A Novel Slow-Growing Gross Error Detection Method for GNSS/Accelerometer Integrated Deformation Monitoring Based on State Domain Consistency Theory

Round 1

Reviewer 1 Report

This paper proposed a new GNSS/Accelerometer Integrated filter method to detect the deformation other than traditional Kalman filter method. This method considers the slow-growing Gross Error.  

  The reviewer think this paper is of engineering significance and can be a meaningful alternative method.

 

  Here are two recommendations:

 

  1、A high light of the proposed method is that “it does not need to consider the dimensional change in the observation matrix during the fusion process, which has better applicability to GNSS/accelerometer integrated deformation monitoring.”  I think the authors should explain the true advantages of your method in the engineering senses , i.e. what is the meaning of “better applicability”?  for example, maybe it can reduce calculation? Save time? …etc.

 

  2、In the line 119 the authors proposed that “the AIME-based method must consider the problem of inconsistent observation matrix dimensions due to different sampling rates, which is difficult to solve in complex monitoring environments. “  But In this paper, In the specific steps of the slow-growing gross error detection algorithm(line 215) the authors also use the Kalman filter as step2, so the authors should explain the  complexity between your method and the traditional Kalman filter method.       

 

Author Response

Dear Reviewers:

Thanks you for your letter and for the reviewers’ comments concerning our manuscript ID 1880132 entitled " A Novel Slow-growing Gross Error Detection Method for GNSS/Accelerometer Integrated Deformation Monitoring Based on State Domain Consistency Theory". Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. Revised portion are marked in the manuscript. Please see  the attachment for the main corrections and revisions of the paper and the reply to the reviewer's comments.

                                                  

Author Response File: Author Response.docx

Reviewer 2 Report

A review of “A novel slow-growing gross error detection method for GNSS/accelerometer … “ by Sun et al.

This contribution is on the Kalman filter based gross error detection of GNSS/accelerometer data for integrated deformation monitoring. Although this is indeed an important research topic, the innovation of the contribution is questionable and should therefore be convincingly presented for this contribution to be acceptable for publication.

The authors are apparently not aware of the available DIA theory that is especially suited for the authors’ application, see e.g. [Teunissen: 1989: A recursive slippage test for use in state=space filtering. Manuscripta Geodaetica, 14, 383-390].

The Kalman-filter based DIA-method is a recursive Detection, Identification and Adaptation method for robustifying against both abrupt as well as slow moving model-errors using UMPI (uniformly most powerful invariant)  test statistics. The method has found widespread application, see also the Handbook of GNSS (Chapter 24: Batch and recursive model validation). If the authors believe to have found innovation they should at least compare their approach with the above state-of-the-art method of recursive testing.

Three further points of attention for the authors are:

1.       In their introduction the authors have missed to mention that the area of low-cost GNSS/accelerometers is also an important area of current research, see e.g. [Lapadat et al (2021): Experimental Evaluation of Smartphone Accelerometer and Low-Cost Dual Frequency GNSS Sensors for Deformation Monitoring. Sensors 2021, 21, 7946] and other references on this topic.

2.       The authors claim that Eq (13) is chi-square distributed and (22) approximately chi-square distributed. They should provide proof of their claim.

3.       The authors should check their text for typos (like e.g. ‘NN’)

 

Author Response

Dear Reviewer,

Thanks you for your letter and for the reviewers’ comments concerning our manuscript ID 1880132 entitled " A Novel Slow-growing Gross Error Detection Method for GNSS/Accelerometer Integrated Deformation Monitoring Based on State Domain Consistency Theory". Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. Revised portion are marked in the manuscript. Please see  the attachment for the main corrections and revisions of the paper and the reply to the reviewer's comments.

Author Response File: Author Response.docx

Reviewer 3 Report

This paper introduces the State-domain Robust Autonomous Integrity Monitoring by Extrapolation (SRAIME) method, which exists as State-domain Robust Chi-Square Test Method, for identifying slow-growing gross errors for GNSS/accelerometer integrated deformation monitoring. The method directly performs gross error identification in the state domain, which does not need to consider the dimension change of the observation matrix in gross error detection. The idea is fine and is probably sound. However, the paper also needs major improvement before proceeding with the publications.

1. Line 136: “NN{X;Xk;Pk} s” Formula error and incomplete sentence.

2. Line 150 and Line 160-170: The Kalman filter state equation and corresponding matrices including the system state transition matrix Phi, the noise driving matrix G, and the covariance matrix Q,  seem not correct. How to give the state equation and corresponding matrices of the Kalman filter, the detailed derivation process must be supplemented.

3. Line 222: How to determine m? And what is the specific value of m in this experiment? “Assuming that epoch ?−? has no faults…”, if there is a fault in epoch ?−? (or the first epoch), can the low-growing gross error be judged effectively in this condition?

4. Figure 1 and figure 8 are poor in quality, please redraw.

5. Line 254: “and the processed GNSS displacement and accelerometer raw data were used as input values.” Whether to consider GNSS and accelerometer systematic errors, such as coordinate system deviation. How to set observation noise when using a GNSS/accelerometer combination?

6. Line 297: “a slow-change gross error of 0.0003*(K-20)ns/s was added in the state update process from 110s to 150s.”, If there is only a slow-change error of 0.0003*k can it still be detected effectively by SRAIME or AIME? This is because the use of 0.0003*(K-20) would lead to a mutation outlier generation. And if the error is nonlinear?

7. In Figure 7(b), after the gross error is added, AIME can effectively detect slow-growing errors between 110s- ~120s, but there is no data after ~120s, why?

Author Response

Dear Reviewer,

Thanks you for your letter and for the reviewers’ comments concerning our manuscript ID 1880132 entitled " A Novel Slow-growing Gross Error Detection Method for GNSS/Accelerometer Integrated Deformation Monitoring Based on State Domain Consistency Theory". Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. Revised portion are marked in the manuscript. Please see  the attachment for the main corrections and revisions of the paper and the reply to the reviewer's comments.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

As the revised version has adequately answered the points raised in the review it can now be accepted for publication

Author Response

Dear Reviewers:
Thanks you for  the reviewers' comments concerning our manuscript ID 1880132 entitled " A Novel Slow-growing Gross Error Detection Method for GNSS/Accelerometer Integrated Deformation Monitoring Based on State Domain Consistency Theory". Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. Thank you for accepting this paper for publication.

Reviewer 3 Report

 

Comments for author File: Comments.pdf

Author Response

Dear Reviewer,

Thanks you for  the reviewers’ comments concerning our manuscript ID 1880132 entitled " A Novel Slow-growing Gross Error Detection Method for GNSS/Accelerometer Integrated Deformation Monitoring Based on State Domain Consistency Theory". Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. Revised portion are marked in the manuscript. Please see the attachment for the main corrections and revisions of the paper and the reply to the reviewer's comments.

Author Response File: Author Response.docx