On-Orbit Geometric Calibration and Performance Validation of the GaoFen-14 Stereo Mapping Satellite

Round 1

Reviewer 1 Report

1.           The key load of Line 254, Optical axis position measurement data, hopes to be emphasized in Chapter 2.

2.           Formula (1) The Collinearity equation lacks a scaling coefficient, f can be extracted as the scaling coefficient m. Formulas (3) - (9) have the same problem.

3.           Does "scheme W" mentioned by Line 344 refer to "scheme W1"; Similarly, is the "scheme N1" mentioned by Line 360 written incorrectly, it should be "scheme N2"?

4.           Using an internal curve chart in Table 3 to compare the difference in inter angles solved by several methods would be more intuitive. It is recommended that the author add one.

5.           Is Table 5 missing a description of Pre-calibration?

6.           Comparing and describing Table 6 with a histogram would be more intuitive.

7.           The constant terms of the External calibration model and the internal geometric model in the article are related and will inevitably affect the solving process. How is this correlation resolved?

8.           Chapter 3.2, it is necessary to introduce the differences in the data used for N1 and N2, and the impact this difference will have on the results, as generally comparative experiments need to be conducted under the same data conditions. For example, how to obtain the stitched panoramic image used for N1.

9.           It is best to list the number of calibration control points/checkpoints and their residual plots in the experimental results, rather than just a comprehensive statistic.

10.          Chapter 3.2, is it necessary to add inter ship geometry constraints, as the general site calibration already utilizes absolute site benchmarks, which can constrain the geometric relationship between CCDs.

11.          Assuming that inter ship geometry constraints are abbreviated as C and Optical axis position measurement data is abbreviated as A, the four calibration strategies in the author's article are: Scheme A (W1+N1); Scheme B (W1+N2+C); Scheme C (W2+N1+A); Scheme D (W2+N2+A+C). However, the above four combinations do not support the conclusion of the authors Line 465 – Line 468. Suggest the author to add an experiment: Scheme E (W1+N2); Scheme F (W1+N1+A); Scheme G (W1+N2+A); Scheme H (W1+N2+C+A); Scheme I (W2+N1); Scheme J (W2+N2); Scheme K (W2+N2+C); Scheme L (W2+N2+A). And discuss the impact of independent variables separately according to their categories.

Author Response

1. The key load of Line 254, Optical axis position measurement data, hopes to be emphasized in Chapter 2.

Answer: Optical axis position measurement data is emphasized in Chapter 2. “This device acquires the relative attitude angles of the forward camera and the backward camera with respect to the reference component during the on-orbit photography. The acquisition angles data describes the attitude changes of the imaging cameras.”

2. Formula (1) The Collinearity equation lacks a scaling coefficient, f can be extracted as the scaling coefficient m. Formulas (3) - (9) have the same problem.

Answer: I am very sorry, is added into Formula (1) and Formulas (3) - (9). The external calibration model (8) and the internal geometric model (9) based on inter-chip geometry constraints are developed based on the new formulas. For the image points p₁(x_p1,y_p1) and p₂(x_p2,y_p2), the scaling coefficientare considered to be the same.

 

3. Does "scheme W" mentioned by Line 344 refer to "scheme W1"; Similarly, is the "scheme N1" mentioned by Line 360 written incorrectly, it should be "scheme N2"?

Answer: I am very sorry, it’s my mistake.

"scheme W" mentioned by Line 344 has been corrected as "scheme W1".

"scheme N1" mentioned by Line 360 has been corrected as "scheme N2".

 

4． Using an internal curve chart in Table 3 to compare the difference in inter angles solved by several methods would be more intuitive. It is recommended that the author add one.

Answer:  Two internal curve charts to Table 3 are added to compare the difference in inter angles solved by several methods.

5. Is Table 5 missing a description of Pre-calibration?

Answer:  The description of Pre-calibration in Table 5 is the same as that of Table 4, so the description of Pre-calibration in Table 5 is omitted.

 

6. Comparing and describing Table 6 with a histogram would be more intuitive.

Answer: Histogram comparing and describing Table 6 has been added.

7. The constant terms of the External calibration model and the internal geometric model in the article are related and will inevitably affect the solving process. How is this correlation resolved?

Answer: The constant terms of the External calibration model and the internal geometric model in the article are related, to resolve this correlation the constant terms of the External calibration model and the internal geometric model are solved in iterative process in Figure 3. Thus the External calibration model and the internal geometric model are solved independently.

8. Chapter 3.2, it is necessary to introduce the differences in the data used for N1 and N2, and the impact this difference will have on the results, as generally comparative experiments need to be conducted under the same data conditions. For example, how to obtain the stitched panoramic image used for N1.

Answer: The stitched panoramic image is generated from direct mosaic of multichip images without any geometric transform. Only the left overlapping area is reserved and the right adjacent area is cropped out. Explanation is added.

9. It is best to list the number of calibration control points/checkpoints and their residual plots in the experimental results, rather than just a comprehensive statistic.

Answer: Take 20 Mar. 22nd, 2021 Songshan data for example, residual plots of the experimental results has been added.

10. Chapter 3.2, is it necessary to add inter ship geometry constraints, as the general site calibration already utilizes absolute site benchmarks, which can constrain the geometric relationship between CCDs.

Answer: Although the general site calibration already utilizes absolute site benchmarks, which can constrain the geometric relationship between CCDs, but the geometric relationship between CCDs may change during launch and running in the orbit. Moreover, the inter ship geometry constraints can also be a validation for the camera performance.

