High-speed sensing for object detection in
underwater bi-static acoustic paths
Angela Digulescu
*†
, Cindy Bernard
*
, Elena Lungu
†
, Ion Candel
*
and Cornel Ioana
*
*
University of Grenoble-Alpes, GIPSA-lab, Saint Martin D’Heres, France
Email: [angela.digulescu, cindy.bernard, ion.candel, cornel.ioana]@gipsa-lab.grenoble-inp.fr
†
Sigintec, 334 rue Tour de l’Eveque, 30000, Nimes, France
Email: elungu@sigintec.fr
Abstract—Detection of objects in underwater environment is
an important operation that can be aimed to assess the pollution
in the region under study as well as to prevent intrusion of
undesired objects in off shore power production facilities or in the
restricted entrance area. The use of acoustic methods has been
proven to be very powerful for the detection and localization
of the underwater objects. This paper proposes a new method
for the detection of an underwater object using bi-static acoustic
paths. The method uses the dynamic evolution the phase space of
the received signals, namely the phase space trajectory, without
any synchronization and it computes the point wise Euclidean
norm. The detection map obtained gives both the amplitude and
time of arrival information. The major advantage brought by this
approach (rather than conventional techniques) is that the signals
need no synchronization, their characterization being based only
on their wave form.
Keywords—phase space; recurrence matrix; detection curve;
time of arrival
I. I NTRODUCTION
Underwater object detection is an important task for the
marine community and it represents a heavy duty for the signal
processing field. Its purpose can relate to the monitoring of the
underwater fauna as least intrusive as possible, as well as to
supervise the pollution in the studied area.
While the detection part has been studied using vari-
ous methods like correlation techniques [1], time-frequency
methods [2], sonar imaging [3], etc., our approach is based
on high speed sensing in order to determine the time of
arrival (TOA) of the object relative to a reference response.
This implies that there is no synchronization between the
emission and reception. Moreover, our approach also proposes
to characterize the trajectory of the object.
Therefore, the application is based on a wide-band active
acoustic system, these types of signals being more robust
to on-site drawbacks like: ambient noise, electronic noise,
interference sources, etc. [2]. