Multi-Node Motion Estimation Method Based on B-Spline of Array Position and Orientation System

Round 1

Reviewer 1 Report

A multi-node motion estimation method for array POS based on B-spline is proposed to realize motion estimation for node without sub-IMU in the article. The semi-physical experiments based on ground loading test are conducted. and the results verified that this estimation method could improve the estimation accuracy of baseline and the roll angle. However, some minor errors should be revised in the further version.

Major comments:

1. The paper should be revised carefully. The formulas and the symbols must be uniform throughout the article. In general, the description of abbreviations and symbols should be given first. 

2. The description about the experiment process should be improved. There is little information available about the experiment process in this article except the load weight. And the data using different methods at different processes should be briefly introduced.

3. In general, the accuracy of the position, velocity, and attitude are the evaluation indicators for the position and orientation system. However, the experiment results only show the accuracy of baseline and roll angle in this paper. Please add some descriptions about other evaluation indicators. 

Specific comments:

1．Equation (14): There is no description of identifiers H and L. H is the measurement matrix in equation (5). It should be better to use different symbols to represent different meanings.

2. Equation (35) and Equation (36): There is an extra comma with the last element of the matrix. 

3. Figure 3: The node vector in figure 3 is different from that of equation (19). The control vertices in figure 3 is also different from that of equation (35). Please confirmed that which is correct.                                                                                

4. Section 4: There is only a limited description of the experimental process, and there is little useful information expect for the weight of the load. Please give more information about them. 

5. Figure 4 (c) should be replaced with a clearer one.

There are some minor mistakes in the grammar, and minor editing of English language is required for this manuscript.

Author Response

The authors thank the reviewer for the valuable comments on the manuscript. The manuscript is revised according to the reviewer’s suggestions. Please refer to the attachment for detailed modification

Author Response File: Author Response.docx

Reviewer 2 Report

A motion estimation method for s Array Position and Orientation System based on B-spline is proposed in this paper, which can realize infinite motion compensation with limited sub-IMU by fully utilized of the space-time characteristics of each interpolation point. The algorithm is derived and the simulation experiments based on ground loading test is carried out. The experiment results show that this algorithm have a superior performance compared to other algorithms. In addition, in my opinion, the description of the methodologies for conducting experiments and the design of the results obtained are not so clear. The work should be better disposed and justified in the context of other contributions, and its originality was better emphasized. I suggest a few proposals for improvement (see below).

1.In this paper, the conclusion shows that the Estimation method Based On B-Spline for array POS have a superior performance compared to other algorithms. But the simulation results only show the accuracy of the baseline and the roll angle. How about the heading and pitch angle? 

2. We can infer from the article that the array POS is mainly used in the field of aerial remote sensing, but the simulation experiment in this paper is based on ground loading test. Simulation results based on real flight test may be more persuasive. 

3. The mathmatical writting including the formulas and the symbols should be uniform. And there are some minor mistakes in the grammar of the paper. The author should revise the paper carefully.

4.    Line 193-194: “As mentioned above, the repeatability of the first and last nodes of the B-spline function is 6. ”Is the repeatability of the first and last nodes of the B-spline function 6? The repeatability of the first and last nodes derived from equation (20) is 4. It is must be confirmed.                                                                     5.  In section 4, there is a lack of explanation of experimental Process. And why the authors did these various experiments should be provided.

1.  Line 14-15: The authors should pay attention to writing format. For example, why are the first letter of many words in line 14 and 15 capitalized?

 2. Line 120: “The mathematical model of the transfer alignment is established on the basis of the inertial navigation system error equation [], which is not repeated here. ”What is the meaning of the symbol “[]”?

Author Response

The authors thank the reviewer for the valuable comments on the manuscript. The manuscript is revised according to the reviewer’s suggestions. Please refer to the attachment for detailed modification.

Author Response File: Author Response.docx

Reviewer 3 Report

This paper proposes a multi-node motion estimation method based on B-Spline of Array Position and Orientation System to realize remote sensing load motion compensation without sub-IMU. A transfer alignment method based on fiber grating multi-dimensional deformation measurement was adopted, making full use of the spacetime characteristics of each interpolation point. The motion information of the main POS and all sub-IMUs are matched using a B-Spline-based estimation method, so that the spatial correlation between the information of each node is fully exploited.

I must congratulate the Authors that the summary of the work interested me enough to somewhat force me to realize the review despite the lack of time . The work does not raise any major doubts on the editorial and content side, although in the second aspect I admit that it is partly beyond the scope of my interest, making the overall assessment difficult.

Despite the fact that the work is quite extensive, I am unsatisfied by the introduction and the number of literature items cited. Sections 2 and 3 presenting the Composition and Mathematical Model of array POS and B-Spline fusion model, respectively, are very extensive. They are characterized by quite careful development of formulas and illustrations. Experimental and analytical results are presented in Section 4. It is advisable to at least slightly expand the Conclusions section.

Despite the diligence of the study, the Authors were not spared from editing errors:

The mathematical model of the transfer alignment is established on the basis of the inertial navigation system error equation [], which is not repeated here. The state equation 120 - [ ] - ?

the system noise matrix as shown in equation (3).w(t) is the system noise driving matrix, 124 - (3). -> Through w(t) marked

Observation equation of main POS; 140 -> Observation equation of main POS:

equation (6). v is the measurement 146 -> By v is denoted...

• Observation equation of sub-IMU; 157 -> • Observation equation of sub-IMU:

Table 1
Accelerometer bias of main POS 20ug - micro g?

Lines 296-308 - different font size

by31.25%, 27.08%, and 28.07% respectively than that obtained by the transfer alignment , 334 -> by 31.25%, 27.08%, and 28.07% respectively than that obtained by the transfer alignment, 334

Author Response

The authors thank the reviewer for the valuable comments on the manuscript. The manuscript is revised according to the reviewer’s suggestions. Please refer to the attachment for detailed modification.

Author Response File: Author Response.docx