A Systematic Error Compensation Method Based on an Optimized Extreme Learning Machine for Star Sensor Image Centroid Estimation  
[PERSON]  
1 Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi'an 710119, China; [EMAIL_ADDRESS] (X.W. ); [EMAIL_ADDRESS] (D.W.); [EMAIL_ADDRESS] (W.Z. ); [EMAIL_ADDRESS] (G.L. ); [EMAIL_ADDRESS] (Z.L.) [PERSON]  
1 Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi'an 710119, China; [EMAIL_ADDRESS] (X.W. ); [EMAIL_ADDRESS] (D.W.); zhangweik  
proposed. Among these existing methods, the center of mass (CoM) centroid estimation method features high speed and simplicity of calculation, so CoM is utilized in engineering projects. However, the location accuracy of the CoM method is influenced by two types of noise, namely, random noise and systematic noise. Random noise, which contains dark current noise, short noise, radiation noise, etc., is related with the hardware system of the star sensor [11]. Systematic noise is caused by the character of the centroid estimation algorithm itself, and it brings about several arc seconds of accuracy loss in the star centroid location. In this paper, we focus on analyzing the systematic error in the CoM method, and then we propose a compensation method to remove the accuracy loss introduced by the systematic error, while the random noise is also discussed briefly. Investigations into the systematic error in the CoM centroid estimation method have been made by several scholars. In general, the systematic error is related with the starlight energy distribution, the sampling window size, and the actual position of the detected star spot. [PERSON] et al. [12] found that the systematic error decreases when the starlight energy is defocused to wider neighboring pixels. [PERSON] et al. [13] pointed out that the relationship curve between the systematic error and the actual position of the star spot roughly satisfies a sinusoid pixel periodic function under fixed Gaussian width. [PERSON] et al. [14] supplemented [PERSON]'s work and studied the systematic error under different blur sizes of star spots, detector fill ratios, and pixel sizes numerically. [PERSON] et al. [15] studied the systematic error for the CoM centroid estimation method and gave a general expression for the systematic error. [PERSON] et al. [16] introduced a numerical model of the defocused point spread function, in which the defocus effects and diffraction were considered, and employed a backpropagation neural network (BP) to reduce the systematic error. [PERSON] et al. [17] presented a theoretical analysis of the systematic error in the CoM method by a frequency field approach considering both the limitation of the detector sampling frequency and the limitation of the sampling window size, and they then proposed a compensation method based on the obtained analytical expression to improve the centroid accuracy. [PERSON] et al. [18] used the least square curve fitting method to estimate several key parameters in a bivariate polynomial model and developed a method utilizing a bivariate polynomial compensation template to correct the systematic error. [PERSON] et al. [19] conducted least squares support vector regression (LSSVR) to eliminate the systematic error, where a trained LSSVR model was applied to predict the systematic error and then compensate for this error. This paper presents an analysis of the systematic error in the CoM method under different Gaussian widths of starlight energy distribution utilizing a frequency field approach and numerical simulations, and it indicates that the systematic error consists of approximate error and truncation error.