Round 1

Reviewer 1 Report

1. line 37 and line 52 the name of the cited author should be ended with (.), please, check, if it is correct or not.
2. please, mention in intorduction, why do you plan to eliminated the systematic error? Are there any other errors which also effect the geo-location accuracy and should be eliminated or compensated? 
3. check the line 132, it should be Xv instead of Xb, i think
4. in the line 136 put space between angle
5. The title of figure 6 is separated from the figure, make them together please.
6. check English grammar.
7. Please, plot differently Figure 13 and Figure 14. The colours are appearing twice (with differen marks), but it is difficult to distinguish them. 

Author Response

Response: We appreciate the reviewer’s comments. We seriously consider the comments from the reviewer, and efforts to improve the manuscript from several aspects. Thank you very much for your help.

 

Point 1: line 37 and line 52 the name of the cited author should be ended with (.), please, check, if it is correct or not.

 

Response 1: Thank you for your correction and I have made the amendment.

 

Point 2: please, mention in introduction, why do you plan to eliminated the systematic error? Are there any other errors which also effect the geo-location accuracy and should be eliminated or compensated? 

 

Response 2:  Thank you for your comment. Eliminating systematic error is the basis for improving the accuracy of target geo-location since it directly affects the geo-location accuracy and the filtering algorithms. And I revised the introduction and make the reason clearer. As for second question, there are truly other errors which also effect the geo-location accuracy. There are lots of articles such as using Kalman filter, moving average filtering and so on to compensated those errors and this also is a question in my future research. In this article, we focus on proposing a method to eliminate the systematic error.

 

Point 3: check the line 132, it should be Xv instead of Xb, i think

 

Response 3: Thank you for your correction and I have made the amendment. Thank you.

 

Point 4: in the line 136 put space between angle

 

Response 4: Thank you for your correction and I have made the amendment. Thank you.

 

Point 5: The title of figure 6 is separated from the figure, make them together please.

 

Response 5:  Thank you for your correction and I have made the amendment. Thank you.

 

 

Point 6: check English grammar.

Response 6:  Thank you for your comment and I had check English grammar carefully.

 

Point 7: Please, plot differently Figure 13 and Figure 14. The colours are appearing twice (with different marks), but it is difficult to distinguish them. 

 

Response 7:  Thank you for your comment and I replot Figure 13 and Figure 14 with different colors and different marks. Please see the Response to Reviewer 1.docx or the draft.

Author Response File: Author Response.docx

Reviewer 2 Report

Summary

The authors describe a boresight calibration method for a UAV mounted laser range finder. The algorithm is based on measurements of one or more ground control points (GCP) from several different UAV positions. The authors then present an algorithm to infer the desired boresight angles (i.e. installation angles of the laser range finder w.r.t airborne platform) from the GCP measurements with a linear least-squares fit. The authors investigate the performance of the proposed boresight calibration method with a synthetic test data set obtained based on Monte Carlo simulations and they present results from a case study, where the proposed calibration method is applied to a real UAV mounted laser ranger finder. The results show, that the proposed boresight calibration technique is capable of improving the absolute accuracy of the geo-location in both cases.

Broad Comments

The research objectives are clearly stated and they are motivated well with a practical application (UAV based geo-location of military and civil targets). The underlying theory is presented extensively with an in-depth presentation of the associated mathematical theory. Since most of the equations describe basic rotations in three dimensions, I would even recommend to shorten the theory section by referring to applicable literature wherever possible. The following description of the numerical and practical validation experiments and their respective evaluation is presented clearly and comprehensibly. The results show, that the algorithm is capable of inferring a sensible set of boresight angles which lead to a significant improvement in the absolute geo-location accuracy.

While the introduction presents a detailed literature overview of related geo-location algorithms and their applications, it lacks a similar overview of relevant literature on GCP based boresight calibration methods and their respective properties. Given the fact, that boresight calibration is the central topic of this publication, this is a prerequisite to evaluate the authors contribution to this field of research, especially since the topic has been investigated extensively for the geo-location of airborne and spaceborne optical remote sensing instruments over the last thirty years. In particular, the authors should state clearly, how the algorithm they propose differs from other published boresight calibration methods (e.g. [1]) and how the results compare to those published methods in terms of accuracy, precision and robustness.

Specific Comments

Section 1 (Introduction)

1. 27 – 29 Sentence seems incomplete. Maybe “Airborne optoelectronic platforms play an important role in military and civilian applications such as search, ….”
2. 34 – 41 How is the choice of the ellipsoid model relevant to your work? How are DEMs relevant, if you measure GCPs by DGPS?
3. 71 – 74 Could the methods you mention here be applied to the data after systematic correction, including e.g. the boresight calibration you propose? Would this increase the overall accuracy even further? Maybe system correction is not mentioned in these publications, because the authors regard is an orthogonal activity?
4. 88: I think you should add a review about state-of-the-art boresight calibration methods here, especially those used within the scope of orthorectification of remote sensing data. E.g., could you also use commercial software such as PARGE (http://dev.rese.ch/software/parge/parge-background.html)?. Why not? Which problem inherent to these algorithms are you trying to solve?

