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Accurate co-estimations of battery states, such as state-of-charge (SOC), state-of-health (SOH,) and remaining useful life (RUL), are crucial to the battery management systems to assure safe and reliable management. Although the external properties of the battery charge with the aging degree, batteries' degradation mechanism shares similar evolving patterns. Since batteries are complicated chemical systems, these states are highly coupled with intricate electrochemical processes. A state-coupled co-estimation method named Deep Inter and Intra-Cycle Attention Network (DIICAN) is proposed in this paper to estimate SOC, SOH, and RUL, which organizes battery measurement data into the intra-cycle and inter-cycle time scales. And to extract degradation-related features automatically and adapt to practical working conditions, the convolutional neural network is applied. The state degradation attention unit is utilized to extract the battery state evolution pattern and evaluate the battery degradation degree. To account for the influence of battery aging on the SOC estimation, the battery degradation-related state is incorporated in the SOC estimation for capacity calibration. The DIICAN method is validated on the Oxford battery dataset. The experimental results show that the proposed method can achieve SOH and RUL co-estimation with high accuracy and effectively improve SOC estimation accuracy for the whole lifespan.