Ki KANG, Kun FANG, Yno ZHU, Yun LIU, Zhipeng WANG,*,Qing LI

a National Key Laboratory of CNS/ATM, School of Electronic and Information Engineering, Beihang University, Beijing 100083, China

b Research Institute for Frontier Science, Beihang University, Beijing 100083, China

KEYWORDS GBAS;Integrity;Inter-frequency bias;Ionosphere-free smoothing;Vertical protection level

Abstract Dual-Frequency Ground-Based Augmentation Systems(GBAS)can be affected by receiver Inter-Frequency Bias (IFB) when Ionosphere-Free (Ifree) smoothing is applied. In the framework of the proposed GBAS Approach Service Type F (GAST-F), the IFB in the Ifree smoothed pseudorange can be corrected. However, IFB residual uncertainty still exists, which may threaten the integrity of the system. This paper presents an improved algorithm for the airborne protection level considering the residual uncertainty of IFBs to protect the integrity of dual-frequency GBAS. The IFB residual uncertainty multiplied by a frequency factor is included in the Ifree protection level together with the uncertainty of other error sources.To verify the proposed protection level algorithm, we calculate the IFB residual uncertainties of ground reference receivers and user receiver based on BDS B1I and B3I dual-frequency observation data and carry out a test at the Dongying Airport GBAS station.The results show that the proposed Ifree protection level with IFB residual uncertainty is 1.48 times the current protection level on average. The probability of Misleading Information (MI) during the test is reduced from 3.2 × 10-4 to the required value. It is proven that the proposed protection level can significantly reduce the integrity risk brought by IFB residual uncertainty and protect the integrity of dual-frequency GBAS.

1. Introduction

Based on the differential structure of the Global Navigation Satellite System (GNSS), the Ground-Based Augmentation System (GBAS) broadcasts differential corrections and integrity information to aircraft to provide accurate, safe and reliable approach guidance. At present, GBAS Approach Service Type D (GAST-D) can meet the requirements of CAT II/III precision approaches.1,2However, GAST-D should introduce several monitors to address ionospheric threats because it supports only single frequency signal.

With the development of GNSS constellations and the application of new signals, Dual-Frequency Multi-Constellation GBAS (DFMC GBAS) can use dual-frequency smoothing techniques to solve the threat from ionospheric activities. In the framework of the proposed GBAS Approach Service Type F (GAST-F), two smoothing techniques are being considered: Divergence-Free (Dfree) and Ionosphere-Free (Ifree).3Accordingly, there are two alternative modes of the current structure: GAST-F SF (DF) and GAST-F IF.4The switching between these two modes depends on whether ionospheric anomalies are detected.5,6Dfree uses singlefrequency code measurement and dual-frequency phase measurements. Although only the temporal ionospheric gradient is eliminated, Dfree can provide more accurate monitoring performance and maintain the same noise level as the single frequency system. Ifree combines both code and phase measurements of two frequencies, which can eliminate all ionospheric delay errors and completely addresss the ionospheric threat. However, the cost is that there will be multiplied measurement noise (related to the carrier frequency used) and receiver Inter-Frequency Bias (IFB) will be introduced into the Ifree smoothed pseudorange.

The IFB is the hardware delay difference between the measurements of different frequencies at the receiver,7which relates to the internal structure of a specific receiver8and may vary with respect to different GNSS satellites, it affects dual-frequency signal processing and positioning in the GNSS receiver.9IFB is a part of Differential Code Bias (DCB), so research on IFB is usually carried out simultaneously with the analysis of DCB and the ionosphere.10The fast method to calculate and remove single-receiver IFB from the dualfrequency measurements utilizes Time Group Delay (TGD)of satellite which can be obtained from public sources.11To achieve real-time solution,IFB can be estimated by combining Kalman filter and ionospheric spherical harmonic model,12but the accuracy of this method is relatively low. An improved TGD ‘‘zero mean” condition was applied to separate IFBs in the IGGDCB method,13which combined the local ionospheric model and least square estimation to calculate DCB. IFB can also be calibrated by the ‘‘zero pseudorange” method at the hardware level.14

Only code IFB will be considered in this research, and IFB in the carrier phase will be ignored. Code IFBs are transformed into biases in the Ifree smoothed pseudorange observation, which may bring errors of a few meters to the GAST-F IF position solution with dual-frequency pseudorange combination. To meet the requirements of the CAT III precision approach, IFB in the Ifree smoothed pseudorange must be eliminated. However, even if the IFB is removed, its residual errors will remain and vary randomly in a certain range,15which may introduce potential integrity risk to dualfrequency GBAS and should be bounded for in the protections levels.16Therefore, it is necessary to protect the integrity of dual-frequency GBAS from IFB residual uncertainties of reference receivers and user receiver.

