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Spatial Compressive Sensing Approach For Field
Directionality Estimation.
I. INTRODUCTION
Variety of techniques for field directionality estimation were
studied in literature [1]-[5]. Thus, a theoretical analysis of
the relationship between the hydrophone array output and the
noise field was conducted in [1]-[5]. The developed techniques
were based on the array beamformer output or the crossspectral
matrix between outputs of array elements [4]-[5]. The
problem of a field directionality estimation in ocean, using
horizontal line towed array was also addressed in literature [5]-
[8]. Recently, problems of direction of arrival and field directionality
estimation for moving sensors arrays have attracted
renewed interest [9]-[12]. It was shown that an array motion
can improve an array performance assuming temporal coherence
of successive samples [10]-[11]. In [12], the wavefield
sampling method that exploits the linear relationship between
the noise field and the collection of beamformer outputs over
various array orientations was proposed. It was shown that
the wavefield sampling (WS) method outperforms other tested
methods. This algorithm was implemented via the recursive
estimation method and its convergence to the unique solution
was promised for a specific set of array orientations and
beamformer look directions. However, a method for a proper
array orientation and beamformer look direction sequence
selection remains an open question.
The quality of the field directionality estimation is determined
by the angular resolution. The higher angular resolution
is, the more accurate estimation of the far field sources,
and better detection performance can be achieved. One of
fundamental relations in the array signal processing is that
the angular resolution is directly proportional to the number
of the array elements [13]. This relation motivates the desire
for longer arrays that can achieve higher resolution. Unfortunately,
the requirement contradicts the implementation and
installation limitations that motivate shorter arrays. Moreover,
implementation of longer arrays for maneuvering platforms
such as unmanned underwater vehicles (UUV) can even be
impossible [14]. These contradictions motivate the quest for
alternative array signal processing methods.
Usually, the field directionality is modeled as a finite set
of strong far-field narrow-band sources and an isotropic lowpower
noise [1]. In this work, the model of the field directionality
is adopted in the following way. First, the bearing angle
space is uniformly sampled into a large number of discrete
angles. Next, it is assumed that ether the high energy that
corresponds to the far-field strong sources or the low-energy
that corresponds to the isotropic noise is received at the sensor
array from every of these discrete azimuth angles.