d-MUSIC, a real time algorithm for estimating the DOA of coherent sources using a single array snapshot

d-MUSIC estimates the DOA of two closely spaced sources using a single array snapshot. To overcome the coherent signal problem d-MUSIC utilizes additional information, specifically the derivative of an array snapshot. The combined vector set produces a full rank signal space projector. The algorithm nearly attains the Cramer-Rao bound for typical air traffic control problems. As it does not require a subspace decomposition (e.g., eigenstructure) and all operations are highly vectorized it can be readily implemented in real-time. The algorithm is tested using vertical linear array data with a low flying helicopter. With a spacing of 16% to 35% of a beamwidth between the direct and surface reflected rays, the d-MUSIC RMS error is 9.6% of a beamwidth for the 4 data collections while MUSIC resolved the two rays for 2 of the 4 cases with a RMS error of 18.1%.