Increasing yield estimation accuracy for individual apple trees via ensemble learning and growth stage stacking

• Revealed the optimal window for apple yield estimation. • SEL outperforms individual machine learning in apple yield estimation accuracy. • Developed a novel apple yield estimation model: Growth Stage Stacking Ensemble. • Achieved orchard-wide apple yield estimation based on GSSE. Accurate prediction of individual apple tree yields during the preharvest stage is essential for precision orchard management and market planning. However, systematic studies focusing on apple yield estimation are scarce. To address this gap, this study targets Fuji apples in the Aksu region of Xinjiang. Multiple images were captured via a UAV during four key growth stages: flowering, fruit formation, fruit expansion, and ripening. On the basis of the extracted vegetation indices, we first developed yield estimation models using random forest (RF), support vector regression (SVR), partial least squares regression (PLS), and ridge regression (RR) methods. We subsequently combined these four models to construct a stacking ensemble learning (SEL) model. To further increase the accuracy of apple yield estimation, we refined the growth stage stacking method and developed a new model, the growth stage stacking ensemble (GSSE). This model maximises the use of spectral information from multiple apple growth stages by employing various machine learning algorithms and integrating multistage spectral data to improve yield estimation accuracy. The results indicate that the optimal period for yield estimation occurs during the fruit expansion stage, with the support vector regression (SVR) model achieving the best performance (R 2 = 0.654, RMSE = 5.307 kg). Compared with individual machine learning models, the SEL approach enhances yield estimation accuracy, reaching a maximum R 2 of 0.686 and an RMSE of 5.058 kg. Furthermore, GSSE significantly enhanced accuracy compared with the single-growth stage estimation models and SEL, with the combination of fruit expansion and fruit ripening stages yielding the best results, with an R 2 of 0.759 and an RMSE of 4.431 kg, with the fruit expansion stage contributing the most. This study is the first to apply the GSSE to apple yield estimation, offering novel insights for UAV-based apple yield estimation.