Research on Partitioning Algorithm Based on Dynamic Star Simulator Guide Star Catalog

Abstract

The simulated star map generated by the dynamic star simulator cannot meet the current demand for calibration of the star map recognition rate of the star sensor due to the huge amount of guide star catalog data and the slow retrieval process. This paper proposes the guide star equipartition method, which makes the constant number of each sub-region of the guide star catalog basically the same. This method first divides the declination at equal intervals through the field of view of the dynamic star simulator, and then determines the interval of the right ascension by the average number of stars with magnitude Mv that can be photographed in the field of view of the star sensor. The SAO (Smithsonian Astrophysical Observatory) catalog containing 5103 stars in the whole celestial sphere is divided into 452 sub-areas by the average number of guide stars. After the division, the guide star retrieval time is about 8ms, and the refresh rate of the simulated star map is increased by more than three times. The real-time requirements of the dynamic star simulator have been improved. Based on this, a star map simulation software is designed, which can realize the division of star catalogs with different fields of view and different magnitude thresholds.

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Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.
Digital Object Identifier 10.1109/ACCESS.2017.Doi Number
Research on Partitioning Algorithm Based on
Dynamic Star Simulator Guide Star Catalog
GUANGXI LI, LINGYUN WANG, RU ZHENG, XIN YU, YUE MA, XIAO LIU, and BO LIU.
Changchun University of Science and Technology, School of Optoelectronic Engineering, Changchun 130022, China
Corresponding author: LINGYUN WANG (wanglingyun_510@163.com).
This work was supported in part by the Science and Technology Development Plan of Jilin Province of China under Grant20170521001HJ, Grant
20180201018GX , Grant 20200401054GX, and in part by the Scientific and Technological Research in the 13th Five-Year Plan period of Jilin Provincial
Education Department of China under Grant JJKH20181133KJ.
ABSTRACT The simulated star map generated by the dynamic star simulator cannot meet the current
demand for calibration of the star map recognition rate of the star sensor due to the huge amount of guide
star catalog data and the slow retrieval process. This paper proposes the guide star equipartition method,
which makes the constant number of each sub-region of the guide star catalog basically the same. This
method first divides the declination at equal intervals through the field of view of the dynamic star
simulator, and then determines the interval of the right ascension by the average number of stars with
magnitude Mv that can be photographed in the field of view of the star sensor. The SAO (Smithsonian
Astrophysical Observatory) catalog containing 5103 stars in the whole celestial sphere is divided into 452
sub-areas by the average number of guide stars. After the division, the guide star retrieval time is about 8ms,
and the refresh rate of the simulated star map is increased by more than three times. The real-time
requirements of the dynamic star simulator have been improved. Based on this, a star map simulation
software is designed, which can realize the division of star catalogs with different fields of view and
different magnitude thresholds.
INDEX TERMS Aerospace simulation, Image sensor, Algorithms, Optical sensor, High-resolution imaging.
I. INTRODUCTION
As a high-precision attitude measurement device, the star
sensor is widely used in the aviation and aerospace fields. It
uses the starlight vector to determine the instantaneous
direction of the visual axis in the celestial coordinate system
to determine the attitude of the aircraft [1,2]. The star map
recognition and attitude determination are based on the guide
star catalog as the information standard [3-5].
The guide star catalog is the description of stars in the
celestial coordinate system, mainly including the star's right
ascension, declination and brightness. The establishment of
the guide star catalog is an important task of starlight
guidance technology. The most important step in establishing
the guide star catalog is to select the guide star. Indicators
such as the brightness and distribution uniformity of the
guide star directly affect the distribution density of the guide
star in the field of view when the star sensor is working, the
minimum number of guide stars that can be detected, and the
minimum number of matching star pairs in the star map
recognition process, and identification navigation the
probability of stars etc. This affects the efficiency and
success rate of star map recognition and star tracking
matching algorithm [6]. Due to the high cost of space
experiments, it is impossible for the debugging of the star
sensor to perform actual starry sky shooting [7]. Therefore,
the dynamic star simulator is used to generate simulated star
map in real time for detection by the star sensor [8].
The dynamic star simulator generates a simulated star map.
First, according to the direction of the optical axis, given the
size of the star simulator's field of view and the angle of the
field of view around the optical axis, extract the guide star
from the guide star catalog, and then perform the coordinates
and magnitude respectively Transform, and finally display it
in the form of a two-dimensional image on the screen of the
star map display device to realize the starry sky simulation.
The star sensor is the "eye" of the spacecraft in space.
With the vigorous development of space missions, the rapid
maneuverability of spacecraft in orbit has become the key to
space missions. Significant demand, and put forward higher
and higher requirements for the dynamic performance of the
autonomous attitude measurement system. The high dynamic

