This study thoroughly scrutinized techniques for initial alignment and random error suppression in hemispherical resonator gyroscopes and inertial navigation systems, both domestically and internationally, identifying angle random walk and bias instability as the primary error sources for gyroscopes through Allan variance analysis of raw data. To alleviate these errors, a novel combined model prediction reconstruction algorithm based on Intrinsic Time scale Decomposition (ITD) is proposed. This algorithm involves decomposing the original signal using ITD, followed by conducting stationarity tests and applying Auto-Regressive Moving Average (ARMA) modeling for completely stationary components, and Long Short-Term Memory (LSTM) neural network modeling for non-stationary components. The final prediction signal is then obtained by recombining the predicted components. Subsequent Allan variance analysis of gyroscope reconstruction signals processed by both prediction algorithms, using short and long-term sampled data, demonstrated a significant reduction in gyroscope random errors for both algorithms. Notably, the proposed algorithm exhibited superior suppression effects compared to its counterpart.