Pre-process algorithm for satellite laser ranging data ... · Pre-process algorithm for satellite...
Transcript of Pre-process algorithm for satellite laser ranging data ... · Pre-process algorithm for satellite...
Geodesy and Geodynamics 2012,3(2) :53-59
http://www. jgg09. com
Doi:l0.3724/SP.J.l246.2012.00053
Pre-process algorithm for satellite laser ranging data based on
curve recognition from points cloud
Liu Yanyu1, Zhao Dongming2 and Wu Shan'
1 Beijing Global Celll<r of Infonrw.tion Application and Developnumt, Beijing 100094, C/Una
'lnstituu of Surveying and Mapping, PIA, Zhengzhou 450052, China
Abstract:The satellite laser ranging (SLR) data quality from the COMPASS was analyzed, and the difference
between curve recognition in computer vision and pre-process of SLR data finally proposed a new algorithm for
SLR was discussed data based on curve recognition from points cloud is proposed. The results obtained by the
new algorithm are 85% ( or even higher) consistent with that of the screen displaying method , furthermore , the
new method can process SLR data automatically, which makes it possible to be used in the development of the
COMPASS navigation system.
Key words: satellite laser ranging(SLR); curve recogoition; points cloud; pre-process algorithm; COM
PASS ; screen displaying
1 Introduction
Satellite laser ranging ( SLR) has become an effective
tool for orbit measurement and orbit assessment for its
high precision. Currently, in the COMPASS system,
the SLR for GEO satellite , which is 40000 km far from
the Earth center, has achieved a precision of 3 em.
SLR has become an indispensable component of the
COMPASS navigation system.
In SLR process , the thermal noise of receivers and
background noise from the sky often mistakenly trigger
the process device, as a result, a great deal of abnor
mal values are observed which should be eliminated in
order to obtain high-quality SLR data. The practical
preceding process includes pre-process, noise separa
tion , abnormal value elimination, documentation of re
maining effective data for validation and calibration of
the navigation system. In common data process, outli
ers only account for 5%- 10% of observations; when
Received:2012-03-22; Accepted: 2012-04-03
Corresponding author: Uu Yanyu, Tel: + 86-13911904261 ; E-mail: liu_
yanyu@ hotmail. com.
there is a lot of abnormal values , conventional outlier
elimination method does not work well for laser data.
The common method is the screen display method, in
which the abnormal values are removed through man
computer dialogue. Although the screen display meth
od has a good effect, human plays an important role in
the process , which means low automation. The screen
display method is applied in the SLR station of Shang
hai Astronomical Observatory and Zimmeiwald SLR sta
tion. Besides, there are many other methods applied in
the process of laser observations , such as the Graz fast
echo identification algorithm , Poisson statistical filte
ring algorithm, etc [I- 'l .
We attempts to introduce the curve reconstruction
method which is widely used in the reverse engineering
and computer vision, and to propose a data pre-process
algorithm of SLR based on curve recognition from
points cloud. The SLR data is regarded as point cloud
data, and the domain that containing SLR data is grid
ded. By iteratively adjustment, the valid domain of la
ser point cloud can be determined, and then curve fit
tings are made by the total points within the valid do
main, while the data with bigger fitting residual than
54 Geodesy and Geodynamics Vol. 3
the threshold value is eliminated. This algorithm uses
computer vision instead of the man-machine dialogue in
screen process method. The new method has a lot of
advantages such as high degree of automation, fast cal
culation , and immune from manual error. We carry out
an experimental verification using the SLR data from
the COMPASS system.
2 Quality assessment of laser observations
Data generated in the process of satellite laser ranging
contains a wealth of information, laser echo time ti,
satellite distance Rani, satellite speed Ratei, elevation
angle H, and azimuth A,. The relationship between dis
tance observation 0 and the calculated value C is ( 0 -
C) = p0 ( t,) - p, ( t,). The number of observations is
usually very large , may be tens of thousands , and the
observations contain a large number of outliers. The
calculations will have an enormous impact on the final
result if the outliers are not removed.
In order to analyze the quality of laser observations,
we used the screen process algorithms to pre-process
the SLR data from the COMPASS. Data 1 : March 20,
2010, from 11:20: 50 to 13:54: 36 ( UTC); Data 2:
March 22, 2010, from 12 : 02 : 20 to 12 : 59 : 33
(UTC); Data 3: April6, 2010, from 14:43:24 to
15:56:46 ( UTC).
As can be seen from table 1 , there are a large num
ber of outliers in the laser observations , and about half
of the data need to be removed even if the observations
have good quality. There are three steps contained in
the screen display method. Firstly, the obvious outliers
are removed by manual intervention; secondly, polyno
mial smoothing is used to process the difference be
tween the measured distance and the calculated dis
tance with epoch as abscissa, and then eliminates the
residual abnormal values with a specific threshold value
(the threshold value is always set as 2a) ; fmally, the
estimation of observation accuracy and internal consis
tency are made. The first two operations are carried out
alternately until the data quality achieving the target re
quirement, and laser data preprocessing is completed.