11. Assuming that inter ship geometry constraints are abbreviated as C and Optical axis position measurement data is abbreviated as A, the four calibration strategies in the author's article are: Scheme A (W1+N1); Scheme B (W1+N2+C); Scheme C (W2+N1+A); Scheme D (W2+N2+A+C). However, the above four combinations do not support the conclusion of the authors Line 465 – Line 468. Suggest the author to add an experiment: Scheme E (W1+N2); Scheme F (W1+N1+A); Scheme G (W1+N2+A); Scheme H (W1+N2+C+A); Scheme I (W2+N1); Scheme J (W2+N2); Scheme K (W2+N2+C); Scheme L (W2+N2+A). And discuss the impact of independent variables separately according to their categories.

Answer: Thanks for such comprehensive scheme designs, Scheme E (W1+N2); Scheme F (W1+N1+A); Scheme G (W1+N2+A); Scheme H (W1+N2+C+A); Scheme I (W2+N1); Scheme J (W2+N2); Scheme K (W2+N2+C); Scheme L (W2+N2+A).

About Scheme E (W1+N2); Scheme F (W1+N1+A); Scheme G (W1+N2+A); Scheme H (W1+N2+C+A); Scheme I (W2+N1); Scheme J (W2+N2); Scheme K (W2+N2+C); Scheme L (W2+N2+A), I have figured out a Table and make comparison among them.

 

In GaoFen-14 satellite calibration, some schemes among Scheme A to Scheme L are adopted in the experiment. But for GaoFen-14 satellite has a very stable geometry relationship, so some schemes don’t exhibit evident differences from other schemes. But we can make a full explanation in combination with our prevision calibration experiences with TH-1 and ZY-3 satellite. Moreover, explanation is also given on the property of GaoFen-14 satellite.

 

Firstly, the condition “C” is designed to ensure the integrity the stitched long CCD. If there exists great displacement among various CCD chips, condition “C” can ensure the seamless mosaic at the CCD overlap region. If the multi CCD chips keep the consistent and stable geometry relationship, condition “C” doesn’t produce obvious effect. Such as in Table 6 schemes C and D get consistent calibration value for probe pointing angles.

Therefore, the calibration accuracy and effect of scheme B and E are at the same level.

The same case is for scheme L and scheme D.

 

Secondly, for the optical axis measurement data records the attitudes change of the forward camera and the backward camera separately, so the optical axis measurement data is only suitable for the external calibration model W2, ie, the forward camera and the backward camera involves two independent sets of alignment angles.

Therefore, condition “A” can be combined with “W2”.

If condition “A” is lacked, the accuracy will decrease greatly.

Scheme A(W1+N1) and Scheme I (W2+N1) are basically the same. In some cases, scheme I is slightly better than scheme A, as scheme W2 can accommodate more independent external errors.

 

Scheme A (W1+N1)	Scheme F (W1+N1+A) is not suitable
Scheme B (W1+N2+C)	Scheme E (W1+N2) Its accuracy is equal to that of scheme B.	Scheme G (W1+N2+A) is not suitable	Scheme H (W1+N2+C+A) is not suitable
Scheme C (W2+N1+A)	Scheme I (W2+N1) Its accuracy is nearly equal to scheme A, but less than scheme C.
Scheme D (W2+N2+A+C)	Scheme J (W2+N2) Its accuracy is less than scheme D.	Scheme K (W2+N2+C) Its accuracy is equal to scheme J.	Scheme L (W2+N2+A). Its accuracy is equal to scheme D.

 

For GaoFen-14, we only choose four schemes A, B, C, D to validate the following goals:

1. Whether the forward and backward images share the same set of alignment angles or involves two independent sets of alignment angles is more appropriate for the GaoFen-14 satellite calibration with the support of the optical axis position measurement data.
2. Does there lie independent and inconsistent geometric distortion among different CCD chips. If the geometric distortion among different CCD chips are consistent and stable, the multiCCD images can be treated as an integral body and scheme C and D can get the same geopositioning accuracy and calibration values for probe angles.

And the chosen four schemes fulfill the demands.

Author Response File: Author Response.docx

Reviewer 2 Report

please see the attachment.

Comments for author File: Comments.pdf

Author Response

1、“This device acquires the relative attitude angles of the forward camera and the backward camera with respect to the reference component during the on-orbit photography. The acquisition angles data describes the attitude changes of the imaging cameras.” can be separated into a paragraph.

Answer: “This device acquires the relative attitude angles of the forward camera and the backward camera with respect to the reference component during the on-orbit photography. The acquisition angles data describes the attitude changes of the imaging cameras.” Is separated into a paragraph.

2、Formula (3) and formula (4) should not have the same quantity , and it is recommended to use and to describe them separately. This is particularly important for the derivation of the author's formula, and the author can carefully deduce it further, especially for formulas (6) - (9).

Answer: It’s right that formula (3) and formula (4) should not have the same quantity in the most strict meaning. It’s not difficult to deduce the following equation based on the different quantity in formula (3) and formula (4). And we have made many experiments based on the different quantity. But the experiment results are not satisfactory, both the geopositioning accuracy and the mosaic accuracy decrease. We analyzed the experiments and found that the different quantity influence the convergence of the solution. Therefore, we treat formula (3) and formula (4) in the same quantity in the later and we think the difference in the quantity is absorbed in the others variations.

 

3、For Figures 10 and 11, I think the author may have misunderstood my meaning. I am not concerned about the actual values of the coefficients solved, and I would prefer the author to draw curves of the internal pointing angles obtained by the methods described by these parameters. In addition, it is necessary to indicate the meaning and units of the horizontal and vertical coordinates in the diagram.

Answer: Thanks for your advice. Figures 10 and 11 of the pointing probes are added.

To compare schemes A, B, C, D and E indepth, we plot out the pointing probe curves for the forward camera in Fig.10 and Fig. 11. Fig.10 plot out the pointing probe curve in the x direction (the obit flight direction), Fig.10 (a) shows the overall curve and Fig.10 (b) displays the local details to give a more vivid description. Fig.11 plot out the pointing probe curve in the y direction (vertical to the obit flight direction), Fig.11 (a) shows the overall curve and Fig.11 (b) displays the local details.

 

 

4、For Table 3, I don't think there should be two C0 for the first row, one of which should be C2.

Answer: The fifth column is corrected as C2.

 

5、Suggest merging Table 4 and Table 5.

Answer: Table 4 and Table 5 are merged together.

 

6、Figure 12 needs to indicate the meaning and units of the horizontal and vertical coordinates in the diagram.

Answer: The meaning and units of the horizontal and vertical coordinates in the diagram are added in Figure 12.

 

7、Is there a way to reduce the correlation between internal and external calibration models during the modeling process, rather than solving them through iteration during the solving process? For example, in the model mentioned in the author's article, the c0/r0 of the internal calibration model is actually highly correlated with the external calibration model /.

Answer: We have tested many approaches to solve the strong correlation, as the incorporation of correlated variations, the ridge and stein estimation method and so on.

But the iteration during the solving, the separation computation of the interior and exterior parameters are most stable and efficient.

 

8、Figure 8/9 requires a scale to be indicated

Answer: The scales of Figure 8/9 are indicated.

 

9、“Although the general site calibration already utilizes absolute site benchmarks, which can constrain the geometric relationship between CCDs, but the geometric relationship between CCDs may change during launch and running in the orbit. Moreover, the inter ship geometry constraints can also be a validation for the camera performance.”  Whether it is the traditional method or the method proposed by the author, calibration is the acquisition of parameters after changes; In addition, both traditional methods and the methods proposed by the author can be a validation for the camera performance, so currently I have not seen the specific advantages of the author's proposed method from the author's response, and from the experimental results, the difference in accuracy is not significant.

Answer: Both the traditional method and the method proposed by the author can realize the calibration of parameters after changes.

The difference between the traditional method and the proposed method is that the traditional method doesn’t consider the integrity of multi slices. But the proposed method tries to ensure the integrity of multi slices while calibrating the camera.

And the newly added Figures 10 and 11 of the pointing probes prove that the proposed method can describe the deformation of each CCD chips in details.

 

10、“In GaoFen-14 satellite calibration, some schemes among Scheme A to Scheme L are adopted in the experiment. But for GaoFen-14 satellite has a very stable geometry relationship, so some schemes don’t exhibit evident differences from other schemes.” I can understand the author's point that due to the stable geometric relationship between the GF-14 satellite and the payload, the current GF-14 data cannot support the author's argument that their method has significant advantages over traditional methods? If so, is it inappropriate to use this data to prove the author's method?

Answer: Thanks for your advice. Scheme E is added to validate the effect of Condition C. Scheme D can achieve best uncontrolled positioning accuracy stably and well illustrate the deformation of each CCD chip.

11、“Firstly, the condition “C” is designed to ensure the integrity the stitched long CCD. If there exists great displacement among various CCD  chips, condition “C” can ensure the seamless mosaic at the CCD overlap region. If the multi CCD chips keep the consistent and stable geometry relationship, condition “C” doesn’t produce obvious effect. Such as in Table 6 schemes C and D get consistent calibration value for probe pointing angles.” Firstly, does this mean that the current data does not help the author argue that their proposed N2 method has significant advantages. “the condition “C” is designed to ensure the integrity the stitched long CCD. If there exists great displacement among various CCD chips, condition “C” can ensure the seamless mosaic at the CCD overlap region” should be placed in the processing phase rather than the calibration phase. It is recommended that the author clarify the relationship between calibration and processing, which steps should be calibrated offline and which steps should be processed online.

Answer: Thanks for your advice. Scheme E is added to validate the effect of Condition C.

Experiments results prove that if there exists great displacement among various CCD chips, the proposed method, condition “C” can ensure the seamless mosaic at the CCD overlap region.

The seamless mosaic is not a simple geometric transformation and it involves the interior parameters and the exterior parameters, so it is advisable to consider condition C during calibration.

If condition C is put before calibration, it will change the actual situation of interior parameters. If condition C is put after calibration, calibration on separate slices will generate great displacements among multi slices and subsequent mosaic will disturb the integrity of whole image.

 

 

Author Response File: Author Response.docx

Reviewer 3 Report

This manuscript focuses on the on-orbit geometric calibration of the GaoFen-14 satellite while conducting internal and external calibration using diverse combinations. On-orbit geometric calibration for the specific satellite is essential for obtaining high precision in geometric positioning. Although the topic is interesting, there are severe revisions necessary, especially in the representation of the manuscript. The followings are detailed comments for improving the manuscript’s quality.

 

-          Abstract: Schemes from A to D are mentioned in the Abstract without any explanation, making it difficult for readers to understand these schemes. Instead of just mentioning the schemes from A to D, a brief explanation of each scheme should be included, enabling readers to understand which kinds of calibrations are important for on-orbit geometric calibration performance.

 

-          L45: There is an incomplete sentence from the first sentence of the manuscript (i.e., “~ remote sensing, sur On-orbit geometric calibration ~”). Not only this one, but there are also many grammar errors and typos throughout the manuscript. Please carefully revise the entire manuscript.

 

-          Full names of abbreviations should be given when they are first used in the manuscript (e.g., CCD, DSM, etc.).

 

-          Citation reference format should follow the Remote Sensing journal guidelines. There are many errors, e.g., Weser, Zhang L., Zhang Yongjun, Wang Tao, etc.

 

-          L122: A brief explanation of the four different calibration schemes should be mentioned here. Schemes A to D should be at least briefly explained in the Introduction.

 

-          L138-L146: It would be better to include a figure regarding the payload.

 

-          P179: The explanation of "f" is missing. Please provide an explanation.

 

-          Figure 1: The notations in the figures seem different from those written in the text. Moreover, some notations are missing in the figure. (e.g., f, w, phi, kappa, etc.) Please unify all the notations between the figure and the text and add all the notations mentioned in the text to the figure.

