The unscented Kalman filter (UKF) is a promising method for system state and structural parameters estimation. However, its performance depends on the process noise and measurement noise covariance matrices, which are usually unknown in practice. Arbitrary selection of these covariance matrices may lead to unreliable or even diverging estimation results. To resolve this critical problem, we propose a Bayesian probabilistic algorithm for the estimation of the noise covariance matrices based on the response measurement. The proposed Noise-Parameters-Identified Unscented Kalman Filter (NPI-UKF) has the following salient features: (1) the divergence problem is resolved; (2) reliable estimation results including uncertainty quantification can be obtained; and (3) NPI-UKF is applicable to nonstationary situations. These salient features are illustrated through the numerical applications to a bridge structure and a laboratory experiment to a shear building model. The efficacy and robustness of NPI-UKF will be validated.