An existing joint input-state estimation algorithm is extended for applications in structural dynamics. The estimation of the input and the system states is performed in a minimum-variance unbiased way, based on a limited number of response measurements and a system model. An additional method is proposed to identify the noise statistics, which are needed for the joint input-state estimation procedure and which can be used to quantify the uncertainty on the estimated forces and system states. The proposed methodology is illustrated using data from an in situ experiment on a footbridge.