Application of Quatemion in Two Dimensional DOA Estimation

Based on quaternion, a new two dimensional parameters estimation method for two parallel uniform linear arrays is proposed in this paper. Unlike the complex algebra, quaternions are multi-dimension algebra numbers. Within the quaternion algebra framework, DOA estimation problem can be solved with high dimensional view. In the paper, the quaternion algebra is first introduced to the estimation problem of two parallel uniform linear arrays, and the quaternion received data model for the array is established. The presented algorithm employs the common character of different base of the quaternion received data, decouples the orthogonal relationship between the quaternion subspace and the steering vector of sources. The algorithm obtains an orthogonal expression between the quaternion subspace and a new steering vector that only involves the information of azimuth angles. Azimuth angles are further estimated by one-dimensional spectral searching. By exploiting estimated azimuth angles, elevation angles of impinging sources are obtained, successively. The simulation experiments are described to validate the benefit of the proposed method.