## 1 Introduction  
Structural parameter identification is one of the most important aspects of the structural health monitoring and has received considerable attention. As a result, various analysis methods for structural parameter identification have been proposed and significant progress has been made over the past few decades. Damage detection techniques can be mainly classified as frequency-domain-based and time-domain-based methods. In particular, the time-domain analyses have been used extensively, such as the least-squares method [1; 2], Monte Carlo method [3; 4; 5], and filtering methods [6; 7; 8]. Besides, the methods of wavelet analysis [9; 10; 11] and Hilbert-Huang transform [12; 13; 14], in which the vibration signals are decomposed into the frequency/time-domain signals, have also received much attention.  
The well-known Kalman filter (KF) [15; 16] has also been applied to the system identification. Based on the KF, [PERSON] [17] has promoted and studied the extended Kalman filter (EKF), which extended the KF theory into the nonlinear field, with great achievements acquired. Afterwards, [PERSON] and [PERSON] [18] used the EKF for identification of the parameters involved in multi-degree-of-freedom (multi-DOF) nonlinear structural dynamic systems under various output noise conditions. [PERSON] [PERSON] [19] analyzed the single-DOF and multi-DOF dynamic systems based on EKF to detect the possible sources of the inaccuracy when the structures suffered the strength degradation. In recent years, several approaches to EKF-based system identification have been made for damage detection in the time domain which shows the good accuracy and arithmetic robustness. [PERSON] and [PERSON] [20] presented a new method working iteratively in the time domain using an EKF and it can also be used as a black box tool for model order reduction. [PERSON] [21] developed an effective methodology based on the EKF to predict the beam tip displacement under Gaussian noises. [PERSON] and [PERSON] [22] employed a constrained version of the dual EKF technique, and its robustness and efficacy was verified by numerical analysis of a six-story shear frame and a three-dimensional space truss. [PERSON] [23] proposed a new method based on an EKF with l1-norm regularization via free vibration responses, which shows good robustness and excellent accuracy of damage identification with the unknown initial structural state. [PERSON] [24] presented a novel real-time structural damage detection method by integrating an EKF and dynamic statistical process control, with which high detection accuracy was provided.  
Generally speaking, the EKF is particularly suitable for real-time damage identification. However, inappropriate integration methods and integration steps will have negative effect on identified results, especially when it is applied to practical structures. On the other hand, observations are usually contaminated with all kinds of noises affecting the convergence of the algorithm and accuracy of the target structural parameters as well, which also should be investigated in depth. In this paper, the EKF will be studied focusing on identification of both stiffness and damping of multi-DOF systems, which are the two most important parameters of structural dynamic systems. Numerical simulation is firstly carried out to choose the suitable integration method and integration step. After that, the identification accuracies under different levels of both Gaussian and non-Gaussian noises are analyzed and compared. To verify the capability of EKF to identify the structural parameters as well as the damages for real structures, experiments on a five-story steel frame structure are further conducted.