Quaternion ESPRIT for direction finding with a polarization sentive array

The problem of direction of arrival (DOA) estimation with a crossed-dipole array is addressed within the quaternionic framework, and a new ESPRIT variant, termed as quaternion-ESPRIT (Q-ESPRIT), is proposed. The proposed algorithm arranges the recorded signals into a quarternion model, and estimates the signal subspace of an array of translational invariance structure via quaternionic low-rank approximation. Then, Q-ESPRIT exploits the underlying rotational invariance between signal subspaces of different sub-arrays with quaternionic matrix operations to obtain the ultimate DOA estimates. Simulations show that Q-ESPRIT significantly outperforms its conventional counterpart in difficult situations with short data length, low signal-to-noise ratio, or unknown model errors.