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VOLUME XX, 2017 9
star sensor technology is an urgent need for the development
of China’s spacecraft and technology, which requires its
ground test equipment——dynamic star simulator is
becoming more and more dynamic. How to quickly extract a
guide star that meets the field of view is the key to increasing
the speed of the simulated star map and realizing the
dynamic simulation of the starry sky environment. In order to
speed up the search speed of the guide star catalog, it is
necessary to divide the guide star catalog. A reasonable
division of the sky area can increase the refresh rate of the
simulated star map, thereby greatly increasing the refresh
frequency of the star simulator.
The division of the guide star catalog is actually the
division of the surface of the celestial sphere. The
arrangement of the guide stars in the guide star catalog is
irregular. If you select a guide star that points to the field of
view with a certain visual axis, you must traverse the entire
guide star catalog once. Obviously, such search efficiency is
very low. How to retrieve the guide star quickly has become
a key step in formulating the guide star catalog.
The guide star catalog can be divided into two major
categories: one is to divide the whole sky star map based on
right ascension and declination. The spatial division of each
block is extremely uneven, which is not conducive to the
organization and scheduling of the guide star catalog. There
is mainly the spherical matrix segmentation method used by
Chen Yuanzhi [9] et al. to divide the surface of the celestial
sphere into 800 regions. This method gradually increases the
surface area of the sub-interval from the north and south
poles to the equator, which is not conducive to the rapid
retrieval of guide stars. Jeffery [10] also uses the declination
belt method, which can directly search for the declination
value when searching for guide stars. However, the
distribution of stars in each sub-region is not uniform, and
the right ascension information is useless, which will cause
redundant guide stars. Wang Lingyun [11] et al. used the
method of equal field of view to divide the surface of the
celestial sphere into 254 areas. Although this method makes
the retrieval area smaller than the entire celestial sphere, it is
still much larger than the projection area of the star sensor’s
field of view, which will lead to the rate of searching for
guide stars is reduced.
The other is the uniform division method of the celestial
sphere. This kind of method completely discards the
longitude and latitude information of the celestial sphere and
obtains the uniform division of the celestial sphere surface.
However, this kind of method boundary division is more
complicated and the retrieval method is not intuitive. Ju [12]
et al. mainly used the cone method to divide the surface of
the celestial sphere into 11,000 regions. The cone regions
divided by this method will overlap each other, which will
cause the same guide star to appear in different cone regions.
At the same time, the storage space becomes very large. In
addition, Zhang Guangjun [13] et al. used the method of
inscribed cubes to divide the surface of the celestial sphere
into 486 sub-regions. This method divided the regions into
uniform and non-overlapping divisions, which can quickly
search for guide stars, but for stars The judgment of the
boundary of the sub-region is more complicated. Li Xing [14]
et al. used a quadrangular pyramid partition method to divide
the surface of the celestial sphere into approximately 60,000
sub-regions. This method may make a navigator star appear
in multiple sub-regions and require a lot of storage space for
data storage.
In 2019, Wang Jun [15] proposed that the average time for
the star sensor to recognize a star map is 10.077ms. In order
to enable the star sensor to recognize the simulated star map
of the dynamic star simulator in real time, the dynamic star
simulator refresh time of the star map should be less than
10.077ms. In 2019, Li Xing [14] proposed the quadrangular
pyramid partitioning algorithm to search the global SAO
catalog data containing 21983 stars. The search time for the
guide star is 110HZ, which is about 9ms. As its calibration
test equipment, the dynamic star simulator is in urgent need
of a new guide star catalog partition algorithm to improve the
star map refresh time.
The guide star equipartition method proposed in this paper
is based on the declination of equal intervals, and considering
the premise that the number of stars in each subregion is
equal in the partition, the right ascension is divided. When
searching for guide stars, search based on right ascension and
declination, so as to achieve the purpose of improving the
refresh rate of the star map.
II. PRINCIPLES OF CONSTRUCTING GUIDE STAR
CATALOG
In the selection of guide stars, in principle, it is required that
under the premise of meeting the identification requirements,
there should be as few guide stars as possible. Generally, it is
based on the field of view of the star sensor, the star sensor’s
limit magnitude, recognition accuracy, storage capacity, and
recognition. Algorithm requirements to build the guide star
library [16-19]. Due to the uneven distribution of stars on the
celestial sphere, the distribution of stars in the field of view is
random in a certain spatial domain. The most important
reference index in the construction of the guide star catalog is
the magnitude sensitivity limit and star sensitivity of the star
sensor. Field of view. The magnitude sensitivity limit of the
star sensor is different from the size of the field of view, and
the number of stars in the field of view will vary greatly [20-
22].
A.
FITTRT GUIDE STAR
In order to screen out effective guide stars, speed up the
retrieval of guide stars and reduce the data capacity of guide
stars, the specific steps of the method adopted in this paper
are as follows:
1)Delete variable stars and double stars in the basic catalogue;
2)The greater the brightness of the guide star, the better;

