Fatigue related damage growth without feasibility of optical assessment can be monitored conveniently by means of the direct current potential drop method in laboratory experiments. By estimating the unknown damage extent of a structure indirectly via observed measurements, the need to relate both quantities, i.e. a calibration of damage extent and measurements, arises. In recent years, Bayesian inference has been applied with a special focus to such inverse problem formulations. In the present paper, a novel approach to the calibration issue is proposed by employing Bayesian filtering and smoothing. A probabilistic state space model incorporating prior information about the damage extent and calibration parameters as well as process describing models is defined and subsequently used to infer the damage extent of fatigue-tested specimens from potential drop measurements. First, the obtained results in the form of joint conditional posterior distribution functions are exploited to facilitate an evaluation of a direct model calibration on the one hand and direct damage extent estimation on the other hand given persistent uncertainties. In a further step, the inferred damage extent estimations and associated uncertainties are propagated in time as to allow an assessment of decision-making-feasibility within the extended scope of structural health monitoring and damage prognosis. A thorough performance analysis in the light of actual damage extend data is undertaken, revealing accurate results.