A Robust Autonomous Star identification Algorithm for ZY3 satellite

Junfeng Xie

Satellite Surveying and Mapping Application Centre, Beijing, P.R.China

junfengxie@gmail.com

Xiao Wang Institute of Remote Sensing Application Chinese Academy

of Sciences, Beijing, P.R.China wangx@irsa.ac.cn

Abstract—ZY-3 is China’s first civilian high-resolution stereo mapping satellite. It equipped multiple star trackers and gyros for attitude determination. The stellar images acquired by the autonomous Active Pixel Sensor (APS) based star tracker on ZY-3 satellite are downlinked to the ground for post-processing. The FOV (Field Of View) of the star tracker is 20º×20º, which is designed large to detect more stars in the FOV. However, the star identification becomes more complex. A robust autonomous star identification algorithm is proposed. The novel algorithm firstly chooses the brightest star in the stellar image as the base star, and links the base star to each neighbouring star for radiant pattern construction. Each “link” is compared with star database, and the star that has most times of meeting the matching condition is considered as the base navigation star. And the adjacent stars are constructed as a directed circularity pattern for unitary matching. The candidate matching group which has the longest chain will be selected as the ultimate matching result. The stellar images downlinked from ZY-3 are used to verify the effectiveness and reliability of this algorithm.

Keywords- Star identification; Angular distance; matching probability; Matching group; The longest matching chain

I. INTRODUCTION ZY-3 is the first civilian original design high-precision

stereo mapping satellite for China, which was successfully launched on January, 2012. Satellite exploits three-line-array CCD for photography, and is mainly used for land survey, 1:50000 stereo mapping and 1:25,000 topographic map update.

High attitude precision is very important for satellite mapping accuracy. Compared with other attitude sensors, as the most accurate sensor, the star tracker has many advantages such as no drift and providing the attitude information of three axis, etc[1~3]. Currently most high-resolution remote sensing satellites including ZY-3 adopt star tracker for attitude determination [4-6]. In order to improve absolute attitude accuracy, the stellar images acquired by the APS based star tracker loaded on ZY-3 are downlinked for the ground processing.

During the process of attitude determination using star sensor, the stars in the inertial frame are considered as the references, which are imaged by CCD camera, and a series of processing will be implemented [7],which involves star acquirement[8,9] ,star identification [10-13], and attitude estimation [14-16] . Star identification is the most important step of data processing, which is related to the efficiency and

the reliability. In order to improve the reliability of attitude determination, The APS star tracker equipped on ZY-3 has the large FOV design with 20º×20º,which ensure the quantity of the detected stars in the FOV, and increase the complexity of star recognition.

The calculation precision of the angular distance may be low due to lots of factors, such as the stellar camera parameters aren’t calibrated on-orbit, or the star centroiding accuracy is low, and so on, which can decrease the success rates of star identification.

A novel star identification algorithm is put forwarded. In this algorithm, the selection of the base star and directed circularity pattern matching and the matching group which has the longest chain as last matching result will improve the success rate of star matching. Lastly, the stellar images from ZY-3 are employed to test and verify it.

II. THE STAR IDENTIFICATION BASED ON THE LONGEST MATCHING CHAIN

A. The principle of the algorithm The proposed algorithm firstly chooses a star in the center

of the stellar image (also called “the Identified Base Star”, IBS). A radial geometry pattern is constituted by linking the identified base star to other neighboring stars in the stellar image.

The compare of each angular distance in the stellar image and in the star catalogue is implemented to identify IBS. For all “links” within matching threshold, the IDentity (ID) of two corresponding stars are recorded and accumulated. The star in the star catalogue that has the most appearance times is regarded as the navigation star (also called “Cataloged Base Star”, CBS) corresponding to the IBS.

Once the CBS is confirmed, the candidate stars groups including CBS will be extracted. The directed circularity pattern is constructed by candidate star groups for unitary matching, and the longest matching chain is considered as the final matching results.

B. Star Database Generation According to the principle of algorithm, the angular

distance is the elementary matching item. The identifying process mainly is frequently searching the qualified angular

distance to identify the star. Therefore, the Angular Distance Index Table (also called ADIT) is required to be computed and stored as the navigation star database. As shown in table I, the angular distance is sort ascendingly. The ID of the star is noted by INDEX, and the magnitude of angular distance is denoted by I12, and two navigation stars of the angular distance in the star catalogue are denoted by ID1 and ID2 respectively.

Considering the range of the FOV, only the angular distance that is less than the size of the FOV can be saved. In order to reduce the false matching, the navigation star should be selected firstly according to the detect ability of the star tracker. And meanwhile, the binary and viable stars will be eliminated in the initial star catalogue.