This paper is organized as follows. Section 2 provides a review of the protection level calculation in GBAS, including protection levels in single-frequency system and dualfrequency system. Then, in Section 3, the calculation formula of the Ifree protection level, which contains the IFB residual uncertainty is derived.In Section 4,the IFB residual uncertainties of ground reference receivers and user receiver used in this research are estimated based on the BDS B1I and B3I dualfrequency observation data collected at the Dongying Airport GBAS station. In Section 5, the process and results of the actual test are shown to verify the proposed Ifree protection level. A corresponding integrity analysis is also conducted.Finally,a brief summary of the paper is presented in Section 6.

2. GBAS protection level calculation

In GBAS, if the time of positioning error exceeding the given alert limit is longer than the required time to alert,an integrity fault is assumed. However, the true value of the positioning error cannot be known during the approach.Thus,the concept of protection level is introduced into GBAS.

2.1. Protection level of single-frequency GBAS

The protection level is a real-time value calculated by the airborne according to its own receiver performance and the integrity parameters provided by the ground subsystem. It can bound the true value of the positioning error with a high confidence probability, which is related to the required integrity risk probability.When the positioning error exceeds the calculated protection level, Misleading Information (MI) will be generated, resulting in a loss of integrity. Furthermore, if the positioning error is greater than the protection level and the protection level is less than the given alert limit, Hazardous Misleading Information (HMI) will be generated, which will seriously threaten the security of the system. Therefore, the accurate calculation of protection level is very important for the integrity of GBAS.

The protection level is divided into the Vertical Protection Level(VPL)and the Horizontal Protection Level(HPL).Considering the stricter requirements on the integrity of the vertical direction in the process of aircraft approach and landing, this paper only studies the VPL under the H0 hypothesis, which refers to normal measurement conditions (i.e., no faults) in all reference receivers and on all ranging sources.17For single frequency GBAS, the calculation of VPL is as follows.17

where σNand h0is the refractivity uncertainty and tropospheric scale height broadcast to the aircraft by the ground system, θ is the elevation of the satellite, and Δh is the altitude of the aircraft. These parameters can be set as constant values to cover the worst-case expected during the operation.

It should be noted that the ionospheric error is frequency dependent but the tropospheric error is not.

2.2. Protection level of dual-frequency GBAS

According to the current proposed GAST-F processing mode,under normal conditions, single-frequency observations are used for positioning, and Dfree is used for monitoring. In this case,the calculation of the airborne protection level is the same as that of the single-frequency system. When the ionospheric anomaly is detected,the system will switch to Ifree positioning and monitoring mode. The smoothing process is shown in Fig.1,where ψ and φ represent the code pseudorange and carrier phase inputs, respectively. For Ifree smoothing, ψ and φ are the forms shown in Eqs. (9) and (10) (taking BDS B1I and B3I for example).3

Fig. 1 GBAS smoothing process.

where R is the true distance between the satellite and user,tsis the satellite clock bias,tris the receiver clock bias,I represents the ionospheric delay, which is related to the frequency of the navigation signal,T represents the tropospheric delay,M is the multipath error and ε is the thermal noise.

The carrier phase measurement has a similar expression.The clock bias of the BDS takes the antenna phase center of frequency B3 as the zero reference. Therefore, the same part of the hardware delay for B1I and B3I pseudorange measurements is included in the clock bias, and the inconsistent parts can be written in the pseudorange expression of B1I only;they are IFB of the receiver and TGD of the satellite. In fact,because GBAS is a differential system,TGD will be eliminated during the process of differential correction,and will not affect positioning and monitoring. To simplify the formula, TGD is omitted from the following analysis. The expression of the Ifree smoothed pseudorange is as follows.19

3. Ifree protection level considering IFB residual uncertainty

IFB is introduced by the Ifree combination,and due to the difference between the ground receiver and airborne receiver,the bias will not be eliminated in the differential process.However,even if the IFB is removed, its residual errors will remain and change randomly in a certain range, which may introduce potential integrity risk to dual-frequency GBAS. Therefore,it is necessary to protect the integrity of dual-frequency GBAS from the IFB residual uncertainties of reference receivers and user receiver by modifying the calculation formula of the Ifree protection level.

3u.n1c.e rRt ealianttiyo nship between σpr air，Ifree and IFB residual

Fig. 2 The variation of σi，Ifree.

Fig. 3 VPL calculation and integrity assessment process.

Fig. 4 IFB + TGD and IFB time sequences of reference receiver No.1 (Nov. 24, 2019).

