On the Recursive Joint Position and Attitude Determination in Multi-Antenna GNSS Platforms
Round 1
Reviewer 1 Report
The paper presents interesting contribution. I think that results will be interesting for potential readers, but it is necessary to make some corrections and improvement i.e. moderate revision of the paper before acceptance.
Quality of presentation is unsatisfactory and should be corrected. First, the abstract is not informative enough although it is long. The abstract should be rewritten, and important stressed. Now it looks as a part of Introduction (three sentences from the beginning of the Abstract should be removed, …). Also, some parts in Sec. 2, 3 and 4 are written so that they are difficult to follow and the reader gets lost in them. I suggest to authors to rewrite them (maybe to move some parts in appendix or remove unnecessary parts). Finally, in Sec. 6. with title ‘Conclusions and Future Work’ what is describe as future work? Authors should change title to Conclusions and Outlook or better point out about future work.
Minor corrections: Authors should read the text carefully and correct technical deficiencies i.e.
- In Authors affiliation ORCID ID of first (corresponding) author is incorrect; in the text, Fig 5 appears before Fig. 4 and it should be corrected; on page 10, titles Prediction step and Correction step should be subsections; text in Figs. 6 and 7 are too small to be useful; etc, …
Author Response
Please see attached pdf for the review report.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The paper “On the Recursive Joint Position and Attitude Determination in Multi-Antenna GNSS Platforms” is devoted to the development and experimental study of the algorithm for translational and angular motion estimation using a set of navigation signals receivers. The paper can be interesting for specialists in motion determination, but in current form it is unclear in a set of aspects.
Main critical comments:
Why do the authors not include the angular velocity vector of the body in the state vector eq. (3)? In the dynamical model presented in eq. (27) a constant linear velocity is assumed, but the why not a constant angular velocity as well? Now the attitude of the body is considered constant which is quite unnatural for a moving object. Moreover, for robotics applications it is necessary to estimate not only the position, velocity and attitude, but also the angular velocity. It is strongly recommended to include it in the state vector and to add in model (27) attitude kinematics.
The discrete dynamical model in eq. (25) is not in correspondence with eq. (28) and (29). Function “f” does not depend on noise w in eq. (25), so F_w is defined incorrectly. Moreover, it is not described what is “x_(t-1)”. The index “t-1” leads to confusion, it is not appropriately chosen designation for a time step. It is not described what is “delta_t” in eq. (27). In eq. (28) process noise is “Q_t”, but in description is another designation “Q”.
It is unclear how the covariance matrix “Q_y” in eq. (37) and (38) is obtained. More details on the measurement covariance matrix derivation is required. The Fig. 3 demonstrates the blocks of the matrix “Q_y” that correspond to the position, attitude covariance and also cross-correlation between them. But how can the covariance measurement matrix contain the covariance of state vector elements? This leads to a complete misunderstanding of what the authors propose. More comments and explanation is necessary.
The section 5 with experimentation should be significantly improved. All the values algorithm parameters used in proposed algorithm (especially covariance matrices) should be presented in the text. The details on the accuracy of the additional equipment, which output values are considered as reference, should be added. The paper main statement is that the joint estimation has advantages over a separate position and attitude estimation, therefore, a comparison of the accuracy of the two approaches should be presented in the text. Moreover, the authors should show the results of the velocity and integer ambiguities estimation, since it is also included in the state vector.
Some minor comments:
The first statement in Section 3.4 is wrong. For attitude determination it is necessary to have at least three GNSS antennas, there should be two non-collinear baselines between them.
Line 106. It is not clear what is the multiplication formula related to? What are i, j and k?
In matrices in eq. (27), (29), (36), (37) all the empty space should be filled with zeros.
There is a mistake in eq. (31) – instead of transpose sign should be inverse of the expression in commas.
Can you explain the local deviation in roll and pitch angle at about 12:40 at Fig. 7?
The appendix on the Quaternion details is redundant in the paper, since it is well-known information.
Author Response
Please see attached pdf for the review report.
Author Response File: Author Response.pdf
Reviewer 3 Report
see attached file
Comments for author File: Comments.pdf
Author Response
Please see attached pdf for the review report.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors successfully corrected the text according to the requests and suggestions. Now the manuscript is ready for acceptance in Remote Sensing in present form.
Good job guys.
Reviewer 2 Report
The authors carefully addressed almost all the reviewer suggestions. The paper can be accepted for the publication.
