As high accuracy and high reliability devices, star sensors play an important role in attitude determination for satellites in celestial navigation system (CNS). The main steps for attitude determination include star point location, star identification and attitude tracking [1
]. Based on the captured star images, stars can be located and identified. Whether the attitude determination of satellite is successful or not, the pattern recognition is very important for star images in the field of view (FOV) [2
]. It indicates that only the available and recognizable star images can ensure star sensor can give an accurate satellite attitude [3
], so it is critical to improve the accuracy of star point location.
In the past many years, some algorithms have been developed to extract star centroids utilizing initial star images. Reference [4
] shows a new sub-pixel interpolation technique to process image centroids. Reference [5
] gives a method of enhancement of the centroiding algorithm for star tracker measure refinement. An analytical and experimental study for autonomous star sensing, including the star centroid process, is presented in [6
]. However, these studies are generally used under static conditions or balanced processes. For many agile maneuver satellites, star sensors work under dynamic conditions as a result of the rotation of the star sensor along with the satellite. Therefore, various noises in star field caused by dynamic factors may affect the quality of imaging. Moreover, due to the large angular rate, the star point moves on the focal plane during the exposure time, which may lead to two changes for the star point: the position shifting on the focal plane and the limited starlight energy dispersing into more pixels. As a result, the SNR (Signal to Noise Ratio) of blurred star images may decrease and the measured star centroid would be inaccurate.
Dynamic conditions stress the need for a very accurate and robust processing method for blurred star images. At present, many investigations tend to concentrate on the exploration and analysis of star location under dynamic condition [3
]. For example, reference [7
] shows the simulation analysis of dynamic working performance for star trackers. Reference [8
] provides an analysis of the star image centroid accuracy of an APS star sensor under rotation conditions. Blind iterative restoration of images with spatially-varying blur is the research topic in reference [9
]. However, most of them are limited to the useless locating capability when the angular rate is larger than 2°/s. In [3
], the method is effective to estimate attitude, but it has the contrary effect when the angular rate is low.
The main theme of this paper is to overcome the difficulties arising from dynamic imaging blur of star sensors, including denoising and restoration of blurred star images by estimating the angular rate. On the one hand, if the angular rate is in the dynamic range of the star sensor, a proposed adaptive wavelet threshold is used for denoising according to the characteristics of the blurred star image, which can guve the accurate centriod within sub-pixels. On the other hand, if the angular rate is larger than the dynamic range, the restoration algorithm based on the angular rate is used to process the “tail” star image. As will be seen later in this paper, the adaptive method outperforms other denoising methods in terms of Power Signal-to-Noise Ratio (PSNR) and visual qualities, and the large variation of the angular rate has little effect on the star centroid determination based on the restoration method.
This paper is divided into six sections. Following this Introduction, the imaging theory of star sensors is outlined in Section 2, as well as the characteristic of blurred star images under dynamic conditions. Then the method of denoising based on adaptive wavelet threshold is described in detail in Section 3. The restoration method is developed in Section 4 by analyzing the Point Spread Function (PSF) of motion blurred star images, where a Wiener filter with an optimal window is used to overcome the edge error. In Section 5, simulation results are shown to demonstrate the proposed methods. At the end, conclusions are drawn in Section 6.