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In this paper, the identification of soft magnetic B - H characteristics when using the single measured hysteresis loop and fitting the discrete dynamic Preisach (DDP) model is addressed. The magnetic measurements with primary and secondary windings are performed to obtain the magnetostatic system response. The constrained least-squares estimation of the Preisach density function yields the global solution even for limited hysteresis data. The uncertainties detected during the measurement and computation of B and H values are discussed.