Peer review of: Descent trajectory reconstruction and landing site positioning of Chang’E-4 on the lunar farside (2019)

Reviewers' comments:  
 
Reviewer #1 (Remarks to the Author):  
 
General Comments  
 
This paper describes the location of where the Chang’E-4 landed on the far side of the Moon and 
the technique used to identify the location. Traditional radiometric techniques are unusable 
because there is no line-of-sight with the far side, so there is no direct telemetry with Chang’E-4. 
As such, optical navigation techniques of triangulation based upon the Moon’s digital terrain model 
were used, both in controlling the spacecraft for soft landing as well as computing where the 
spacecraft finally landed.  
 
The paper is well written and clear with only a few awkward sentences.  
 
The paper does a good job describing the sequence of events and the data that was available to 
the spacecraft and later the reconstruction team. The reviewer would have liked to see more detail 
in the method section of the specific mathematics and techniques used, especially the bundle 
adjustment applied.  
 
In the discussion section: the comment about the gentle topography (L173) for the Chang’E-4 site 
compared to the Chang’E-3 site lacked sufficient detail to draw effective conclusions. A 3km 
variation vs a 6000m (please use the same units) does not seem like a drastic enough change. It 
seems like there was something significant, but the text was hard to follow. The phrase “avoid the 
discontinuity” (L176) needs more clarity.  
 
L87 More information about the Automatic on-orbit analysis would be useful, either here or in 
methods. Is this software available? Does it have a name? Has it been used before?  
 
L109 More information about the three-dimension laser imaging should be provided.  
 
L139 Figure 4 shows a shaded relief map of the landing site. This shaded relief map has significant 
pixelation and artifacts (surface is too flat, lack of craters near the site, etc.) Can you provide any 
discussion for this? Also, it would be useful to have an image that shows which regions where done 
at what resolution. While the text says 2cm DEM were produced, I expect that wasn’t done over all 
of the region. Thus, showing where the data has higher resolution would improve people’s 
understanding of the process and where the data is best.  
 
L146 How was the 5 laser reflectors integrated into your analysis? How where they measured? 
When where these measurements taken?  
 
L233 More discussion about why LROC positions are so different than Chang’E-4 would be useful.  
L245 Define RANSAC  
L250 What is a vertical ground control point.  
L256 Define EO  
L270 Define TIN  
L271 Define LACM, or did you mean LCAM?  
 
 
Minor Comments   
L14 successful should be successfully  
L17 Recommend changing “real time” with “a” (It wasn’t real time when the reconstruction was 
done)  
L28-31 Sentence “After…” is awkward. Suggest replacing “experienced” with “conducted”. 
“descending” with “descent”  
L31 Remove comma after Moon  
L45 Define DOM and DEM  
L49 Suggest replacing “Combined with the” with “Using combined”  
L59 Caption. Suggest adding a comment that the + is the identified landing location  
L70 Only use etc. for a list of items that are known. If you are making a list of items, give the full 
list. In this case, you might be able to remove etc altogether.  
L78-82 Awkward sentence. This may be because the concept of vertical attitude isn’t defined.  
L81 Likewise “horizontal to the vertical direction” isn’t clear  
L89 Sentence starting with “Therefore…” is confusing.  
L93 After hovered, replace comma with “and”  
L113 Can you provide the speed of the “slow vertical descent?”  
L117 Provide a reference for the bundle adjustment technique.  
L123 Either provide the residuals for the bundle adjustment here or refer readers to the method 
section. 
Table 1. Suggest putting error values next to the lat/lon rather than in comments  
L157-159. I suggest putting a dashed line around the next image’s footprint. It would make it 
easier for people to follow the progress of images. Thus, image C would have a small box that 
matched the full field of view of image D. Also, a scale bar on each would be beneficial.  
L189-192 Suggest referring the reader to the methods section to understand where the RMS error 
comes from.  
L195-196 Sentence starting with “Apparently, …” is awkward.  
L232 Where are the reflectors located? Are they on the near or far side? If so, how sampled?  
 

