage of the GNSS network. In addition, only a limited number of studies have been conducted on TEC validation and the rate of TEC (ROT) analysis using different signal combinations of QZSS [26,29].

In this study, we estimate ionospheric TEC by using combinations of L1, L2, and L5 observations from QZSS satellites only, based on data obtained from nine GNSS stations in the Korean Peninsula. To assess the consistency of TEC estimates, TEC values derived from different signal combinations (L1-L2, L1-L5, and L2-L5) are compared with those from the CODE GIM. In addition, the corresponding DCB of QZSS satellites is analyzed for each signal combination. Furthermore, the ROT is calculated to evaluate the noise characteristics of each signal combination. From these results, we suggest the most appropriate frequency pair for accurate ionospheric TEC retrieval.

2. QZSS Constellation and Data Description

The QZSS is a Japanese regional satellite navigation system designed to provide continuous Positioning, Navigation, and Timing (PNT) services across the East Asia and Oceania regions. The current QZSS constellation comprises one GEO satellite and three IGSO satellites. The GEO satellite maintains a semi-major axis of approximately 42,164 km, with an inclination of 0°, and is positioned near 127°E longitude. The three IGSO satellites share the same orbital period and semi-major axis as the GEO satellite but are inclined at approximately 39° or 41°, with an orbital eccentricity of about 0.075. While these satellites occupy different orbital planes, they exhibit similar ground track patterns.

Figure 1 shows the ground tracks of the four QZSS satellites derived from broadcast ephemeris data on 1 January 2024. The IGSO satellites trace characteristic figure-eight-shaped ground tracks, displaying north–south asymmetry. Furthermore, the QZSS constellation is scheduled for expansion in 2025 with the addition of two new GEO satellites and one Quasi-Geostationary Earth Orbit (QGEO) satellite.

Figure 2a presents the spatial distribution of nine GNSS reference stations selected for QZSS-based TEC estimation. These stations are geographically located between approximately 33° and 39° north latitude and 126° to 129° east longitude, covering the Korean Peninsula. Detailed specifications for each GNSS station, including the geographic coordinates, receiver models, and antenna types, are summarized in

Table 1. The list of GNSS stations with geographic coordinates.

Site Name	Geographic Latitude (Degrees)	Geographic Longitude (Degrees)
skch	38.25°N	128.56°E
skma	37.49°N	126.91°E
sbao	36.93°N	128.45°E
daej	36.39°N	127.37°E
bhao	36.16°N	128.97°E
mlyn	35.49°N	128.74°E
mkpo	34.81°N	126.38°E
kohg	34.45°N	127.51°E
jeju	33.28°N	126.46°E

. All stations are equipped with identical instrumentation, specifically the Trimble NetR9 GNSS receiver and the TRM59800.00 SCIS antenna manufactured by Trimble Inc. (Westminster, CO, USA), ensuring consistency in data acquisition and minimizing hardware-related biases in the TEC estimation.

The types of observations generated by a GNSS receiver can differ based on the satellite system and the receiver manufacturer. The Trimble NetR9 receiver supports a wide range of observation types compliant with the Receiver Independent Exchange Format (RINEX) version 3 format.

Table 2. QZSS observation types at selected GNSS stations.

Signal	Observation Types
L1	C1C, L1C, C1X, L1X, C1Z, L1Z
L2	C2X, L2X
L5	C5X, L5X

summarizes the frequency bands utilized by QZSS along with the corresponding observation codes for each frequency. Although several observation types are available for the L1 frequency band, this study specifically employed the C1C and L1C signal types to ensure consistency and compatibility. In Table 2, L1C, L1X, and L1Z types are all GNSS signals transmitted on the L1 carrier phase. They utilize distinct modulation techniques. In addition, C1C, C1X, and C1Z represent the code measurement types transmitted by the L1C, L1X, and L1Z signals, respectively. The observables C1C, C2X, and C5X are derived from signals transmitted on different frequency bands. All GNSS measurements were recorded at 30 s intervals following the RINEX version 3.02.

