Review of Visual Navigation Technology Based on Craters

Fig. 2. Examples of DEM, infrared, and visible light images of craters^[32]. Craters pictured in (a) come from Mercury/Messenger^[33]; (b) infrared data from Mars/Themis; (c) visible light data from Moon/Wide Angle Camera Global^[34]

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Fig. 3. Schematic diagram of crater-based visual navigation method^[43]

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Fig. 4. Test results of segmentation network on images of craters. (a) Head structure of Mask R-CNN^[62]; (b) numbers shown near craters are detection certainty^[61]

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Fig. 5. Test results of detection network with images of craters^[41]

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Fig. 6. Basic flow chart of tracking recognition

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Fig. 7. Crater image matching^[40]. (a) Direct matching with different perturbing; (b) triangle matching

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Fig. 8. Diagram of pyramid algorithm which continuously increases fourth crater l to form a pyramid structure and reduces redundant matches^[79]

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Fig. 9. Flow chart of matching system including direct matching, triangle matching, and LIS matching^[40]

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Fig. 10. World coordinate $O_{x y z}^{w}$ , machine coordinate $O_{x y z}^{m}$ , camera coordinate $O_{x y z}^{c}$ , and image coordinate $O_{x y z}^{i m a g e}$ . Pose includes rotation matrix R and translation matrix t^[79]

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Fig. 11. Block diagram of ATON system^[117]

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Table 1. Summary of TRN methods

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Table 1. Summary of TRN methods

Number	Type of collected images	Feature/Other measurement	Object to match	Output parameter	Passive imaging	Active imaging	Pattern recognition	Correlaction
1	Visible images	Craters^［14］	Craters in database	Absolute position and attitude	√	—	√	—
2	Visible images	Scale-invariant feature transformation（SIFT）features	Celestial surface map	Absolute position and attitude	√	—	√	—
3	Visible images	Surface features^［29］/Estimated attitudes	On-orbit map of landing site	Absolute position and updating attitude	√	—	√	√
4	Visible images	Estimated attitudes	On-orbit map of landing site	Horizontal speed	√	—	—	√
5	Visible images	Estimated attitudes	Descending sequence images	Horizontal speed	√	—	—	√
6	Visible images	Height	Descending sequence images	Average velocity and angular acceleration	√	—	—	√
7	Digital elevation model（DEM）data	Signatures/Motion correction data	DEM data of landing area	Absolute position and attitude	—	√	√	—
8	DEM data	Motion correction data/Estimated attitudes	Global DEM data	Absolute position	—	√	—	√

Table 2. Crater datasets

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Table 2. Crater datasets

Name of dataset	Data source	Quantity and size	Type	Planetary	Open data
Andersson et al^［15］（1982）	—	—	—	Moon	Table
Rodionova et al（2000）	—	19308 craters（>10 km）	—	Mars	Table
Salamunic’car et al^［21］（2008）	Some previous work	57633 craters	THEMIS	Mars	Non-open
Head et al^［16］（2010）	LOLA	5185 craters（≥20 km）	DTM	Moon	Table
Salamunic’car et al^［22-23］（2012）	MDIM，THEMIS-DIR，and MGS MOC datasets	132843 craters	Optical images	Mars	Table
Bandeira et al^［24］（2012）	HRSC	3050 craters	Optical images	Mars	Images/Table
Robbins et al^［25-26］（2012）	THEMIS Daytime IR mosaics	384343 craters（≥1 km）	THEMIS	Mars	Non-open
Salamunic’car et al^［27］（2013）	—	9224 craters	DEM and optical images	Phobos	Table
Neumann et al^［17-18］（2015）	GRAIL and LOLA	74 basins（>200 km）	Gravitational data	Moon	Non-open
Povilaitis et al^［19］（2018）	LROC WAC	22746 craters（5-20 km）	Monochrome mosaic and DTM	Moon	Images
Robbins et al^［20］（2018）	LRO WAC and Kaguya Terrain Camera	2000000+ craters（ $\geq$ 1-2 km）	CTX mosaics	Moon	Non-open

Table 3. Domestic and foreign research institutions/personnel

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Table 3. Domestic and foreign research institutions/personnel

