•There have been very few researches on unscented Kalman filter with unknown input.•A novel UKF-UI is proposed for recursive state-input-system identification of nonlinear systems.•The proposed UKF is derived analogously to the procedures of the conventional UKF.•Data fusion of partially measured accelerations and displacements is used to prevent the drifts in identification.•Such a presented analytical solution of UKF-UI is not available in previous literatures. The unscented Kalman filter (UKF) has proven to be an effective approach for the identification of nonlinear systems from limited output measurements. However, the conventional UKF requires that measurements of the input excitations are available to successfully perform nonlinear system identification, which limits its application in cases where it is difficult or impractical to measure the inputs. In this paper a novel unscented Kalman filter with unknown input (UKF-UI) is proposed for the simultaneous identification of nonlinear structural systems and external excitations. Based on the estimation-based procedures of the conventional UKF, the analytical recursive solutions of the proposed UKF-UI are derived in an analogous fashion resulting in a recursive nonlinear least-squares problem for the unknown input. Moreover, data fusion of partially measured acceleration and displacement responses is used to alleviate the drifts typically observed in the estimated inputs and displacements. Numerical and experimental validation examples are used to demonstrate the effectiveness of the proposed UKF-UI algorithm for the simultaneous identification of nonlinear parameters and unknown external excitations using data fusion of partially measured system responses.