Section 2 (Materials and Methods)

l. 99 Maybe add who developed/manufactured the UAV system and what are its main applications

l. 116 “… and the airborne …” -> omit “and”

l.119 Could you also use the camera for boresight calibration, e.g. to obtain more GCPs with one measurement (i.e. perform the ‘classical’ boresight calibration used for imaging remote sensing instruments)? What are the advantages/disadvantages compared to your approach?

Figure 1 Maybe you could indicate where the IMU and the GPS antenna are located.

l. 132 Do all optical instruments share a common principal point? How can this be guaranteed?

l. 133 “points to the front of the platform” -> unclear since front is diagonally above the platform. Maybe “points upwards if the camera is oriented in flight direction / along vehicle x-axis”?

ll.135-136 “the outer gimbal rotates around the Z_V axis” Are you sure this should not be Z_b?

ll. 143 – 147 Is this the standard ARINC frame with origin shifted to the center of the optical platform reference frame? If so, you could just state this and omit the lengthy description.

ll. 150 -153 Since this seems to describe the standard NED (north, east, down) reference frame, you could state this and shorten the explanation. What exactly do you mean by “aircraft’s center”? The center of gravity, the center of the IMU, the principal plane of the optical system …?

ll. 155 – 158 I think it would be sufficient, to state that you are using the WGS-84 reference ellipsoid.

Figure 3 to Figure 5: I find the pseudo-3d sketches in combination with the many angles a little confusing. Maybe reduce the number of coordinate systems shown per figure?

Eq (1) Replace x_g by y_g, z_g in second and third term, respectively

170 – 187, eqs (2) – (6) These seem to be standard coordinate transformations. I would recommend to simply cite applicable literature and omit the details in the manuscript. It is clear, that you can transform the coordinate systems into each other by a sequence of rotations and translations.

Eq (8) What is P_g? Should there not be a shift of origin from the center of gravity of the aircraft to the origin of the imaging system coordinate frame?

Eq (9) Did you develop this algorithm yourself? If so, please explain how, otherwise please cite the source. In case there is a source, you could actually leave the equation out entirely.

Eq (10) Is this detail really relevant?

l. 202 “influence of the error items” -> “individual sources of measurement uncertainty” ?

l. 208 Maybe “These are normally distributed random errors”? Also: How do you know the GNSS position error is random with gaussian distribution? Could there be systematic offsets, too, on time scales of several minutes? On which time scales do the errors become normally distributed?

l. 215 Does the additional POS move with the optoelectronic platform? Where is the GNSS antenna for this POS located? Does the antenna lever arm change when the optical platform moves? If so, is this accounted for during data processing? If not, what’s the estimated additional uncertainty caused by this effect compared to the uncertainty of the gimbal encoder uncertainty?

l. 220 Does 200” mean 200 arc-seconds? I would recommend to use either deg or mrad.

ll. 223/224 Maybe “[…] the rotation matrix […] can be approximated by”?

eq (19) Should the last element of the fit vector not be \delta_\beta instead of \delta_\chi ?

eqs (14) – (22) The least squares fit seems to follow established techniques. I would recommend to evaluate, whether equations could be replaced by references to suitable publications.

ll. 250,254 “least squares method” (with an ‘s’)

Please describe, how the method proposed here deviates from other state-of-the art boresight calibration techniques. Which advantages over those methods do you expect with the method proposed here. Please cite the works upon which you built the development of the algorithm shown here.

Section 3 (Results)

ll. 259 – 272 I would argue that the Monte Carlo method is a well-established technique, so I would recommend to refer to applicable literature wherever possible to shorten the text.

Table 1 There seem to be 4 columns but only 3 headings. Maybe a more descriptive term than Symbol could be chosen as heading?

ll. 278,279 Are the aircraft locations from which measurements are taken also obtained by a random process or are they chosen following a pre-defined pattern?

ll. 282, 283 Sentence seems incomplete

ll. 289, 290 Looking at figure 7 it seems to be, that the errors of ψ and α converge slower than the other errors (see Discussion). Why does the agreement become worse, with more than 200 measurements? It is not immediately clear to me that 100 measurements are better than 50 from figure 7.

ll. 296 “[…] corresponds to 22.13m” -> “[…] or 22.13 m”? Also, please check space between numbers and units everywhere.

Figure 7 Maybe it would be possible to find a more meaningful caption? Number of measurements indicates the number of measurements entering the least squares fit?

l. 305 “[…] is shown in Table 2”?

ll. 307,308 “[…] which makes preliminary preparations […]” I do not understand this sentence. Could you try to rephrase it?

