Reliable and precise extraction of features plays a critical role in predicting the State of Health (SOH) of lithium batteries. Nevertheless, noise-tainted measurement signal can cause the distortion of differential curves, consequently compromising the accuracy of feature extraction. This paper develops an online two-dimensional filtering framework by fusing the Adaptive Taylor Kalman filter (ATKF) and the Improved Gaussian filter (IGF), applying it to both incremental capacity analysis and differential thermal voltammetry methods. Firstly, the Taylor series is harnessed to construct a state model for the noise-affected measurement signal. Then, an adaptive algorithm is introduced to diminish the dependence on human judgment when configuring variances. Finally, the IGF filters the curve from the two-dimensions of time and period. Experimental results demonstrate that the two-dimensional filtering method exhibits robust noise mitigation capabilities, enhancing the stability of feature extraction while maintaining system causality. Furthermore, this method has strong robustness to battery inconsistency and temperature uncertainty. When applying the proposed filter to extract aging features from battery data provided by CALCE and Oxford datasets, the correlation coefficient between the extracted aging features and SOH increases by 34.75% and 10.71%, respectively. Additionally, the RMSE of the SOH prediction results decreases by 60.57% and 59.46%, respectively.