 

-          All equations: The notations used in the equations should be defined in the text (e.g., R1, R2, A, etc.). Additionally, like Figure 1, some notations are different between the equations and text (e.g., x_1, y_1 in equation 3, x_p1, y_p1 in text).

 

-          Figure 2 is too simple to clearly understand the concept of the alignment angle correction. It would be helpful to add some notations in the figure.

 

-          (cont.) As I understand it correctly, two points should know the positions (i.e., A and B in figure 2) to calibrate the unknown area (i.e., C in figure 2). What if there is only one known position or more than three known positions? In those cases, can the same alignment angle correction (i.e., equations 10, 11, and 12) be applied?

 

-          L310-L363: Section 3.4 should be moved before section 3.1 so that sections from 3.1 to 3.3 will be easier to understand. Alternatively, section 3.4 should be reorganized as an independent section.

 

-          L312-L313, “two calibration models: the first model ~ constraints.”: it would be better to clarify that the first model includes the external calibration, and the second model includes the internal calibration. Since all the four schemes conducted both external and internal calibrations, it is wrong to say that the first model excludes the internal calibration. The same applies to L537-L538.

 

-          L320-L322: x and y coordinates can be obtained from the DOM. Then, what about height information?

 

-          Figure 4 and Figure 5: Information regarding scale, coordinates, etc. should be added in the Figures.

 

 

-          It would be better to add some limitations of this research together with future works that can address such limitations.

Extensive editing of English language required

Author Response

This manuscript focuses on the on-orbit geometric calibration of the GaoFen-14 satellite while conducting internal and external calibration using diverse combinations. On-orbit geometric calibration for the specific satellite is essential for obtaining high precision in geometric positioning. Although the topic is interesting, there are severe revisions necessary, especially in the representation of the manuscript. The followings are detailed comments for improving the manuscript’s quality.

 

1. Abstract: Schemes from A to D are mentioned in the Abstract without any explanation, making it difficult for readers to understand these schemes. Instead of just mentioning the schemes from A to D, a brief explanation of each scheme should be included, enabling readers to understand which kinds of calibrations are important for on-orbit geometric calibration performance.

Answer: Scheme A and scheme B utilize the same set of alignment angles for the forward and backward images, and differ in the set of interior calibration parameters. Scheme A takes a single set of interior calibration parameters for all chips within the same view, while scheme B sets independent interior calibration parameters for each chip in both the forward and backward views. Scheme C and scheme D are also the same in the exterior calibration model, which involves two sets of alignment angles for the forward and backward views respectively. In addition, Schemes C and D utilized GaoFen-14’s specific real-time recording data of the optical axis, incorporating a slight revision of the alignment angle calibration value using dichotomous search. The interior models of scheme A and C are the same and those of scheme B and D are the same. These four schemes are taken to validate the most suitable exterior model and the interior model for the GaoFen-14 satellite.

For GaoFen-14 satellite, it is more appropriate to adopt two sets of alignment angles for the forward and backward views. Since GaoFen-14 satellite has consistent geometry relationship, a single set of interior calibration parameters for all chips within the same view and independent inner calibration parameters for each chip in the forward/backward view image are both suitable.

 

2. L45: There is an incomplete sentence from the first sentence of the manuscript (i.e., “~ remote sensing, sur On-orbit geometric calibration ~”). Not only this one, but there are also many grammar errors and typos throughout the manuscript. Please carefully revise the entire manuscript.

Answer: The manuscript is carefully checked for more times.

 

3. Full names of abbreviations should be given when they are first used in the manuscript (e.g., CCD, DSM, etc.).

Answer: Full names of abbreviations are added into the manuscript. 

4. Citation reference format should follow the Remote Sensing journal guidelines. There are many errors, e.g., Weser, Zhang L., Zhang Yongjun, Wang Tao, etc.

Answer: Errors in citation reference format are corrected to follow the Remote Sensing journal guidelines.

 

5. L122: A brief explanation of the four different calibration schemes should be mentioned here. Schemes A to D should be at least briefly explained in the Introduction.

 Answer: A brief explanation of the four different calibration schemes is added to the Introduction.

 

6. L138-L146: It would be better to include a figure regarding the payload.

Answer: I am very sorry that I don’t get the figure regarding the payload

 

7. P179: The explanation of "f" is missing. Please provide an explanation.

Answer: "f" is the focus of the camera and the explanation is added.

 

8. Figure 1: The notations in the figures seem different from those written in the text. Moreover, some notations are missing in the figure. (e.g., f, w, phi, kappa, etc.) Please unify all the notations between the figure and the text and add all the notations mentioned in the text to the figure.

Answer:  All the notations between the figure and the text are unified. Fig. 1 displays the geometric relationship of probe pointing angles in the image space coordinate system without considering its relationship to the ground coordinate system. So some notations in the exterior models are missing. Explanation on Fig. 1 has been changed.

9. All equations: The notations used in the equations should be defined in the text (e.g., R1, R2, A, etc.). Additionally, like Figure 1, some notations are different between the equations and text (e.g., x_1, y_1 in equation 3, x_p1, y_p1 in text).

Answer: The notations used in the equations are added in the text.

And the image point p₁(x_p1,y_p1) on the left chip and the corresponding image point p₂(x_p2,y_p2) on the right chip are corrected as p₁(x₁,y₁) and p₂(x₂,y₂). 

 

10. Figure 2 is too simple to clearly understand the concept of the alignment angle correction. It would be helpful to add some notations in the figure.

(cont.) As I understand it correctly, two points should know the positions (i.e., A and B in figure 2) to calibrate the unknown area (i.e., C in figure 2). What if there is only one known position or more than three known positions? In those cases, can the same alignment angle correction (i.e., equations 10, 11, and 12) be applied?

 Answer: Some notations are added in the figure. If there are more than three known positions, the same alignment angle correction (i.e., equations 10, 11, and 12) can also be applied. Two separate known positions can get one group of estimation and more than three known positions can get several groups estimation. The average estimation values can be generated from these several groups and are more accurate.