Figure 8 This figure extends over three pages. Maybe try to split it into two figures? Are you sure the lines in subfig (j) are correct (i.e. errors after correction is larger than before)?

l. 321 Why do you use an INS (Inertial navigation system) to measure the position of a static target? How does it improve the DGPS measurement?

l. 321 “geographical positions”

l. 341 “was shown in figure 9” -> “is shown in figure 11”?

Figure 10 “the plane flied” -> “the plane flew”

Table 5 It would be interesting to know, how long the phases took to complete, especially the calibration phase S0. Maybe this information could be added to the table.

Figure 11 The rate of convergence seems to be slower than in figure 7. Maybe you could elaborate on possible explanations for this behavior? Based on this figure, would you still recommend to use 100 measurements for the boresight calibration process?

Section 4 (Discussion)

ll. 386-389 Could you propose an optimal or suitable flight path based on your analysis? Could you define criteria which help to improve calibration accuracy?

Please add, how these results compare to other common boresight calibration techniques in terms of accuracy. How much time do you need to perform the calibration? How does this compare to the time required if you would obtain the boresight angles from images with the RGB camera system? Would this lead to comparable accuracy?

Section 5 (Conclusions)

This section basically states that you performed an in-flight boresight calibration and obtained better results than without such a calibration. I would argue, that this is established knowledge and therefore not unexpected. I would expect some guidelines here, in which scenarious you would recommend the method proposed here compared to other methods and why. Especially, why would you recommend your approach over commercially available software?

 

References

[1] M. Bäumker and F.J. Heimes, New Calibration and Computing Method for Direct Georeferencing of Image and Scanner Data Using the Position and Angular Data of an Hybrid Inertial Navigation System, Proc. OEEPE Workshop on Integrated Sensor Orientation, 2002.

Author Response

Response to Reviewer 2 Comments

 

Response: We appreciate the reviewer’s comments. We seriously consider the comments from the reviewer, and efforts to improve the manuscript from several aspects.

From the revision comments, we know that the reviewers are very familiar with this direction, and the reviewer’s comments are very professional and conscientious. The reviewer gave comments on the principles, comparations, grammar, and sentence expression in the article. Thank you very much for your help.

 

 

Summary

The authors describe a boresight calibration method for a UAV mounted laser range finder. The algorithm is based on measurements of one or more ground control points (GCP) from several different UAV positions. The authors then present an algorithm to infer the desired boresight angles (i.e. installation angles of the laser range finder w.r.t airborne platform) from the GCP measurements with a linear least-squares fit. The authors investigate the performance of the proposed boresight calibration method with a synthetic test data set obtained based on Monte Carlo simulations and they present results from a case study, where the proposed calibration method is applied to a real UAV mounted laser ranger finder. The results show, that the proposed boresight calibration technique is capable of improving the absolute accuracy of the geo-location in both cases.

Broad Comments

The research objectives are clearly stated and they are motivated well with a practical application (UAV based geo-location of military and civil targets). The underlying theory is presented extensively with an in-depth presentation of the associated mathematical theory. Since most of the equations describe basic rotations in three dimensions, I would even recommend to shorten the theory section by referring to applicable literature wherever possible. The following description of the numerical and practical validation experiments and their respective evaluation is presented clearly and comprehensibly. The results show, that the algorithm is capable of inferring a sensible set of boresight angles which lead to a significant improvement in the absolute geo-location accuracy.

While the introduction presents a detailed literature overview of related geo-location algorithms and their applications, it lacks a similar overview of relevant literature on GCP based boresight calibration methods and their respective properties. Given the fact, that boresight calibration is the central topic of this publication, this is a prerequisite to evaluate the authors contribution to this field of research, especially since the topic has been investigated extensively for the geo-location of airborne and spaceborne optical remote sensing instruments over the last thirty years. In particular, the authors should state clearly, how the algorithm they propose differs from other published boresight calibration methods (e.g. [1]) and how the results compare to those published methods in terms of accuracy, precision and robustness.

Specific Comments

Section 1 (Introduction)

Point 1: 27 – 29 Sentence seems incomplete. Maybe “Airborne optoelectronic platforms play an important role in military and civilian applications such as search, ….”

 

Response 1: Thank you for your comments. The sentence had changed to the following:

Airborne optoelectronic platform, which can realize a wide range of search, identification, tracking and measurement, is playing an important role in military and civilian applications such as search, rescue of the wounded and target reconnaissance, etc.

 

Point 2: 34 – 41 How is the choice of the ellipsoid model relevant to your work? How are DEMs relevant, if you measure GCPs by DGPS?

Response 2: The choice of the ellipsoid model refers to the relevant literatures. Because the system uses a laser rangefinder to obtain the distance between the target and the photoelectric load, so the geo-location of target can be obtained without DEM. The GCPs measured by DGPS are mainly for the calibration of the systematic error.

 

Point 3: 71 – 74 Could the methods you mention here be applied to the data after systematic correction, including e.g. the boresight calibration you propose? Would this increase the overall accuracy even further? Maybe system correction is not mentioned in these publications, because the authors regard is an orthogonal activity?