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VOLUME XX, 2017 9
3)The number of stars in the field of view meets the
minimum number of stars required for star chart recognition;
4)Under the condition of meeting (3), the fewer stars in the
field of view, the better;
5)The guide star is distributed as evenly as possible on the
celestial sphere;
6)According to the imaging of the dynamic star simulator,
select stars within 6.0 apparent magnitudes as guide stars.
B.
PROCESSING DOUBLE STARS
Double stars refer to two stars that are close apart on the line
of sight (the actual distance may be far away), and the star
points on the imaging surface of the dynamic star simulator
cannot be distinguished from each other. The traditional
approach is to delete it directly. When there are fewer guided
stars in the field of view, directly removing double stars
means losing part of the available information.
The judgment of binary stars can be determined by the
angular distance between stars. The schematic diagram of
binary stars is shown in Fig.1. Let the right ascension and
declination of stars A and B be respectively (
α
i,
β
i) and (
α
j,
β
j),
Then the angular distance
θ
of stars A and B in the celestial
coordinate system is as follows.
( ) ( )
( )
arccos cos cos
ij ij
θ αα ββ
= −⋅ −
(1)
FIGURE 1. Schematic diagram of binary stars
In the imaging process of the dynamic star simulator, the
defocus of the image plane is 3×3 or 5×5 pixels. There are
1024×1024 pixels on the imaging surface of the dynamic star
simulator, and the field of view is 10°×10°. Then, the angular
distance
ξ
corresponding to each pixel is as follows.
10 /1024 0.0098
FOV
N
ξθ
= =°= °
(2)
Then, a 5×5 pixels guide star is defocused, the
corresponding angle
ζ
size of the star is as follows.
=5 5 0.0098 0.05
ζξ
× = × °= °
(3)
When the angular distance between A and B stars is
θ≤0.05°, the two stars are regarded as binaries, which will
not be distinguished when the navigational star is extracted,
so the two stars are removed. In addition, the imaging of
binary stars in the phase plane is a large spot connected
together, which cannot correctly determine the center of mass.
Therefore, binary stars will be removed from the guide star
catalog.
In this paper, the stellar table of The Smith Astrophysical
Observatory (SAO) is taken as the original stellar table. After
removing variable stars and binary stars from the stellar table,
5,103 stars whose brightness is higher than (or equal to) 6Mv
are left as guide stars. Its distribution of stars in the celestial
sphere is shown in Fig.2.
FIGURE 2. Stellar distribution map
It can be seen from Figure 2 that the distribution of stars in
the celestial sphere is not uniform and random, the
distribution of stars near the North-South Pole is relatively
sparse, and the distribution of stars near the equator is
relatively dense. Therefore, rationally expanding and
homogenizing the star distribution can reduce the amount of
data in the guide star catalog to a certain extent, and improve
the refresh rate of the star map.
III. RESEARCH ON PARTITION ALGORITHM OF GUIDE
STAR CATALOG
A. PARTITION ALGORITHM
The celestial sphere is divided into non-overlapping regions
by right ascension and declination, and the separation
interval can be close to the radius of the field of view of the
dynamic star simulator. For a FOV 10°×10° square field of
view, it should be covered with a circular field of view
during partitioning to ensure that all guide stars are included
in the field of view, then the field of view radius
θ
r is as
follows.
2 10 7.07
2
r
θ
°
⋅°
= =
(4)
In order to facilitate the partitioning of the star catalog, the
celestial declination is divided equally, and the partition
interval should not be too large. Because the range of
declination changes in the range of 180° between the South
Pole -90° and the North Pole +90°. So the partition interval is
taken as 7.5°, the celestial declination interval can be equally
divided into 24 parts and labeled with Mi(i=1,2,3,…,24).
The common algorithm for homogenizing the distribution
of guide stars is orthogonal grid method [23-26]. The basic
idea is to imagine a sphere as a plane region. If the stars in
any field of view show a uniform distribution, the

