Bayesian filters are classic engineering tools for estimating the states and the parameters of a dynamic system, often applied in the context of structural health monitoring (SHM) to detect and quantify structural damage. The unmeasured inputs, the modelling errors and the sensor noise give birth to the process and measurement noise that perturb the state and output equations, which affects the state estimation and the subsequent damage quantification. In applications, the noise covariance are generally unknown and their values are oftentimes tuned to optimize user-defined criteria that characterize filtering performance. This can be cumbersome and may not always yield the optimal covariance matrices. Optimization and inversion-based methods have also been developed to estimate these covariances, but such methods are computationally inefficient. The present paper utilizes an existing subspace-based identification method to estimate process and measurement covariances, which are then used in a Bayesian inference-based SHM strategy to estimate states and damage in elements of a structural system. A comparative study is made to determine the effect of using the estimated covariances on the damage detection efficiency and accuracy of the SHM strategy.