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The electromagnetic localization and orientation method is based on 2-axis generation and 3-axis sensing of a quasi-static magnetic field. Two mutually orthogonal coils fed with phase-quadrature signals comprise the excitation source, which is equal to a rotating magnetic dipole. Using the amplitude and phase information of the sensing signals from the 3-axis sensing coils, the position of the sensor can be calculated directly by simple and explicit analytical expressions, then the orientations of the sensor can be determined by using rotation matrix. In this paper, a novel method is proposed to realize the direct calculation, which is easy and fast to determine the position and orientation of the 3-axis sensor in a single period of excitation. Experimental results demonstrate a promising performance of this method.