The ionospheric pierce point (IPP) refers to the specific point where a GNSS signal passes through the ionosphere. To analyze the spatial distribution of the IPP by the QZSS constellation, we examined the coverage of the IPP derived from QZSS satellite signals received at nine GNSS stations in the Korean Peninsula. Figure 2b displays the IPP, which is represented by green lines. The location of the IPP is sensitive to the assumed height of the ionospheric thin shell above the Earth’s surface. In this study, an altitude of 350 km was adopted for the fixed ionospheric thin shell [30,31,32,33]. Furthermore, observations with a mask angle greater than 10 degrees were processed to ensure TEC quality. Cycle slips frequently occur below an elevation angle of 10 degrees due to environmental obstructions near the GNSS stations. As shown in Figure 2b, the resulting IPP distribution spans approximately 22° to 38° in latitude and 125° to 135° in longitude. Due to the orbital characteristics of QZSS satellites, observations are often unavailable, or signal interruptions may occur, particularly at latitudes below approximately 24°.

3. TEC Estimation Method

The GNSS network makes it possible to measure ionospheric TEC in high spatial and temporal resolutions. The dual-frequency GNSS observables enable us to monitor ionospheric TEC precisely. The estimation methods for ionospheric TEC from dual-frequency GPS measurements have been suggested in the literature [2,34,35,36,37]. As the QZSS includes GEO satellites, it has the advantage of being able to monitor ionospheric TEC at a specific location. Therefore, there have been some reports of cases using QZSS data in ionospheric studies [26,29,38].

QZSS observations can be utilized to estimate ionospheric TEC through the use of multi-frequency combinations, specifically L1-L2, L1-L5, and L2-L5. By applying both code and carrier phase measurements, the slant TEC (STEC) is derived, which represents the integral of electron density along the line-of-sight path between a satellite and a ground-based receiver [4]. TEC is commonly expressed in TEC units (TECU), where 1 TECU corresponds to approximately ${10}^{16}$ electrons per square meter column (electrons/m²) [39].

$$STEC={\displaystyle \frac{f_i^2·f_j^2}{K·\left(f_i^2-f_j^2\right)}}·\left[\left(P_i-P_j\right)-{DCB}_{ij}\right]$$

(1)

where $P_i(i=1, 2)$ and $P_j(j=2, 5)$ represent the pseudorange measurements of the QZSS signals. The constant $K$ is 40.3 ${\mathrm{m}}^3/{\mathrm{s}}^2$, which is a physical constant related to ionospheric refraction. $f_i$ and $f_j$ denote the carrier frequencies of the corresponding signals. ${DCB}_{ij}$ represents the differential code bias between two signals $f_i$ and $f_j$. This value includes the combined hardware biases of the satellite and receiver. DCB should be removed as it causes a large error source in calculating TEC [2,40]. In this study, we employed a least squares (LSQ) approach to obtain DCB values for receivers and satellites. In consideration of the limited number of QZSS observations and the narrow spatial distribution of the IPP, the DCB values are estimated once per day using daily observations to ensure their stability.

In addition, to separate the receiver and satellite DCBs, we applied the following common constraint by setting the sum of satellite DCBs to zero.

$${\sum }_{i=1}^n{DCB}_{L1L2}^i=0$$

(2)

$${\sum }_{i=1}^n{DCB}_{L1L5}^i=0$$

(3)

$${\sum }_{i=1}^n{DCB}_{L2L5}^i=0$$

(4)

STEC can be converted to vertical TEC (VTEC) using a single-layer mapping function as follows [18,41]:

$$\mathrm{V}\mathrm{T}\mathrm{E}\mathrm{C}=\cos \left(\mathsf{\chi }\right)·STEC$$

(5)

$$\mathsf{\chi }=\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{s}\mathrm{i}\mathrm{n}\left({\displaystyle \frac{R_E·\cos \left(ϵ\right)}{R_E+H}}\right)$$

where $\mathsf{\chi }$ is a zenith distance at the IPP, $R_E$ is the mean radius of the Earth ($R_E~$6378 km), $ϵ$ is the elevation angle, and $H$ is the height of the single-layer model that is assumed to be 350 km.

