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Estimating flaw profiles from measurements is a typical inverse problem in electromagnetic nondestructive evaluation (NDE). This paper proposes a novel state-space approach for solving such inverse problems. The approach is robust in the presence of measurement noise. It formulates the inverse problem as a tracking problem with state and measurement equations. The state-space model resembles the classical discrete-time tracking problem. The model allows recursive Bayesian nonlinear filters based on sequential Monte Carlo methods to be applied in conjunction with numerical models that represent the measurement process (i.e., solution of the forward problem). We apply our approach to simulated eddy-current and magnetic flux leakage NDE measurements (with and without measurement noise) from known flaw shapes, and the results indicate the feasibility and robustness of the proposed method.