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VOLUME XX, 2017 9
distribution of guide stars in this plane region (i.e., the whole
celestial region) is also uniform.
For star map recognition, the number of observed stars in
the field of view should not be too small and must meet the
minimum requirement of recognition ( ≥3). In order to
ensure the accuracy of attitude calculation, the average
number of stars in the field of view should not be too small,
usually ≥6.
Within the whole sky area, the total number of stars N
with magnitude Mv is as follows.
1.08
6.57
v
M
Ne=
(5)
For a star sensor with a field of view of B (B is the
opening angle of the star sensor optical lens), the ratio K of
the sky area within the field of view that it can capture to the
whole sky area is as follows.
2
11
arccos sin
22
FOV
K
θ
π


= − 



(6)
For a star sensor with a lens angle of
θ
FOV, the average
number
θ
FOV of stars with magnitude Mv that can be
photographed in the field of view is as follows.
1.08 2
11
=6.57 arccos sin
22
v
MFOV
FOV NK e
θ
θπ




=⋅−







(7)
Bring the magnitude threshold to 6 magnitude stars and
the field of view of 10°×10° into formula (7), it can be
obtained that the average number of stars of magnitude 6 that
can be photographed in the field of view is 10.2°To ensure
the smooth recognition of the star map, the average number
θ
FOV of stars in the field of view should be taken as 11.
(1) Divide the declination of the entire sky area equally at
intervals of 7.5°;
(2) Screen the number of stars in each declination interval,
denoted as NMi ;
(3) Divide the number of stars NMi in each declination
interval and the corresponding right ascension into blocks,
and N
θ
≥
θ
FOV stars in each subregion, and arrange the right
ascension in ascending order. The number of stars N
θ
in the
subregion is calculated as follows.
i
M
FOV
N
N qr
θ
θ
= = ⋅⋅⋅
(8)
q is the number of right ascension divisions in the
declination strip, and r is the number of stars left in the
declination zone;
1) If r=0, the number of right ascension sub-blocks in each
declination subregion is q, and the number of stars N
θ
in
each zone is
θ
FOV.
2) If r
＜
q
＜θ
FOV , in block r in the declination subregion,
