A Novel Optimal Robust Adaptive Scheme for Accurate GNSS RTK/INS Tightly Coupled Integration in Urban Environments
Round 1
Reviewer 1 Report
Position, velocity, and attitude information at higher accuracy and better reliability are very important for different communities. A robust adaptive method utilizes the observation information of both systems to optimize the filtering system, overcoming the shortcomings of Kalman filter in complex urban environments. We propose a novel robust adaptive scheme based on a multi-condition decision model suitable for tightly coupled RTK/INS architecture, which can reasonably determine whether the filtering system performs robust estimation or adaptive filtering. The method is novel and the results are solid to support the claimed novelty. Therefore, the paper should meet the caliber of the journal. To further improve the paper, below is my comments:
-The acronym when it first appears should be defined. Please check the paper thoroughly from the abstract to the conclusions.
- Please highlight the contributions in the introduction instead of just stating what has been done in the paper.
- Please provide information in the caption on the system diagram in Figure 1 and also define the acronym. Also, the context in Figure 7 is hard to read. Larger font can be used or the color can be changed to make the context visible.
- The method proposed in this paper in particular for the loosely coupled version is general and can be used in other areas such as integrating the imu with lidar, camera, or onboard sensors. In this case, I hope the author can mention these merits in the method design by including some related works: an automated driving systems data acquisition and analytics platform; hydro-3d: hybrid object detection and tracking for cooperative perception using 3D lidar; yolov5-tassel: detecting tassels in rgb uav imagery with improved yolov5 based on transfer learning; estimation on imu yaw misalignment by fusing information of automotive onboard sensors. In this way, the paper will be more interesting.
- The title of the last section should be Conclusions instead of Discussion. Discussion should be included in the results section.
- For the loosely coupled integration between the GNSS and IMU, some research based on the adaptive Kalman filter is missing in the literature, please consider including them: autonomous vehicle kinematics and dynamics synthesis for sideslip angle estimation based on consensus kalman filter; automated vehicle sideslip angle estimation considering signal measurement characteristic; imu-based automated vehicle body sideslip angle and attitude estimation aided by gnss using parallel adaptive kalman filters; vision‐aided intelligent vehicle sideslip angle estimation based on a dynamic model.
-Also, I have a suggestion about the drawing of the figure. The lines in the figures of results should be differentiated by not only the color but also the line types.
Author Response
Response to Reviewer 1 Comments
Position, velocity, and attitude information at higher accuracy and better reliability are very important for different communities. A robust adaptive method utilizes the observation information of both systems to optimize the filtering system, overcoming the shortcomings of Kalman filter in complex urban environments. We propose a novel robust adaptive scheme based on a multi-condition decision model suitable for tightly coupled RTK/INS architecture, which can reasonably determine whether the filtering system performs robust estimation or adaptive filtering. The method is novel and the results are solid to support the claimed novelty. Therefore, the paper should meet the caliber of the journal. To further improve the paper, below is my comments:
Comment 1: The acronym when it first appears should be defined. Please check the paper thoroughly from the abstract to the conclusions.
Response 1: Thank you very much for your comments. We have checked the entire manuscript for acronyms and made corresponding modifications. It has been highlighted in yellow in the manuscript.
Comment 2: Please highlight the contributions in the introduction instead of just stating what has been done in the paper.
Response 2: Thank you very much for your comments. We have revised the relevant statements in the introduction to highlight our contribution more. Yellow highlighted in manuscript.
Comment 3: Please provide information in the caption on the system diagram in Figure 1 and also define the acronym. Also, the context in Figure 7 is hard to read. Larger font can be used or the color can be changed to make the context visible.
Response 3: Thank you very much for your comments. We have added a more detailed and necessary description to Figure 1, while also modifying the issue of acronyms. Highlighted in yellow in the manuscript. In Figure 7, we have adjusted the font size and color to make the context visible.
Comment 4: The method proposed in this paper in particular for the loosely coupled version is general and can be used in other areas such as integrating the imu with lidar, camera, or onboard sensors. In this case, I hope the author can mention these merits in the method design by including some related works: an automated driving systems data acquisition and analytics platform; hydro-3d: hybrid object detection and tracking for cooperative perception using 3D lidar; yolov5-tassel: detecting tassels in rgb uav imagery with improved yolov5 based on transfer learning; estimation on imu yaw misalignment by fusing information of automotive onboard sensors. In this way, the paper will be more interesting.
Response 4: Thanks for your recommendations, the referred references enriched our literature review. We have integrated the referred references in our revised manuscript. Yellow highlighted in manuscript.
Comment 5: The title of the last section should be Conclusions instead of Discussion. Discussion should be included in the results section.
Response 5: Thank you very much for your comments. We have adjusted the title of the last section and added a Discussion section.