For regional ionospheric TEC modeling and DCB estimation, we applied the spherical harmonic expansion technique [42], as presented in Equation (6).

$$VTEC\left(\beta ,s\right)={\sum }_{n=0}^N{\sum }_{m=0}^n{\overline{P}}_{nm}\left(sin\beta \right)({\overline{C}}_{nm}\cos \left(ms\right)+{\overline{S}}_{nm}\sin \left(ms\right))$$

(6)

where $\beta$ and $s$ are the geocentric latitude and solar-fixed longitude of the IPP, respectively. ${\overline{P}}_{nm}$ represents the normalized associated Legendre function with the degree n and the order m. $N$ denotes the maximum degree of the spherical harmonic expansion. A degree of $N$ = 8 was adopted in the model. ${\overline{C}}_{nm}$ and ${\overline{S}}_{nm}$ are the TEC unknown coefficients of spherical harmonics.

The corresponding TEC values are derived from a high-accuracy ionospheric TEC estimation program developed by the Korea Astronomy and Space Science Institute. Figure 3 presents a flow chart for the ionospheric TEC and DCB estimation procedure. The estimation of ionospheric TEC and DCB is carried out through a systematic multi-step procedure for QZSS observations and broadcast ephemeris. First, dual-frequency observables are extracted from RINEX version 3 observation files. Simultaneously, we use the RINEX navigation files for satellite position computation. In addition, a pre-processing procedure is carried out for outlier detection and cycle slip identification. Subsequently, ambiguity resolution is performed to address phase ambiguities in the carrier phases. In this study, the phase ambiguities are resolved through a combination of dual-frequency code and carrier-phase observations. The integer ambiguities are then determined by simply rounding the float ambiguity values.

The IPP is determined using the station coordinates and the satellite’s position. A geometry-free linear combination is then applied to calculate ionospheric TEC and DCB. In the case of the GPS, the abundance of observations allows for the stable estimation of DCB and VTEC simultaneously. However, the insufficient observations from the QZSS satellites may pose challenges in the simultaneous estimation of TEC and DCB. Therefore, we initially compute the satellite and receiver DCBs by using the daily QZSS data. Subsequently, the computation of ionospheric TEC is based on the use of predetermined DCBs for both satellites and receivers.

4. Results

4.1. QZSS Satellite DCB

In this study, the DCBs of QZSS satellites only were estimated using data over six months, collected from DOY 1 to DOY 182 in 2024 at nine GNSS stations. All stations are capable of receiving C1C, C2X, and C5X code observations. A regional ionospheric modeling approach was employed to estimate the QZSS satellite DCBs. Figure 4 show the time series of satellite DCB estimates for each QZSS satellite with different signal combinations (C1C-C2X, C1C-C5X, and C2X-C5X).

The stability of the daily DCB values is critical for accurate TEC estimation. As shown in Figure 4, the DCB values for each signal combination remained relatively stable throughout this period, with day-to-day variations confined within approximately ±0.3 nanoseconds.

All satellite DCB values for QZSS satellites ranged approximately from −2 ns to +2 ns. It is noted that satellites J04 and J07 exhibited highly similar DCB values with all signal combinations. In addition, the DCB values of J07 exhibit relatively larger variability compared to those of J04. This may be associated with the slow geometry of the geostationary satellite J07.

The DCB values for satellite J03 were estimated to be smaller compared to those of the other satellites. Furthermore, the C1C-C2X and C1C-C5X DCB values for J03 show a high similarity. The remarkable thing is that the C1C-C5X DCBs for all satellites were observed to remain within the range of −0.6 ns to +0.6 ns.

Figure 5 shows the average and RMS values of the different DCB values presented in Figure 4 for each satellite. In Figure 5, the average and RMS of satellite DCB values are represented as bar graphs and error bars, respectively. The absolute values for the C1C-C2X DCBs are smallest for the J03 satellite and largest for the J02 satellite. Similarly, as can be seen in Figure 5c, the C2X-C5X DCBs show the largest absolute value for J02 and the smallest value for the J03 satellite. Moreover, the detailed values for the average and RMS of different DCB values are presented in Table 2.