Research institutions /personnel	Crater detection method	Crater recognition method	Pose calculation method	Navigation accuracy
NASA JPL/Yang Cheng^［36］（2003）	Edge detection，rim edge grouping，ellipse fitting，precision fitting，and crater confidence evaluation	Correlation matching，context matching，and conic invariance matching	Orbit determination filter	Position error is <100 m
Chad Hanak^［37］（2010）	Hough transform and ellipse detection	Using triangle affine invariants by voting matching	—	Matching rate is 82%（evaluation of crater recognition）
Harbin Institute of Technology/Hutao Cui^［38］（2014）	MSER feature extraction，image region pairing method，and ellipse fitting	Using area ratio as invariants to match	—	Position error is <0.97 pixel
Guilherme F. Trigo^［39］（2018）	Extract neighboring illuminated and shadowed sections，centroids trace，and fit ellipse	—	EPnP algorithm in conjunction with QCP solver	Position error is <15 m，velocity error is <0.8 m·s^-1，and attitude error is < 5 $°$
Yang Tian^［12］（2018）	Image region pairing method and ellipse fitting	—	A distributed extended Kalman filter	Position error is <200 m and attitude error is < 1 $°$
DLR，German Aerospace Center^［40］（2020）	Image segmentation and fitting ellipse craters	Direct，triangle，and LIS matching	EPNP and Kalman filter	Position error is <500 m， velocity error is <40 m·s^-1，and angular velocity is <0.001 rad·s^-1
Beihang University^［41］（2021）	Dense point crater detection network	Using encoded features	EPNP and Kalman filter	Position error is <10 m and attitude error is <1.5 $°$
Delft University of Technology^［42］（2022）	Ellipse R-CNN	Using coplanar invariants for ellipse triads	Extended Kalman filter	Position error is >160 m

Table 4. Evaluation indicators in crater detection

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Table 4. Evaluation indicators in crater detection

Evaluation indicator	Meaning
S_TP	True positive（S_TP）means that some positive samples are predicted to be positive
S_FP	False positive（S_FP）means that some negative samples are predicted to be positive
S_FN	False negative（S_FN）means that some positive samples are predicted to be negative
S_TN	True negative（S_TN）means that some negative samples are predicted to be negative
T_DT	Total detection time（T_DT）
R=S_TP/（S_TP+S_FN）	Recall（also known as sensitivity）is number of true positive results divided by number of all samples that should have been identified as positive
P=S_TP/（S_TP+S_FP）	Precision（also called positive predictive value）is number of true positive results divided by number of all positive results，including those not identified correctly
F_DR=S_FP/（S_TP+S_FP）	Fraction of false instances among all detected positive instances. It evaluates fraction of false samples
B=S_FP/S_TP	Branching factor，which is ratio of number of false instances to number of positive instances. It evaluates classification performance
Q=S_TP/（S_TP+S_FP+S_FN）	Quality factor which evaluates overall performance of algorithm
$F 1 = \frac{2 \times P \times R}{P + R}$	F-score or F-measure is a measure of a test’s accuracy. It is calculated from precision and recall of test
ROC curve	Horizontal axis is ‘false positive rate’ and vertical axis is ‘true positive rate’
AUC	Area under curve（AUC）is defined as area under ROC curve surrounded by a coordinate axis

Table 5. Evaluation indicators in crater recognition
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Table 5. Evaluation indicators in crater recognition
Evaluation indicator Meaning
M_TN Total matching number
M_CN Correct matching number
M_FN False matching number
M_CN/（M_CN+M_FN） Matching rate
M_FN/（M_CN+M_FN） False matching rate

Table 6. Comparison of crater identification methods

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Table 6. Comparison of crater identification methods

Researcher	Feature	Matching method	Application scenario	Matching rate
Hanak^{［37，76］}（2010）	Affine invariants of crater tuples	Vote matching	LIS identification of orbital segment	82%
He^［14］（2010）	Affine invariants of curve pair	Vote matching	Tracking identification of landing segment	>85%
Park^［77］（2019）	30 projective invariants of craters	Vote matching	LIS identification of landing segment	41.7%
Alfredo^［28］（2021）	Projective invariants of craters	Template matching	Tracking identification of orbital segment	Position error is <400 m
Chen^［41］（2021）	Characteristic patterns of crater combinations	Weighted bipartite graph best matching method	Tracking identification of landing segment	98.5%
Doppenberg^［42］（2021）	Seven projective invariants of craters	Direct matching	LIS identification of orbital segment	14%
Christian^［78］（2021）	Seven projective invariants of craters	Hierarchical matching	LIS identification of orbital segment	>80%
Xu^［79］（2022）	Tow projective invariants of crater pair	Iterative pyramid matching	LIS identification of landing segment	>80%

Table 7. Evaluation indicators in pose calculation

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Table 7. Evaluation indicators in pose calculation

Evaluation indicator	Meaning
X	Position error in X axis
Y	Position error in Y axis
Z	Position error in Z axis
Yaw angle	Yaw rotation around yaw axis
Roll angle	Roll rotation around roll axis
Pitch angle	Pitch rotation around pitch axis
Velocity	Velocity of detector
Angular velocity	Angular velocity of detector
Height	Height of detector
$E_{A, a l l}$	Absolute trajectory error
$E_{A, t r a n s}$	Average translational error
$E_{R, a l l}$	Relative pose error
$E_{R, t r a n s}$	Relative translational error