Subspace-based coherent source localisation with forward/backward covariance matrices

Coherent signals arriving at a uniform linear array can be localised using the sum of the spatially smoothed forward covariance matrix and the backward one. A basis for the signal subspace can be estimated directly from its columns without computationally expensive eigendecomposition. However, the terms of noise power present at the sum matrix result in an inaccurate estimate of the basis, even if an infinite number of samples are available. In the paper, the author proposes a new subspace method which exploits the difference between the forward and the backward covariance matrices as well as their sum. The introduction of the difference matrix can allow better estimation of a basis for the signal subspace because it has no noise power terms. As a result, the estimation performance of arrival angles may be improved. Simulation results are included to demonstrate the usefulness of the approach