The guided projectiles experience extreme dynamic conditions during launch, including high rotational speeds, high overloads, and large ranges. To address the issue that onboard low-to-medium precision MEMS gyroscopes are easily affected by time-varying and nonlinear random errors, a prediction model combining adaptive waveform EMD (Empirical Mode Decomposition) and Gated Recurrent Unit (GRU) is proposed (EMD-GRU). This model uses the GRU neural network to learn and predict the IMF (Intrinsic Mode Function) components obtained from the adaptive waveform extended EMD decomposition and then reconstructs them. Simulation results show that the proposed method outperforms traditional EMD and neural network methods on multiple evaluation metrics, demonstrating its effectiveness in complex, non-stationary, and nonlinear onboard environments. This provides a new approach for improving the attitude solution accuracy of guided projectile.