The screen processing algorithms have a very good effect
and demonstrate a strong signal extraction capability ,
Table 1 SLR data quality evaluation
Quantity of Quantity after Data utilization original elimination rate
observations outlier (%)
Data I 16061 3127 19.4
Data2 8519 4497 52.7
Data3 23248 12661 54.5
but this method requires manual intervention , which
may cause a waste of human resources and lead to con
siderable results with arbitrariness [ 1•3 l .
3 Laser data preprocess algorithm based on point-cloud curve recognition
3. 1 Basic concept
Curve reconstruction has been widely used in reverse
engineering and computer vision. The core issue of re
verse engineering is how to rebuild curve and swface
models from the sampling point set. In computer vi
sion, the problem is how to reconstruct the geometric
model using discrete data points obtained from an im
age or scan to facilitate shape analysis and recogni
tion[4-71. The two fields require one or more fitted
curves to reflect the point set based on the disordered
aod noised sample. Figure 1 shows the data obtained
by one laser observation of the COMPASS.
As shown by figure 1 , due to the numerous back
ground thermal noise , the laser echo contains both the
actual satellite position and lots of abnormal observa
tions , which makes the identification of effective echo
very difficult.
The slant range residuals caused by the orbit forecast
error are consisted of two parts : the distance deviation
RB and time deviation TB; aod t.p, = RB +Ran, X TB,
where Ran, is the projection of the satellite speed rate
onto the p vector direction at t, moment. Therefore, the
data points were regarded to be sampled from a smooth
and simple curve, and then reconstructed.
The sampled point cloud in reverse engineering and
laser observations have some common points : ( 1 )
both are sampled point set with noise ; ( 2) both have
physical meanings. Their geometric model can be
reconstructed by the discrete points of the point cloud.
No.2
liu Y anyu, et al. Pre-process algorithm for satellite laser ranging data based on
curve recognition from points cloud 55
200
-200 0.42
I 0.44 0.46 0.48 0.5 0.52
UTC/day
0.54
---0.56 0.58 0.6 0.62
Figure 1 The original SLR data
Otherwise, they have some differences : ( 1 ) The point
cloud sampled in reverse engineering is disordered and
discrete , but laser observations are orderly series ; ( 2 )
Many things must be considered in reverse engineer
ing , such as endpoint shape of the point cloud and
curve self-intersection. However, laser observations al
ways show a simple smooth curve. ( 3 ) The noise in re
verse engineering usually obeys normal distribution ,
but noise of laser observations is uniformly distributed
in background.
Generally speaking , laser observations can he ab
stracted as a simple continuous curve with no comer,
no branch and self-intersection, and then pre-pro
cessed in a similar way to the reconstruction of orderly
chaos points in reverse engineering.
3.1 Pre-process algorithm
When gridding the point cloud , the region where the
known laser point cloud located is gridded firstly, with
the time span T, the difference between the observed
distance 0 and the calculated distance C is D , then the
validity of each grid is verified by checking whether the
number of the sampled points is the largest within its
time span , if yes , the grid region is a valid one , other
wise ' invalid. All the valid regions form a set n. Due to the unevenness of the regional distribution of
the point cloud and the consistency of grid size, the
valid region {},i of one selected time span may locate at
the edge of laser point cloud curve ; some regional
curve would be distorted , and valid regions should he
adjusted.
( 1 ) Merge all data in a valid area n, into a charac
teristic value Pi· The determination of Pi can adopt one
of the two following options : 1 ) The average coordinate
of all points that fall into the region is the characteristic
value. 2) Search out the characteristic value of one re
gion using adaptive genetic algorithm[81 •
( 2) Adjust the location of the valid region n, center
ing on the characteristic point p,, and then re-deter
mine the domain of {},i as well as the incorporated point
sets.
( 3) In the adjusted n, , there is a new characteristic
value p, replacing Pi , and determines a new domain by
Pi, repeats the steps iteratively until p, and p, overlap
completely.
( 4 ) Implement curve fitting to all points in all valid
regions. Set the polynomial order to be k , and then a
kth-ordered polynomial with time ti as variable will fit
the distance difference between the 0 and C using least
square method. Eliminate the data bigger than the
threshold value of fitting residual till the number of re
moved outlier is zero.
4 Numerical experiment and analysis
In order to verify the validity of the proposed method ,
the SLR data from the COMPASS was used to carry out
a series of tests. Two methods are used in laser data
pre-process. One is screen displaying method; the oth
er is curve recognition from point cloud.
In the calculation, the grid size is 0. 0003 day
( UTC ) X 1 m , with a 4 -order fitting polynomial , and
the residual value greater than 2u will he removed un
til there is no gross error. Although the average coor
dinate method and adaptive genetic algorithm have the
equivalent results, considering the computer work-
56 Geodesy and Geodynamics Vol. 3
2010, from 14:43:24 to 15:56:46 (UTC). load , the fonner is chosen to calculate the characteris
tic value. Data 1 : March 20, 2010, from 11: 20: 50
to 13:54:36 (UTC); Data 2: March 22,2010, from
12: 02: 20 to 12: 59: 33 ( UTC) ; Data 3: April 6,
Figures 2 - 4 and table 2 show that SLR data pre
process algorithm can realize the automatic process of
the laser observations , and have the similar result and
(..) 400
1 0 I the original SLR data I
l~ 200
.~ 0 • I
J -200 lS 0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6
(..) 0 1
0 .-~ I -20 g ---·-.c -40
" __.
i I the data after screen displaying I
-60 0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6
(..)
1 0
----------0 ~ ~ -20
~g .c -40 8 I the data after proposed algorithm I
~ -60 L__ __ _L__ __ ___J_ __ _____i ___ _J__ __ __J__ __ ____(
j:j 0.46 0.48 0.5 0.52 0.54 0.56 0.58
UTC/day
Figure 2 Comparison between two results with two methods for the first data set
(..) 400 1 0 . G
200 i • i!: • .c 0 = JB L usa sse• " I the original SLR data I i -200
0.5 0.505 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55
(..) -14 1
flllllll'l""' --0 i -14.2 ••• rs-~ -14.4 I the data after screen clisplaying I 8
~ -14.6 ~ 0.5 0.505 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55
(..) -14
1
~· ......._
0 -14.2 G j !:-14.4 ..
1 the data after proposed algorithm 1
"
i -14.6 0.5 0.505 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55
UTC/day
Figure 3 Comparison between two results with two methods for the second data set
No.2
liu Y anyu, et al. Pre-process algorithm for satellite laser ranging data based on
curve recognition from points cloud 57
·+ • ••• ·t • ••
I the original SLR data I
0.5 0.52 0.54 0.56 0.58 0.6 0.62
1.)
1 c I the data after screen displaying I
1]: I •
-2 0.48 0.5 0.52 0.54 0.56 0.58 0.6 0.62
1.)
1 c 1 the data after proposed algorithm 1
1]: •
J -2 ~ 0.48 0.5 0.52 0.54 0.56 0.58 0.6 0.62
UTC/day
Figure 4 Comparison between two results with two methods for the third data set
Tablel Evaluation of the aceordance between the two algorithms
Screen displaying Number
Data of Deletion points Number ratio
of points (%)
Datal 16059 3127 80. 5
Data2 8519 4497 47.2
Data3 23248 12661 45.5
data deletion ratio with the screen display method.
In order to further check the data quality after laser
data pre-process, the satellite orbit is assessed using
the pre-processed laser data obtained by the two pre
processing algorithms. The satellite orbit is calculated
using three-day observations on March 23, 2010.
Therefore Datal and Data2 are in the arcs of orbit de-
termination.
Figures 5 and 6 show that the two algorithms have
the similar mean when assessing orbit by the laser da
ta. The proposed algorithm can even acquire a better
mean square error. At Datal, the carryover of the data
at the end of the observation arc was avoided by pro
posed algorithm which appeared in the screen process
ing method. Therefore, the proposed algorithm can
meet the quality requirements of the navigation system.
Proposed algorithm Number of points in
Consistency Deletion ratio Number of ratio terml! of (%) points (%) consistency
3339 79. 2 2867 85. 9
4554 46.5 4423 97.1
10955 52.8 10327 94.3
To analyze the effect of pre-set threshold value on
the laser data pre-process algorithm based on curve
recognition, Data 2 is taken as an example to demon
strate the impact of grid size, order of polynomial fit
ting and the Root Mean Square ( RMS) of curve fitting
on the algorithm. Results show that properly adjust
ment of grid size and fitting polynomial order have no
effect on computations , while the impact of the fitting
RMS on the algorithm is shown in figure 7.
There is multi-echo in Data 2 , and the echo interval
is very small. This is a common case in the SLR obser
vation , and in screen processing algorithm extra echoes
will be manually removed , otherwise , in the proposed
algorithm , the threshold value of residual fitting has a
quite big effect on the method: too strict threshold val
ue will cause a lot of useful observations to be elimina-
58 Geodesy and Geodynamics Vol. 3
ted , while too loose threshold value will cause the
multi-echo of SLR to be contained in data process. As
shown in figure 7 , when the threshold is set at a proper
value, multi-echo will be removed, and the points to
be processed decrease suddenly, which lead to a cor
rect computation. Due to the fact, 2u is selected as
the threshold value for residual fitting to ensure that all
the redundant echoes will be removed.