It can be seen that the C1C-C5X DCBs have relatively small values compared to the C1C-C2X and C2X-C5X DCBs. However, their RMS values are relatively high, except for the J03 satellite. As shown in

Table 3. Average and RMS values of satellite DCBs with three different signal combinations.

PRN	Signal Combination	Average Value (ns)	RMS Value (ns)
J02	C1C-C2X	−1.58	0.11
	C1C-C5X	−0.26	0.14
	C2X-C5X	1.34	0.12
J03	C1C-C2X	−0.55	0.11
	C1C-C5X	−0.53	0.12
	C2X-C5X	0.04	0.12
J04	C1C-C2X	1.03	0.12
	C1C-C5X	0.49	0.14
	C2X-C5X	−0.52	0.13
J07	C1C-C2X	1.10	0.14
	C1C-C5X	0.30	0.22
	C2X-C5X	−0.86	0.19

, the RMS of C1C-C2X DCBs is small for all QZSS satellites.

The accuracy and stability of DCB estimates can be dependent on the distribution of ground GNSS stations and the number of observations [43]. In this study, DCBs were estimated using nine GNSS stations located in a narrow area, which may affect the accuracy and stability of DCB. Moreover, the poor geometry of GNSS reference stations within a limited area is clearly linked to the spatial distribution of the IPP. As a result, there are inherent limitations in improving the accuracy of TEC and DCB estimation. However, using receivers and antennas of the same type can improve the DCB estimation accuracy.

Figure 6 presents the variations in receiver DCBs for nine GNSS stations in South Korea, specifically for the QZSS constellation, during the period from DOY 1 to 182, 2024. From top to bottom on Figure 6, three panels show the time series of receiver DCBs to different frequency pair combinations (C1C-C2X, C1C-C5X, and C2X-C5X). The C1C-C2X DCB values range between approximately −10 ns and −15 ns. They exhibited stable behavior over this period. In comparison with the satellite C1C-C2X DCB values, the absolute receiver C1C-C2X DCB values are observed to be significantly larger. A similar trend is consistently observed for both the C1C-C5X and C2X-C5X DCBs as well. This indicates that the receiver DCBs can serve as a major error source in TEC estimation.

As can be seen in the middle panel of Figure 6, the C1C-C5X DCBs exhibit slightly more negative values, ranging between roughly −20 ns and −30 ns. In contrast to the satellite C1C-C5X DCBs, the receiver C1C-C5X DCBs showed significantly larger bias magnitudes. This may reflect increased sensitivity in this frequency combination to hardware. In addition, the receiver C2X-C5X DCBs have values roughly within the range of −10 ns to −18 ns. It can be observed that these values were consistently estimated during the entire period.

4.2. QZSS TEC

Ionospheric TEC can be retrieved using dual-frequency combinations, including L1-L2, L1-L5, and L2-L5 observations. Figure 7 presents the time series of VTEC for the QZSS J07 satellite. VTEC values are derived at intervals of 300 s. These are also calculated using combined QZSS L1, L2, and L5 observations received at the ‘daej’ station from DOY 1 to 182 in 2024.

For a clear distinction between the different VTEC values, the L1-L2, L1-L5, and L2-L5 TEC series are presented separately in three individual panels in Figure 7. The different TEC values demonstrate similar behavior, both in trend and magnitude.

To assess the performance of the CODE GIM in the regional area, we calculated the GPS TEC using data obtained from the ‘daej’ station. Figure 8 presents the GPS TEC and CODE GIM TEC for 182 days. In Figure 8, the GPS TEC was derived using satellite signals only with elevation angles greater than 40 degrees. Despite the mismatch between the GPS IPPs and the CODE GIM grid points, the GPS TEC and GIM TEC show strong agreement with each other.

To validate the derived QZSS TEC values, each was compared with the CODE GIM. The GIM TEC was calculated by aligning it with the IPP locations of the QZSS satellite J07. In this study, TEC was estimated at 5 min intervals, whereas the CODE GIM is provided at an hourly resolution. Consequently, differences in TEC values may occur due to the discrepancy in temporal resolution between the two datasets. To facilitate the comparison between the two datasets, statistical values are calculated based on the temporal resolution of the CODE GIM.