Response 3: In fact, if the systematic error is corrected, the boresight error has already been calibrated. The boresight calibration method mentioned in the literature mainly aims at the installation error between the camera and the POS system. The method proposed in this article not only includes these error items, but also includes the azimuth and pitch angle errors of the load itself. After system error correction, the calibration of the boresight has been achieved, so the positioning accuracy of the system can no longer be improved. The method proposed in this article is a little different from the classical boresight calibration: Optoelectronic equipment generally has azimuth, pitch or more rotation axes, which can realize search and reconnaissance in a large area. Conventional orthorectification of remote sensing data is mainly for vertical downward viewing to achieve mapping images of the target area. Besides, the method proposed in this article uses a laser rangefinder to obtain the distance between the target to develop the equation, which also different from the method mention in the literature of boresight calibration.

 

 

Point 4: 88: I think you should add a review about state-of-the-art boresight calibration methods here, especially those used within the scope of orthorectification of remote sensing data. E.g., could you also use commercial software such as PARGE (http://dev.rese.ch/software/parge/parge-background.html)?. Why not? Which problem inherent to these algorithms are you trying to solve?

 

Response 4: Thank you for your suggestion and I have added a review about state-of-the-art boresight calibration methods. However, there are some difference between classical boresight calibration method and the method proposed by this article.

The object of application is different. This article mainly focuses on the calibration of photoelectric payload geo-location. Optoelectronic equipment generally has azimuth, pitch or more rotation axes, which can realize search and reconnaissance in a large area. Conventional orthorectification of remote sensing data is mainly for vertical downward viewing to achieve mapping images of the target area;

There are differences in system errors. Because of its azimuth and pitch axis, the error of the photoelectric payload is not only the installation error of the three angles between the POS system, but also the systematic error of the azimuth and pitch axis. Ortho correction and commercial software such as PARGE are not considered the azimuth and pitch axis, but simplify the error to three angles installed with the POS system.

The method of establishing the equation is different. Commercial software such as PARGE and conventional optical axis correction methods generally use buddle adjustment or GCPs to obtain the three angles of the optical axis of the image. The method proposed in this article uses a laser rangefinder to obtain the distance between the target. In this way we established the equation to solve the systematic error.

Therefore, it is not possible to simply rely on boresight calibration and commercial software to solve the problem of systematic errors in the target positioning process of the photoelectric pod.

Section 2 (Materials and Methods)

Point 5: l. 99 Maybe add who developed/manufactured the UAV system and what are its main applications

Response 5: Thank you for your comments and I added the information about the UAV as follows:

The geo-location system introduced in this article is composed of a ground control station, a digital & image transmission link, an UAV with an airborne optoelectronic platform, as shown in the figure 1. The UAV was developed by Changchun Institute of Optics Fine Mechanics and Physics, Chinese Academy of Science for civilian applications such as rescue of the wounded and forest fire prevention. The ground control system is responsible for the control and status display of the UAV and the airborne optoelectronic platform. The transmission link is responsible for real-time downloading of video data. The airborne optoelectronic platform is composed of visible camera, Thermal imaging camera, laser rangefinder, stabilized platforms, image trackers, inertial measurement unit (IMU) etc. The stabilized platforms include the azimuth axis and the pitch axis, and each axis has an encoder which can output the current azimuth and pitch angle in real time.

Point 6: l. 116 “… and the airborne …” -> omit “and”

Response 6: Thank you for your comments and the “and” was omitted.

Point 7: l.119 Could you also use the camera for boresight calibration, e.g. to obtain more GCPs with one measurement (i.e. perform the ‘classical’ boresight calibration used for imaging remote sensing instruments)? What are the advantages/disadvantages compared to your approach?

Response 7：This method is based on active geo-location with laser ranging, and only one target point can be obtained for each measurement. This method is aimed at the payload with azimuth and pitch axis. Using laser rangefinder for active geo-location, and the systematic error of azimuth and pitch angle can be solved. However, the classic boresight calibration is often aimed at the down-view image, and what is obtained is the boresight direction installed on the aircraft, and it is impossible to solve the azimuth and pitch angle errors of the load.

Point 8: Figure 1 Maybe you could indicate where the IMU and the GPS antenna are located.

Response 8: Thank you for your suggestion and the revised images is show as follows:

Figure 1. The geo-location system introduced in this article (The top left figure shows the ground control station and the figure on the bottom left shows the inside of the station; the top right figure shows the UAV with the airborne optoelectronic platform, and the bottom right figure shows the detail of the airborne optoelectronic platform).

Point 9: l. 132 Do all optical instruments share a common principal point? How can this be guaranteed?

Response 9: In this platform, the IR camera and Visible camera don’t share a common principle point but they are very close (about 100mm). Compared with the geo-location error, this is relatively small. In order to obtain a better result, I have changed the origin of the coordinate to the rotation center of the payload, because the center is the closest to the laser ranging, the visible light camera and the infrared camera.