 
Reviewer #2 (Remarks to the Author):  
 
Review of Paper  
 
This is a most interesting report on the first historic landing on the lunar far-side, quite appropriate for publication in Nature.  
 
However, the text would benefit from improvements. While the spelling is good, the wording and 
phrasing need some more work effort. Many sentences are not sufficiently specific. Besides, the 
text leaves some open questions.  
There is confusion about the instruments and the data that were used. Some critical information is 
only given late in the paper and should be moved up.  
 
From the reading, I have the impression that in many places the paper is researching what the 
spacecraft was doing. I suggest to improve the phrasing to correct this impression.  
 
I tried to point out problems and make some suggestions, see my comments below.  

Generally speaking, I recommend publication of the exciting material, pending on a number of 
improvements of the text.  
 
 
Specific comments:  
 
Title:  
..on Moon’s farside -- > ..on the Moon’s farside (or: on the lunar farside)  
 
 
Abstract:  
Because it is impossible to directly measure the farside of the Moon ... -- >  
As Earth-based radio tracking is impossible for a spacecraft moving over the lunar farside ...  
 
to use real-time series of image data -- >  
to use image data obtained during descent, which were transmitted to the ground after landing via 
a relay satellite (perhaps you may want to give the name of the satellite and mention its important 
mission)  
 
It was found that CE-4 … realized a safe soft landing  
-- > it seems that the paper is researching what the spacecraft was doing. I suggest to rephrase 
this (and in other places the main text of the paper.)  
 
L 34 - 37  
It is impossible to perform… real-time control based on the measurement and control network of 
earth -- > ? not clear, need to rephrase  
 
L 40  
It is expected that slight movement … -- > We reconstructed the descent trajectory, showing even 
barely perceivable maneuvers of the spacecraft during the landing approach (ok?)  
 
L 45  
-- > please explain to the non-expert reader: what are DOM and DEM?  
 
L 67  
One general comment: It is not clear what is described in this chapter.  
Is it the trajectory from the autonomous navigation or is it the reconstruction of the trajectory 
from the images, after the landing. The topic of trajectory reconstruction is only introduced later in 
the paper.  
 
L 72  
Autonomous navigation control was adopted in the whole landing process  
-- > there is little information in the paper. Did the autonomous navigation use the LCAM images?  
General question: Is the information on the autonomous navigation solution available, and was it 
used in the reconstruction of the trajectory?  
 
L 73  
obstacle avoidance -- > How was this accomplished?  
 
L 78  
… started acquiring image …  
-- > started acquiring images … (or: acquired the first image…)  
 
… started acquiring image 5m11s … after onset of CE-4 power descent -- >  
Can you give more information? What was the time of the touch-down?  

(Perhaps, it is a good idea give a time line or a plot showing time, spacecraft speed and height?)  
 
L 87  
automatic onboard orbit analysis … revealed … surface slope -- > can you explain what was done?  
 
L91  
by optical imaging sensor on CE-4 -- >  
Is this LCAM?  
 
L 93  
performed detailed detection and determined the landing site -- > performed detailed assessment 
of the morphology of the ground and a choice for a final landing site was made.  
 
L 109  
laser imaging sensor -- > can you explain?  
 
L 115  
General question: “We made LCAM topographic maps” -- > considering that the LCAM images 
were all taken from above, stereo angles between images were probably very small. How did you 
manage to produce the topography?  
 
Were topographic maps produced after the trajectory reconstruction, assuming that the spacecraft 
position and attitude were fixed for each image? Or was this a combined approach?  
 
Were the laser images available to support the map production?  
 
