Monitoring and estimating the state of electric vehicle power batteries are of great significance for ensuring their safe and stable operation. To address the challenges in estimating the battery state of health (SOH) and remaining useful life (RUL), specifically the difficulty in extracting health-related features and the strong sensitivity of models to noise, a highly robust estimation model based on ICEEMDAN-DO-GRU is proposed, fully accounting for the impact of data noise on model performance. First, the ICEEMDAN decomposition method is used to perform signal decomposition on NASA’s publicly available battery dataset to extract health features for model estimation. Second, the dandelion optimizer (DO) is used to optimize the number of hidden layer neurons and the initial learning rate of the gated recurrent unit (GRU), thereby improving its performance. Finally, the effectiveness of the proposed model under different noise conditions is studied, and the DO-GRU results are comprehensively compared with four other typical neural networks. The experimental results prove that the proposed ICEEMDAN-DO-GRU model achieves high accuracy and strong robustness in both SOH and RUL estimation.