An Adaptive Multi-Scale Star Centroid Localization Algorithm with Bayesian Iterative Weighting and Performance Analysis

Abstract. Star centroid localization accuracy fundamentally limits spacecraft attitude determination precision. Existing methods face a critical accuracy-efficiency trade-off: traditional intensity-weighted approaches achieve computational efficiency (<1 ms/star) but suffer from poor noise robustness, while Gaussian fitting and deep learning methods provide high accuracy at prohibitive computational costs. We address this fundamental limitation by developing a principled Bayesian Multi-Scale Adaptive Iteratively Weighted (BMAI) centroid localization algorithm that achieves high accuracy approaching theoretical limits while maintaining real-time computational efficiency. The algorithm integrates four key technical contributions: (1) SNR-adaptive window extraction with robust threshold estimation, (2) regularized iteratively weighted framework with proven convergence properties, (3) multi-scale fusion with SNR-dependent weighting, and (4) gradient-based refinement to mitigate systematic bias. Rigorous theoretical analysis establishes convergence guarantees, derives error bounds, and evaluates Cramér-Rao Lower Bound (CRLB) efficiency. Comprehensive evaluation on 16,500 synthetic star images across six diverse imaging scenarios demonstrates that under high-SNR conditions (SNR >25, n=2,000), BMAI achieves mean RMSE of 0.0120 pixels (95% CI: [0.0116, 0.0124] pixels), representing a 98.6% relative improvement over intensity-weighted centroiding (0.857 pixels), 35.8% improvement over Gaussian fitting (0.0187 pixels) and 95.3% improvement over CNN methods(0.2566 pixels). The algorithm maintains computational efficiency of 0.89ms per star—8.7× faster than Gaussian fitting—while achieving CRLB efficiency of 79.2%. Robustness analysis demonstrates stable performance across SNR range 3-100 with graceful degradation under challenging conditions. The BMAI algorithm fundamentally resolves the accuracy-efficiency trade-off in star centroid localization through principled Bayesian inference and multi-scale processing.