Point 10: l. 133 “points to the front of the platform” -> unclear since front is diagonally above the platform. Maybe “points upwards if the camera is oriented in flight direction / along vehicle x-axis”?

Response 10: Thank you for your suggestion and it is truly clearer in this way. The sentence now presents as follow:

This frame has its origin at the principal point of the imaging system. The  axis points upwards if the camera is along vehicle x-axis, and the  axis is along the light of sight (LOS) of the imaging system and pointing to the target, and  forms an orthogonal right-handed frame set.

Point 11: ll.135-136 “the outer gimbal rotates around the ZV axis” Are you sure this should not be Zb?

Response 11: Thank you for your correction and I had corrected the wrong expression.

Point 12: ll. 143 – 147 Is this the standard ARINC frame with origin shifted to the center of the optical platform reference frame? If so, you could just state this and omit the lengthy description.

Response 12: Thank you for your suggestion and this is the standard ARINC frame with origin shifted to the center of the optical platform reference frame. I have omitted the lengthy description as suggested.

Point 13: ll. 150 -153 Since this seems to describe the standard NED (north, east, down) reference frame, you could state this and shorten the explanation. What exactly do you mean by “aircraft’s center”? The center of gravity, the center of the IMU, the principal plane of the optical system …?

Response 13: Thank you for your suggestion and this is the standard NED (north, east, down) reference frame. I have omitted the lengthy description as suggested. In this article the aircraft’s center means the center of the IMU.

Point 14: ll. 155 – 158 I think it would be sufficient, to state that you are using the WGS-84 reference ellipsoid.

Response 14: Thank you for your suggestion and I have shortened the explanation.

Point 15: Figure 3 to Figure 5: I find the pseudo-3d sketches in combination with the many angles a little confusing. Maybe reduce the number of coordinate systems shown per figure?

Response 15: Thank you for your suggestion and I replot those sketches and reduce the number of coordinate systems shown in per figure.

Figure 3 has been changed from

To

And Figure 4 has been changed from

To.

The Figure 5 have only to coordinate and maybe it’s OK compare to the figure 3 and figure 4.

Point 16: Eq (1) Replace xg by yg, zg in second and third term, respectively

Response 16: Thank you for your correction and I had corrected the wrong expression.

Point 17: 170 – 187, eqs (2) – (6) These seem to be standard coordinate transformations. I would recommend to simply cite applicable literature and omit the details in the manuscript. It is clear, that you can transform the coordinate systems into each other by a sequence of rotations and translations.

Response 17: Thank you for your suggestion. It is truly clear, that we can transform the coordinate systems into each other by a sequence of rotations and translations. I have tried to cite applicable literature and omit the details in the manuscript; however, the symbols are named differently. It may be a little confused if I cite without those transformations.

Point 18: Eq (8) What is Pg? Should there not be a shift of origin from the center of gravity of the aircraft to the origin of the imaging system coordinate frame?

Response 18: Thank you for your comment and I haven’t given the meaning of of Pg. I had added the meaning of Pg:

Then the target position  in geodetic coordinate frame can be expressed as

(8)

 is a shift of origin from the center of gravity of the aircraft to the origin of the imaging system coordinate frame.

Point 19: Eq (9) Did you develop this algorithm yourself? If so, please explain how, otherwise please cite the source. In case there is a source, you could actually leave the equation out entirely.

Response 19: I have given the cite the source and I think maybe it is more complete to explain in this way.

Point 20: Eq (10) Is this detail really relevant?

Response 20: Thank you for your suggestion and this part shows how to get the longitude of the target points and I think it is more complete to explain in this way.

Point 21: l. 202 “influence of the error items” -> “individual sources of measurement uncertainty” ?

Response 21: Thank you for your suggestion and It’s more concise and clearer in this way. Thank you.

Point 22: l. 208 Maybe “These are normally distributed random errors”? Also: How do you know the GNSS position error is random with gaussian distribution? Could there be systematic offsets, too, on time scales of several minutes? On which time scales do the errors become normally distributed?

Response 22: Thank you for your suggestion and I have changed the sentence in this way. We usually consider the GNSS position error as random with gaussian distribution, see literature [2,3].

Point 23: l. 215 Does the additional POS move with the optoelectronic platform? Where is the GNSS antenna for this POS located? Does the antenna lever arm change when the optical platform moves? If so, is this accounted for during data processing? If not, what’s the estimated additional uncertainty caused by this effect compared to the uncertainty of the gimbal encoder uncertainty?

Response 23: Yes the additional POS moves with the optoelectronic platform. The GNSS antenna located at the top of the UAV as shown in figure 1. Antenna lever arm doesn’t change when the optical platform moves. There is a three-dimensional displacement between the antenna and the platform, and the accurate value can be obtained through the structural drawing. The geo-location error caused by this displacement error is very small compared with the geo-location error caused by the encoder angle error of the payload, which is not considered in this article.

