System identification usually assumes that the considered system is driven by known inputs and/or stationary random noises. This paper considers the case involving unknown inputs, which are arbitrary disturbances. A typical example is a mechanical structure naturally excited by wind, which changes direction from time to time. To address such disturbances, subspace methods for system identification will incorporate techniques of unknown input observers, which are state estimators with the ability to reject arbitrary unknown disturbances, provided a mathematical model of the system under consideration is available. Simulation results are reported to illustrate the proposed method for system identification while rejecting unknown disturbances.