Utilizing statistical information for interval analysis: A method for analyzing the interval uncertainty of line-of-sight measurement error of space-borne observation platforms

Abstract

Analyzing the space-borne observation platform's line-of-sight measurement error (SOPLME) is of great significance for the improvement of the space-borne optical tracking system. In this regard, we consider the space-borne observation platform (SOP) as a multi-body system and build both the target imaging model from the inertial space to the optical camera image plane and the line-of-sight measurement model. The relationship between the SOPLME and the satellite's orbit error, attitude error, platform angular vibration error, inner and outer frame rotation error, and position quantization error of target image point is deduced theoretically. However, since there are many error sources and the modeling process is highly nonlinear, the amplification of the output range caused by the 'wrapping effect' may occur when using the interval calculation method to analyze the output range of the SOPLME. To solve this problem, we propose a novel method of interval analysis by using statistical information. This method combines the convenience of interval representation with the high accuracy of probability calculation, which can effectively avoid the overestimation problem caused by the inherent 'wrapping effect' of the interval calculation method. Firstly, we describe the parameters of each error source with the interval constructed by upper and lower bounds. Secondly, the optimal Latin hypercube sampling (LHS) matrix of error source parameters is designed by the quasi-optimization method. Then we use the Gaussian mixture model (GMM) to approximate the distribution function of the SOPLME. Finally, the output range of the SOPLME is estimated by Taylor expansion. The simulation test verifies the reliability of the model and interval calculation method in this paper. The simulation example shows that the proposed method can get a more reliable error output interval with less sampling amount, which is suitable for analyzing the dynamic process of the output interval of the SOPLME.