Point 24: l. 220 Does 200” mean 200 arc-seconds? I would recommend to use either deg or mrad.

Response 24: Yes 200” mean 200 arc-seconds. Now I am using mrad as recommended.

Point 25: ll. 223/224 Maybe “[…] the rotation matrix […] can be approximated by”?

Response 25: Thank you for your suggestion and It’s more concise and clearer in this way. Thank you.

Point 26: eq (19) Should the last element of the fit vector not be \delta_\beta instead of \delta_\chi ?

Response 26: Thank you for your correction and I have made the amendment. Thank you.

Point 27: eqs (14) – (22) The least squares fit seems to follow established techniques. I would recommend to evaluate, whether equations could be replaced by references to suitable publications.

Response 27: Although this process is a conventional least squares method, due to the inconsistency of the variables, citing literature descriptions may cause readers to misunderstand, here is thrown to keep the original state

Point 28: ll. 250,254 “least squares method” (with an ‘s’)

Response 28: Thank you for your correction and I have made the amendment. Thank you.

 

Point 29: Please describe, how the method proposed here deviates from other state-of-the art boresight calibration techniques. Which advantages over those methods do you expect with the method proposed here. Please cite the works upon which you built the development of the algorithm shown here.

Response 29: Thank you very much for your suggestion. I have added the state-of-the art boresight calibration techniques in introduction. However, the method proposed here aim at different imaging system: this imaging system with rotation axis in the platform, not just misalignment between POS and the imaging system. I have cited the works upon which you built the development of the algorithm in the article.

Section 3 (Results)

Point 30: ll. 259 – 272 I would argue that the Monte Carlo method is a well-established technique, so I would recommend to refer to applicable literature wherever possible to shorten the text.

Response 30: Thank you for your suggestion and I referred to other literature and have shortened the text.

Point 31: Table 1 There seem to be 4 columns but only 3 headings. Maybe a more descriptive term than Symbol could be chosen as heading?

Response 31: Thank you for your suggestion and the table have been changed as follows:

Error type	Name of Error Variable       Symbol		Error value
Systematic error	POS installation error	Roll	0.2°
		Pitch	-0.05°
		Yaw	0.3°
	Payload installation error	Pitch	0.1°
		Azimuth	-0.2°
Random error	Platform position	Latitude	0.0001°(10m)
		Altitude	0.00012°(10m)
		Altitude	10m
	Platform attitude	Roll	0.02°
		Pitch	0.02°
		Yaw	0.05°
	Payload angle	Pitch	0.027°
		Azimuth	0.027°
	Laser range	Laser	5m

 

Point 32: ll. 278,279 Are the aircraft locations from which measurements are taken also obtained by a random process or are they chosen following a pre-defined pattern?

Response 32: Yes, the aircraft locations also obtained by a random process.

Point 33: ll. 282, 283 Sentence seems incomplete

Response 33: Thank you for your correction and I have made the amendment. Thank you.

The sentence has been changed from:

Performed 256 times measurements on the control point, and gotten the installation error as shown in Figure 7.

to:

After performed 256 times measurements on the control point, we got the installation error as shown in Figure 7.

Point 34: ll. 289, 290 Looking at figure 7 it seems to be, that the errors of ψ and α converge slower than the other errors (see Discussion). Why does the agreement become worse, with more than 200 measurements? It is not immediately clear to me that 100 measurements are better than 50 from figure 7

Response 34: If the pitch angle and roll angle errors between the POS and the platform are close to 0, then the heading axis of the POS and the azimuth axis of the platform are parallel, so it converges slower. But the sum of azimuth and heading errors is stable. If you look at it from this perspective, 50 iterations are enough to be stable. However, if the pitch angle and roll angle between the POS and the platform have a large error, the heading of the carrier aircraft and the azimuth of the load are no longer parallel, and it can converge quickly.

Point 35: ll. 296 “[…] corresponds to 22.13m” -> “[…] or 22.13 m”? Also, please check space between numbers and units everywhere.

Response 35: Thank you for your suggestion and I had made the revise as recommended.

Point 36: Figure 7 Maybe it would be possible to find a more meaningful caption? Number of measurements indicates the number of measurements entering the least squares fit?

Response 36: Thank you for your suggestion and I have changed the caption to “The iteration curve of the installing errors for simulation data.” And I have changed the caption for figure 11 too. Yes, the number of measurements indicates the number of measurements entering the least squares fit.

Point 37: l. 305 “[…] is shown in Table 2”?

Response 37: Thank you for your suggestion and I had made the revise as recommended.

Point 38: ll. 307,308 “[…] which makes preliminary preparations […]” I do not understand this sentence. Could you try to rephrase it?

Response 38: Thank you for your suggestion and I had rephrased the sentence as follows.

After the systematic error were corrected, the root mean square error is reduced to 1/3 of the original, and the mean value of the geo-location error is closer to zero. The methods such as Kalman filter etc. used for geo-location would be more accurate after the systematic error were corrected.

