  A blind Direction-of-Arrivals (DOAs) estimate of narrowband signals for
Acoustic Vector-Sensor (AVS) arrays is proposed. Building upon the special
structure of the signal measured by an AVS, we show that the covariance matrix
of all the received signals from the array admits a natural low-rank 4-way
tensor representation. Thus, rather than estimating the DOAs directly from the
raw data, our estimate arises from the unique parametric Canonical Polyadic
Decomposition (CPD) of the observations' Second-Order Statistics (SOSs) tensor.
By exploiting results from fundamental statistics and the recently re-emerging
tensor theory, we derive a consistent blind CPD-based DOAs estimate without
prior assumptions on the array configuration. We show that this estimate is a
solution to an equivalent approximate joint diagonalization problem, and
propose an ad-hoc iterative solution. Additionally, we derive the Cram\'er-Rao
lower bound for Gaussian signals, and use it to derive the iterative Fisher
scoring algorithm for the computation of the Maximum Likelihood Estimate (MLE)
in this particular signal model. We then show that the MLE for the Gaussian
model can in fact be used to obtain improved DOAs estimates for non-Gaussian
signals as well (under mild conditions), which are optimal under the
Kullback-Leibler divergence covariance fitting criterion, harnessing additional
information encapsulated in the SOSs. Our analytical results are corroborated
by simulation experiments in various scenarios, which also demonstrate the
considerable improved accuracy w.r.t. a competing state-of-the-art blind
estimate for AVS arrays, reducing the resulting root mean squared error by up
to more than an order of magnitude.