This algorithm can be suitable for the conditions that the star magnitudes aren’t measured accurately or even unknown. If the appearance magnitude of the star can be measured accurately, this algorithm becomes more effective. The visual magnitude in the star catalogue can be considered as the matching elements, which are added to the ADIT, as shown in last two columns of the table I. INDEX I12 ID1 ID2 MAG1

(×100) MAG2 (×100)

100 0.10880 13619 14058 567 496 … … … … … …

101 0.10901 6063 5441 524 591 102 0.10907 9523 9538 401 485 … … … … … …

TABLE I. ANGULAR DISTANCE INDEXED TABLE(ADIT).

The MAG1and MAG2 respectively denotes the two star magnitudes of the angular distance in star catalog, which is magnified 100 times. As the important matching element, the star magnitude can be used to eliminate the fasle candidate matching result further. The regulation is described by formula (1). The mag1 and mag2 denote two star magnitudes of angular distance in the stellar image, and TE and TMag denote angular distance and magnitude threshold respectively. The algorithm becomes more effective when the visual magnitudes are acquired. The matching conditions and formulas are shown below.

1 1 2 2( & & )i j E

mag mag

E E T

MAG mag T MAG mag T

⎧ − <⎪⎨

− < − <⎪⎩

…… (1)

C. Implementation steps Based on the design idea of the algorithm, the ADIT is

founded firstly, and the star identification can be implemented. The identification process is described as follows:

a) The brightness of the star is an important reference to know the guide star can be detected by star tracker. The brightest star in the FOV is considered as the IBS. In the stellar image pre-processing, the double stars and very bright body (such as the moon, the sun, etc.) are removed to avoid being selected as the IBS, as shown in figure 1.

b) The IBS is treated as the origin, and the radiant pattern is constructed by linking the origin with the neighboring stars in the FOV.

c) The new image central coordinates are established, in which the IBS is origin, and the x and y axis is parallel to the corresponding axes of the old image central coordinate respectively. The adjacent stars are indexed from new x axis in counterclockwise direction, which are expresses as 0, 1…5. As shown in figure 1, the radicalized pattern is formed as (IBS-> (0->1->2->3->4->5)).

d) Each angular distance of radicalized star map ((IBS-0), (IBS-1)… (IBS-5)) is matched with the angular distances in the ADIT(as shown in Table I), and the candidate navigation stars satisfying matching condition are obtained. The numbers of repeated candidate navigation stars are recorded and sort descending. The navigation stars who has largest times will be chosen as the CBS, As seen from figure 2, the ID of the CBS is 2041 when other navigation stars only appear one or two times. In generally, in order to avoid rejecting the right CBS, the candidate navigation star isn’t only one. Those navigation stars whose repeated number is larger than the amount of neighboring stars will be chosen as candidate CBS, while the corresponding neighboring groups of the candidate CBS will be recorded, which are listed as table II.

e) The candidate neighboring stars of each candidate CBS are confirmed in order. As seen in table 2, the corresponding neighboring stars of the identified CBS (2041) have multiple candidate stars, for example, the star 0 in stellar image have candidate navigation star 2047, 1839 in the star catalogue. The directed pattern matching is implemented to eliminate the false candidate navigation stars. From figure 2, the links connected by lines denote the angular distance matching successfully. The longest matching chain will be determined as the final result. The matching result is 2047-2048-1861-1857-1858-2049-2047. If the chain is broken, the longest matching chain still is selected as the final result. For example, the star 1 is pseudo star in the stellar image, the longest matching chain （1861->1857->1858->2049->2047） corresponding to（2->3->4->5->0）in the stellar image also considered as final result.

TABLE II. STATISTIC OF THE CANDIDATE NEIGHBORING STARS

Image Star Link

Candidate navigation star groups

Candidate Guide Star

Image Star ID

navigation star ID

(IBS-0) (2041,2047)(2041,1835) 0 2047,1839 (IBS-1) (2041,2048)(2041,1854)

(2041,1860) 1 2048,1854,

1860 (IBS-2) (2041,1861)(2041,1844)

(2041,1845) 2 1861,1844,

1845 (IBS-3) (2041,1857),(2041,1854)

(2041,2046)(2041,2048) 3 1857,1854,

2046,2048 (IBS-4)

(2041,1858)(2041,1855) (2041,1844)(2041,2043) (2041,2051)