If there is only one known position, the same alignment angle correction (i.e., equations 10, 11, and 12) can be also be applied. But  can only take the previous calculated value or set to be the unit value 1. 

 

11. L310-L363: Section 3.4 should be moved before section 3.1 so that sections from 3.1 to 3.3 will be easier to understand. Alternatively, section 3.4 should be reorganized as an independent section.

 Answer: Section 3.4 is reorganized as an independent section “Section 4”.

12. L312-L313, “two calibration models: the first model ~ constraints.”: it would be better to clarify that the first model includes the external calibration, and the second model includes the internal calibration. Since all the four schemes conducted both external and internal calibrations, it is wrong to say that the first model excludes the internal calibration. The same applies to L537-L538.

Answer: L312-313 has been corrected as “The on-orbit geometric calibration process for the GaoFen-14 dual-line-array stereo mapping satellite is designed to incorporate two steps: the external calibration process and the internal calibration process. The two steps are independent and iterative to resolve the strong correlation among the exterior parameter and the interior parameters. The workflow diagram illustrating the steps of this calibration process is presented in Fig. 3.”

L537-L538 are corrected as “The first model treats all the CCD chips in the same view as a whole and considers just one set of interior parameter for each camera, while the second model incorporates geometry constraints between the chips.”

 

13. L320-L322: x and y coordinates can be obtained from the DOM. Then, what about height information?

Answer: The height information are interpolated from DEM.

 

14. Figure 4 and Figure 5: Information regarding scale, coordinates, etc. should be added in the Figures.

Answer:  Information regarding scale, coordinates, etc. are added in the Figure 4 and Figure 5:.

 

15. It would be better to add some limitations of this research together with future works that can address such limitations.

Answer: Some limitations of this research together with future works are addressed in the paper. “However, there still remains a residual systematic error of approximately 1m in the plane X direction, which requires further investigation and analysis. In the future, we will continue to exploit the properties of the optical axis position measurement data and hope to advance the uncontrolled geopositioning accuracy to a higher level.”

 

16. Comments on the Quality of English Language

Extensive editing of English language required

Answer: English language are given extensive editing.

 

Author Response File: Author Response.docx

Reviewer 4 Report

Dear authors,

The calibration of satellite instruments is a very interesting and crucial topic for the creation of surveying products such as DEM, DSM and Orthophotomosaics. GaoFen-14 is a new (2020) satellite constellation which provide stereo-images and also it is equipped with an altitude measurement system.

First and foremost the manuscript should contain five sections, regarding the mdpi instruction for authors area, which are

1. Introduction

2. Materials and Methods

3. Results

4. Discussion

5. Conclusions

In this manuscript there are not "Materials and Methods", "Results" and "Discussion".

 I recommend the authors to restructure there manuscript based on the requirements. Maybe the sections 2 and 3 of the manuscript could be included to "Materials and Methods" while the "Experiment and verification" to Results and Discussion but after all the authors should find the best fit to each section.

 

In this paper, an on orbit calibration process for the GaoFen-14, is proposed in which the altitude measurements are included to improve the calibration process.

 

In general there are:

external calibration scheme W1 and W2

internal calibration scheme N1 and N2

The difference is that W2 and N2 use parameters for each sensor independently while W1 and N1 share the parameters among the sensors. To investigate the on-orbit calibration process the authors evaluate four calibration schemes i.e., A, B, C and D. In fact they, test every possible scheme i.e., (W1,N1), (W1, N2) etc.

 

Maybe the authors should change:

- Line 344 -> W1 and not W

- Line 360-> N2 and not N1

- Line 396 -> nine and not 9 (only for consistency)

- Table 5 not includes pre calibrated values

- Table 4 and 5 need units.

 

 

The authors use two test fields (Ningxia and Songshan) and four validation sets.

Ningxi:

- What they mean by "The positions of image points were then further refined through manual editing" The matching points ?

- The authors use matching points as GCPs from which they use 20 points as control points for evaluation. Maybe an image displaying the distribution of such points would be beneficial for the reader. Also they should provide how they select the 20 control points.

 

Shongsan:

Twenty GCPs were obtained through field measurements and used as checkpoints for accuracy evaluation. These points were obtained through field measurements. A short paragraph explaining the measurement process will be beneficial for the reader e.g., using a GPS etc.

Also a further clarification of how they match the high resolution digital orthophoto with all chip images should be provided. They use a commercial software or a in-house one ?

 

Validation set:

-  Apart from the number of GCPs is beneficial to add the captured area i.e., the image boundaries like ig5 etc. to display the distribution of GCPs in respect to the captured image.

 

After all I thing that the proposed manuscript, describes in detail the calibration process and also includes a well detailed literature review and a vast amount of results. Additionally, the authors conduct a well designed research including a sufficient number of evaluation schemes, test and validation areas.

I accept this paper after minor revisions.

Minor editing of English language required

Author Response

1． First and foremost the manuscript should contain five sections, regarding the mdpi instruction for authors area, which are

1. Introduction
2. Materials and Methods
3. Results
4. Discussion
5. Conclusions

In this manuscript there are not "Materials and Methods", "Results" and "Discussion".

 I recommend the authors to restructure there manuscript based on the requirements. Maybe the sections 2 and 3 of the manuscript could be included to "Materials and Methods" while the "Experiment and verification" to Results and Discussion but after all the authors should find the best fit to each section.

Answer: The titles are corrected.

 

2. In this paper, an on orbit calibration process for the GaoFen-14, is proposed in which the altitude measurements are included to improve the calibration process.

 In general there are:

external calibration scheme W1 and W2

internal calibration scheme N1 and N2

The difference is that W2 and N2 use parameters for each sensor independently while W1 and N1 share the parameters among the sensors. To investigate the on-orbit calibration process the authors evaluate four calibration schemes i.e., A, B, C and D. In fact they, test every possible scheme i.e., (W1,N1), (W1, N2) etc.

Maybe the authors should change:

- Line 344 -> W1 and not W

Answer: The error is corrected.

 

- Line 360-> N2 and not N1

Answer: The error is corrected.

- Line 396 -> nine and not 9 (only for consistency)

Answer: The error is corrected.

 

3. Table 5 not includes pre calibrated values

Answer:  The description of Pre-calibration in Table 5 is the same as that of Table 4, so the description of Pre-calibration in Table 5 is omitted.

 

4. Table 4 and 5 need units.

 Answer: The units are added in Table 4 and 5.

 

5. The authors use two test fields (Ningxia and Songshan) and four validation sets.

Ningxi:

- What they mean by "The positions of image points were then further refined through manual editing" The matching points ?

Answer: For these control points are obtained through matching, there are some mismatches in the results. So the mismatched control points will be edited through manual editing, ie, the positions of image points were then further refined through manual editing

- The authors use matching points as GCPs from which they use 20 points as control points for evaluation. Maybe an image displaying the distribution of such points would be beneficial for the reader. Also they should provide how they select the 20 control points.

Answer: The distribution of such points is added in Fig.4. The 20 control points should be in an even and wide distribution pattern.

6. Shongsan:

Twenty GCPs were obtained through field measurements and used as checkpoints for accuracy evaluation. These points were obtained through field measurements. A short paragraph explaining the measurement process will be beneficial for the reader e.g., using a GPS etc.
Answer: These points were obtained through field measurements with RTK (Real-time kinematic) equipment.

 

7. Also a further clarification of how they match the high resolution digital orthophoto with all chip images should be provided. They use a commercial software or a in-house one ?

 Answer: The high resolution digital orthophoto are matched with all chip images using our self-developed software.

8.Validation set:

-  Apart from the number of GCPs is beneficial to add the captured area i.e., the image boundaries like Fig5 etc. to display the distribution of GCPs in respect to the captured image.

 Answer：In Fig5，the distribution of GCPs is displayed.

 

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

 

1、“This device acquires the relative attitude angles of the forward camera and the backward camera with respect to the reference component during the on-orbit photography. The acquisition angles data describes the attitude changes of the imaging cameras.” can be separated into a paragraph.

2、Formula (3) and formula (4) should not have the same quantity , and it is recommended to use and to describe them separately. This is particularly important for the derivation of the author's formula, and the author can carefully deduce it further, especially for formulas (6) - (9).

3、For Figures 10 and 11, I think the author may have misunderstood my meaning. I am not concerned about the actual values of the coefficients solved, and I would prefer the author to draw curves of the internal pointing angles obtained by the methods described by these parameters. In addition, it is necessary to indicate the meaning and units of the horizontal and vertical coordinates in the diagram.

4、For Table 3, I don't think there should be two C0 for the first row, one of which should be C2.

5、Suggest merging Table 4 and Table 5.

6、Figure 12 needs to indicate the meaning and units of the horizontal and vertical coordinates in the diagram.

7、Is there a way to reduce the correlation between internal and external calibration models during the modeling process, rather than solving them through iteration during the solving process? For example, in the model mentioned in the author's article, the c0/r0 of the internal calibration model is actually highly correlated with the external calibration model /.

8、Figure 8/9 requires a scale to be indicated

9、“Although the general site calibration already utilizes absolute site benchmarks, which can constrain the geometric relationship between CCDs, but the geometric relationship between CCDs may change during launch and running in the orbit. Moreover, the inter ship geometry constraints can also be a validation for the camera performance.”  Whether it is the traditional method or the method proposed by the author, calibration is the acquisition of parameters after changes; In addition, both traditional methods and the methods proposed by the author can be a validation for the camera performance, so currently I have not seen the specific advantages of the author's proposed method from the author's response, and from the experimental results, the difference in accuracy is not significant.

10、“In GaoFen-14 satellite calibration, some schemes among Scheme A to Scheme L are adopted in the experiment. But for GaoFen-14 satellite has a very stable geometry relationship, so some schemes don’t exhibit evident differences from other schemes.” I can understand the author's point that due to the stable geometric relationship between the GF-14 satellite and the payload, the current GF-14 data cannot support the author's argument that their method has significant advantages over traditional methods? If so, is it inappropriate to use this data to prove the author's method?

11、“Firstly, the condition “C” is designed to ensure the integrity the stitched long CCD. If there exists great displacement among various CCD chips, condition “C” can ensure the seamless mosaic at the CCD overlap region. If the multi CCD chips keep the consistent and stable geometry relationship, condition “C” doesn’t produce obvious effect. Such as in Table 6 schemes C and D get consistent calibration value for probe pointing angles.” Firstly, does this mean that the current data does not help the author argue that their proposed N2 method has significant advantages. “the condition “C” is designed to ensure the integrity the stitched long CCD. If there exists great displacement among various CCD chips, condition “C” can ensure the seamless mosaic at the CCD overlap region” should be placed in the processing phase rather than the calibration phase. It is recommended that the author clarify the relationship between calibration and processing, which steps should be calibrated offline and which steps should be processed online.

 

Comments for author File: Comments.pdf

Author Response

1、“This device acquires the relative attitude angles of the forward camera and the backward camera with respect to the reference component during the on-orbit photography. The acquisition angles data describes the attitude changes of the imaging cameras.” can be separated into a paragraph.

Answer: “This device acquires the relative attitude angles of the forward camera and the backward camera with respect to the reference component during the on-orbit photography. The acquisition angles data describes the attitude changes of the imaging cameras.” Is separated into a paragraph.

2、Formula (3) and formula (4) should not have the same quantity , and it is recommended to use and to describe them separately. This is particularly important for the derivation of the author's formula, and the author can carefully deduce it further, especially for formulas (6) - (9).

Answer: It’s right that formula (3) and formula (4) should not have the same quantity in the most strict meaning. It’s not difficult to deduce the following equation based on the different quantity in formula (3) and formula (4). And we have made many experiments based on the different quantity. But the experiment results are not satisfactory, both the geopositioning accuracy and the mosaic accuracy decrease. We analyzed the experiments and found that the different quantity influence the convergence of the solution. Therefore, we treat formula (3) and formula (4) in the same quantity in the later and we think the difference in the quantity is absorbed in the others variations.

 

3、For Figures 10 and 11, I think the author may have misunderstood my meaning. I am not concerned about the actual values of the coefficients solved, and I would prefer the author to draw curves of the internal pointing angles obtained by the methods described by these parameters. In addition, it is necessary to indicate the meaning and units of the horizontal and vertical coordinates in the diagram.

Answer: Thanks for your advice. Figures 10 and 11 of the pointing probes are added.

To compare schemes A, B, C, D and E indepth, we plot out the pointing probe curves for the forward camera in Fig.10 and Fig. 11. Fig.10 plot out the pointing probe curve in the x direction (the obit flight direction), Fig.10 (a) shows the overall curve and Fig.10 (b) displays the local details to give a more vivid description. Fig.11 plot out the pointing probe curve in the y direction (vertical to the obit flight direction), Fig.11 (a) shows the overall curve and Fig.11 (b) displays the local details.

 

 

4、For Table 3, I don't think there should be two C0 for the first row, one of which should be C2.

Answer: The fifth column is corrected as C2.

 

5、Suggest merging Table 4 and Table 5.

Answer: Table 4 and Table 5 are merged together.

 

6、Figure 12 needs to indicate the meaning and units of the horizontal and vertical coordinates in the diagram.

Answer: The meaning and units of the horizontal and vertical coordinates in the diagram are added in Figure 12.

 

7、Is there a way to reduce the correlation between internal and external calibration models during the modeling process, rather than solving them through iteration during the solving process? For example, in the model mentioned in the author's article, the c0/r0 of the internal calibration model is actually highly correlated with the external calibration model /.

Answer: We have tested many approaches to solve the strong correlation, as the incorporation of correlated variations, the ridge and stein estimation method and so on.

But the iteration during the solving, the separation computation of the interior and exterior parameters are most stable and efficient.

 

8、Figure 8/9 requires a scale to be indicated

Answer: The scales of Figure 8/9 are indicated.

 

9、“Although the general site calibration already utilizes absolute site benchmarks, which can constrain the geometric relationship between CCDs, but the geometric relationship between CCDs may change during launch and running in the orbit. Moreover, the inter ship geometry constraints can also be a validation for the camera performance.”  Whether it is the traditional method or the method proposed by the author, calibration is the acquisition of parameters after changes; In addition, both traditional methods and the methods proposed by the author can be a validation for the camera performance, so currently I have not seen the specific advantages of the author's proposed method from the author's response, and from the experimental results, the difference in accuracy is not significant.

Answer: Both the traditional method and the method proposed by the author can realize the calibration of parameters after changes.

The difference between the traditional method and the proposed method is that the traditional method doesn’t consider the integrity of multi slices. But the proposed method tries to ensure the integrity of multi slices while calibrating the camera.

And the newly added Figures 10 and 11 of the pointing probes prove that the proposed method can describe the deformation of each CCD chips in details.

 

10、“In GaoFen-14 satellite calibration, some schemes among Scheme A to Scheme L are adopted in the experiment. But for GaoFen-14 satellite has a very stable geometry relationship, so some schemes don’t exhibit evident differences from other schemes.” I can understand the author's point that due to the stable geometric relationship between the GF-14 satellite and the payload, the current GF-14 data cannot support the author's argument that their method has significant advantages over traditional methods? If so, is it inappropriate to use this data to prove the author's method?

Answer: Thanks for your advice. Scheme E is added to validate the effect of Condition C. Scheme D can achieve best uncontrolled positioning accuracy stably and well illustrate the deformation of each CCD chip.

11、“Firstly, the condition “C” is designed to ensure the integrity the stitched long CCD. If there exists great displacement among various CCD  chips, condition “C” can ensure the seamless mosaic at the CCD overlap region. If the multi CCD chips keep the consistent and stable geometry relationship, condition “C” doesn’t produce obvious effect. Such as in Table 6 schemes C and D get consistent calibration value for probe pointing angles.” Firstly, does this mean that the current data does not help the author argue that their proposed N2 method has significant advantages. “the condition “C” is designed to ensure the integrity the stitched long CCD. If there exists great displacement among various CCD chips, condition “C” can ensure the seamless mosaic at the CCD overlap region” should be placed in the processing phase rather than the calibration phase. It is recommended that the author clarify the relationship between calibration and processing, which steps should be calibrated offline and which steps should be processed online.

Answer: Thanks for your advice. Scheme E is added to validate the effect of Condition C.

Experiments results prove that if there exists great displacement among various CCD chips, the proposed method, condition “C” can ensure the seamless mosaic at the CCD overlap region.

The seamless mosaic is not a simple geometric transformation and it involves the interior parameters and the exterior parameters, so it is advisable to consider condition C during calibration.

If condition C is put before calibration, it will change the actual situation of interior parameters. If condition C is put after calibration, calibration on separate slices will generate great displacements among multi slices and subsequent mosaic will disturb the integrity of whole image.

 

 

Author Response File: Author Response.docx

Reviewer 2 Report

The paper has been revised according to my comments and can be accepted for publication.

Reviewer 3 Report

The revised manuscript has addressed most of my comments.

 

None

 

Author Response

1、“This device acquires the relative attitude angles of the forward camera and the backward camera with respect to the reference component during the on-orbit photography. The acquisition angles data describes the attitude changes of the imaging cameras.” can be separated into a paragraph.