Point 39: Figure 8 This figure extends over three pages. Maybe try to split it into two figures? Are you sure the lines in subfig (j) are correct (i.e. errors after correction is larger than before)?

Response 39: Thank you for your correction and I am shamed for my error -.-.

Point 40: l. 321 Why do you use an INS (Inertial navigation system) to measure the position of a static target? How does it improve the DGPS measurement?

Response 40: I have to say that you are very familiar with the entire system, and the questions you raise are also critical. INS (Inertial navigation system) can’t improve the DGPS measurement of the position of a static target. In fact, it’s a DGPS/INS integrated navigation system which we always used in outfield. Here in order to make it less confuse, I change it to use a DGPS device to measure these static targets.

Point 41: l. 321 “geographical positions”

Response 41: Thank you for your correction and I have made the amendment. Thank you.

Point 42: l. 341 “was shown in figure 9” -> “is shown in figure 11”?

Response 42: Thank you for your correction and I have made the amendment. Thank you.

 

Point 43: Figure 10 “the plane flied” -> “the plane flew”

Response 43: Thank you for your correction and I am shamed for my error -.-.

Point 44: Table 5 It would be interesting to know, how long the phases took to complete, especially the calibration phase S0. Maybe this information could be added to the table.

Response 44：The UAV flew about 60m/s, and the total distance of phase S0 is about 30km, but the UAV had to climb from 2500 to 3000. During the flight, we flew the path of each altitude, that mean L1->L2->K4->L5->L3, so it difficult to estimate the time each phase cost. If we just consider the valid route, the phase S0 cost about 12min.

Point 45: Figure 11 The rate of convergence seems to be slower than in figure 7. Maybe you could elaborate on possible explanations for this behavior? Based on this figure, would you still recommend to use 100 measurements for the boresight calibration process?

Response 45: If the pitch angle and roll angle errors between the POS and the platform are close to 0, then the heading axis of the POS and the azimuth axis of the platform are parallel, so it converges slower. But the sum of azimuth and heading errors is stable. If you look at it from this perspective, 50 iterations are enough to be stable. However, if the pitch angle and roll angle between the POS and the platform have a large error, the heading of the carrier aircraft and the azimuth of the load are no longer parallel, and it can converge quickly. I would recommend to use 200 measurements for the calibration process.

Section 4 (Discussion)

Point 46: ll. 386-389 Could you propose an optimal or suitable flight path based on your analysis? Could you define criteria which help to improve calibration accuracy?

Response 46: Since different platforms have different laser rangefinder, it difficult to give a suitable flight path for all the calibration. But through simulation and flight experiment, it is recommended that the UAV flies on the left side and right side of the target, and take sample during the azimuth angle near 45deg,135deg,225deg and 325deg respectively.

 

Point 47: Please add, how these results compare to other common boresight calibration techniques in terms of accuracy. How much time do you need to perform the calibration? How does this compare to the time required if you would obtain the boresight angles from images with the RGB camera system? Would this lead to comparable accuracy?

Response 47: There are differences between this method and the common boresight calibration: first, this method introduce more calibration items than just misalignment between imaging coordinate system and body coordinate system with inertial instrument; second, this method applies to platform with laser rangefinder to measure the distance between the imaging coordinate system and targets, which is different from get boresight angle from images. Now I have difficult to build equations using boresight angles from image with RGB camera system with the azimuth and pitch angle of the payload considered. I will still focus on this topic and give a overall answer.

Section 5 (Conclusions)

Point 48: This section basically states that you performed an in-flight boresight calibration and obtained better results than without such a calibration. I would argue, that this is established knowledge and therefore not unexpected. I would expect some guidelines here, in which scenarious you would recommend the method proposed here compared to other methods and why. Especially, why would you recommend your approach over commercially available software?

Response 48: I have added the following to the conclusions:

The method proposed here mainly focus on the systematic error correction for airborne optoelectronic platform with laser rangefinder, which has multiple rotation axis such as azimuth and pitch axis. Through this method, we can not only get the misalignment between the platform and the body coordinate system established by the inertial instruments, but the systematic error of the rotation axis inside the platform. As for more rotation axis platform, we just need to add more systematic error items and expand the equation. There are differences between this method and the common boresight calibration: first, this method introduce more calibration items than just misalignment between imaging coordinate system and body coordinate system with inertial instrument; second, this method applies to platform with laser rangefinder to measure the distance between the imaging coordinate system and targets, which is different from get boresight angle from images .

 References

[1] M. Bäumker and F.J. Heimes, New Calibration and Computing Method for Direct Georeferencing of Image and Scanner Data Using the Position and Angular Data of an Hybrid Inertial Navigation System, Proc. OEEPE Workshop on Integrated Sensor Orientation, 2002.

[2] Qiao, C.; Ding, Y.; Xu, Y. Ground target geolocation based on digital elevation model for airborne wide-area reconnaissance system. J. Appl. Remote Sens. 2018, 12, 016004.

