Bayesian filtering based approaches for diagnosis of structural damage have been widely employed in structural health monitoring (SHM) research. The approach however may lead to an inaccurate alarm/decision due to the presence of faulty sensor/s. Nevertheless, sensor faults are inevitable during real field SHM in which sensor may malfunction or get detached from the structural surface, registering completely irrelevant information as measurement. Eventually, such erroneous information induce error in the estimation which leads to an inaccurate, sometimes divergent and impractical solution. The current study deals with Bayesian filtering based structural damage detection in the presence of one or multiple (consecutive) sensor faults. The damage detection is addressed with joint state-parameter estimation approach while a switching filtering strategy is employed for sensor fault detection. Switching approach employs multiple possible sensor fault models which are subsequently integrated to the measurement model of the joint estimation approach. The selection of the competent model (/switching between model ensembles) is undertaken recursively based on their likelihood against measured response. The proposed approach is tested on a numerical lumped mass model of a shear frame building, followed by a laboratory experiment on a cantilever beam. It has been perceived that estimation of health for structures measured with faulty sensors can actually lead to a false (positive and negative) alarm which can, however, be avoided by the employment of the proposed approach. The performance of the proposed approach is further established for healthy and damaged system with pre-existing and sudden sensor faults.