A Polar Coordinate System Based Grid Algorithm for Star Identification

38

Table 1. The results of the simulations

Performances of the algorithm Algorithm in [10] Algorithm in this paper

Rate of successful identification 99.36% 99.74%

Mean time spent by the algorithm 18.50 mS 11.40 mS

Memory for star catalog About 0.5 MB About 0.7 MB

As demonstrated in Table 1, the algorithm presented in

the paper is superior to the algorithm in the Cartesian

coordinate system in both the identification rate and the

time spent. The improvement in rate of success results

from the consideration that the reference star may be near

the brim of the FOV, as well as from the smaller radial

grids adopted. The failure cases are associated with the

noises inserted into the centroids of the stars.

Another improvement of the algorithm is to use the

pixel-distribution of the stars in an angular polar coordi-

nate system to coarsely identify the reference star. As the

coordinates of the stars are denoted by angles, the time-

consuming trigonometric functions and vector functions

are not needed to compute the inter-star angles. However,

as the smaller grids are adopted, the memory required for

the catalog patterns enlarges. For the radial pattern

represents the angular separations between the reference

star and the neighbor stars, the smaller grids are neces-

sary to guarantee the rate of success and the robustness.

As in the most patterns, there is no star in most of the

radial ring strips, so most of the radial patterns include

many zero bits. A data compressing method can be

adopted to reduce the memory requirement for the star

catalog. Nevertheless, that may somewhat delay the al-

gorithm.

5. Conclusions

To speed up the star identification algorithm, an angular

polar coordinate system is adopted in star sensor and a

grid algorithm in the polar coordinate system is intro-

duced. As in the angular polar coordinate system, the

coordinates are all angular representations, the algori-

thms in the coordinate system are potential to be compu-

tationally efficient and of high identification rate. As the

night sky tests and the simulations demonstrate, the algo-

rithm proposed is excellent in both computational effi-

ciency and identification rate. It can be used in the star

sensors for high precision and high reliability in space-

craft navigation.

6. Acknowledgements

The work was supported by the key program of National

Natural Science Foundation of China under grant

No.60736010.

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