3.2. Ifree VPL with IFB residual uncertainty

Fig. 5 Unified reference receiver IFB.

Fig. 6 Standard deviation of reference receiver IFB residual errors (32 days).

The first three terms in Eq.(28)can be calculated using navigation data,but σIFB，Gand σIFB，Aneed to be estimated according to the ground and airborne receivers, which will be introduced in the next section. The flow chart of the VPL calculation and integrity assessment in this paper is shown in Fig. 3.

4. IFB and its residual uncertainty

IFB is the hardware delay difference between the measurements of different frequencies, which relates to the internal structure of the ground reference receiver and airborne receiver.8Data from Dongying GBAS Station is collected to estimate receiver IFB,and verify the proposed protection level.The four reference receivers’ type of Dongying GBAS Station is 639A from Tianjin 712 Communication&Broadcasting Co.,Ltd, and the receiver board is K505 GNSS mainboard from ComNav Technology Ltd.The user receiver’s type is NovAtel PwrPak7, and the mainboard is OEM7700. The IFB and its residual uncertainty can be estimated using dual frequency observation data.

4.1. Estimation method

Before introducing the estimation method, it is necessary to make an explanation for the choice of frequencies we used.The BDS-2 B1I and B3I measurements are used in this section to estimate IFB and in Section 5 to verify the proposed VPL.The reason is that B1I and B3I are test signals(without B2I)of dual-frequency BDS system now. This will contribute to the future dual-frequency BDS Open Service (BDS OS) which is based on a combination of the B1C and B2a signals.22

Eq.(29)can obtain the difference of pseudoranges between the two frequencies used by combining the measurements in Eqs. (13) and (14).12

It should be noted that in theory, Eq. (29) should also include the difference of antenna Group Delay Variations(GDV) between this two frequencies, which is a function of the elevation,azimuth and the frequency used.23But according to the latest research,24the difference of GDV at 1561.098 MHz (center frequency of B1I) and 1268.520 MHz(center frequency of B3I) is much smaller compared with IFB even in the worst case. Therefore, GDV is ignored and not taken into account in Eq. (29).

To obtain the IFB,the ionospheric Total Electron Content(TEC) product is used to deduct I1-I3first, and this step relates to the estimation accuracy of the receiver IFB.25According to the relationship between the TEC and ionospheric delay, Eq. (29) is rewritten as follows.12

where F is the slant factor and VTEC represents the TEC in the vertical direction.

Next, the IFB needs to be separated from IFB + TGD.One method is to apply the TGD ‘‘zero mean” condition,26assuming that the mean value of all satellite TGDs is 0,which makes the equations full rank and solves the IFB. However,considering the satellite visibility, this method is not suitable for single stations such as GBAS stations. Therefore, in this paper,the TGD is deduced by using the satellite DCB product published by IGS MGEX.The accuracy of this product is high enough to meet the requirements of IFB estimation. The standard deviation of IFB residual errors is used to characterize the IFB residual uncertainty after correction.

4.2. IFB estimation results

In this paper, 32-day observation data(from Nov. 24,2019 to Jan.2,2020;8 days were not selected due to data interruption)collected at the Dongying Airport (ZSDY) GBAS station are used to estimate the ground receiver IFB and its residual uncertainty. The ground reference receivers are multimode GNSS receivers. The ionospheric delay difference of the two frequencies is deduced from the pseudorange difference using the Global Ionospheric Map TEC product published by Beihang University(BUAA GIM,BUAG).The annual mean precision of the VTEC values is better than 0.25 TECU in where Dongying airport is located,27which is one order of magnitude smaller than other errors in GBAS.

As shown in Fig.4(a),the IFB+TGD time sequence conforms to the characteristics of random variables. Using the separation method mentioned in Section 4.1, IFB time sequence is obtained, as shown in Fig. 4(b). Although the IFB values tend to be consistent among different satellites,there are still differences,which is in accordance with the analysis in previous study.9In this research,a conservative IFB calculated with these values is used as the unified value to simplify the processing, as shown in Fig. 5, which does not affect the analysis. Because the estimated IFB result is negative, the absolute value of the IFB is drawn in Fig.5(a)for convenience of understanding. The absolute value of the receiver IFB will vary from 4 m to 4.5 m, which may impact the real-time positioning errors.Fig.5(b)shows the daily mean value of the reference receiver IFB over 32 days. The maximum difference of the daily mean value is less than 0.3 m. The final result of the reference receiver IFB is -4.2651 m.