L 121  
Can you explain to the non-expert reader: what are GCPs?  
What is the positioning accuracy of the CE-2 maps (from which GCPs were taken)?  
(Information is given only later in the text)  
 
L 134 Figure 3:  
Please use consistently decimals of degree (preferred) -- or degree, minute, second!  
Is the image on the right showing a detail within the image on the left?  
It is confusing that the images right and left use identical numberings for different control points 
(if I am not mistaken?). Please choose better example to demonstrate control point work.  
 
L 163 Figure 3 caption  
I do not see the “red triangle”  
 
Adjustment -- > adjustment  
images Adjustment -- > image adjustment  
 
L 167  
Discussion -- > It is strange to have the discussion so early, even before description of Methods.  
 
L 171  
It is confusing to mix discussions of CE4 and CE3. What are we to learn from CE3 here?  
 
L 177 fluctuating terrain -- > (?)  
 
Figure 6: can you please mark the surface level?  
The plot combines topography and spacecraft height. Would it make sense to show topography 
and spacecraft height separately?  
 
L 174  
our results reveal that the spacecraft switched from oblique downward to vertical downward…  
-- > not clear (it seems that the paper is researching what the spacecraft was doing)  
 
L 176  
… which effectively avoid the discontinuity -- > discontinuity? not clear  
 
… which effectively avoid -- > … which effectively avoided  
 
L 178  
distance measuring sensor -- > can you explain?  
General question: were the data from distance measuring sensor and the above mentioned laser 
imaging sensor used in the reconstruction of the trajectory?  
(Note that these instruments are not listed in the “Instrument Description”)  
 
L 186  
Based on the sequence images of the LCAM, we reconstructed the power descent trajectory of the 
CE-4 lander through the photogrammetry method  
-- > this is coming very late (in the Discussion?). If I understand correctly, results are already 
shown earlier in the paper.  
 
L 191 and L 232: CE2TMap2015 absolute accuracy...  
-- > how did the map achieve this excellent accuracy? Unfortunately, the relevant papers that are 
referenced are all in Chinese.  
 
L 195: Why is the difference in position so large? Does it mean that the LRO reference frame and 
CE2TMap2015 differ by ~500m? It seems there is some confusion about the reference frame in 
use.  
 
L 206  
Instrument descriptions -- > This information is coming very late in the paper. The complete list of 
instrument and relevant data used in the analysis should be briefly introduced earlier in the paper. 
The details may be moved to the end. It appears that critical instruments are not listed (laser 
imager, distance sensor?)  
 
L 249: what is the NAC image used for? It is also not mentioned in Fig.7? Please clarify  
 
L 369 We thank the team ... -- > perhaps this statement should go into the acknowledgements?  
 
L 374 data … available on reasonable request -- > “reasonable” ?  
 
 

 
Reviewer #3 (Remarks to the Author):  
 
The manuscript submitted by Liu et al presents the photogrammetric methodology utilized to 
determine the descent trajectory and surface coordinates of the Chang’e 4 lander.  
 
 
1) What are the major claims of the paper?  
- The authors derived a detailed reconstruction of the descent trajectory, which included 
autonomous hazard avoidance. They describe how the onboard systems avoided hazards and 
allowed the vehicle to land safely on the lunar farside. The trajectory and surface coordinate 
reconstructions were the result of standard photogrammetric bundle block adjustment techniques.  
The authors provide the following coordinates for the lander 45.4446°S latitude, 177.5991°E, 
elevation -5935 meters and state that (lines 199-201) “As a permanent artificial landmark on the 
farside of the Moon, the location of the CE-4 lander was precisely confirmed using CE-2 and CE-4 
image, and can serve as a potential control point on the farside of the Moon.”  
 
Absolute coordinate control for the Chang’e 4 images was provided by tying the bundle block 
adjustment to the Chang’e 2 global image mosaic / control network, with a stated uncertainty of 
21-97 m horizontal and 2-19 m elevation. The Chang’e 2 coordinate system is in turn tied to the 5 
laser retroreflectors located on the nearside. Note that in the caption to Table 1 a footnote states 
(line 149): “...the elevation data was accurate to meter.” It is not clear to the reviewer where the 
accurate to a meter was derived when previously it was stated that the uncertainty in elevation 
was 2-19 m.  
 
