Regional Real-Time between-Satellite Single-Differenced Ionospheric Model Establishing by Multi-GNSS Single-Frequency Observations: Performance Evaluation and PPP Augmentation

Round 1

Reviewer 1 Report

This paper tended to model the ionospheric delay with multi-GNSS single-frequency observations. And to remove the receiver differential code bias, the between-satellite single-differencing operations are adopted. Subsequently, the authors applied the ionospheric modeling results to real-time PPP applications, attempting to improve the positioning accuracy.

The authors have done substantial work. And the pictures in this article are very beautiful and impressive. However, the feasibility and application scenarios of the proposed methods need to be discussed more fully. Therefore, I suggest that the author elaborate more on the significance of the proposed method.

My detailed comments and questions are as follows:

• Is ionospheric-enhanced and ionospheric-constrained same concept? Please confirm this.

• The term "regional between-satellite SD ionospheric-enhanced RT SF-PPP" could be further simplified to improve clarity.

• The organization and logical structure of the section "Introduction" can be further optimized. The first half of the second paragraph (i.e. line 55-68) should be a separate paragraph, describing the superiority of extraction ionospheric delay with UU-PPP. Line 68-86 should be consolidated into one paragraph, describing the necessity of using between-satellite single differece. Subsequently, the innovatoin (such as line 55-58) shoud be summarized.

• Line 200: When the nine estimated coefficients are updated, do you use the data collected from the past 20 miniutes?

• Besides, what means of communication do you plan to use to broadcast the updated parameters? How many kilometers are these parameters valid in the surrounding area? Is such a design feasible for mobile phones or smartwatches, which you have mentioned in the section Introduction? Please clarify.

• As mentioned in the section Introduction, the main purpose of modeling ionospheric delay with single-frequency observations is to help single-frequency devices such as mobile phones to eliminate ionospheric errors. Then, by using the method proposed in this paper, can mobile phone users estimate ionospheric delay independently?

• Moreover, for fixed base stations, does it make sense to use only single-frequency observations in the ionospheric modeling?

• Line 226: The quality of the observations provided by MGEX stations is very high. If real low-cost single-frequency devices were used as user receivers, the test results would be more convincing.

• There are still some English language problem in this version, such line 91, line5, line 224, line 142 (equation ciation error), line 206 and so on. Please carefully proofread the manuscript and fix the existing flaw.

Minor editing of English language required

Author Response

This paper tended to model the ionospheric delay with multi-GNSS single-frequency observations. And to remove the receiver differential code bias, the between-satellite single-differencing operations are adopted. Subsequently, the authors applied the ionospheric modeling results to real-time PPP applications, attempting to improve the positioning accuracy. The authors have done substantial work. And the pictures in this article are very beautiful and impressive. However, the feasibility and application scenarios of the proposed methods need to be discussed more fully. Therefore, I suggest that the author elaborate more on the significance of the proposed method. My detailed comments and questions are as follows:

1. Is ionospheric-enhanced and ionospheric-constrained same concept? Please confirm this.

Reply: thank you for your comments. The terms “ionospheric-enhanced” and “ionospheric-constrained” have the same meaning in this manuscript. To prevent misunderstanding and ambiguity for readers, the term “ionospheric-enhanced” has been removed in the revised manuscript.

2. The term "regional between-satellite SD ionospheric-enhanced RT SF-PPP" could be further simplified to improve clarity.

Reply: thank you for your suggestions. The term “regional between-satellite SD ionospheric-enhanced RT SF-PPP” has been simplified to “SD ionospheric-constrained RT SF-PPP” in the revised manuscript.

3. The organization and logical structure of the section "Introduction" can be further optimized. The first half of the second paragraph (i.e. line 55-68) should be a separate paragraph, describing the superiority of extraction ionospheric delay with UU-PPP. Line 68-86 should be consolidated into one paragraph, describing the necessity of using between-satellite single difference. Subsequently, the innovation (such as line 55-58) should be summarized.

Reply: thank you for your suggestions. The second paragraph of the section “Introduction” has been divided into two paragraphs in the revised manuscript.

4. Line 200: When the nine estimated coefficients are updated, do you use the data collected from the past 20 minutes?

Reply: thank you for your comments. Yes, the observations with the interval of 30 s collected from the past 20 min are used to fit nine estimated coefficients, and this sliding window of observations is set to move forward for 10 min each time. Some descriptions have been added to the revised manuscript as follows:

“The nine estimated coefficients are fitted by the observations with the interval of 30 s collected from the past 20 min, and this sliding window of modeling moves forward for 10 min each time. Thus, all coefficients are updated every 10 min and broadcast to positioning users in real-time.”