the number of stars N
θ
in the ascension subregion is
θ
FOV+1 ,
and the number of stars N
θ
in the remaining q-r subregions
is
θ
FOV .
3) If q
＜
r
＜θ
FOV, then the calculation is as follows.
qr
rNN
q= ⋅⋅⋅
(9)
a. If Nr=0, then the number of stars N
θ
in the right
ascension subregion of block q in the declination subregion
is
θ
FOV+Nq.
b. If Nr
≠
0, then the number of stars Nq in the right
ascension subregion of block in the declination zone
is
θ
FOV+Nq+1, and the number of stars N
θ
in the right
ascension subregion of the remaining q-Nq block is
θ
FOV+Nq.
(4) Mark each subregion of right ascension as
Mij(i=1,2,3…,Mi, j=1,2,…q) , then calculate the total number
of subregions Msum of the star catalogue as follows.
11
=
i
Mq
ij
ij
MM
= =
∑∑
sum
(10)
1) When j=q=1, then calculate the right ascension DecMi1
interval of subregion Mi1 as follows.
(j 1)
(max ,Dec ]
ij i
M MN
Dec Dec
θ
−

∈
(11)
2) When j
＜
q, then calculate the right ascension interval
DecMij of subregion Mij as follows.
(j 1)
(max ,Dec ]
ij i
M MN
Dec Dec
θ
−

∈
(12)
3) When j=q
≠
1, then calculate the right ascension
interval DecMiq of subregion Miq as follows.
(
( 1)
max ,360 ,( 1)
iq i q
MM
Dec Dec j q
−


∈ °=
≠


(13)
According to the above subregion steps, the guide star
catalog is divided into 452 subregions, and its subregion
information is shown in Ⅰ, and Fig.3 is its guide star catalog
subregion map. TABLE Ⅰ
PARTITION INFORMATION
Declination
Partition
number Mi
Declination interval
i
M
Ra
Number of star
i
M
N
Number of
declination
subregions q
1
-90 -82.5
i
M
Ra°≤ < °
18
1
2
-82.5 -75
i
M
Ra
°≤ < °
68
6
3
-75 -67.5
i
M
Ra°≤ < °
111
10
4
-67.5 -60
i
M
Ra°≤ < °
212
19
5
-60 -52.5
i
M
Ra°≤ < °
217
19
6
-52.5 -45
i
M
Ra°≤ < °
266
24
7
-45 -37.5
i
M
Ra°≤ < °
309
28
8
-37.5 -30
i
M
Ra°≤ < °
272
24
9
-30 -22.5
i
M
Ra°≤ < °
313
28
10
-22.5 -15
i
M
Ra°≤ < °
282
25
11
-15 <-7.5
i
M
Ra°≤ °
290
26
12
-7.5 0
i
M
Ra°≤ ≤ °
281
25
13
0 7.5
i
M
Ra°< ≤ °
265
24
14
7.5 15
i
M
Ra°< ≤ °
291
26
15
15 22.5
i
M
Ra°< ≤ °
332
30
16
22.5 30
i
M
Ra°< ≤ °
303
27
17
30 37.5
i
M
Ra°< ≤ °
274
24
18
37.5 45
i
M
Ra°< ≤ °
250
22
19
45 52.5
i
M
Ra°< ≤ °
230
20
20
52.5 60
i
M
Ra°< ≤ °
205
18
21
60 67.5
i
M
Ra°< ≤ °
150
13
22
67.5 75
i
M
Ra°< ≤ °
90
8