4
(.)
1 2 0
j]:o j -2
iS
0.48 0.5
4
(.)
1 2 0
J]:o .., I -2 __.. a ......
.-_,.. ....... ~ ............ __ ~
, • •
I • lhe data after screen displaying:Mean:-1.710m Std:0.264m I
0.52 0.54 0.56 0.58
I • the data after proposed algorithm:Mean:-l.716m Std:0.163m I
0.6
-4L_ ______ ~ ______ _L ________ L_ ______ ~ ______ _J ________ ~------~
0.46
(.) 0.55
1 0 0.5
6 J]: 0.45
~ 0.35
0.4
0.5
0.55 l)
1 0
0.5
j]: 0.45
j 0.4
0.35 ~
0.5
0.48 0.5 0.52 0.54 0.56 0.58 liTC/day
Figure 5 Radial component errors of orbit using the first data set
..
I· ..... ~. 0.505 0.51 0.515
I • ·-. 0.505 0.51 0.515
I • the data after screen displaying:Mean: 0.412m St.d:0.030m I
0.52 0.525 0.53 0.535 0.54 0.545 0.55
I• the data after proposed algorithm:Mean: 0.408m Std:0.025m I .. -r
lt
0.52 0.525 0.53 0.535 UTC/day
0.54 0.545 0.55
Figure 6 Radial component errors of orbit using the second data set
liu Y anyu, et al. Pre-process algorithm for satellite laser ranging data based on
No.2 curve recognition from points cloud 59
6000
! 4000 ll
1 ;z; 2000
number of points after proposed algorithm I
--- number of points in terms of COIISistency
OL--------L _______ J_ ______ _J _______ ~
1.5 2 2.5 3 3.5 sigma
Figure 7 Influence of fitted sigma on the effect of the algorithm
5 Conclusion
In order to develop a satellite navigation system with
automatic pre-process of laser ranging data , the author
discussed the automatic process technique of SLR ob
servations , and proposed a SLR data preprocess algo
rithm based on point cloud curve recognition. The
method makes it free from manual intervention, mean
while has the equivalent accuracy with the screen dis
play method.
'Through analyzing actual SLR observations of multi
ple circles from GEO satellite , it was found that the
two methods got rather consistent results ( consistency
rate reaching 85% ) . When the SLR data was applied
to orbit assessment using SLR data , close means were
obtained from the two methods, meanwhile the new
method has advantages of better RMS error and better
adaptability due to the fact that different observations
are not sensitive to grid size, polynomial fitting order
and the threshold value of residual fitting. The new
method realizes automatic process of SLR data. Howev
er, the research has just commenced, and there are
some points need further discussion , such as adaptive
adjustment of the algorithm, partially replacing the
screen display method , for the unpredictable cases in
actual SLR observations.
References
[ 1] Fang Qinghai and Zhao Y ongli. The research progress in data pro
cessing algorithm of satellite laser ranging[ J]. Laser Technology,
2008, 32(4): 417-419. (in Chinese)
[ 2] Wu Zhibo, Zhang Zhongping, Yang Furnin, et al. Statistical anal
ysis of successful detection probability of the returns in Satellite la
ser Ranging [ J ]. Science of Surveying and Mapping, 2006 , 31
(3): 28 -29. (in Chinese)
[ 3] Sun Baosan, Zhang Zhongping and Yang Fumin. Screen process
ing for 8Btellite laser ranging at high repetition rate [ I ] . Annals of
Shanghai Observatory Academia Sinica, 2006 , 27: 129 - 134. ( in
Chinese)
[ 4 ] Cai Runhin. Registraion of range images and planar regions extrac
tion from TL'l point cloud [ D]. Tongji University, 2008. (in Chi
nese )
[5] Zhong Gang , Yang Xunnian and Wang Guomao. Planar curve Re
construcion from unorganized point trough field representation [ J] .
Journal of Computer-Aided Design & Computer Graphics ,2002 ,14
( 11) :1074-1079. (in Chinese)
[ 6] Lee I K. Curve reconstruction from unorganized points [ J]. Com
puter Aided Geometric Design ,2000 ,17 ( 2) : 161 - 177.
[ 7] Du Xiaohui , Yin Baocai and Kong Dehui. Mixed simplification al
gorithm of point clouds [ J] . Computer Engineering and Applica
tions,2007 ,43(34) :43 -45. (in Chinese)
[ 8] Cheng Y angyuan, Man Jiaju and Quan Huiyun. Curve reconstruc
tion from points cloud based on adaptive ~netic algorithm [ J] .
Journal of Image and Graphics , 2006, 11 ( 9 ) : 1293 - 1298. ( in
Chinese)