5. Besides, what means of communication do you plan to use to broadcast the updated parameters? How many kilometers are these parameters valid in the surrounding area? Is such a design feasible for mobile phones or smartwatches, which you have mentioned in the section Introduction? Please clarify.

Reply: thank you for your comments. These updated parameters can be broadcasted over the internet based on Networked Transport of RTCM via Internet Protocol (NTRIP), similar to the broadcast of IGS SSR corrections.

The service scope of these parameters is directly related to the number and distribution of modeling stations. We have not yet studied the effectiveness of these parameters beyond the coverage range of ionospheric model, and this issue is worth exploring in future research.

In theory, if the mobile phone or smartwatch has ability to receive these ionospheric parameters, the SD ionospheric-constrained RT SF-PPP can be implemented. However, the kinematic RT SF-PPP based on the observations of smart device has not been implemented yet. The focus of the proposed method in this research is to verify whether single frequency observations can be used to construct a high-precision ionospheric model. In fact, the application of this model in practical scenarios still requires a lot of work to be done, which is also the direction and focus of our future research.

6. As mentioned in the section Introduction, the main purpose of modeling ionospheric delay with single-frequency observations is to help single-frequency devices such as mobile phones to eliminate ionospheric errors. Then, by using the method proposed in this paper, can mobile phone users estimate ionospheric delay independently?

Reply: thank you for your comments. Different from the previous ionospheric models like Klobuchar, NeQuick, and GIM, the between-satellite SD ionospheric model cannot provide absolute ionospheric delays of each satellite. Hence, the ionospheric delay of mobile phone users cannot be estimated and eliminated using the SD ionospheric model. In fact, the SD ionospheric delay calculated from the proposed ionospheric model is treated as a virtual observation, which can improve the (re-)converge performance of the UU-PPP through precise ionospheric parameter constraints.

7. Moreover, for fixed base stations, does it make sense to use only single-frequency observations in the ionospheric modeling?

Reply: thank you for your comments. In our study, only single-frequency observations are used to establish the SD ionospheric model. On the one hand, the feasibility of extracting ionospheric observables from the multi-GNSS single-frequency UU-PPP is worth investigating, as it can provide a theoretical basis and data support for constructing low-cost ionospheric models. On the other hand, the method proposed in the paper is fully applicable to constructing ionospheric models using real low-cost single-frequency receivers. In summary, our research objective is to attempt to reduce the hardware cost of ionospheric modeling and provide an effective solution for building high-precision regional ionospheric models only using affordable single-frequency receivers in the future.

8. Line 226: The quality of the observations provided by MGEX stations is very high. If real low-cost single-frequency devices were used as user receivers, the test results would be more convincing.

Reply: thank you for your comments. Although the MGEX observations are used to carry out the SD ionospheric-constrained SF-PPP test, the reference positioning results (i.e., GRAPHIC SF-PPP) are also based on the same data. This fully demonstrates that the proposed SD ionospheric-constrained SF-PPP has better positioning performance, especially in terms of (re-)convergence. On the other hand, this novel method is fully applicable to real low-cost SF-PPP in theory. In our future work, the RT SF-PPP tests using real low-cost single-frequency receivers will be implemented, and this is also an issue that we are very concerned about. Some descriptions have been added to the section “Conclusions” in the revised manuscript as follows:

“To verify the effectiveness of the proposed algorithm on real low-cost SF-PPP users, the truly SF observations collected from the affordable SF devices or chips need to be used for carrying out RT SF-PPP tests in our future research.”

9. There are still some English language problem in this version, such line 91, line5, line 224, line 142 (equation ciation error), line 206 and so on. Please carefully proofread the manuscript and fix the existing flaw.

Reply: thank you very much for your reminder. All English language problem in the original manuscript have been corrected one by one.

Reviewer 2 Report

this manuscript proposed a regional high-precision ionospheric model using low-cost GNSS single-frequency observations. The novel method has made significant contributions to improving the positioning performance of low-cost single-frequency GNSS users, especially in terms of convergence. However, some descriptions and technical details need to be further explained to enhance readability. In summary, the manuscript can be accepted after revision.

 (1) 3.2 Processing strategies. “The weight of observations… 0.3 and 0.003 m”. The quality of RTS orbits and clocks for the BDS IGSO satellite is inferior to other MEO satellites, how to set the weight of observations?

 (2) Table 1. Why did not GLONASS observations be used for multi-GNSS PPP? At present, quad-system (GPS+GLONASS+Galile+BDS) combined positioning technology has developed very maturely.

