Periodic health assessment of large civil engineering structures is an effective way to ensure safe performance all through their service lives. Dynamic response-based structural health assessment can only be performed under normal/ambient operating conditions. Existing Kalman filter-based parameter identification algorithms that consider parameters as the only states require the measurements to be sufficiently clean in order to achieve precise estimation. On the other hand, appending parameters in an extended state vector in order to jointly estimate states and parameters is reported to have convergence issues. In this article, a constrained version of the dual extended Kalman filtering (cDEKF) technique is employed in which two concurrent extended Kalman filters simultaneously filter the measurement response (as states) and estimate the elements of state transition matrix (as parameters). Constraints are placed on stiffness and damping parameters during the estimation of the gain matrix to ensure they remain within realistic bounds. The proposed method is compared against the existing Kalman filter-based parameter identification techniques on a three-degrees-of-freedom mass-spring-damper system adopting both unconstrained and constrained estimation approaches. cDEKF is then employed on a numerical six-story shear frame and a 3D space truss to validate its robustness and efficacy in identifying structural damage. The results suggest that cDEKF algorithm is an efficient online damage identification scheme that makes use of ambient vibration response.