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Vector Sensor Cross-Product for Direction of Arrival Estimation

A vector sensor is composed of three electric dipoles and three magnetic loops, measuring the full six components of electric field and magnetic field at one point in the space. This paper introduces an easy way on understanding how the vector sensor receives signals, and using the basic cross-product method with considering of the antenna pattern compensation, it can give out the more exact direction of arrival of the electromagnetic wave propagated with arbitrary polarization. In the direction of arrival estimation application, usually the signal transmitted from the ground. For Low-Grazing-Angle, without considering the antenna pattern compensation, the cross-product of a reduced vector sensor can give the azimuth of the signal arrived. In this paper, we give out the mathematical transformation matrix directly by using the spherical to rectangular coordinate transfer and the relationship between electric field and magnetic field. It is easy to understand and easy to check the sign of the response of the vector sensor. In the model we consider the antenna pattern of vector sensor's each element. Our mathematical model of the vector sensor is more close to the real response. Vector sensor cross-product can handle all kinds of polarizations of the arrival. Our simulation is circular polarization. We give out the estimation error without antenna pattern compensation and with antenna pattern compensation at different signal to noise ratio.