 (3) Figure 8. Why does the positioning errors start from 03:00:00 instead of 00:00:00?  

(4) Conclusions. When it comes to positioning accuracy, the vertical component of this PPP-enhanced algorithm may be decreased. Please add some improvement measures or outlooks for this proposed method.

Minor editing of English language required

Author Response

This manuscript proposed a regional high-precision ionospheric model using low-cost GNSS single-frequency observations. The novel method has made significant contributions to improving the positioning performance of low-cost single-frequency GNSS users, especially in terms of convergence. However, some descriptions and technical details need to be further explained to enhance readability. In summary, the manuscript can be accepted after revision.

1. 3.2 Processing strategies. “The weight of observations… 0.3 and 0.003 m”. The quality of RTS orbits and clocks for the BDS IGSO satellite is inferior to other MEO satellites, how to set the weight of observations?

Reply: thank you for your comments. Due to the lower accuracy of RTS orbits and clocks for BDS IGSO satellites, the weight of IGSO observations should be reduced to half in comparison with other MEO satellites. The relevant descriptions have been added to the revised manuscript as follows:

“Considering the lower accuracy of SSR orbits and clocks for BDS-3 inclined geosynchronous orbit (IGSO) satellites (i.e., C38-40), the weight of IGSO observations needs to be set as 1/2 of other medium earth orbit (MEO) satellites [24].”

[24] Chen, J.; Wang, J.; Yu, C.; Zhang, Y.; Wang, B. Improving BDS broadcast ephemeris accuracy using ground‑satellite‑link ob-servations. Satellite Navigation 2022, 3, 11.

2. Table 1. Why did not GLONASS observations be used for multi-GNSS PPP? At present, quad-system (GPS+GLONASS+Galile+BDS) combined positioning technology has developed very maturely.

Reply: thank you for your comments. Since the GLONASS satellite-specific IFB (inter-frequency biases) and estimated ionospheric parameters have strong linear correlation in SF UU-PPP, the partial ionospheric delays can be absorbed by IFB parameters. At present, the accuracy of ionospheric observables extracted from GLONASS observations is not ideal, which may affect the quality of the SD ionospheric model. Meanwhile, the available satellites of GPS+BDS-3+Galileo are sufficient for regional SD ionospheric modeling. Therefore, the GLONASS observations are excluded from our study.

3. Figure 8. Why does the positioning errors start from 03:00:00 instead of 00:00:00?

Reply: thank you for your comments. Due to the poor convergence of RT SF-PPP, only the ionospheric observables after 3 h in daily solution are used to build the regional SD ionospheric model. Hence, the SD ionospheric-constrained SF-PPP tests were conducted in the period of 3 h to 24 h.

4. Conclusions. When it comes to positioning accuracy, the vertical component of this PPP-enhanced algorithm may be decreased. Please add some improvement measures or outlooks for this proposed method.

Reply: thank you for your suggestions. Some descriptions have been added to the revised manuscript as follows:

“With the increase of the number of monitoring stations in the region or the improvement of RTS products quality, the spatial-temporal resolution and accuracy of extracted ionospheric observables can be improved, and result in higher accuracy of the SD ionospheric model. As long as the SD ionospheric model is accurate enough, the vertical positioning accuracy of the SD ionospheric-constrained RT SF-PPP can be improved.”

Reviewer 3 Report

Review on the manuscript "Regional Real-Time Between-Satellite Single-Differenced Ionospheric Model Establishing by Multi-GNSS Single-Frequency Observations: Performance Evaluation and PPP Augmentation" submitted by Wang et al. to Remote Sensing

The manuscript summarizes and characterizes the regional real-time between-satellite single-differenced single-frequency multi-GNSS ionospheric model. The approach and results are of interest in opinion of this reviewer, and the next minor points are the only ones found:

1) [Lines 50-52] The authors state than

"Global ionospheric map (GIM) as one of the most accurate ionospheric models at present can provide correction accuracy within 2 total electron content units (TECU), but it cannot support RT positioning [9]."

(...)

[9] Cai, C.; Gong, Y.; Gao, Y.; Kuang, C. An approach to speed up single-frequency PPP convergence with quad-constellation GNSS and GIM. Sensors 2017, 17, 1302.

Why GIMs cannot support RT positioning? The RT-GIMs exists, with accuracies some of them very close to the post-process GIMs (see Liu et al. 2021).

