Modeling of non-Gaussian array data using cumulants: DOA estimation of more sources with less sensors

Multichannel, non-Gaussian linear processes are modeled via direct and inverse cumulant-based methods using noisy, multivariate output data. The proposed methods are theoretically insensitive to additive Gaussian noise (perhaps colored, with unknown covariance matrix), and are guaranteed to uniquely identify the system matrix within a post-multiplication by a permutation matrix. Asymptotically optimal and computationally less intensive modeling criteria are also discussed. Further, it is proved that using higher-than-second-order cumulants, it is possible to estimate more angles-of-arrival (or harmonics) with fewer sensors. The problem of detecting the number of sources (or inputs) using output cumulants only is also addressed. Simulation results show that the proposed algorithms outperform the traditional correlation-based methods.