The ionospheric delay differences between various GNSS frequency pairs were analyzed to evaluate the consistency and residual biases in multi-frequency combinations.

Figure 9 presents a comparison between the QZSS-derived TEC and the CODE GIM TEC. The QZSS TEC and CODE GIM TEC are represented by the black solid and red solid lines, respectively. Strong agreement is observed between the two datasets in terms of both magnitude and temporal variation. Figure 9a shows a comparison of the L1-L2 TEC with the CODE GIM TEC. For the L1-L2 combination, a mean value of +0.29 TECU was observed. This suggests that the bias is very small compared to the CODE GIM. Since the GIM is generally reported to have ionospheric errors ranging from 2 to 8 TECU, the L1-L2 TEC estimates obtained in the study can be considered reliable. In addition, the corresponding RMS value of 3.71 TECU reflects the variability between the L1-L2 derived TEC and the CODE GIM TEC. Figure 9b presents a comparison between the L1-L5 TEC estimates and the TEC values derived from the CODE GIM. The L1-L5 combination yielded a mean of +0.25 TECU with an RMS of 3.59 TECU, indicating a similar magnitude of bias and variability compared to the L1-L2 combination. Based on the statistical results, the L1-L5 combination appears to show stronger agreement with the CODE GIM compared to the L1-L2 combination.

For the L2-L5 combination, a negative mean of −0.33 TECU was observed. In contrast to the L1-L2 and L1-L5 combinations, the L2-L5 TEC tends to be slightly underestimated relative to the CODE GIM, as shown in Figure 9c. In addition, there was a higher RMS of 5.18 TECU in this combination. This may suggest greater variability in the ionospheric response between these two frequencies, possibly due to increased noise or hardware-dependent effects in the L2 and L5 bands.

To analyze the differences in TEC values generated by various signal combinations, the L1-L2 and L1-L5 combinations, as well as the L2-L5 and L1-L5 combinations, were considered. Figure 10 illustrates the time series of TEC differences (L1-L2 minus L1-L5) from DOY 1 to 182 in 2024. In this study, the TEC differences between the two signal combinations were calculated individually for each GNSS station. As seen in Figure 10, the blue dots in all panels represent the TEC differences between the two combinations. A linear regression was applied to the time series to examine any long-term trends, with the resulting fit depicted as a solid red line. The 95% confidence level for the linear fit is shown as cyan dashed lines, providing a statistical measure of the reliability and variability.

The mean of TEC differences exhibits both positive and negative values, suggesting station-dependent behavior likely influenced by local ionospheric conditions or hardware-related biases. The averaged TEC differences observed at each station are as follows: ‘jeju’ (−0.76 TECU), ‘kohg’ (0.03 TECU), ‘mkpo’ (−0.11 TECU), ‘mlyn’ (0.08 TECU), ‘bhao’ (0.09 TECU), ‘sbao’ (0.01 TECU), ‘daej’ (−0.04 TECU), ‘skch’ (0.05 TECU), and ‘skma’ (0.90 TECU).

TEC differences between the L1-L2 and L1-L5 combinations can be considered relatively small overall. However, some stations, such as ‘jeju’ and ‘skma’, exhibit remarkable TEC biases that cannot be disregarded. These discrepancies may be partially attributed to site-specific factors, such as the occurrence rate of cycle slip in the different observations or the environment surrounding each GNSS station. Such factors could influence the ambiguity resolution process and contribute to the observed TEC differences.

Similarly, the TEC differences between the L2-L5 and L1-L5 combinations were also analyzed. Figure 11 shows the time series of TEC differences (L2-L5 minus L1-L5). The mean value of TEC differences observed at each GNSS station is as follows: ‘jeju’ (2.13 TECU), ‘kohg’ (−0.39 TECU), ‘mkpo’ (0.66 TECU), ‘mlyn’ (−0.22 TECU), ‘bhao’ (0.29 TECU), ‘sbao’ (0.69 TECU), ‘daej’ (−0.04 TECU), ‘skch’ (−1.07 TECU), and ‘skma’ (−1.08 TECU).