Comment 6: For the loosely coupled integration between the GNSS and IMU, some research based on the adaptive Kalman filter is missing in the literature, please consider including them: autonomous vehicle kinematics and dynamics synthesis for sideslip angle estimation based on consensus kalman filter; automated vehicle sideslip angle estimation considering signal measurement characteristic; imu-based automated vehicle body sideslip angle and attitude estimation aided by gnss using parallel adaptive kalman filters; vision‐aided intelligent vehicle sideslip angle estimation based on a dynamic model.
Response 6: Thanks for your recommendations, the referred references enriched our literature review. We have integrated the referred references in our revised manuscript. Yellow highlighted in manuscript.
Comment 7: Also, I have a suggestion about the drawing of the figure. The lines in the figures of results should be differentiated by not only the color but also the line types.
Response 7: Thank you very much for your comments. We have updated Figure 10 to distinguish between different line types and adjusted the color scheme to maintain a consistent and aesthetically pleasing overall style of the manuscript.
Author Response File: 
Author Response.docx
Reviewer 2 Report
1. Regarding the Tokyo dataset, it is necessary for the authors to provide further details on whether the IMU mounting angles and lever arm were calibrated in advance and the reasonable of using NHC constraint.
2. It is recommend the authors to add unit to Figure 2 and Figure 9 to ensure readability and accuracy of the figures.
3. Regarding Figure 10, Figure 11, and Figure 12, I suggest the authors refer to the Figure 8 and use the same x-axis for these figures. This will enhance the consistency and comparability of the figures, enabling readers to easily compare and analyze the data. Furthermore, for Figure 1 and Figure 6, the color scheme appears somewhat abrupt. I recommend the authors consider making adjustments to maintain visual consistency throughout the paper.
4. In sections 3.1 and 3.2, it is important to discuss the differences between the proposed approach and the existing M-M model(Yang 2006) in detail. It is necessary to identify and highlight the specific disparities and conduct a comparative analysis with the existing research. This will help readers better understand the novelty and distinctiveness of your study.
5. In section 3.3.2, where it is mentioned that "some literature points out that the threshold is set to 75%", it is recommend the authors add specific references to support this statement.
Moderate editing of English language required
Author Response
Response to Reviewer 2 Comments
The manuscript presents a high level of originality. Testing the applicability of low-cost GNSS receivers plays an important role nowadays. Especially, using low-cost GNSS receivers for contemporary navigation and positioning is a vibrant topic, which the authors have proved. Both the article's structure, as well as its language, are exemplary. The text is comprehensively written, and the methods are presented fairly and understandably. Nevertheless, while reading the text, I spotted some minor ambiguities, which would need explanations before publishing.
Comment 1: Regarding the Tokyo dataset, it is necessary for the authors to provide further details on whether the IMU mounting angles and lever arm were calibrated in advance and the reasonable of using NHC constraint.
Response 1: Thank you very much for your comments. For this set of open-source data, the lever arm value was set to [0, 0, 0,] during processing, and the IMU mounting angles was not considered. These errors will be directly reflected in the final positioning error, which is also one of the factors causing significant positioning errors in the test results. We have added relevant descriptions in the manuscript and highlighted them in blue. In different solutions, we use the same lever arm and mounting angles. This set of open-source data is very valuable and our main goal is to reflect the limitations of the loosely coupled solution and complement the second set of experiments.
Comment 2: It is recommend the authors to add unit to Figure 2 and Figure 9 to ensure readability and accuracy of the figures.
Response 2: Thank you very much for your comments. We have updated Figures 2 and Figure 9. Highlighted in blue in the manuscript.
Comment 3: Regarding Figure 10, Figure 11, and Figure 12, I suggest the authors refer to the Figure 8 and use the same x-axis for these figures. This will enhance the consistency and comparability of the figures, enabling readers to easily compare and analyze the data. Furthermore, for Figure 1 and Figure 6, the color scheme appears somewhat abrupt. I recommend the authors consider making adjustments to maintain visual consistency throughout the paper.
Response 3: Thank you very much for your comments. We have updated Figures 1, 6, and 10 to maintain a consistent and aesthetically pleasing overall style of the manuscript
Comment 4: In sections 3.1 and 3.2, it is important to discuss the differences between the proposed approach and the existing M-M model (Yang 2006) in detail. It is necessary to identify and highlight the specific disparities and conduct a comparative analysis with the existing research. This will help readers better understand the novelty and distinctiveness of your study.
Response 4: Thank you very much for your comments. The main contribution of this manuscript is to propose a multi-condition decision model to correctly judge whether to implement robust estimation or adaptive filter, and to propose a dual-factors robust estimation for the different random characteristics of double-differenced carrier phase and double-differenced pseudo range in RTK/INS tight coupling integration, which essentially still meet Yang's M-M model.
Comment 5: In section 3.3.2, where it is mentioned that "some literature points out that the threshold is set to 75%", it is recommend the authors add specific references to support this statement.
Response 5: Thank you very much for your comments. We have added literature supporting this empirical threshold. Highlighted in blue in the manuscript.
