The ESVC(Ellipse-based Segmental Varying Curvature) foot, a robot foot design inspired by the rollover shape of the human foot, significantly enhances the energy efficiency of the robot walking gait. However, due to the tilt of the supporting leg, the error of the contact model are amplified, making robot state estimation more challenging. Therefore, this paper focuses on the noise analysis and state estimation for robot walking with the ESVC foot. First, through physical robot experiments, we investigate the effect of the ESVC foot on robot measurement noise and process noise. and a noise-time regression model using sliding window strategy is developed. Then, a hierarchical adaptive state estimator for biped robots with the ESVC foot is proposed. The state estimator consists of two stages: pre-estimation and post-estimation. In the pre-estimation stage, a data fusion-based estimation is employed to process the sensory data. During post-estimation, the acceleration of center of mass is first estimated, and then the noise covariance matrices are adjusted based on the regression model. Following that, an EKF(Extended Kalman Filter) based approach is applied to estimate the centroid state during robot walking. Physical experiments demonstrate that the proposed adaptive state estimator for biped robot walking with the ESVC foot not only provides higher precision than both EKF and Adaptive EKF, but also converges faster under varying noise conditions.