Bearing estimation based on orthogonal projections technique with a horizontal linear array in shallow water

A new signal-subspace high-resolution bearing estimation method based on the orthogonal projections technique is proposed in this paper. Firstly, the received data are calculated step by step to form a set of basis vectors for the signal-subspace, utilizing an orthogonal projections algorithm that does not construct and eigen-decompose the covariance matrix. This procedure retains a linear complexity in computation and guarantees maximum signal energy in the spanned signal-subspace. Then the algorithm exploits the singular value decomposition of the matrix, comprised of the signal-subspace and the modal subspace that is obtained also from the received data, and the source bearings are estimated by detecting the intersection between the estimated signal-subspace and the modal subspace. The computational complexity of the proposed method is compared to that of the subspace intersection method, and its performance is compared to that of the conventional bearing estimation method, including conventional beamforming (CBF), and minimum variance distortionless response beamforming (MVDR). The performance of the proposed method under different condition such as sensor number, sensor inter-space, received signal-noise ratio (SNR), snapshot number is also investigated. Numerical simulation results in typical shallow water demonstrate the effectiveness of the proposed method.