Accurate information about the vehicle state such as sideslip angle is critical for both advanced assisted driving systems and driverless driving. These vehicle states are used for active safety control and motion planning of the vehicle. Since these state parameters cannot be directly measured by onboard sensors, this paper proposes an adaptive estimation scheme in case of unknown measurement noise. Firstly, an estimation method based on the bicycle model is established using a square-root cubature Kalman filter (SQCKF), and secondly, the expectation maximization (EM) approach is used to dynamically update the statistic parameters of measurement noise and integrate it into SQCKF to form a new expectation maximization square-root cubature Kalman filter (EMSQCKF) algorithm. Simulations and experiments show that EMSQCKF has higher estimation accuracy under different driving conditions compared to the unscented Kalman filter.