Abstract: During the straightening process of a scraper conveyor in a fully mechanized mining face, the system is affected by sensor measurement errors and hydraulic support advancing errors. The sensors used for trajectory detection on hydraulic supports and the scraper conveyor are subject to noise interference with evident non-Gaussian and heavy-tailed characteristics and unknown statistical properties under complex coal dust, illumination disturbance, and mechanical impact conditions. Traditional filtering algorithms exhibit low trajectory prediction accuracy, resulting in poor straightening performance. To address this problem, a scraper conveyor straightening method based on a Variational Bayesian Adaptive Kalman Filter (VBAKF) algorithm with hierarchical Bayesian modeling was proposed. The process noise and measurement noise were jointly modeled as Student-t distributions, and the noise covariance was estimated online through scale variables, thereby constructing a trajectory prediction model for the scraper conveyor suitable for complex non-Gaussian environments. On this basis, a calculation procedure for the compensation amount of scraper conveyor advancement based on the predicted trajectory was further established to achieve the straightening objective. Under conditions of unknown noise statistical characteristics, simulations were conducted for error scenarios in which process noise and measurement noise exhibited different degrees of heavy-tailedness and slowly varying covariance characteristics. The results showed that: ① the VBAKF algorithm maintained stable trajectory prediction performance under unknown noise statistical characteristics and heavy-tailed interference. ② The mean squared error between the predicted trajectory and the actual trajectory of the scraper conveyor was about 1.6 mm, which was reduced by approximately 20%, 25%, and 40% compared with the unscented Kalman filter, maximum correntropy Kalman filter, and adaptive Kalman filter, respectively. ③ After applying the proposed method for straightening, the maximum straightness deviation of the scraper conveyor was reduced by about 70%. These results indicate that the proposed method effectively improves the trajectory prediction and straightening accuracy of the scraper conveyor in a fully mechanized mining face.