The maglev gyroscope torque feedback orientation measurement system, equipped with abundant sampling data and high directional accuracy, plays a crucial role in underground engineering construction. However, when subjected to external instantaneous vibration interference, the gyroscope rotor signal frequently exhibits abnormal jumps, leading to significant errors in azimuth measurement results. To solve this problem, we propose a novel noise reduction algorithm that integrates Moving Average Filtering with Autoregressive Integrated Moving Average (MAF-ARIMA), based on the noise characteristics of the rotor jump signal. This algorithm initially adaptively decomposes the rotor signal, subsequently extracting the effective components of the north-seeking torque with precision and applying MAF processing to effectively filter out noise interference. Furthermore, we utilize the stable sampling trend data of the rotor signal as sample data, employing the ARIMA model to accurately predict the missing abnormal jump trend data, thereby ensuring the completeness and coherence of the rotor signal trend information. Experimental results demonstrate that, compared to the original rotor signal, the reconstructed signal processed by the MAF-ARIMA algorithm exhibits an average reduction of 70.58% in standard deviation and an average decrease of 47.31% in the absolute error of azimuth measurement results. These findings fully underscore the high efficiency and stability of the MAF-ARIMA algorithm in processing gyroscope rotor jump signals.