  This paper introduces the maximal eigengap estimator for finding the
direction of arrival of a wideband acoustic signal using a single
vector-sensor. We show that in this setting narrowband cross-spectral density
matrices can be combined in an optimal weighting that approximately maximizes
signal-to-noise ratio across a wide frequency band. The signal subspace
resulting from this optimal combination of narrowband power matrices defines
the maximal eigengap estimator. We discuss the advantages of the maximal
eigengap estimator over competing methods, and demonstrate its utility in a
real-data application using signals collected in 2019 from an acoustic
vector-sensor deployed in the Monterey Bay.
