A nonlinear system identification-based structural health assessment procedure is presented in this paper. The procedure uses the unscented Kalman filter (UKF) concept. The weighted global iteration with an objective function is incorporated with the UKF algorithm to obtain stable, convergent, and optimal solution. An iterative least squares technique is also integrated with the UKF algorithm. The procedure is capable of assessing health of any type of structures, represented by finite elements. It can identify the structure using limited noise-contaminated dynamic responses, measured at a small part of large structural systems and without using input excitation information. In order to demonstrate its effectiveness, the proposed procedure is compared with the extended Kalman filter (EKF)-based procedure. For numerical verification, a two-dimensional five-story two-bay steel frame is considered. Defect-free and two defective states with small and severe defects are considered. The study shows that the proposed UKF-based procedure can assess structural health more accurately and efficiently than the EKF-based procedures for nonlinear system identification.