In structural health monitoring, Bayesian updating is widely utilised in the analysis of noisy sequential data of dynamic systems with the objective of determining the state of damage of a structure or identifying its unknown dynamic characteristics or both. In the present work, this approach is enhanced to encompass the simultaneous handling of insufficient knowledge of sensor features – i.e. a non-applicable relation between state of damage and observations due to high uncertainty introduced by unknown measuring parameters – while given the nature of damage propagation as in fatigue-driven applications. Thereby, the statistical inversion problem of inferring unknown states of damage as well as unknown measuring and dynamic model parameters is addressed solely on the basis of observations and parameter-dependent functional expressions linking these quantities. As Bayesian updating provides the posterior belief on the unknown quantities in form of probability density functions, the question of state observability and parameter identifiability can be approached simultaneously. The methodology is applied to potential-drop measuring in a fatigue-loading scenario and its effectiveness is successfully demonstrated. © 2019 Elsevier Ltd