2-D DOA estimation in the presence of Gaussian noise with quaternion

In this paper, quaternion was introduced in estimating azimuth and elevation of two dimensional direction of arrival (2-D DOA). We proposed a new quaternion signal model instead of classical complex signal model. Then, two definitions of multiplicative rules of quaternion were introduced. At last, we drew out azimuth and elevation using two definitions of quaternion and isomorphic complex expression of Hamilton´s quaternion. Some simulations illustrated this new idea