Micro-electro-mechanical system (MEMS) gyroscopes have found widespread application across various fields due to their core characteristics of low cost, compact size, and high practicality. However, their output accuracy deteriorates significantly under coupled temperature-vibration environments. Under combined wide-range temperature variations and persistent vibration, temperature drift and vibration errors overlap in the gyroscope output, weakening traditional single-factor compensation. Currently, research on systematic error compensation under coexisting temperature and random vibration is limited, with technical solutions still lacking. To address signal aliasing under temperature-vibration coupling, this paper proposes a variational mode decomposition-long short-term memory-Sage-Husa adaptive Kalman filter (VMD-LSTM-SHAKF) error compensation model based on virtual gyroscope technology, achieving simultaneous compensation of temperature drift and vibration errors in MEMS gyroscopes for the first time. In the proposed method, VMD is employed to separate the coupled signal, extracting temperature drift components while suppressing vibration interference. An LSTM network is then used to compensate the temperature drift, and an improved SHAKF fuses the outputs of a four-gyroscope array to further suppress random vibration errors and enhance overall accuracy. A static temperature-varying experiment was designed to collect gyroscope array data under different temperature and vibration conditions. Experimental results show that after VMD-LSTM-SHAKF processing, the system′s 1σ standard deviation decreases to 0.033 9°/s, angle random walk to 0.555 8°/h, with a 94.32% error reduction compared to the best single gyroscope. This study provides an effective solution for MEMS gyroscope error compensation in complex environments, offering engineering application insights.