Direction-of-arrival and frequency estimations for narrowband sources using two single rotation invariance algorithms with the marked subspace

In array signal processing, one is frequently interested in simultaneously estimating the directions of arrival and the centre frequencies of the uncorrelated narrowband radiating sources having different centre frequencies. By using single spatial rotation invariance and temporal rotation invariance algorithms, e.g. the original ESPRIT, the authors can individually estimate the spatial frequencies α_i and the temporal frequencies ω_i of the sources. If detecting radiating sources only in azimuths is of interest, the spatial frequency α_i is defined as α_i=ω_i sin (θ_i ), where θ_i is the location of the ith source relative to the broadside of the array, and they need decide which of the ω_i and α_i values belong to the same radiating source to obtain the pair {θ_i,ω_i} for each source. They propose a technique, the marked subspace technique, which is applied to the original ESPRIT to obtain the parameter pair {θ_i,ω_i}. By using both single spatial invariance and single temporal invariance algorithms along with the marked subspace, the parameter pair {θ_i,ω_i } of each radiating source can be more easily obtained than using the original ESPRIT without the marked subspace