Uncertainty Estimation and Multi-FOV Data Fusion for Star Sensors Based on Directional Statistics

The uncertainty of star sensors refers to the uncertainty of star observation and attitude determination. These uncertainty parameters are important performance criteria and also the basis for multisensor data fusion. In this article, the Fisher and matrix Fisher distributions in directional statistics are used to model the observed star vectors and star sensor attitude, respectively. Based on their mathematical properties and parameter estimation methods, a novel uncertainty estimation method for single-frame measurement of star sensors is proposed and derived. This method can estimate the concentration of the observed star vectors, filling a gap in previous studies. Through the maximum-likelihood estimation of attitude, this method can directly obtain the propagation of vector concentration to the attitude concentration. Under high-precision conditions, the conversions between the concentration parameters and covariances are also derived, and based on this, a multi-field-of-view (multi-FOV) data fusion method with uncertainty parameter weighting is proposed, where the uncertainty of installation matrices is also considered. The simulation results demonstrate the proposed uncertainty estimation method's effectiveness, and the fusion method can effectively reduce the attitude measurement error of multi-FOV star sensors. Finally, the uncertainties of the three types of star sensors are evaluated and analyzed in a night-sky experiment, which further validates the proposed method's practicality.