There are currently two types of methods for calculating the accuracy of star sensors, one is theoretical calculation formulas; The other type is Monte Carlo algorithm. In the research process of star sensors, various formulas have emerged to characterize the accuracy of star sensors, mainly including attitude angle measurement accuracy, optical axis pointing accuracy, noise equivalent angle, and single star measurement accuracy. However, they are only an approximate representation of some influencing factors on the accuracy of attitude measurement, and cannot estimate the accuracy of star sensors in real-time. Taking the Abreu formula, which is widely used in the design of star sensors, as an example, it is an approximate estimation of the impact of star image point extraction error on the accuracy of attitude angle measurement. It cannot estimate the accuracy of attitude angle measurement when the star sensor is aligned with a specific sky area, or the real-time accuracy of attitude measurement of the star sensor; It is also not possible to evaluate the impact of other factors, such as catalog errors and orientation element errors within star sensors, on attitude measurement. The use of Monte Carlo algorithm is a very direct method for calculating the accuracy of star sensors, but it requires hundreds or thousands of simulation experiments to achieve the convergence of indicator parameters to true values, which cannot meet the requirements of real-time evaluation of star sensor attitude measurement accuracy.
This article aims to comprehensively evaluate the impact of various factors on the measurement accuracy of star sensors. Firstly, based on the representation of star sensor spatial attitude using Euler angle, a star sensor attitude measurement model based on active frame theory is proposed, which avoids the dependence of attitude measurement accuracy on coordinate system selection and overcomes the problem of Euler angle singularity. Then, the error transfer formula for the multivariable implicit function overdetermined equation system was derived, and the error analysis theoretical model was improved. It was applied to the specific scenario of star sensor attitude measurement accuracy analysis. After the star sensor completes attitude capture, each frame of star map matching results can synchronously output the corresponding attitude measurement accuracy, achieving real-time output of star sensor attitude accuracy. Furthermore, theoretical analysis was conducted on the impact of random errors in star image point extraction, star catalog random errors, and the systematic errors of orientation elements within the star sensor on the attitude measurement accuracy of the star sensor. Finally, the effectiveness of the real-time analysis algorithm for attitude measurement accuracy in characterizing the real-time accuracy of star sensor operation was verified through simulation and outfield star sensor data.
Choose Euler angle to represent the attitude of the star sensor and describe the attitude measurement accuracy of the star sensor from an intuitive perspective. By using the active frame theory, the shortcomings of Euler angle representation of spatial attitude in star sensor accuracy analysis have been overcome, including the dependence of attitude measurement accuracy on the selection of coordinate systems and the singularity of Euler angle. The error transfer formula for multivariable implicit function overdetermined equations was derived, which improved the theory of error analysis. On this basis, an error transfer model for analyzing the attitude measurement accuracy of star sensors was established, including a random error transfer model and a system error transfer model. The error transfer model of star sensors was specifically analyzed from three aspects: random error in star image point extraction, random error in star catalog, and systematic error in internal orientation elements.
In the influence of internal orientation element system error on the attitude measurement accuracy of star sensors, the system error of the main point will introduce a large attitude measurement system error, which can be eliminated by installing the calibration of the attitude matrix. The system error of the focal length is relatively small compared to the system error of the main point, which contributes to the attitude measurement system error. However, the system error of the focal length can cause the star map matching to fail, resulting in incorrect attitude output or no attitude output. High order distortion can lead to star point extraction errors, reduce the accuracy of single star measurement, and in turn affect the accuracy of attitude measurement. Therefore, the calibration of internal orientation elements is crucial for high-precision star sensors. In addition, the accuracy of star sensors is approximately proportional to the square root of the number of sensitive navigation stars, and the detection performance of star points to a certain extent determines the attitude measurement accuracy of star sensors. In the case of few or a large number of false navigation stars, star map recognition fails, and the attitude measurement error of the star sensor manifests as accidental error. Accidental errors do not have a definite error transmission relationship or a random distribution pattern.
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