The authors compared their derived coordinates to those derived by the Lunar Reconnaissance 
Orbiter Camera (LROC) team values (45.457°S, 177.589°E, plus minus 20 meters) and state that 
there is a 376 m and 215 m difference in latitude and longitude (respectively), for a total 433 m 
positional offset. The authors state that: “The total positional deviation is 433 m. Apparently, the 
positioning data of this study is more sufficient and detailed, and the results are more accurate. 
The latitude and longitude disagreement with that of LRO data can be accounted for by different 
reference map.” Lines 195-198. [Note: a degree on the Moon is ~30.3 kilometer so 0.001° is ~30 
meters]  
 
2) Are they novel and will they be of interest to others in the community and the wider field?  
- While the methods presented in this work to derive the trajectory and lander coordinates are not 
novel, the reconstruction of a robotic lander under autonomy as it sets down on the lunar farside is 
novel and will be of interest to others in the community and the wider field.  
 
3) If the conclusions are not original, it would be helpful if you could provide relevant references.  
The conclusions seem to be original, though partially unsubstantiated. Authors might add a 
standard reference to the bundle block adjustment technique that goes back 60 years (see 
below).  
 
4) Is the work convincing, and if not, what further evidence would be required to strengthen the 
conclusions?  
- For the most part the work is convincing. I do have one quibble with the comparison to the LROC 
team coordinates of the lander summarized above (see also lines 194-198 in manuscript). One 
could justifiably argue that the CE-2 coordinate system tied to the 5 nearside retroreflectors will 
not be as accurate on the opposite side of the Moon for several reasons (i.e. the lumpy gravity 
field of the Moon, small uncertainties in camera model (distortion, FL) adding up over “distance”, 
etc.). For example, a control network derived from Clementine UVVIS images was also shown to 
have km offsets due to the aforementioned reasons (Speyerer et al., 2016).  
 
The authors did not fully document the coordinate system used in their work (a key reference is in 
Chinese and this reviewer was unable to read the paper) thus the claim that discrepancy is due to 
“different reference map” is left ambiguous. The LROC coordinates derived have a stated accuracy 
much smaller than the 433 meters reported in this manuscript.  
 
Lunar Reconnaissance Orbiter radiometric tracking data were combined with the GRAIL gravity 
model to significantly improve the Lunar Reconnaissance Orbiter spacecraft ephemeris and thus 
geodetic accuracy of each LOLA spot to less than 10 m horizontally and 1 m vertically (Lemoine et 
al. 2014; Mazarico et al. 2012; Mazarico et al. 2013 ). Subsequent, in-flight calibration has 
improved the mapping of a single NAC image to < 20 m (Speyerer et al., 2016). The methods 
used to control LROC NAC images to the LOLA framework (and associated uncertainties) are 
documented in Wagner et al (2017) and Henriksen et al (2017).  
 

Archinal, B.A., M.R. Rosiek, R.L. Kirk, and B.L. Redding, 2006. The Unified Lunar Control Network 
2005. U.S. Geological Survey Open-File Report 2006-1367, 12 p.  
Henriksen, M. R, M. R. Manheim, K. N. Burns, P. Seymour, E. J. Speyerer, A. Deran, A. K. Boyd, E. 
Howington-Kraus, M. R. Rosiek, B. A. Archinal, and M. S. Robinson (2017), Extracting accurate and 
precise topography from LROC narrow angle camera stereo observations, Icarus, 283, 122-137, 
doi: 10.1016/j.icarus.2016.05.012.  
 
Lemoine, F.G., Goossens, S., Sabaka, T.J., et al., 2014. GRGM900C: A degree 900 lunar gravity 
model from GRAIL primary and extended mission data. Geophys. Res. Lett. 41, 3382–3389. doi: 
10.10 02/2014GL060 027.  
 
