A Multi-GNSS/IMU Data Fusion Algorithm Based on the Mixed Norms for Land Vehicle Applications

Round 1

Reviewer 1 Report

All necessary changes and queries are pointed out in the pdf file.

Comments for author File: Comments.pdf

Author Response

RESPONSE TO THE REVIEWER:

 

Dear Reviewer:

Thank you very much for your comments and suggestions concerning our manuscript entitled “A Multi-GNSS/IMU Data Fusion Algorithm Based on the Mixed Norms for Land Vehicle Applications”. These comments and suggestions are all very helpful and important for revising and improving this manuscript. We have studied these comments and suggestions carefully and have made many corrections. Revised portion are marked in the revised manuscript. The main corrections and replies to your comments are as follows:

Main comments and replies:

• Too many errors are done with this strangely writing format.

Reply: Thank you very much for reminding. These errors are mainly caused by the change of the margins. We have checked the whole manuscript, and the spelling and format errors are corrected. Please see the detailed corrections in the revised manuscript.

• Did the “……multiple GNSS measurements” mean multiple GNSS constellation?

Reply: Thank you very much for your comment. The sentence has been changed into “……to receive the signals of multiple GNSS constellations”.

• Do not use its abbreviation when it is used for the first time.

Reply: Thank you very much for your comment. “IE” means “Inertial Explorer”, and we have checked and modified all the abbreviations of this manuscript. Please see the detailed corrections in the revised manuscript.

• Why Pz was not estimated? Despite that, Fig 3-6, show the Pz components.

Reply: Thank you very much for your comment. Pz and Vz are added into the related Tables. Please see the detailed corrections in the revised manuscript.

 

Dear reviewer, thank you very much for your warm work earnestly, we have checked the whole manuscript and modified the corresponding sections, and we hope that the corrections will meet with approval. Once again, thank you for your comments and suggestions. Please don’t hesitate to contact us if you have any questions. We look forward to your information about our revised paper.

Yours sincerely,

Chen Jiang

Author Response File: Author Response.docx

Reviewer 2 Report

1) Abbreviations in the text are not taken care of.

2) “…in military, airline, vehicle, robots et al.” This sentence should be rewritten.

3) Real world experiments should also be applied. Land vehicle images and sensor information should be explained graphically.

4) Only individual and fusion state estimates were compared. The fact that the fusion is more successful proves that the method works. But the results can be compared using another filter that uses the same data. For example, the particle filter.

5) Actual values and predicted state values should be plotted.

6) Related Works is insufficient. Previous studies fusing with similar state estimation filters should be discussed. For example, the following study can be used

https://doi.org/10.1016/j.measurement.2020.107704

Author Response

RESPONSE TO THE REVIEWER:

 

Dear Reviewer:

Thank you very much for your comments and suggestions concerning our manuscript entitled “A Multi-GNSS/IMU Data Fusion Algorithm Based on the Mixed Norms for Land Vehicle Applications”. These comments and suggestions are all very helpful and important for revising and improving this manuscript. We have studied these comments and suggestions carefully and have made many corrections. Revised portion are marked in red in the revised manuscript. The main corrections and replies to your comments are as follows:

Main comments and replies:

• Abbreviations in the text are not taken care of.

Reply: Thank you very much for your comment. We have checked and modified the abbreviations in this manuscript, and the full name of these abbreviations are provided when they are used for the first time. Please see the detailed corrections in the revised manuscript.

• “…in military, airline, vehicle, robots et al.” This sentence should be rewritten.

Reply: Thank you very much for your comment and this sentence has been modified as “…and it has been widely applied in the navigation of kinematic carriers”.

• Real world experiments should also be applied. Land vehicle images and sensor information should be explained graphically.

Reply: Thank you very much for your comment. The experiments in the initial manuscript are the real world experiments, but we didn’t provide the land vehicle images in the initial manuscript. Therefore, in the revised manuscript, the land vehicle images are provided and the sensor information is explained in the Table. Please see the detailed corrections in the revised manuscript.

• Only individual and fusion state estimates were compared. The fact that the fusion is more successful proves that the method works. But the results can be compared using another filter that uses the same data. For example, the particle filter.

Reply: Thank you very much for your comments. The applications of the particle filter are limited by the problem of particle degradation, and this problem can be improved with the suitable and precise importance density function [1,2]. Therefore, in order to improve the performance of the particle filter, the extended Kalman filter (EKF), the unscented Kalman filter (UKF) and the cubature Kalman filter (CKF) are usually applied to construct the importance density function [3]. Namely, performance of the particle filter may be inferior to that of the CKF, and the particle filter needs a heavy calculation burden. Thus, we didn’t compare the results with the particle filter in the initial manuscript. The figure below depicts the performance of the CKF and the PF algorithms.

