Statistical approach of truncation order selection for evaluating wavefront aberration effect in cold atom gravimeters

Wavefront aberration (WAE) is a major source of error in cold atom gravimeters (CAGs). In conventional CAGs, due to the limited range of modifiable parameters, it is challenging to obtain sufficient samples to determine the truncation order (TO) of the Zernike polynomials in WAE assessment. To address this, this paper proposes an approach combining Leave-One-Out Cross-Validation (LOOCV) with <i>F</i>-statistic to determine the TO: LOOCV pre-screens candidate orders with optimal generalization performance, followed by <i>F</i>-statistic to validate whether the higher-order model yields significant improvements, ultimately balancing model complexity and predictive performance. We conduct modulated Raman beam aperture experiments under three different system wavefront conditions. The results demonstrate that our approach can accurately evaluate the TO of the Zernike polynomial model in the conventional CAG, whereas the conventional approach fails. Moreover, we performed a joint fitting of the data from these three sets of wavefronts. Compared to the individual fitting, the joint fitting reduced the evaluation uncertainty by approximately 64% on average.