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.

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