4.3. IFB residual uncertainty

In this paper, the IFB residual uncertainty is characterized by the standard deviation of IFB residual errors after correction.Fig. 6 shows the standard deviation of the reference receiver IFB residual errors over 32 days, and its average value is the mean square deviation of these 32 values, which is 0.1357 m.

The standard deviation of IFB residual errors needs to be bounded before it can be used for the calculation of the Ifree protection level as IFB residual uncertainty. Fig. 7(a) and (b)show the probability distributions of IFB residual errors on Nov. 24, 2019 and for all 32 days, respectively. In both cases,the residual distribution of IFB is a‘‘thin tail”Gaussian distribution with zero mean,which means there is no need to find a larger standard deviation for bounding to meet the integrity requirements. However, in this research, the IFB residual uncertainty σIFB，Gis determined to be 0.14 m for conservation.

The IFB and its residual uncertainty of the user receiver are estimated by the same method, and the results are shown in Table 1.

5. Verification and integrity analysis

To verify the Ifree VPL with IFB residual uncertainty proposed in this paper and to assess the integrity, we carried out a test in vehicles near the Dongying Airport GBAS station on Jan. 25, 2021 and collected the experimental data needed.

Fig. 7 Probability distributions of reference receiver IFB residual errors.

Table 1 IFB and its residual uncertainty results of the reference receiver and user receiver.

5.1. Testing

The test route was from our laboratory to the GBAS station,as shown in Fig. 8(a). To meet the requirements of test duration and sample size, three repetitions were made along this route during the test.Fig.8(b)shows the layout of the ground reference receiver and VDB antenna at the GBAS station.28All four receivers were equipped with the same choke ring antenna, and their positions had already been calibrated accurately.

During the test,a Beidou/GNSS precise timing receiver was used to receive the B1I and B3I measurements, together with Pseudorange Correction (PRC) to attain the user’s position.The data update interval was 0.5 s and the filtering time was 100 s.

A sky plot of the satellites used during the test period is shown in Fig. 9(a). There were seven satellites used for positioning, including four GEO satellites (C01, C02, C03 and C04) and three IGSO satellites (C06, C09 and C10). The visibility of these satellites remained unchanged due to the limited test duration. Fig. 9(b) shows the change in baseline length during the test, in which the unevenness represents stopping caused by the local traffic conditions.

Meanwhile, to calculate the Vertical Positioning Error(VPE), the test vehicle was also equipped with a receiver as the user receiver, together with another receiver placed in our laboratory as the base station to perform RTK positioning.Because RTK can achieve millimeter-size positioning with very high accuracy, we use its positioning result as the user’s true position in this research.The VPE is obtained by subtracting the RTK solution from the Ifree positioning result.

Fig. 8 Test scenario.

Fig. 9 Test process.

Fig. 10 VPE vs. current Ifree VPL and proposed Ifree VPL.

5.2. VPL verification

To verify the proposed Ifree VPL, we analyze two verification scenarios.In the first scenario,simulated VPE is used to prove the correctness of the algorithm proposed in Section 3,and the second scenario uses the true VPE from the test described in Section 5.1. The Ifree VPLs with and without IFB residual uncertainty are calculated and compared with the VPE.

The results of these two verification scenarios are shown in Fig.10.The black points are the VPEs during the test.The red curve is the current Ifree VPL without considering IFB residual uncertainty, and the blue curve is the proposed Ifree VPL with IFB residual uncertainty. Fig. 10(a) shows the simulated VPE assuming that there are no IFB residuals. All VPE values are far smaller than the current Ifree VPL, and the margin between them is very large. However, when IFB residual errors are added,as shown in Fig.10(b),the variation range of the simulated VPE increases. Although most of the VPE points are still below the current Ifree VPL curve, there are several values the exceeding VPL, which means integrity risk of the system.In contrast,the Ifree VPL with IFB residual uncertainty calculated by the formula described in Section 3,as shown by the blue curve in Fig. 10(b), can mark all simulated VPE points below the VPL curve.The actual test result is similar, as shown in Fig. 10(c). Several VPEs exceed the current VPL, but they are all smaller than the Ifree VPL with IFB residual uncertainty. The results above verify that the Ifree VPL proposed in this paper is able to protect the integrity of dual-frequency GBAS from IFB residual uncertainty. The detailed integrity analysis will be shown in the next section.