Answer: “This device acquires the relative attitude angles of the forward camera and the backward camera with respect to the reference component during the on-orbit photography. The acquisition angles data describes the attitude changes of the imaging cameras.” Is separated into a paragraph.

2、Formula (3) and formula (4) should not have the same quantity , and it is recommended to use and to describe them separately. This is particularly important for the derivation of the author's formula, and the author can carefully deduce it further, especially for formulas (6) - (9).

Answer: It’s right that formula (3) and formula (4) should not have the same quantity in the most strict meaning. It’s not difficult to deduce the following equation based on the different quantity in formula (3) and formula (4). And we have made many experiments based on the different quantity. But the experiment results are not satisfactory, both the geopositioning accuracy and the mosaic accuracy decrease. We analyzed the experiments and found that the different quantity influence the convergence of the solution. Therefore, we treat formula (3) and formula (4) in the same quantity in the later and we think the difference in the quantity is absorbed in the others variations.

 

3、For Figures 10 and 11, I think the author may have misunderstood my meaning. I am not concerned about the actual values of the coefficients solved, and I would prefer the author to draw curves of the internal pointing angles obtained by the methods described by these parameters. In addition, it is necessary to indicate the meaning and units of the horizontal and vertical coordinates in the diagram.

Answer: Thanks for your advice. Figures 10 and 11 of the pointing probes are added.

To compare schemes A, B, C, D and E indepth, we plot out the pointing probe curves for the forward camera in Fig.10 and Fig. 11. Fig.10 plot out the pointing probe curve in the x direction (the obit flight direction), Fig.10 (a) shows the overall curve and Fig.10 (b) displays the local details to give a more vivid description. Fig.11 plot out the pointing probe curve in the y direction (vertical to the obit flight direction), Fig.11 (a) shows the overall curve and Fig.11 (b) displays the local details.

 

 

4、For Table 3, I don't think there should be two C0 for the first row, one of which should be C2.

Answer: The fifth column is corrected as C2.

 

5、Suggest merging Table 4 and Table 5.

Answer: Table 4 and Table 5 are merged together.

 

6、Figure 12 needs to indicate the meaning and units of the horizontal and vertical coordinates in the diagram.

Answer: The meaning and units of the horizontal and vertical coordinates in the diagram are added in Figure 12.

 

7、Is there a way to reduce the correlation between internal and external calibration models during the modeling process, rather than solving them through iteration during the solving process? For example, in the model mentioned in the author's article, the c0/r0 of the internal calibration model is actually highly correlated with the external calibration model /.

Answer: We have tested many approaches to solve the strong correlation, as the incorporation of correlated variations, the ridge and stein estimation method and so on.

But the iteration during the solving, the separation computation of the interior and exterior parameters are most stable and efficient.

 

8、Figure 8/9 requires a scale to be indicated

Answer: The scales of Figure 8/9 are indicated.

 

9、“Although the general site calibration already utilizes absolute site benchmarks, which can constrain the geometric relationship between CCDs, but the geometric relationship between CCDs may change during launch and running in the orbit. Moreover, the inter ship geometry constraints can also be a validation for the camera performance.”  Whether it is the traditional method or the method proposed by the author, calibration is the acquisition of parameters after changes; In addition, both traditional methods and the methods proposed by the author can be a validation for the camera performance, so currently I have not seen the specific advantages of the author's proposed method from the author's response, and from the experimental results, the difference in accuracy is not significant.

Answer: Both the traditional method and the method proposed by the author can realize the calibration of parameters after changes.

The difference between the traditional method and the proposed method is that the traditional method doesn’t consider the integrity of multi slices. But the proposed method tries to ensure the integrity of multi slices while calibrating the camera.

And the newly added Figures 10 and 11 of the pointing probes prove that the proposed method can describe the deformation of each CCD chips in details.

 

10、“In GaoFen-14 satellite calibration, some schemes among Scheme A to Scheme L are adopted in the experiment. But for GaoFen-14 satellite has a very stable geometry relationship, so some schemes don’t exhibit evident differences from other schemes.” I can understand the author's point that due to the stable geometric relationship between the GF-14 satellite and the payload, the current GF-14 data cannot support the author's argument that their method has significant advantages over traditional methods? If so, is it inappropriate to use this data to prove the author's method?

Answer: Thanks for your advice. Scheme E is added to validate the effect of Condition C. Scheme D can achieve best uncontrolled positioning accuracy stably and well illustrate the deformation of each CCD chip.

11、“Firstly, the condition “C” is designed to ensure the integrity the stitched long CCD. If there exists great displacement among various CCD  chips, condition “C” can ensure the seamless mosaic at the CCD overlap region. If the multi CCD chips keep the consistent and stable geometry relationship, condition “C” doesn’t produce obvious effect. Such as in Table 6 schemes C and D get consistent calibration value for probe pointing angles.” Firstly, does this mean that the current data does not help the author argue that their proposed N2 method has significant advantages. “the condition “C” is designed to ensure the integrity the stitched long CCD. If there exists great displacement among various CCD chips, condition “C” can ensure the seamless mosaic at the CCD overlap region” should be placed in the processing phase rather than the calibration phase. It is recommended that the author clarify the relationship between calibration and processing, which steps should be calibrated offline and which steps should be processed online.

Answer: Thanks for your advice. Scheme E is added to validate the effect of Condition C.

Experiments results prove that if there exists great displacement among various CCD chips, the proposed method, condition “C” can ensure the seamless mosaic at the CCD overlap region.

The seamless mosaic is not a simple geometric transformation and it involves the interior parameters and the exterior parameters, so it is advisable to consider condition C during calibration.

If condition C is put before calibration, it will change the actual situation of interior parameters. If condition C is put after calibration, calibration on separate slices will generate great displacements among multi slices and subsequent mosaic will disturb the integrity of whole image.

 

 

Author Response File: Author Response.docx