TEC differences between the L2-L5 and L1-L5 combinations are relatively larger than those observed between the L1-L2 and L1-L5 combinations. This suggests that the TEC values derived from the L2-L5 combination have greater inconsistency. Moreover, it may suggest increased variability in the ionospheric response, increased noise levels between L2 and L5 frequencies, and the occurrence rate of cycle slips.

4.3. ROT Analysis

To analyze the observational noise associated with different signal combinations, the ROT was considered. The VTEC values were re-computed using QZSS measurements sampled at 30 s intervals to analyze the ROT. Subsequently, the time series of the ROT was derived using the standard formulation described in previous studies [44,45,46] as follows:

$$ROT=(VTEC{t}_k-VTEC{t}_{k-1})/\delta t$$

(7)

where δt is the time interval. We used 30 s for δt. In addition, potential cycle slips were detected using the Melbourne–Wübbena (MW) combination. We calculate the change in MW data recorded at 30 s intervals. If the MW values exceed the established threshold (>2 m), we assume that a cycle slip has occurred. When a cycle slip is identified, the ambiguity of the MW combination must be re-estimated to prevent abrupt discontinuities in the ROT time series. This step is essential to ensure the reliability of the ROT.

Figure 12 shows the ROT derived from three different signal combinations of QZSS satellite J07 observed at the ‘daej’ station on 1 January 2024. The L1-L2, L1-L5, and L2-L5 combinations are represented by red, blue, and gray lines, respectively.

A comparative analysis of the ROT values reveals notable differences in the magnitude of short-term fluctuations among the combinations. The L2-L5 combination shows the highest level of variability, with an RMS of 0.083 TECU, indicating greater susceptibility to observational noise or ionospheric irregularities. Compared to L2-L5, the L1-L2 and L1-L5 combinations have lower RMS values of 0.039 TECU and 0.033 TECU, respectively. These results indicate that the L2-L5 combination may be more affected by noise, whereas the L1-L5 combination demonstrates the lowest ROT variability, making it potentially more robust for ionospheric monitoring applications.

To conduct a more detailed investigation of the ROT RMS values, we extended our analysis to include all GNSS stations. Figure 13 shows the time series of the ROT derived from the three different GNSS signal combinations (L1-L2, L1-L5, and L2-L5) observed at the GNSS stations from 1 to 6 January 2024. Three time series of ROT variations for each station are presented over six consecutive days. Similarly to Figure 12, the L2-L5 combination consistently exhibits the highest level of ROT fluctuations at all stations. Conversely, the L1-L5 combination shows the lowest level of ROT fluctuations. Heki and Fujimoto [26] reported that the L1-L5 combination exhibits slightly lower noise levels compared to the L1-L2 combination, which is in good agreement with our results. To provide a quantitative measure of ROT variability for both signal combinations and GNSS stations, we performed an additional analysis by calculating the RMS values of the ROT.

Table 4. RMS values of ROT derived from three different QZSS signal combinations (L1-L2, L1-L5, and L2-L5) observed at GNSS stations from 1 to 6 January 2024.

Site Name	Signals	RMS Value (TECU)
	L1-L2	0.034
skma	L1-L5	0.028
	L2-L5	0.073
	L1-L2	0.036
skch	L1-L5	0.030
	L2-L5	0.079
	L1-L2	0.039
daej	L1-L5	0.033
	L2-L5	0.083
	L1-L2	0.029
sbao	L1-L5	0.025
	L2-L5	0.064
	L1-L2	0.033
bhao	L1-L5	0.028
	L2-L5	0.073
	L1-L2	0.028
mlyn	L1-L5	0.025
	L2-L5	0.059
	L1-L2	0.028
mkpo	L1-L5	0.025
	L2-L5	0.059
	L1-L2	0.035
kohg	L1-L5	0.029
	L2-L5	0.072
	L1-L2	0.028
jeju	L1-L5	0.025
	L2-L5	0.059