[1] Gustafsson F. Particle filter theory and practice with positioning applications[J]. IEEE Aerospace and Electronic Systems Magazine, 2010, 25(7): 53-82.

[2] Doucet A, Godsill S, Andrieu C. On sequential Monte Carlo sampling methods for Bayesian filtering[J]. Statistics and Computing, 2000, 10(3):197-208.

[3] Sun W and Liu J Z. Cooperative navigation method based on the Huber robust cubature fission particle filter[J]. Chinese Journal of Scientific Instrument, 2022, 43(2):166-175.

 

Figure 1. Position errors of the CKF.             Figure 2. Position errors of the PF.

The Table below provides the RMSE of the CKF and the PF algorithms.

Table 1. RMSE of CKF and PF algorithms

Algorithm	Px (m)	PY (m)	Pz (m)
CKF	0.12	0.17	0.15
PF	0.14	0.20	0.19

 

The above figures demonstrate that the error amplitudes of the PF algorithm are a little bigger than those of the CKF algorithm, and the CKF algorithm performs better than the PF algorithm in this experiment of our manuscript. Meanwhile, the RMSE values of the position errors can provide the same conclusion.

• Actual values and predicted state values should be plotted.

Reply: Thank you very much for your comments. In this manuscript, the GNSS double-difference carrier phase results calculated from the commercial IE (Inertial Explorer) software were adopted as the actual values, and they were plotted in Figure 3 of the revised manuscript.

In terms of the predicted state values, there are 15 elements in the state vector, and they are the error variables of the position, the velocity and the attitude of the kinematic carrier and the bias of the accelerometer and the gyroscope. Then the error variables of the position in the predicted state vector, namely, the first three elements of the predicted state vector, are taken as examples and plotted in the revised manuscript. It should be noticed that the errors of the position in the predicted state vector are not the final position errors as plotted in Figures 3-10 in the initial manuscript, and they are just the process variables to calculate the estimates. In the revised manuscript, the position error variables of the predicted state vector of different algorithms are plotted in Figures 4-7. Please see the detailed corrections in the revised manuscript.

• Related Works is insufficient. Previous studies fusing with similar state estimation filters should be discussed. For example, the following study can be used

https://doi.org/10.1016/j.measurement.2020.107704

Reply: Thank you very much for your comments. The previous studies fusing with similar state estimation filters are added into the “Introduction” of the revised manuscript, and the related references are cited and added into the reference list. Please see the detailed corrections in the revised manuscript.

Dear reviewer, thank you very much for your warm work earnestly, we have checked the whole manuscript and modified the corresponding sections, and we hope that the corrections will meet with approval. Once again, thank you for your comments and suggestions. Please don’t hesitate to contact us if you have any questions. We look forward to your information about our revised paper.

Yours sincerely,

Chen Jiang

Author Response File: Author Response.docx

Reviewer 3 Report

The manuscript proposed a mixed norm-based data fusion framework, and the hypothesis test statistics are constructed and adopted based on the chi-square distribution. Also, the land vehicle data collected through the multi-GNSS and the IMU, has been used to corroborate the effectiveness of the proposed algorithm. A comprehensive comparison with the conventional filtering algorithms confirms the performance of the algorithm as well. On the contrary, in literature, this kind of work has never been touched, i.e., the mixed-norm-based data fusion algorithm is rarely discussed. The data fusion algorithm of the GNSS/INS integrated navigation and positioning systems is performed under a certain norm, and the performance of the conventional filtering algorithms is improved only under this fixed and limited frame. With the statement above, I think the contributions, method, and results are well-positioned to be published in the journal. Before publication, I hope the authors can address my following comments.

1. Please highlight the contributions in the introduction. The existing introduction only describes the existing literature, it is better to add a paragraph to emphasize the contributions of the proposed algorithm from the comparative perspective.

2. Please elaborate more on the caption of figure 1. I hope with the caption, the readers can understand the work in this work well.

