Full Covariance Fitting DoA Estimation Using Partial Relaxation Framework

The so-called Partial Relaxation approach has recently been proposed to solve the Direction-of-Arrival estimation problem. In this paper, we extend the previous work by applying Covariance Fitting with a data model that includes the noise covariance. Instead of applying a single source approximation to multi-source estimation criteria, which is the case for MUSIC, the conventional beamformer, or the Capon beamformer, the Partial Relaxation approach accounts for the existence of multiple sources using a non-parametric modification of the signal model. In the Partial Relaxation framework, the structure of the desired direction is kept, whereas the sensor array manifold corresponding to the remaining signals is relaxed [1], [2]. This procedure allows to compute a closed-form solution for the relaxed signal part and to come up with a simple spectral search with a significantly reduced computational complexity. Unlike in the existing Partial Relaxed Covariance Fitting approach, in this paper we utilize more prior-knowledge on the structure of the covariance matrix by also considering the noise covariance. Simulation results show that, the proposed method outperforms the existing Partial Relaxed Covariance Fitting method, especially in difficult conditions with small sample size and low Signal-to-Noise Ratio. Its threshold performance is close to that of Deterministic Maximum Likelihood, but at significantly lower cost.