presents the RMS values of the ROT for both signal combinations and GNSS stations. The mean RMS values computed for each signal combination reveal distinct differences in ROT fluctuation levels. In particular, the L2-L5 combination yields the highest mean RMS value of about 0.069 TECU, which is more than 2.5 times greater than that of the L1-L5 combination (~0.027 TECU) and more than twice that of L1-L2 (~0.032 TECU). The L1-L5 combination demonstrates the lowest mean RMS value, indicating its better performance in terms of ROT stability. In addition, although the difference between the L1-L5 and L1-L2 combinations is relatively small, the L1-L5 combination has an approximately 16% lower mean RMS value compared to the L1-L2 combination.

5. Discussion

This study presents a comprehensive assessment of DCBs for QZSS satellites and evaluates the performance of three different signal combinations for QZSS ionospheric TEC estimation. The DCB estimates, derived from 182 days of continuous observations from nine GNSS stations, demonstrated high temporal stability, with daily variations generally constrained within ±0.3 ns. This level of consistency indicates the robustness of the estimation methodology. The strong agreement in DCB values for satellites J04 and J07 with all signal combinations further suggests high hardware stability in the satellite design. While C1C-C5X DCBs for all QZSS satellites showed smaller magnitudes, their RMS values were relatively higher. The relatively large RMS values observed in the C1C-C5X DCBs may reflect frequency-dependent biases inherent in the signal paths or satellite hardware.

GNSS stations with narrow spatial distribution represent a constraint that may have influenced the accuracy of the DCB results. However, employing GNSS receivers and antennas of identical models helps reduce inter-station variability in DCB estimates. Furthermore, DCB estimates may be affected by factors such as hardware temperature variations at reference stations [47,48,49] and the grounding conditions of antennas [50]. Regarding ionospheric TEC, three different signal combinations (L1-L2, L1-L5, and L2-L5) were analyzed using QZSS satellite J07 observations. The TEC time series for all combinations exhibited similar trends and magnitudes. When compared to the CODE GIM TEC, both L1-L2 and L1-L5 combinations showed small positive biases of +0.29 and +0.25 TECU, respectively. The corresponding RMS values are in the range of 3.6~3.7 TECU. The accuracy of GIM TEC is known to range between 2 and 8 TECU [51]. Therefore, our results are in good agreement with the CODE GIM TEC.

Compared to other combinations, the L1-L5 combination demonstrated the lowest ROT variability, indicating high robustness for ionospheric TEC monitoring. These findings are consistent with the previous study [29]. The results suggest that the L1-L5 signal pair yields the most reliable performance for both accuracy and stability for QZSS TEC estimation. Therefore, this study provides valuable insights into QZSS multi-frequency TEC measurement.

6. Conclusions

In this study, we evaluated the ionospheric TEC estimation performance and ROT of three QZSS signal combinations (L1-L2, L1-L5, and L2-L5) using data from nine GNSS stations distributed across the Korean Peninsula. QZSS satellite DCBs were estimated with high temporal stability, ensuring reliable TEC estimation.

The comparison between QZSS-derived TEC and the CODE GIM showed that the L1-L5 combination has the smallest mean bias and RMS error, indicating the highest agreement with the reference value. Furthermore, the analysis of ROT variations for all GNSS stations revealed that the L2-L5 combination has the highest RMS values, while the L1-L5 combination consistently resulted in the lowest RMS values. This suggests that the L1-L5 signal pair is less sensitive to observational noise due to the large frequency separation. Although the performance difference between the L1-L5 and L1-L2 combination is relatively small, the L1-L5 combination demonstrated approximately 16% lower ROT RMS, highlighting its improved stability.

In conclusion, the L1-L5 signal combination offers enhanced performance in both TEC estimation accuracy and ROT stability. We confirmed its effectiveness as a reliable frequency pair for QZSS TEC. In addition, this study provides valuable empirical evidence on QZSS DCB behavior and multi-frequency TEC performance. To enhance the validity and applicability of these results, future research should expand the spatial distribution of GNSS stations and evaluate the effects of diverse environmental variables.