Modeling and Suppression of Star Positioning Errors Induced by Atmospheric Turbulence for Terrestrial Star Sensors

To address the issue that star positioning in terrestrial star sensors (TSSs) is affected by atmospheric turbulence (AT), this article models AT-induced star positioning errors based on Kolmogorov’s AT theory and mitigates them. First, we analyze disturbed star irradiance grounded in the statistical laws of phase variation and amplitude fluctuation in the light field perturbed by AT, and further establish a stochastic process model for jitter error by leveraging both the temporal and spatial characteristics of point spread function (PSF)’s position jitter. Then, for TSS capturing star images with long exposure times, we can suppress jitter error by utilizing the temporal smoothing effect of PSF’s position jitter. For TSSs capturing star images with short exposure times, a jitter-error-incorporating star position H∞ filtering framework is proposed. In this framework, a state equation that integrates a star kinematic model with the established random process model and a measurement equation incorporating jitter error are constructed. Finally, simulations and night sky experiments were conducted. The results show that the estimated uncertainty of observed star vectors σ<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>wi</i></sub> ’s mean for the real star images captured with a short exposure time decreased by over 70% after error suppression.