Mazarico, E., Rowlands, D.D., Neumann, G.A., et al., 2012. Orbit determination of the lunar 
reconnaissance orbiter. J. Geod. 86 (3), 193–207. doi: 10.1007/ s00190-011-0509-4.  
 
Mazarico, E., Goossens, S.J., Lemoine, F.G, et al. , 2013. Improved orbit determination of lunar 
orbiters with lunar and gravity fields obtained by the GRAIL mission. In: Proceedings of the 44th 
Lunar and Planetary Science Conference. The Wood- lands, TX, Abstract #2414.  
Speyerer, E.J., Wagner, R.V., and Robinson, M.S., 2016. Geometric Calibration of the Clementine 
UVVIS Camera Using Images Acquired by the Lunar Reconnaissance Orbiter. In: The International 
Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLI-
B4  
Speyerer, E.J., R.V. Wagner, M.S. Robinson, A. Licht, P.C. Thomas, K. Becker, J. Anderson, S.M. 
Brylow, D.C. Humm, M. Tschimmel, 2016. Pre-flight and On-orbit Geometric Calibration of the 
Lunar Reconnaissance Orbiter Camera, Space Science Reviews, 200, 357-392.  
Wagner, R. V., D. M. Nelson, J. B. Plescia, M. S. Robinson, E. J. Speyerer, and E. Mazarico (2017), 
Coordinates of anthropogenic features on the Moon, Icarus, 283, 92-103, doi: 10.1016/ 
j.icarus.2016.05.011.  
 
Yes, different reference maps were used: LOLA vs Chang’e 2 for the LROC vs Chang’e 4 work. The 
manuscript does not in any way document the assertion: “Apparently, the positioning data of this 
study is more sufficient and detailed, and the results are more accurate.” The authors need to 
compare the Chang’e 2 coordinate system with the LOLA system in a global sense and make some 
quantitative assessment of any discrepancies between the two products to support the statement 
quoted above (lines 195-196 in the manuscript).  
 
5) On a more subjective note, do you feel that the paper will influence thinking in the field?  
The description of the descent trajectory and derivation of the coordinates is certainly of broad 
interest, however I do not think the manuscript will influence thinking in the field.  
 
 
General Comments To Authors  
1) There are a few instances of inappropriate word usage and faulty grammar, likely due to 
translation to English. Some logical inconsistencies may wholly or partially be due to a language 
issue.  
 
Examples:  
1) Line 15 16: “Because it is impossible to directly measure the farside of the Moon, we cannot 
acquire the descent trajectory and the landing site of the spacecraft.” It is possible to directly 
measure the lunar farside and the Chinese L2 relay satellite Queqiao should have been able to 
receive telemetry during the descent I cannot understand what is meant by this sentence. I can 
guess, but the authors should clarify. Perhaps the lander did not have the ability to transmit to 
Queqiao during the descent?  
 
2) Please spell out terms before using abbreviations/acronyms (i.e. DOM, DEM)  
3) “farside of the Moon” appears multiple times. After the first instance you can drop the “of the 
Moon” and just say farside.  
 
4) “5m/p, 1m/p, 10cm/p, 5cm/p resolution” appears multiple times throughout the manuscript. 
Once or twice is plenty.  
 
5) The values in Table 4 and 5 (and elsewhere in the manuscript) may be overly precise. Are three 
decimal places really justifiable (mm precision)?  
 
 
Consider adding Classic Bundle Block Adjustment References:  
 
Schmid, H.H., 1958, Eine allgemeine analytische Lösung für die Aufgabe der Photogrammetrie, 
Bildmessung und Luftbildwesen 1958, pp.103-113, 1959 pp.1-12. [German]  
 
Brown, D. C., 1958. A Solution to the General Problem of Multiple Station Analytical Stereo- 
angulation. Air Force Missile Test Center Report No. 58-8, Patrick AFB, Florida. [English]