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VOLUME XX, 2017 9
23
75 82.5
i
M
Ra°< ≤ °
54
4
24
82.5 90
i
M
Ra°< ≤ °
20
1
FIGURE 3. Guide star catalog subregion
B. EXTRACT GUIDE STAR
To display the position of the guide star on the plane, the
position (
α
i,
β
i) of the guide star in the celestial coordinate
system needs to be rotated and transformed into the star
sensor coordinate system, and then the position (xi, yi, zi) of
the guide star in the star sensor coordinate system is
transformed by projection. Get the position (Xi, Yi) in the
plane image coordinate system.
FIGURE 4. Celestial Cartesian Coordinate System
Convert the coordinates of all the guide stars in the SAO
catalog in the celestial coordinate system to the direction
vector in the rectangular coordinate system in Fig.4. let the
right ascension and declination of the guide be (α0, β0), and
calculate the direction vector of the guide star in the celestial
coordinate system as follows.
0 00
0 00
00
cos cos
sin cos
sin
x
y
z
αβ
αβ
β
⋅
 
 
= ⋅
 
 
 
(14)
1) Rotation transformation
The optical axis of the star sensor is (
α
i,
β
i), and the
rotation angle around the optical axis is
γ
i
. its attitude angle
(
α
i,
β
i,
γ
i
) indicates that the guide star S(
α
i,
β
i) rotates
around the Z axis
γ
i
, around the Y axis
β
i, and finally
around the X axis
α
i. T According to Z-Y-X, a 3 × 3 rotation
matrix C1 is obtained, the calculation is as follows.
1
111
222
333
cos sin 0 cos 0 sin 1 0 0
sin cos 0 0 1 0 0 cos sin
0 0 1 sin 0 cos 0 sin cos
=
ii i i
ii i i
i i ii
C
abc
abc
abc
γγ β β
γγ αα
β β αα
−
  

  

=−⋅ ⋅
  

  
 −

  





(15)
Get its coordinate (xi, yi, zi) in the coordinate system of the
star sensor, the calculation is as follows.
111 0 0
222 0 0
333 0
cos cos
sin cos
sin
i
i
i
x abc
y abc
z abc
αβ
αβ
β
⋅
    
    
= ⋅
    
    
    
(16)
2) Projection transformation
The imaging process of a guide star on the photosensitive
surface can be represented by a perspective projection
transformation as shown in Fig.5. Through perspective
projection, after perspective projection, the coordinates of the
guide star in the plane image coordinate system, the
calculation is as follows.
FIGURE 5. Star sensor, plane image coordinate system
101010
303030
202020
303030
i
ii
i
ii
x ax by cz
Xf f
z ax by cz
y ax by cz
Yf f
z ax by cz
++
=⋅=⋅
++

++
=⋅=⋅
++

(17)
The focal length f of the optical system of the star
simulator is calculated as follows.
2tan( 2) 2tan( 2)
yv
xh
xy
Nd
Nd
fFOV FOV
= =
(18)
Where:
Nx and Ny are the number of row and column pixels
respectively;
FOVx and FOVy respectively represent the field of view
in the X-axis direction and the Y-axis direction;
dh and dn are the width and height of the pixel respectively;
The range of coordinates Xi∈[-Nx/2, Nx/2], Yi∈[-Ny/2,
Ny/2].

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VOLUME XX, 2017 9
The position coordinates of the guide star on the plane
image coordinate system are calculated, and the origin of the
image coordinate system is located in the center of the
imaging plane. When displaying an analog star map on a
computer display, it is also necessary to translate the
coordinates so that the simulated star map can be displayed
normally on the computer screen. The coordinate origin of
the computer display is in the upper left corner of the display,
the calculation is as follows.
2
2
x
ii
y
ii
N
XX
N
YY
′= +



′= +


(19)
The range of coordinates Xi∈[0, Nx], Yi∈[0, Ny].
The rotation matrix C2 of quaternions is calculated as
follows.
2222
1 2 3 4 12 3 4 13 24
2222
2 12 3 4 1 2 3 4 23 14
2222
13 24 23 24 1 2 3 4
2(q q q q ) 2(q q q q )
2(q q q ) 2(q q q q )
2(qq qq) 2(qq qq)
qqq q
C q qqqq
qqqq