3. In the latest literature, instead of just fusing the GNSS and imu, researchers have started adding vehicle dynamics or kinematics in the framework, and more model or sensor errors will be included. I suggest authors discuss these kinds of works in the literature as well to highlight the necessity of this work. The following work should be discussed at least: autonomous vehicle kinematics and dynamics synthesis for sideslip angle estimation based on consensus kalman filter; estimation on imu yaw misalignment by fusing information of automotive onboard sensors; automated vehicle sideslip angle estimation considering signal measurement characteristic; improved vehicle localization using on-board sensors and vehicle lateral velocity.

4. The scale of y-axis from Figure 3-figure 10 can be adjusted properly. Much space has not been used in the existing figures. For example in Figure 10, the range of y-axis should only be -0.5-0.5 to enlarge the data points for the readers.

5. It will be interesting if the authors can discuss more on the future work at the end of case studies. Is the work proposed in this paper can be used to fuse more information such as from the camera, and lidar? Please incorporate the following works in the paper：vision‐aided intelligent vehicle sideslip angle estimation based on a dynamic model; automated driving systems data acquisition and processing platform; yolov5-tassel: detecting tassels in rgb uav imagery with improved yolov5 based on transfer learning. Discuss the potential involvement of these different sensors and their benefits. I believe discussing them will improve the interest of more readers significantly.

6. Please add the key technical specifications of the GNSS as well to the paper.

Author Response

RESPONSE TO THE REVIEWER:

 

Dear Reviewer:

Thank you very much for your comments and suggestions concerning our manuscript entitled “A Multi-GNSS/IMU Data Fusion Algorithm Based on the Mixed Norms for Land Vehicle Applications”. These comments and suggestions are all very helpful and important for revising and improving this manuscript. We have studied these comments and suggestions carefully and have made many corrections. Revised portion are marked in red in the revised manuscript. The main corrections and replies to your comments are as follows:

Main comments and replies:

• Please highlight the contributions in the introduction. The existing introduction only describes the existing literature, it is better to add a paragraph to emphasize the contributions of the proposed algorithm from the comparative perspective.

Reply: Thank you very much for your comment. We have organized a new paragraph to highlight the contributions. Please see the detailed corrections in the revised Introduction.

• Please elaborate more on the caption of figure 1. I hope with the caption, the readers can understand the work in this work well.

Reply: Thank you very much for your comment. More description about the proposed algorithm has been supplemented on the caption of figure 1. Please see the detailed corrections in the revised manuscript.

• In the latest literature, instead of just fusing the GNSS and imu, researchers have started adding vehicle dynamics or kinematics in the framework, and more model or sensor errors will be included. I suggest authors discuss these kinds of works in the literature as well to highlight the necessity of this work. The following work should be discussed at least: autonomous vehicle kinematics and dynamics synthesis for sideslip angle estimation based on consensus kalman filter; estimation on imu yaw misalignment by fusing information of automotive onboard sensors; automated vehicle sideslip angle estimation considering signal measurement characteristic; improved vehicle localization using on-board sensors and vehicle lateral velocity.

Reply: Thank you very much for your comment. These related works have been discussed and emphasized in the Introduction of the revised manuscript. Please see the detailed corrections in the revised Introduction.

• The scale of y-axis from Figure 3-figure 10 can be adjusted properly. Much space has not been used in the existing figures. For example in Figure 10, the range of y-axis should only be -0.5-0.5 to enlarge the data points for the readers.

Reply: Thank you very much for your comment. The scale has been adjusted properly according to the amplitudes of the errors.

• It will be interesting if the authors can discuss more on the future work at the end of case studies. Is the work proposed in this paper can be used to fuse more information such as from the camera, and lidar? Please incorporate the following works in the paper：vision‐aided intelligent vehicle sideslip angle estimation based on a dynamic model; automated driving systems data acquisition and processing platform; yolov5-tassel: detecting tassels in rgb uav imagery with improved yolov5 based on transfer learning. Discuss the potential involvement of these different sensors and their benefits. I believe discussing them will improve the interest of more readers significantly.

Reply: Thank you very much for your comments. The corresponding works are incorporated at the end of the case studies. Please see the detailed corrections in the revised manuscript.

• Please add the key technical specifications of the GNSS as well to the paper.

Reply: Thank you very much for your comments. The key technical specifications of the GNSS have been added into the Table 1.

 

Dear reviewer, thank you very much for your warm work earnestly, we have checked the whole manuscript and modified the corresponding sections, and we hope that the corrections will meet with approval. Once again, thank you for your comments and suggestions. Please don’t hesitate to contact us if you have any questions. We look forward to your information about our revised paper.

Yours sincerely

 

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

The authors made the necessary revisions. This article is acceptable.