[3] Bai, G.; Liu, J.; Song, Y.; Zuo, Y. Two-UAV Intersection Localization System Based on the Airborne Optoelectronic Platform. Sensors 2017, 17, 98.

 

 

Author Response File: Author Response.docx

Reviewer 3 Report

The study entitled "Systematic Error Correction for Geo-location of Airborne Opto- electronic Platform"

 

The authors of this study demonstrated a method for systematic error correction for geo-location is provided in order to increase the geo-location accuracy of the airborne optoelectronic platform and reduce the influence of assembly systematic error on the accuracy.

The geo-location model was first constructed based on the kinematics features of the airborne optoelectronic platform. The mistake items that affect geo-location accuracy were then examined.

The installation error between the platform and the POS was examined, and the platform's pitch and azimuth installation errors were introduced. The least square form of systematic error is produced after excluding higher-order infinitesimals.

 

As a result, the systematic error may be calculated using a series of measurements. The findings of Monte Carlo simulation analysis and in-flight experiment suggest that this method can successfully obtain the systematic error. Correction lowered the root-mean-square value of the geo-location error from 45.65m to 12.62m and the mean error from 16.60m to 1.24m. This technology has the potential to be widely applied in the systematic error correction of relevant photoelectric equipment.

This is an intriguing study, as the authors have compiled a one-of-a-kind dataset using a cutting-edge methodology. In general, the work is nicely written and organized. As I'm very impressed with their work, I will give the first-round pass as is.  

Author Response

Response to Reviewer 3 Comments

 

Response: Thank you for your letter and for the reviewers’ comments concerning our manuscript. These comments are all valuable and very helpful to guiding our researches. We will keep working on relevant research. Thanks.

Round 2

Reviewer 2 Report

I think the changes made by the authors significantly improve the readability of the manuscript.

The main argument, that the existence of the laser range finder allows a simpler algorithmic treatment compared to the standard bundle block adjustment used in photogrammetry sounds convincing to me.

I would like to add, though, that it is not uncommon to mount aerial camera systems on gimballed plattforms to decouple them from the motion of the aircraft. In this case one obtains equations almost identical to those presented by the authors (except for the additinal distance information obtained from the laser range finder). According to my experience it is common to mount the IMU directly to the camera in those cases, so the gimbal encoder values are only used to determine the antenna lever arm, if camera & IMU rotate relative to the airframe/GPS antenna. This reduces the influence of gimbal encoder inaccuracies.

If I understand correctly, you argue that you also calibrate the gimbal encoder along with the installation angles of the optical system. If this is true, I think it would help to answer two additional questions:

1. Is it possible to calibrate the gimbal system in the laboratory with comparable accuracy?
2. You fit a fixed offset for the gimbal encoder wrt. the POS. Can you motivate this choice compared to an offset changing with gimbal angle or time?

To me the usage of the english language seems a little awkward at several places in the text (I am not a native speaker, though). Thus I would recommend editing of style and language by a third party.

The Bäumker and Heimes (2002) article was more or less a random suggestion, because it is one of the earliest publications I could find. If you think it is relevant enough to cite it, please make sure to cite it correctly (according to google it was a contribution to the OEEPE Workshop on Integrated Sensor Orientation).

Author Response

Response to Reviewer 2 Comments

 

Response:

Thank you very much for your comments again. I am glad you agree with the difference of this method with the standard bundle block adjustment used in photogrammetry. I must admit, the questions you mentioned are very professional. We do have airborne optoelectronic platforms that the IMU mounted directly to the camera when there has enough space. This would reduce the influence of gimbal encoder inaccuracies and leads to a better geo-location result. But still we also need a calibration between the IMU and the camera.

 

Point 1: Is it possible to calibrate the gimbal system in the laboratory with comparable accuracy?

Response 1:

 

Yes, we have methods to calibrate the optical system with the azimuth and pitch axis in the laboratory, but there is no good method to calibrate the systematic error between IMU and the optical system now, and we can only rely on the mechanical installation. Better results can be obtained by using the method of flight calibration.

Point 2: You fit a fixed offset for the gimbal encoder wrt. the POS. Can you motivate this choice compared to an offset changing with gimbal angle or time?

Response 2:

Yes, we are using a fixed offset for the gimbal encoder wrt. There is no evidence that the offset of the encoder will change with gimbal angle or time. We will do more tests to see if using dynamic offsets will make the system more accurate.

I check with the https://www.researchgate.net/ about Bäumker, Manfred & Heimes, F.’s article, and I did make a mistake. Now I had corrected it and thank you for your correction. As for the usage of the English language, I asked a colleague who have study in USA for two years to help me and he had made some revision. Thank you for your suggestion.

Are you Chinese? Have you ever been to China? If possible, you can come to the institute I am working for work or academic exchanges. We welcome you who are professional and have a deep understanding of the system.

 

 

Author Response File: Author Response.docx