Space time MUSIC: consistent signal subspace estimation for wide-band sensor arrays

Wide-band Direction of Arrival (DOA) estimation with sensor arrays is an essential task in sonar, radar, acoustics, biomedical and multimedia applications. Many state of the art wide-band DOA estimators coherently process frequency binned array outputs by approximate Maximum Likelihood (ML), Weighted Subspace Fitting or focusing techniques. This paper shows that bin signals obtained by filter-bank approaches do not obey the finite rank narrow-band array model, because spectral leakage and changes of the array response with frequency within the bin create \emph{ghost sources} dependent on the particular realization of the source process. Therefore, existing DOA estimators based on binning are not consistent even when the array response is perfectly known. In this work, under a more realistic array model, which still has finite rank under a space-time formulation, signal subspaces at arbitrary frequencies can be consistently recovered under mild conditions by applying Space Time, MUSIC-type (ST-MUSIC) estimators to the dominant eigenvectors of the wide-band, space-time sensor cross-correlation matrix. A novel, consistent ML based ST-MUSIC subspace estimate is developed to estimate the number of sources active at each frequency by Information Theoretic Criteria. Empirical ST-MUSIC subspaces are fed to any subspace fitting DOA estimator at single or multiple frequencies. Simulations confirm that this approach allows better performance over binning approaches at sufficiently high signal to noise ratio, when model mismatches exceed the noise floor.