Reference: Liu, Q., Hernández-Pajares, M., Yang, H., Monte-Moreno, E., Roma-Dollase, D., García-Rigo, A., Li, Z., Wang, N., Laurichesse, D., Blot, A. and Zhao, Q., 2021. The cooperative IGS RT-GIMs: A reliable estimation of the global ionospheric electron content distribution in real time. Earth System Science Data, 13(9), pp.4567-4582.

2) [Line 114, carrier phase equations in (1)] and [Line 209, carrier phase equations in (15)]: The carrier phase wind-up is missing. Please introduce it and discuss how it is treated, maybe connecting with the mention you do in the manuscript in line 254.


3) [Line 167, equation (9)] Please justify the usage of 40.28 as the fundamental constant to transform electron content in ionospheric delay, instead of the value of 40.309 in S.I. units provided by the IERS Conventions (see Petit & Luzum eds, 2010, page 138).

Reference: Petit, G. and Luzum, B., 2010. IERS technical note no. 36. IERS conventions, 179 (https://iers-conventions.obspm.fr/content/tn36.pdf)

4) [Lines 173-174] Please justify why are you using the specific value of Hiono = 506.7 km (and not, for instance, Hiono = 450 km such as in IGS community).

5) [Lines 244-247] Why are you using broadcast ephemeris instead of precise ultrarapid (predicted) GNSS orbits, distributed by IGS in real-time?

6) [Line 268] There is a typo here: "Figure 2" should be fixed as "Figure 3".

The English is quite good in my opinion and just a minor check would be needed.

Author Response

The manuscript summarizes and characterizes the regional real-time between-satellite single-differenced single-frequency multi-GNSS ionospheric model. The approach and results are of interest in opinion of this reviewer, and the next minor points are the only ones found:

1. [Lines 50-52] The authors state than "Global ionospheric map (GIM) as one of the most accurate ionospheric models at present can provide correction accuracy within 2 total electron content units (TECU), but it cannot support RT positioning [9]." (...)

[9] Cai, C.; Gong, Y.; Gao, Y.; Kuang, C. An approach to speed up single-frequency PPP convergence with quad-constellation GNSS and GIM. Sensors 2017, 17, 1302.

Why GIMs cannot support RT positioning? The RT-GIMs exists, with accuracies some of them very close to the post-process GIMs (see Liu et al. 2021).

Reference: Liu, Q., Hernández-Pajares, M., Yang, H., Monte-Moreno, E., Roma-Dollase, D., García-Rigo, A., Li, Z., Wang, N., Laurichesse, D., Blot, A. and Zhao, Q., 2021. The cooperative IGS RT-GIMs: A reliable estimation of the global ionospheric electron content distribution in real time. Earth System Science Data, 13(9), pp.4567-4582.

Reply: thank you very much for your recommended literature. Some descriptions of this literature (Liu et al. 2021) have been added to the section “Introduction” in our revised manuscript as follows:

“The post-processed global ionospheric map (GIM) as one of the most accurate ionospheric models can provide correction accuracy within 2 total electron content units (TECU), but it cannot support RT positioning [9]. With the development of the Real-Time Working Group (RTWG) of the International GNSS Service (IGS), an RT-GIM has been provided by some IGS real-time ionosphere centers. The accuracy of RT-GIM is slightly lower than that of post-processed GIM and can reach around 3 TECU [10]. Due to the limited accuracy of the current RT ionospheric models, it is necessary to establish an RT ionospheric model with cm-level accuracy using regional reference networks to improve the performance of RT SF-PPP.”

2. [Line 114, carrier phase equations in (1)] and [Line 209, carrier phase equations in (15)]: The carrier phase wind-up is missing. Please introduce it and discuss how it is treated, maybe connecting with the mention you do in the manuscript in line 254.

Reply: thank you for your suggestions. The term of “carrier phase wind-up” has been added to the Equation (1) and (15) in the revised manuscript. The corresponding correction is adopted by the method of (Wu et al. 1992), and some descriptions have been added to the section “3.2 Processing Strategies” in the revised manuscript as follows: “The phase wind-up is corrected by using the method of literature [26].”

[26] Wu, J.T.; Wu, S.C.; Hajj, G.A.; Bertiger, W.I.; Lichten, S.M. Effects of antenna orientation on GPS carrier phase. In Proceedings of the AAS/AIAA Astrodynamics Conference, Durango, CO, San Diego, CA, 1992, 1647-1660.

3. [Line 167, equation (9)] Please justify the usage of 40.28 as the fundamental constant to transform electron content in ionospheric delay, instead of the value of 40.309 in S.I. units provided by the IERS Conventions (see Petit & Luzum eds, 2010, page 138).