−−+ + −

= − −+ − + +


+ − −− + +

(20)
C1=C2, quaternion q1
、
q2
、
q3
、
q4 can be obtained by
combining the two formulas. The calculation is as follows.
( )
( )
( )
1 23 4
2 31 4
3 12 4
4 123
4
4
4
12
q cb q
q ac q
q ba q
q abc
= −

= −

= −

= +++

(21)
When a circular field of view is used to search for stars
that can be imaged, for stars that can be imaged on a
photosensitive plane, the red longitude and declination (
α
i,
β
i)
coordinates satisfy the calculation as follows.
()
cos , cos
(,)
ir r
i rr
ααθβαθβ
β βθβ θ
∈− +

∈− +

(22)
IV. EXPERIMENTAL VERIFICATION AND ANALYSIS
A. EXPERIMENTAL VERIFICATION
The experimental software simulation platform adopts
Matlab2016a version, according to the algorithm flow of the
guide star number equalization method, and uses MATLAB
to program the software to generate the star map simulation
software shown in Fig.6. Star map simulation software
mainly includes star map selection, simulation parameter
setting, attitude setting, star map display, time display,
attitude display, star information and data preservation
functions.
Use the screened guide star catalog with 5103 guide stars
as test data. The view angle of the dynamic star simulator
(FOV) is 10°×10°, the magnitude threshold is 6Mv, its star
map display device resolution is 1024×1024, and the pixel
size is 16um×16um. The optical axis of the dynamic star
simulator points to (75°,63°) 0° rotation about the optical
axis, and the change speed of the optical axis is 0°. Input the
above data into the star map simulation software, and
compare and analyze the refresh time of the star table before
partition and after partition.
FIGURE 6. Star map simulation software interface
B. RESULTS ANALYSIS
In order to verify the consistency of the simulated star map
when the guide star catalog is not partitioned and when it is
partitioned, three optical axis directions are randomly
selected for testing from the north pole to the south pole.
During the test, the rotation angle is 0°, and the optical axis
change speed is 0. The test results are shown in Fig.7 to Fig.9.
Table 2 is the time used to retrieve the guide when generating
3 simulated star maps.
a) Without catalog partition b) Catalog partition
FIGURE 7. Celestial Cartesian Coordinate System Optical axis direction
is(300°,72°)
a) Without catalog partition b) Catalog partition

