Array Element Localisation

Abstract

Abstract—This article have been written in cooperation with
The Swedish Defense Research Agency (FOI). The article proposes a method to calibrate hydrophone positions for improved
underwater survailence in The Baltic Sea. The idea with the
method is to use the sound of a powerboat and a novel beamforming algorithm for array element localisation (AEL). There are
strategic military advatages to this method since it is a cost-saving
method and do not risk to reveal the array positions to other
intelligence agencies. The essence of the algorithm is optimisation
over the array output of a delay-and-sum beamformer.
Keywords—Beamform, FOI, AEL.
I. U NDERWATER SURVAILANCE IN THE BALTIC SEA
Ever since World War I the submarine have been an
essential piece of naval warfare. With the introduction, the need
for underwater surveillance increased dramatically and still
occupy the minds of intelligence agencies around the world.
The developed surveillance techniques can also be used in nonmilitary applications such as deep-sea pollution monitoring,
assessing impacts of offshore infrastructure on local ecosystems and oil leakage control. One primary tool for underwater
surveillance is the study of sound propagation under water. The
acoustic signals are measured by microphones underwater, so
called hydrophones, and the received signal is then treated
mathematically to, for example detect passing submarines.
In order to accomplish this, several hydrophones are usually
placed out together and synchronised into what is called arrays.
Some arrays used by FOI to intercept signals, in the Baltic Sea,
from different ships, are passive arrays on the sea floor, which,
for estimation purposes, are about a hundred meters long and
consist of more than fifty hydrophones.
A. Sinking the array
The hydrophones are all attached to a flexible cord which
is connected to a computer, that processes the signal received.
When placing the array on the sea floor, it needs to be sunk
from a boat. A typical desired array structure, or geometry, on
the sea floor is a perfect linear structure. The linear structure
simplifies the processing of intercepted signals in the application of submarine detection. Therefore it is important that
the array is sunk properly. The computer, or signal transmitter,
along with an anchor is sunk from the boat and at the same
time the array needs to be stretched. Due to the arrays size,
waves and currents, this is problematic and the geometry of
the array will shift. Also the topography of the sea floor
is problematic since it is likely not to be flat. Rocks and
inclination will cause the array to be placed in a sub-optimal
position. This sub-optimal position will introduce bias in the
array applications and therefore it is needed to calibrate the
array by estimating the exact hydrophone positions within the
array.
Fig. 1. Picture of array cord in laboratory with hydrophones and signal
transmitter attached to its end. Source Chen et al. 2013
B. Classified array positions
There are several methods to calibrate the array on the sea
floor. One method would be to ping the array from several
locations nearby, using a boat. The pings appear as spikes
in the data transmitted from the array, making them easy to
process for array calibration. However this method is very
costly because of the need of expensive equipment and also
it’s a time consuming task. Another, perhaps more important,
aspect of this method is that it might reveal the position of the
array. The position of the array is often classified information
due to the strategic military advantage it provides. If FOI
would be seen by other Intelligence Agencies conducting ping
experiments, it is not difficult for them to conclude that they
are calibrating arrays.
C. Calibrating the array with a powerboat
A potentially advantageous method to calibrate an array,
would be to, instead of using pings, drive a powerboat nearby
for a short period of time. This is a cheap method and it can
be done without any risk of revealing the array position. One
such method would be a so called Beamforming calibration
method. In the case of a powerboat, the data transmitted from
the array are no longer nice peaks that are easily identified
to compute time differences, instead the signal is messy. The
beamforming method builds upon estimating the covariance
of the signal intercepted at each hydrophone to understand the
time difference for the signal to reach each hydrophone. When
this is done, each hydrophone is delayed by its individual
time difference, to some reference point, so that the exact
same signal is intercepted at each hydrophone at the same
time. By then summing over each output signal, the energy
of the output will be maximized. To implement this, firstly
some basic spectral analysis knowledge is needed. Secondly
it requires a lot of data. Since one array usually consists of
more than 50 hydrophones, this is a high dimensional nonlinear equation system.
D. Implementation tools and performance
Several gigabytes of data is needed to positions over
50 hydrophones. To process this large amount of data, and
implement the beamforming calibration method, a powerful
computer program such as MatLab can be used. Working
with large data sets and complex algorithms, it is in general
a good idea to break down the problem into smaller parts.
This can be done by building a step-by-step simulation of the
real world problem in MatLab and understand the parameters
of the model. The beamforming calibration method works
with high precision in a simulated environment, however the
underwater world is very complex and it is hard to encapsulate,
for instance, reflections of the propagating sound on the surface
that disturb the method.
Fig. 2. A simulation of beamforming calibration method in MatLab. The
algorithm locates the hydrophone positions very well and suggests that a
powerboat might work in practice to calibrate arrays.
E. Powerboat results on real data
As mentioned earlier, the underwater environment is complex with reflections of the propagating sound and the topography. However the beamform calibration seem to work well

• author: Sundberg, Axel and Bristedt, Olle
• supervisor: Andreas Jakobsson
• organization: Mathematical Statistics
• alternative title: Locating array elements in underwater environment using the sound from a powerboat
• course: FMS820 20171
• year: 2017
• type: H2 - Master's Degree (Two Years)
• subject: Mathematics and Statistics
• language: English
• id: 8917827
• date added to LUP: 2017-06-21 10:02:12
• date last changed: 2017-06-21 10:02:12