Robust DOA estimation of harmonic signals using constrained filters on phase estimates

In array signal processing, distances between receivers, e.g., microphones, cause time delays depending on the direction of arrival (DOA) of a signal source. We can then estimate the DOA from the time-difference of arrival (TDOA) estimates. However, many conventional DOA estimators based on TDOA estimates are not optimal in colored noise. In this paper, we estimate the DOA of a harmonic signal source from multi-channel phase estimates, which relate to narrowband TDOA estimates. More specifically, we design filters to apply on phase estimates to obtain a DOA estimate with minimum variance. Using a linear array and harmonic constraints, we design optimal filters based on estimated noise statistics. Therefore, the proposed method is robust against different noise scenarios. In colored noise, simulation results confirm that the proposed method outperforms an optimal state-of-the-art weighted least-squares (WLS) DOA estimator.