For the ASO-S/HXI payload, the accuracy of the flare reconstruction is reliant on important factors such as the alignment of the dual grating and the precise measurement of observation orientation. To guarantee optimal functionality of the instrument throughout its life cycle, the Solar Aspect System (SAS) is imperative to ensure that measurements are accurate and reliable. This is achieved by capturing the target motion and utilizing a physical model-based inversion algorithm. However, the SAS optical system's inversion model is a typical ill-posed inverse problem due to its optical parameters, which results in small target sampling errors triggering unacceptable shifts in the solution. To enhance inversion accuracy and make it more robust against observation errors, we suggest dividing the inversion operation into two stages based on the SAS spot motion model. First, the as-rigid-as-possible (ARAP) transformation algorithm calculates the relative rotations and an intermediate variable between the substrates. Second, we solve an inversion linear equation for the relative translation of the substrates, the offset of the optical axes, and the observation orientation. To address the ill-posed challenge, the Tikhonov method grounded on the discrepancy criterion and the maximum a posteriori (MAP) method founded on the Bayesian framework are utilized. The simulation results exhibit that the ARAP method achieves a solution with a rotational error of roughly ±35 (1/2-quantile); both regularization techniques are successful in enhancing the stability of the solution, the variance of error in the MAP method is even smaller—it achieves a translational error of approximately ±18 μm (1/2-quantile) in comparison to the Tikhonov method's error of around ±24 μm (1/2-quantile). Furthermore, the SAS practical application data indicates the method's usability in this study. Lastly, this paper discusses the intrinsic interconnections between the regularization methods.

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