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VOLUME XX, 2017 9
FIGURE 8. Celestial Cartesian Coordinate System Optical axis direction
is(85°,2°)
a) Without catalog partition b) Catalog partition
FIGURE 9. Celestial Cartesian Coordinate System Optical axis direction
is(118°,53°)
From the observation of Fig.7 to Fig.9, it can be concluded
that the simulated star map generated when the star catalog is
not partitioned is consistent with the simulated star map
generated during partition, which verifies the consistency of
the partition algorithm of the star catalog.
TABLE Ⅱ
COMPARISON OF REFRESH TIME OF STAR MAP
Optical axis pointing
Star map refresh time/ ms
Without catalog partition
catalog partition
(300°，72°)
23.4392
6.9
(85°，2°)
24.5676
8.7
(118°，-53°)
24.3425
7.6
It can be seen from fig.2 and Ⅱ that the time difference
between the generation of simulated star maps when the
guide star catalog is partitioned and not partitioned is
relatively large. The retrieval time after partition is about
three times the retrieval time before partitioning. In order to
verify the universality of this phenomenon the random
selection of the optical axis points to 1000 to test the refresh
time of the star map, and the test results are shown in Fig.10
and 11.
FIGURE 10. Test results of star map refresh time for without guide star
catalogue partition
FIGURE 11. Test results of star map refresh time for guide star
catalogue partition
It can be seen from Figure 10 that the refresh time of the star
map when the star catalog is not partitioned is between 22
and 27ms. After calculation, the average time for star chart
refresh is 24.59ms. It can be seen from Figure 11 that the
refresh time of the star map after the star catalog is
partitioned is between 7 and 9ms. After calculation, the
average time for star chart refresh is 7.98ms. After the star
catalog is partitioned, there are more stars in some sub-
regions. When searching, the refreshing time of the star map
is 2~3 times longer than when the catalog is not partitioned,
and the average search time for navigating stars is about 3
times. Compared with the currently commonly used star
catalog division algorithm, it has also been greatly improved,
and the generality of the algorithm is verified.
V. CONCLUSION
The guide star equipartition method proposed in this paper.
Through screening and processing the limit magnitude, the
capacity of the guide star catalogue is determined to be 5103.
The declination interval is determined according to the field
of view, and the right ascension interval is determined
according to the number of stars, so that the number of stars
in 452 subregions is approximately equal. Software
programming and star map simulation system are designed
by using the method of average number of guide stars, which
can accomplish the partitioning of guide star catalogs with
different view fields and magnitude limits and realize the
function of star map simulation. Use the star map simulation
system to randomly test the star chart refresh time pointed to
by 1,000 optical shafts, with an average refresh time of about
8ms. In this paper, the partition algorithm of guide star
catalog greatly improves the refresh rate of star map, and also
verifies the consistency and universality of the algorithm.
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10.1109/ACCESS.2021.3070408, IEEE Access
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GUANGXI LI, received the B.E. degree from the
School of Information and Electrical Engineering,
Hebei University of Technology in 2015, and the
M.E. degree from the School of Optoelectronic
Engineering, Changchun University of Science
and Technology, in 2019. He is currently studying
for Ph.D. degree from the School of
Optoelectronic Engineering, Changchun
University of Science and Technology. His current research interests include
spacecraft simulation test and calibration technology and photoelectric
detection technology. LINGYUN WANG, received the D.E. degree in
optical engineering from Changchun University of
Science and Technology in 2009. she served as
associate professor and professor in Changchun
University of Science and Technology, In 2011
and 2016. Her current research interests include
electrical detection technology, spacecraft ground
calibration technology and range testing
technology. RU ZHENG, received the B.E. degree and the
M.E. degree from the School of Optoelectronic
Engineering, Changchun University of Science and
Technology, in 2009 and 2012. And received the
Ph.D. degree from the School of Optoelectronic
Engineering, Changchun University of Science and
Technology, in 2016. She is currently a lecturer in
the School of Optoelectronic Engineering,
Changchun University of Science and Technology. Her current research
interests include spacecraft ground simulation and calibration techniques.
XIN YU, received the B.E. degree and the M.E.
degree from the School of Optoelectronic
Engineering, Changchun University of Science
and Technology, in 2011 and 2014. And received
the Ph.D. degree from The University of
Electronic Science and Technology of China and
the Institute of Photoelectric Technology, Chinese
Academy of Sciences, in 2018. He is currently a
lecturer in the School of Optoelectronic Engineering, Changchun University
of Science and Technology. His current research interests include aberration
detection, calibration and precision instrument design.
YUE MA, received the B.E. degree from the
School of Optoelectronic Engineering, Changchun
University of Science and Technology, in 2018.
She is currently studying for the M.E degree in the
School of Optoelectronic Engineering, Changchun
University of Science and Technology. Her current
research interests include spacecraft simulation
tests and calibration techniques.
XIAO LIU, received the B.E. degree, in 2019. He
is currently studying for the M.E degree in the
School of Optoelectronic Engineering, Changchun
University of Science and Technology. His current
research interests include spacecraft simulation
tests and calibration techniques.

This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI
10.1109/ACCESS.2021.3070408, IEEE Access
VOLUME XX, 2017 9
BO LIU, received the B.E. degree from the
Control Technology and Instruments,
Pingdingshan University, in 2018. He is currently
studying for the M.E degree in the School of
Optoelectronic Engineering, Changchun
University of Science and Technology. His current
research interests include spacecraft simulation
tests and calibration techniques.