Reference: Petit, G. and Luzum, B., 2010. IERS technical note no. 36. IERS conventions, 179 (https://iers-conventions.obspm.fr/content/tn36.pdf)

Reply: thank you for your reminder and sorry for our mistakes. After careful inspection, the fundamental constant 40.3 was used in our software of ionospheric modeling. A reference cited for this constant is as follows:

[23] Li, Z.; Wang, N.; Hernández-Pajares, M.; Yuan, Y.; Krankowski, A.; Liu, A.; Zha, J.; García-Rigo, A.; Roma-Dollase, D.; Yang, H.; Laurichesse, D.; Blot, A. IGS real-time service for global ionospheric total electron content modeling. J Geod. 2020, 94, 32.

4. [Lines 173-174] Please justify why are you using the specific value of Hiono = 506.7 km (and not, for instance, Hiono = 450 km such as in IGS community).

Reply: thank you for your careful reminder and sorry for our mistakes. After a rigorous examination of the software used in this study, the height of single layer was set as 450 km to be consistent with the IGS GIM model. It has been modified in our revised manuscript.

5. [Lines 244-247] Why are you using broadcast ephemeris instead of precise ultrarapid (predicted) GNSS orbits, distributed by IGS in real-time?

Reply: thank you for your comments. In our study, the real-time precise orbits and clocks are derived from the broadcast ephemeris and CNES SSR orbit and clock corrections. The accuracy of this real-time precise product is significantly better than that of ultrarapid precise product (GBU). Besides, the satellite DCB is also corrected by the CNES SSR code bias corrections. Nowadays, the SSR products provided by the IGS real-time service have been widely used in real-time GNSS processing.

6. [Line 268] There is a typo here: "Figure 2" should be fixed as "Figure 3".

Reply: thank you very much for your reminder. This mistake has been modified in our revised manuscript.

Reviewer 4 Report

1.The topic of the study has certain practical significance, and the background and significance of the research can be elaborated in more detail.

2.What are the principles for selecting the study area and whether the location of the site will affect the conclusions of the study?

Author Response

1.The topic of the study has certain practical significance, and the background and significance of the research can be elaborated in more detail.

Reply: thank you for your suggestions. Some descriptions have been added to the section “Introduction” in our revised manuscript as follows:

“The post-processed global ionospheric map (GIM) as one of the most accurate ionospheric models can provide correction accuracy within 2 total electron content units (TECU), but it cannot support RT positioning [9]. With the development of the Re-al-Time Working Group (RTWG) of the International GNSS Service (IGS), an RT-GIM has been provided by some IGS real-time ionosphere centers. The accuracy of RT-GIM is slightly lower than that of post-processed GIM and can reach around 3 TECU [10]. Due to the limited accuracy of the current RT ionospheric models, it is necessary to establish an RT ionospheric model with cm-level accuracy using regional reference net-works to improve the performance of RT SF-PPP.”

“Due to the presence of hardware bias in retrieved ionospheric observables, it is necessary to simultaneously estimate both satellite and receiver DCB parameters when modeling ionospheric VTEC. The satellite DCB has great long-term stability, so its solution accuracy is high and reliable [15]. Unfortunately, the receiver DCB is easily influenced by various factors such as ambient temperature and hardware alternation, thus its apparent short-term time-varying characteristics can be observed [16-17]. If the receiver DCB as an additional parameter was estimated in UU-PPP, although pure slant ionospheric delays can be obtained [18], the increase in estimated parameters reduces the strength and computational efficiency of the UU-PPP model. Meanwhile, the high-frequency parameterization of receiver DCB will inevitably increase the burden and cost of data transmission, making it difficult to apply to RT ionospheric modeling based on dense reference networks.”

“In summary, this contribution is to attempt to reduce the hardware cost of ionospheric modeling and provide an effective solution for building high-precision regional iono-spheric models only using affordable SF devices or chips in the future.”

2.What are the principles for selecting the study area and whether the location of the site will affect the conclusions of the study?

Reply: thank you for your comments. The selection of the study area is based on the sufficient monitoring stations and uniform distribution. Four user sites used in our study are located in different directions of the ionospheric modeling area (as seen in Figure 1). After comparison, the improvement of performance in the SD ionospheric-constrained SF-PPP can always be observed. Hence, the location of the site has little effect on the results of the study. On the other hand, if more monitoring sites are used in constructing ionospheric model, the accuracy of the SD ionospheric model can be improved with the increasing the spatial resolution of the ionosphere pierce point in theory.