Subspace-based direction-of-arrival estimation using nonparametric statistics

The problem of subspace estimation using multivariate nonparametric statistics is addressed. We introduce new high-resolution direction-of-arrival (DOA) estimation methods that have almost optimal performance in nominal conditions and are robust in the face of heavy-tailed noise. The extensions of the techniques for the case of coherent sources are considered as well. The proposed techniques are based on spatial sign and rank concepts. We show that spatial sign and rank covariance matrices can be used to obtain convergent estimates of the signal and noise subspaces. In the proofs, the noise is assumed to be spherically symmetric. Moreover, we illustrate how the number of signals may be determined using the proposed covariance matrix estimates and a robust estimator of variance. The performance of the algorithms is studied using simulations in a variety of noise conditions including noise that is not spherically symmetric. The results show that the algorithms perform near optimally in the case of Gaussian noise and highly reliably if the noise is non-Gaussian.