Discrete-Time Incremental Backstepping Control with Extended Kalman Filter for UAVs
Round 1
Reviewer 1 Report
Please find them in the attached PDF.
Comments for author File: 
Comments.pdf
The paper is badly written in terms of common English usage and style found on scientific literature. It also shows that inadequate time has been given for reviewing before submitting it, given the many references that have not been correctly given in the text, which made the review almost impossible.
Author Response
Thank you for your comments. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have carefully studied the comments and respond to your comments as follows:
- Response: Thanks for your advice. English is not my native language, so I can't express myself well in English when I write. However, We have made a detailed check and asked someone who is good at English to help us make modifications. See the attachment for details.
- Response: The image is correctly referenced in the version we uploaded, but may be incorrectly referenced due to software version or other reasons. We have modified the reference of the picture, please see the attachment for the modified content
- ”The mathematical symbols in the text are being rendered different than in the equations above.”
Response: Thank you very much for your suggestion. We have supplemented the definition of some parameters in the Equations from lines 127 to 131 and deleted the definition of some unused parameters. The detailed modification can be seen in lines 132 to 141 of the paper.
- “Loose statement? You should introduce to the reader why the following assumptions are needed.”
Response: We introduce Ref. [35] to prove the rationality of assumption 1. In Ref. [35], a detailed explanation is given as to why this assumption was made. We included a quote in Line 145 of the article.
Author Response File: Author Response.pdf
Reviewer 2 Report
The paper reports how to apply EKF to DTIBS. The progress from Ref.7 can be admitted. However, there are some correction points in the paper as follows.
1) Figure reference notations are unlinked as indicated by "Error! Reference...".
2) In the abstract and the introduction, you wrote the target in your paper is small unmanned aerial vehicle. You should desribe the definition of small at your target.
3) Describe the response speed of the acuator. In Fig.2, it seems the acuator works at moment.
4) Descirbe why your simulation conditions are enought to your control algorithm.
Author Response
Big thanks for your kindly suggestions and sufficient patience! Your suggestions are of great significance for us to improve the paper, and we have made modifications to your suggestions as follows:
- “Figure reference notations are unlinked as indicated by "Error! Reference...". ”
Response: The image reference is correct in the version we uploaded. It may be due to the software version or other reasons that the image reference is wrong. We have carefully checked the article and revised the places where the quotation errors occurred. Please see the attachment for details of the modifications.
2.” In the abstract and the introduction, you wrote the target in your paper is small unmanned aerial vehicle. You should desribe the definition of small at your target.”
Response: In Section 2, we have explained that the research plant is a small UAV, and the parameters of the UAV are added in the appendix. The changes are shown on Line 120.
- “Describe the response speed of the acuator. In Fig.2, it seems the acuator works at moment.”
Response: Thanks for your suggestion, which is very important to improve our paper. We added the figure that the response of the actuator in the article, as shown in Figure 5 (Line 490, Page 16), and carried out a simple analysis of it.
- “Descirbe why your simulation conditions are enought to your control algorithm.”
Response: In the sumulation test, we have set a series of step signal in the control commands to test the tracking performance of the controller, including rapidity and accuracy. We have set the parameter changes, which is equivalent to disturbance. It can verify the anti-interference ability of the controller. The addition of noise have simulated the real environment, and the filtering effect of EKF can be tested.
Author Response File: Author Response.pdf
Reviewer 3 Report
The contribution presented in this paper, titled "Discrete-Time Incremental Backstepping Control with 2 Extended Kalman Filter for UAVs," is of great importance in the field of drones. This document highlights an innovative control approach based on the incremental backstepping method and the use of two extended Kalman filters in a discrete framework. The mathematical aspect of this contribution is particularly developed, providing a solid foundation for understanding and applying the proposed method. The authors demonstrate in detail the equations, models, and algorithms used, ensuring the scientific rigor of their approach. Readers interested in technical and mathematical aspects will find a wealth of valuable information in this paper. Furthermore, this paper stands out for its variety of results. The authors present thorough simulations and experiments to validate the efficiency and robustness of their control approach. The performance of the proposed control system is compared to other existing methods, highlighting the advantages and significant improvements brought by this new approach.
Author Response
Thank you very much for your approval of our paper.
Author Response File: Author Response.pdf
Reviewer 4 Report
This work aims to use the DTIBS control method with EKF to solve the problem of closed-loop flight state estimation of small UAVs under strong noise conditions. Although this work has been evaluated, I wrote some comments for better improvement, which should be addressed for possible acceptance in this journal.
- The authors need to illustrate clear problem formulation.
- Assumption 1 needs to be clearer.
- The authors need to write understandable steps for DTIBS Controller with EKF.
- More clarification is required for Eq (12). All elements of this matrix need to be inserted in the appendix.
- Eq (13) is not clear.
Author Response
Thank you for your advice to us. We have carefully considered the suggestion of Reviewer and make some changes. We have tried our best to improve and made some changes in the manuscript. The following are our modifications to the paper.
- “The authors need to illustrate clear problem formulation.”
Response: In the part of the problem formulation, we clearly stated that our controlled plant is a small UAV, and put the parameter table in the appendix. We have added it on Line 121, Page 3.
- “Assumption 1 needs to be clearer.”
Response: In this paper, we cited Ref. [35] to explain the rationality of assumption 1. In Ref. [35], Lee et al. have explained in detail why can make this assumption. See Line 145 for the detailed modification.
- “The authors need to write understandable steps for DTIBS Controller with EKF.”
Response: We input the drone state estimate from the EKF into the controller. In Section 3.2, we have explained the connection between EKF and DTIBS, with specific modifications on Line 243, Page 7.
- “More clarification is required for Eq (12). All elements of this matrix need to be inserted in the appendix.”
Response: Thanks for your suggestion. We have carefully checked Eq. 12, whose parameters have been defined in Section 2, so we have not defined them here.
- “Eq (13) is not clear.”
Response: The discrete time in Eq. 13 is defined on Line 191. The continuous control input matrix is described in Eq. 14.
Author Response File: Author Response.pdf
Reviewer 5 Report
The paper is good written, all variables and constants are good explained. The calculations presented, for the UAVs are based on a well-known backstepping method. It is true that in this case the calculations are and the presented conclusions of the simulations can provide some value. Moreover, the system is linearized at the operating point (linearization by means of a Taylor series), which results in a high sensitivity of a change of this point (which is understandable in the case of moving the object under consideration), and consequently this implies stability problems. A good solution is linearization through the use of Lie derivatives of vector fields, which is not affected by the operating point (see for example Isidori, Nonlinear Control, Springer or Marino, Tomai, Nonlinear Control Design). Without the support of experimental studies, the presented work cannot be considered of full value both scientifically and applications points.
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Author Response
Thank you very much for your advice. Our response to the comments is as follows:
Response: As we know, the backstepping control method is a feedback linearization method with the Lie derivative. Linearization of EKF is using a Taylor series, not Lie derivatives of vector fields. Although the linearization results are not as accurate as the Lie derivative, the EKF is used to filter out noise and error. It is means that the effect of Taylor expansion on the EKF is less. Moreover, the Lie derivative often requires an accurate mathematical model. Unfortunately, the matematical model of UAVs is usually not accurate enough. If we use the Lie derivative to linearize the states of uncertain dynamic system, it may cause some problems, resulting in poor filtering effect of the EKF.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Equations (3), (10), (12), (14) and (15) need to be fixed, since the delimiters [], { are not being rendered properly. I suspect this is due to the typesetting software used.
Reviewer 4 Report
Thanks to the authors for their feedback.
The work has improved.
Reviewer 5 Report
No comments.