Author Response File: Author Response.docx
Reviewer 3 Report
Aiming at the shortcomings of Kalman filter in complex urban environment, a robust adaptive filter scheme based on multi-condition decision is proposed in this paper. The scheme performs robust and adaptive filtering through automatic adjustment of different decision conditions, and adopts two-factor robust filtering which takes into account ambiguity variance. In this paper, the proposed algorithm is tested by two sets of vehicle-mounted experiments, and it is verified that it can improve the positioning accuracy of the integrated system. However, the method is described unclearly, with some incorrect expressions. In addition, more detailed analysis and comparison should be made to verify the effectiveness of the proposed method. So, this paper needs major revision before it can be published.
Comments to the Author:
1. Lines 220-221, the standardized residual in Formula 5 is incorrectly described.
2. Line 230, Why c2 is less than c1 is not explained in detail in formula 6.
3. Lines 238-240, How to set n in formula 7 is not explained in detail, and why is the variance of the single-differenced ambiguity set to 30 when the variance of the observation residual is larger than the threshold.
4. Does formula 10 customized? And when α is 0, formula 14 will be singular, how to deal with it?
5. This article does not cover the threshold setting in Step 13 in Algorithm 1 in Section 3.3.3.
6. The header of table 7 is wrong.
7. In this paper, TCAKF, TCRKF and the proposed method are compared by vehicle-mounted experiment. I suggest but do not insist that some analysis can be added to the experimental part, such as whether the strategy proposed in this paper makes a correct choice for the filtering method in the abnormal period of the system.
none
Author Response
Response to Reviewer 3 Comments
Aiming at the shortcomings of Kalman filter in complex urban environment, a robust adaptive filter scheme based on multi-condition decision is proposed in this paper. The scheme performs robust and adaptive filtering through automatic adjustment of different decision conditions, and adopts two-factor robust filtering which takes into account ambiguity variance. In this paper, the proposed algorithm is tested by two sets of vehicle-mounted experiments, and it is verified that it can improve the positioning accuracy of the integrated system. However, the method is described unclearly, with some incorrect expressions. In addition, more detailed analysis and comparison should be made to verify the effectiveness of the proposed method. So, this paper needs major revision before it can be published.
Comment 1: Lines 220-221, the standardized residual in Formula 5 is incorrectly described.
Response: Thank you very much for your comments. We have updated the description and highlighted it in blue in the manuscript.
Comment 2: Line 230, Why c2 is less than c1 is not explained in detail in formula 6.
Response: Thank you very much for your comments. The RTK pseudo-range double-differenced and carrier phase double-differenced have different random characteristics, so the normalization innovation of calculation also has different accidental characteristics. From the vertical coordinates of Figure 2, it can be seen that the normalization innovation of pseudo-range double-differenced is smaller than that of carrier phase double-differenced, which is the reason why c2 is set smaller than c1 when setting the empirical threshold. We have provided a detailed and necessary explanation for the size of the experience threshold setting, which has been highlighted in blue in the manuscript.
Comment 3: Lines 238-240, How to set n in formula 7 is not explained in detail, and why is the variance of the single-differenced ambiguity set to 30 when the variance of the observation residual is larger than the threshold.
Response: Thank you very much for your comments. Both n and 30 are the empirical threshold obtained by debugging the robust adaptive program, which provides a reference for the same model of multi-sensor integrated modules and provides debugging direction for different models of modules.
Comment 4: Does formula 10 customized? And when α is 0, formula 14 will be singular, how to deal with it?
Response: Thank you very much for your comments. Yes, Formula 10 is customized, and we have added its source. Highlighted in blue in the manuscript. The adaptive factor model includes two segment function, three segment function and exponential function model. Three segment function model used in the manuscript. When α is 0, the standard Kalman filter will degenerate into a special form of the least square solution. We have added relevant introductions to the manuscript and highlighted in blue.
Comment 5: This article does not cover the threshold setting in Step 13 in Algorithm 1 in Section 3.3.3.
Response: Thank you very much for your comments. Step 13 in Algorithm 1 is the condition for determining the outage time of GNSS, which is effective and easy to code but simple. We have added relevant descriptions in Section 3.3.3 and highlighted them in blue in the manuscript.
Comment 6: The header of table 7 is wrong.
Response: Thank you very much for your comments. We have reviewed the manuscript and you should have pointed out that the title of our Table 2 is wrong. Thank you for your comment. We have corrected the title of Table 2.
Comment 7: In this paper, TCAKF, TCRKF and the proposed method are compared by vehicle-mounted experiment. I suggest but do not insist that some analysis can be added to the experimental part, such as whether the strategy proposed in this paper makes a correct choice for the filtering method in the abnormal period of the system.
Response: Thank you very much for your comments. We have added relevant analysis in the experimental section and descriptions in the Discussion section, which have been highlighted in blue in the manuscript.
Author Response File: Author Response.docx
Round 2
Reviewer 3 Report
no comments
