In a suspension bridge, the damping ratio as an index suppressing bridge vibration could be considered as one of the important dynamic characteristics. But, in general, estimation of damping ratios can be a laborious task when the existing bridges are under ambient vibration conditions. In this paper, the damping ratios on Sorok Bridge, a suspension bridge in Korea, were estimated by using two damping estimation methods that can be properly applied under ambient vibration conditions. The first is method using Hilbert-Huang Transform and the other is method using the extended Kalman filter(EKF), a nonlinear system identification techniques. When ambient vibration signals are measured from a bridge, it is not simple to separate extract viscous, Coulomb friction damping and aerodynamic damping properties from apparent damping ratios directly using the measured signals But, if the viscous and Coulomb friction damping properties are classified as structural damping, the apparent damping ratios can be separated into structural and aerodynamic damping properties. Here, the aerodynamic damping properties can be linearly affected by wind speed level (J. Macdonald, 2005). Hence, it could be expected that wind velocity is one of the critical factors in estimating damping ratios. The ambient vibration signals have been measured from Sorok Bridge, as a target bridge in this study, which is under wind-induced vibration condition without traffic during measurement term. Thus, some correlation of wind speed, aerodynamic damping and structural damping could be investigated. If the aerodynamic damping could be neglected under very low wind speed conditions, the apparent damping ratios can be assumed as structural damping and varied with vibration levels. On the other hand, under medium or high wind speed conditions, the apparent damping ratios can be separated into both aerodynamic and structural damping properties by using the relationship of wind speed, aerodynamic damping and structural damping varying with vibration levels. Thus, it could be possible that pure structural damping ratio could be estimated using ambient vibration signals and various wind speeds. But, it was still hard to distinguish structural damping and aerodynamic damping from appearance damping only using appearance damping and wind components.