For the results in Fig. 10, there are two points to explain.First, the VPL curves in Fig. 10 are very smooth, with almost no mutation or discontinuity.This is because the test duration is limited and there is no change of the satellites that the user and base station can observe simultaneously as mentioned in Section 5.1. In addition, the protection level is a function of satellite geometry and satellite elevation angle, but the positions and elevation angles of the four GEO satellites used remained nearly constant. Thus, the VPL curves only change smoothly and slowly.Another point that needs to be explained is that the case of a relatively large VPE shown in Fig. 10 is mainly affected by multipaths.Fig.8(a)shows that nearly half of the test route passes through urban streets, where the multipath effect is obvious.Moreover,the Ifree smoothed pseudorange combines B1I and B3I measurements,and the noise and multipath error are nearly 3.5 times those of the singlefrequency GBAS, which makes VPE increase significantly.Baseline length will also affect the VPE. Comparing Fig. 9(b)and Fig. 10(c), it is obvious that a smaller VPE corresponds to shorter baseline length. Note that since the ionospheric delay is eliminated,benefiting from Ifree and σionois no longer included in σi, which explains why VPL does not show a correlation with baseline length.

The density distribution histograms of the two types of VPL are shown in Fig. 11, and their variation ranges are shown in Table 2. In the actual test scenario, the minimum and maximum values of VPL without IFB residual uncertainty are 12.0124 m and 14.3660 m, respectively, with a variation range of 2.3536 m. The minimum and maximum values of VPL with IFB residual uncertainty are 17.8778 m and 21.0787 m, respectively, with a variation range of 3.2009 m.The proposed Ifree VPL is approximately 1.48 times the current Ifree VPL and the average difference between them is 6.1415 m (Table 3).

Fig. 11 Density distribution histograms of two kinds of Ifree VPL.

Table 2 Comparison of two kinds of Ifree VPL.

Table 3 Integrity comparison.

5.3. Integrity analysis

This section analyzes the impact of IFB residual uncertainty on the integrity of dual-frequency GBAS. Eq. (28), as derived in Section 3.2, is rewritten as Eq. (31). σtropois so small that it can be ignored in this formula. Meanwhile, σIFB，Gand σIFB，Aare merged and expressed as σIFB.

However, this problem is solved when IFB residual uncertainty is included in the Ifree VPL, as shown in Figs. 12(e)

Fig. 12 Constraints of IFB residual uncertainty on noise and multipath error levels.

Fig. 13 Triangle plots for two scenarios.

Fig.13 shows the triangle plots of VPE vs.VPL of the two scenarios in Section 5.2. MI will occur when the data points are located in the lower right triangle area,which indicates that VPE is larger than VPL. Figs. 13(a) and (c) show that for the current VPL without IFB residual uncertainty, there are three and four data points in the lower right triangle area, and the MI probabilities are 2.4 × 10-4and 3.2 × 10-4, respectively.However,when the IFB residual uncertainty is included in the Ifree VPL, as shown in Figs. 13(b) and (d), all data points are located in the upper left triangle area in both scenarios. There is no MI occurrence in the test now and its probability is back to meet the integrity requirements (due to the limited sample size,we cannot obtain the exact probability of MI).The above analysis proves that the Ifree VPL proposed in this paper can significantly reduce the MI caused by IFB residual uncertainty and better protect the integrity of the dual-frequency GBAS.

6. Conclusions

An Ifree protection level with receiver IFB residual uncertainty is proposed in this paper.It is tested and verified at the Dongying Airport GBAS station and its integrity is analyzed.The test results show that the probability of misleading information is reduced from 3.2×10-4to the required value after the consideration of IFB residual uncertainty. This indicates that the proposed Ifree protection level is able to reduce the integrity risk caused by IFB residual uncertainty and better protect the integrity of dual-frequency GBAS, which provides a reference for the future GAST-F protection level monitoring algorithm.

In addition, due to the multipath effect of the test environment and the geometry of single constellation satellites, the positioning error and protection level are slightly larger in this research. With the completion of Beidou-3 and the improvement of other constellations, the Ifree protection level will be greatly reduced in the future, which will further improve the monitoring performance of dual-frequency GBAS.

7. Data availability statement

The daily DCBs products were retrieved from the FTP (ftp://igs.ign.fr/pub/igs/products/mgex/dcb). The daily GIMs products BUAG are openly accessible via FTP (ftp://pub.iono sphere.cn/product/).

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors would like to thank many people at the National Key Laboratory of CNS/ATM for their advice and interest.The work was carried out with financial support from the National Natural Science Foundation of China (Nos.61871012, 62022012, U1833125, U2033215), the National Key Research and Development Program of China (Nos.2020YFB0505602,2018YFB0505105),the Civil Aviation Security Capacity Building Fund Project,China(Nos.CAAC Contract 2020(123),CAAC Contract 2021(77)),Open Fund Project of Intelligent Operation Key Laboratory of Civil Aviation Airport Group, China (No. KLAGIO20180405), and the Beijing Nova Program of Science and Technology, China (No.Z191100001119134).