This paper investigates robust state estimation for systems with non-Gaussian noise within the statistical similarity measure framework. To address the limitation of existing approaches, which often overlook the differences in noise vector elements and their impact on estimation accuracy, we first introduce the concept of hierarchical mixture statistical similarity measure (HMSSM), which effectively enhances the adaptive capability of local metrics to capture higher-order statistical properties. Building upon this, the optimal posterior estimate is approximated by maximizing Jensen""s lower bound of HMSSM. To further enhance the adaptability of noise covariance, we introduce matrix similarity into the framework. Within the HMSSM framework, the system state together with the inaccurately predicted covariance and measurement covariance matrices are jointly estimated by optimizing the lower bound of the defined combination of cost functions through alternating fixed-point iterations. Simulation experiments for target tracking show that our proposed algorithm delivers superior estimation accuracy and robustness compared to similar algorithms.