4 1858,1855, 1844,2043,2051

(IBS-5) (2041,2049) (2041,2047) 5 2049,2047

0

1

2

3

4 5

Identified Base star

Figure 1. the scheme of directed ring model

20482047• 2048• 1854

• 1860

1861• 1861• 1844• 1845• 1861

1857• 1857

• 1854• 2046• 2048

1858 2049 2047• 1858• 1855• 1844• 2043• 2051

• 2049• 2047

• 2047• 1835

2047,…

2048,…

1861,…

1857, …

1858,… 2049,…2041

• 2047• 1835

Cataloged Base star

Figure 2. the scheme of matching chain

III. EXPERIMENTAL ANALYSIS AND VALIDATION ZY-3 satellite takes three star trackers for the attitude

determination. The stellar images acquired by one star tracker are downlinked and used for post-process. The Active Pixel Sensor (APS) based star tracker configuration used for the proposed algorithm verification makes use of a 20×20 deg FOV with an image plane consisting of 1024×1024 pixels. The image center is (512,512), and the pixel size is 15 um×15 um. The sensitivity of star magnitude is 6.5 Mv. The raw stellar image is shown as below.

The stellar images are transited to ground when ZY-3 satellite flies over China’s territory. The raw stellar images acquired on February, 2012 are elected for the experimental analysis and algorithm validation when satellite flies smoothly.

Figure 3. stellar images from ZY-3 satellite

The navigation stars in the tycho2n (J2000) star catalog are employed [17]. The main data types includes the star index, the

visual magnitude(MV), the right ascension (hours ,minutes and seconds) and declination (degree, arcminute and arcsecond), etc.. The range of MV is 0 to 6.0, and 5001 navigation stars are selected after the double stars and variable stars are removed to constitute the basic star catalogue.

Due to the position errors, the absence of camera calibration, and the appearance location of navigation star being not completely corrected, etc., the angular distances is set relatively larger to identify the star image based on this algorithm. In this experiment, the matching threshold is set 70 arcseconds, which is the angular resolution of star tracker. The 1090 stellar images of one track are unpacked and employed for this experiment. The amount of the detected stars in the FOV is 5 at least. Before the star identification, the star centroiding is implemented.

The first image plane coordinates are shown in the table below. The first column is the star index in the stellar image, and the next two columns are plane coordinates in the x, y-axis (unit: pixel).

Stellar image Index

Image Coordinate（x axis）,pixel

Image Coordinate（y axis）,pixel

IBS 391.16 -0.209148 0 363.982 46.0158 1 184.97 3.98845 2 4.99304 241.997 3 -117.962 26.024 4 -444.923 -355.982 5 151.033 -1.01778

TABLE III. THE RESULT OF STAR CENTROIDING

According to the algorithm design, The IBS is firstly identified, and based on which, the other neighboring stars are recognized. The matching result (figure 3) is shown in table 4.

Stellar image Index

Star index

Right Ascension （degree）

Declination (degree)

IBS 297 236.067 6.42552 0 298 236.611 7.35323 1 789 234.123 10.0105 2 1295 236.547 15.4219 3 1283 231.447 15.4281 4 1271 221.31 16.9644 5 788 233.701 10.5389

TABLE IV. THE MATCHING RESULT

The algorithm was performed on a Windows XP based PC

(2.99 GHz speed) using C/C++ languages. After all images are batch-processed, the result indicates all images are identified correctly, the total time consumed is 2001 seconds, and the average time for one image achieve 2 seconds, which can meet the demand of the post-processing that has no real-time requirement.

The algorithm is still effective when the stellar camera is uncalibrated or the precision of star centroiding (even to 2-3 pixels) is very low. But in such a case, the matching threshold is needed to set large, and then the candidate matching groups

will be more, the matching speed is slower, compared to the usual.

When the initial condition is bad, the star matching can be implemented by this algorithm, and then the stellar camera can be on-orbit calibrated using these successful matching data [18-19], which can be improve the accuracy of angular distance, lastly the matching threshold can be decreased to increase matching speed.

IV. CONCLUSION The proposed star recognition algorithm based on the

longest matching chain mainly uses the angular distance information and the supplemented magnitude information. This algorithm optimizes the base star choice, and adopts the global match for the adjacent stars with directed circularity pattern. The matching group with the longest chain is considered as the matching result, these strategies are used to improve the reliability of the proposed algorithm. The experiment with real data from ZY-3 satellite shows that the algorithm retains the merit that insensitive to magnitude error, and the high identification rate and efficiency, which has practical application value for attitude determination of high resolution remote sensing satellite.

ACKNOWLEDGMENT This work was supported by the National Key Technology

Support Program under Grant 2011BAB01B02.

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