Instrumentation & Measurement Magazine 24-4 - 77

Direction of Arrival Estimation
Using Four Isotropic Receivers
Jonghoek Kim
W
e consider the micro positioning platform
which is equipped with only four receivers.
This paper considers estimating the Direction
Of Arrival (DOA) using four isotropic receivers. As a signal is
reflected or scattered, its amplitude attenuates significantly.
Thus, as we estimate the DOA, we use receivers with high signal
amplitude, since they have more probability to receive a
direct signal (not a reflected signal), compared to other receivers
with low signal amplitude. Every receiver uses both the
phase difference and the signal amplitude, in order to estimate
the DOA. The efficiency of the proposed DOA estimation is
verified by comparing it with the MUltiple SIgnal Classification
(MUSIC) algorithm using computer simulations.
Direction Of Arrival
In signal processing, Direction Of Arrival (DOA) denotes the
direction from which usually a propagating wave arrives at a
point, where usually a set of sensors are located. This set of sensors
forms a sensor array. The problem is to find the direction
relative to the array where the sound source is located.
With the further development of embedded systems, the
DOA estimation based on micro location platform (such as
unmanned underwater vehicle or unmanned ground vehicle)
has aroused great interest in recent years. Micro-platform
has more flexibility and higher safety. This paper considers
the micro positioning platform which is equipped with only
four receivers. We handle estimating the signal direction using
only four receivers (e.g., hydrophones in underwater
environments). Every receiver is isotropic and collects signals
uniformly in all directions. Each receiver is synchronized
to every other receiver and can measure the signal strength
with respect to sampling time. The readings of all receivers are
sampled and processed on a Digital Signal Processing (DSP)
computer for DOA estimation.
Considering a hydrophone array in underwater environments,
[1] presented a simulated analysis on the effect of array
geometry in the beamforming response (beam-pattern). The
authors considered two geometries, the linear and the circular
geometry. The beamforming response analysis was performed
June 2021
with computer simulations. In this paper, we consider four
isotropic receivers forming the circular geometry. The beamforming
response with four isotropic receivers can be derived
using [1], thus is not handled in this paper.
There are many papers on estimation of the DOA based on
the signal measurements at multiple receivers. In [2], the received
signal powers are measured while the antenna switches
over a set of measured directive beam patterns. The pattern
that exhibits the maximum received signal power is chosen.
Then, the ratio between the pattern adjacent to the chosen pattern
and the chosen pattern is used to find the DOA by using
a lookup table or by performing a linear regression approximation.
However, the authors of [2] require a switched beam
antenna as its hardware platform.
Many DOA methods (e.g., Minimum Variance Distortionless
Response (MVDR) beamformer [3], [4], Estimation
of Signal parameters via rotational invariance technique (ESPIRIT)
[5], [6], and MUltiple SIgnal Classification (MUSIC)
[7]-[9]) use the phase differences at every receiver in order to
estimate the signal direction.
In MVDR beamformer [3], [4], the DOA is estimated using
a peak in the spatial power spectrum, by steering the
beams electronically and estimating the power spectrum of
the received signal. ESPIRIT [5], [6] exploits an underlying
rotational invariance among signal subspaces induced by
an array of sensors with a translational invariance structure.
MUSIC [7]-[9] estimates the frequency content of a signal
or autocorrelation matrix using an eigenspace method. The
performance of these algorithms is achieved at a cost in computation
(searching over parameter space) and storage (of
array calibration data).
As far as we know, every DOA estimation method is based
on the traditional direct-path-only assumption, where multipath
effect is ignored. As a signal is reflected or scattered,
its amplitude attenuates significantly. Hence, to estimate the
DOA, this paper uses receivers with high signal amplitude,
since they have more probability to receive a direct signal (not
a reflected signal) compared to other receivers with low signal
amplitude. Each receiver uses both the phase difference and
IEEE Instrumentation & Measurement Magazine
1094-6969/21/$25.00©2021IEEE
77

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