The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
The training samples X. for equation(3) in hyper planes 
H 2 , are the most close points to the classified plane in the two 
types of samples. Because H 2 looks like supporting the 
optimized classified plane, so we can call X. support 
vector(SV). In Equation(5), corresponding non-SV, /1. = 0, it 
only need to sum up SV X, . The alphabet b is the classified 
threshold. 
If samples cannot classify in given input space, it should be 
mapped to a high dimension space by kernel function 121 , thereby, 
in the transform space the samples can be classified by 
optimized classified plane. The classifier function getting from 
SVM is similar with from neural network. The output of SVM 
is the linearity combination of middle layer nodes, and every 
middle layer node is dot metrix of an input sample and a support 
vector. The process of classifying by SVM is showed as Figure. 
3: 
output 
SV • Sample 
mapping 
suport vector 
input:samples 
Step 6 
Step 7 
Step 8 
Step 9 
Record every stars in S star ‘ as a sample; 
Whether done with the samples? 
YES: getting Samples, to 
Step 8 ; 
training SVM with samples 
Classify all stars in the catalogue with trained SVM; 
if the output is “1”,select the stars as navigation 
stars; record the other stars as non-navigation stars. 
NO: to Step 3; 
Because SVM is iterative optimization process, so it is 
necessary to verify continually what the right SVM parameters 
is and select samples for training SVMs again and again until 
the catalogue can support navigation applications perfectly. 
5. TEST AND ANALYSIS 
Taking SAO catalogue as basic catalogue, we designed some 
tests for verifying the method mentioned in this paper. Firstly, 
given threshold VMT=8.0, we got a temporary catalogue 
include 46,136 stars by filtering basic catalogue with MFM. 
Then, given FOVg =3°x3°, sampled the temporary catalogue 
randomly by FOV§ for getting training samples data. 
Then the samples data were separated into two parts, one part 
was used as training samples for confirming SVM parameters, 
the other part was used as inspection samples for testing the 
performance of SVM and optimizing SVM parameters 
according to classified results. At last, all stars in the temporary 
catalogue were classified by trained SVM, and then we got 
navigation-stars catalogue for determining attitude of satellites. 
The classification was executed 1,000 times randomly and the 
experiment results can be shown by Table 2. FOV is given field 
of view when extracted training samples from temporary 
catalogue. 
Figure3. Operation of SVM 
4. NAVIGATION STARS SELECTION BASED ON SVM 
Navigation stars selection based on SVM include some steps as 
Table.! shown: 
Table. 1 Navigation stars selection based on SVM 
g 1 Support VMT=8.0, initialize basic catalogue based on 
CP MFM; 
Select samples in the whole celestial sphere 
^ te P ^ according to a given sample interval FOV Inlerva ,; 
Select the stars in every sample FOVs FOV' 
Step 3 
(FOV;<FOV). getting SJ , 
Arrange the stars in S star ‘ from bright to dark 
^ te P ^ based on their brightness (Vmag), only reserve 
n(n>3) stars from the beginning of list; 
Consider 3 of the most brightness stars in S star ‘ as 
^ navigation stars, and label with “1” ;the other stars 
labeled with “0”,as non-navigation stars; 
Method 
Capability 
of 
catalogue 
Density 
navigation-stars 
FOV 
of 
in 
0 
<3 
<5 
>=5 
MFM8.0 
46136 
- 
- 
. 
- 
SVM8.0 
9117 
0 
0 
46 
954 
MFM7.0 
15914 
0 
0 
0 
1000 
MFM6.5 
9023 
0 
4 
37 
959 
SVM6.5 
(FOV=3) 
6936 
0 
1 
29 
970 
SVM6.5 
(FOV=6) 
7685 
0 
0 
43 
957 
Table.2 Experiment results 
From Table.2, we can find that the capability of catalogue based 
on SVM is obvious smaller than that based on MFM and the 
density of FOVs has notable change. For example, when 
VMT=6.5, the capability of catalogue based on MFM is 9,023 
and the probability of stars fewer than 3 in FOVS is 0.4 %. But 
the capability and probability of catalogue based on SVM is 
6,936 and 0.1%. When adopted MFM, in order to avoid empty 
hole of field, the VMT must be 7.0 and the capability is 15,914.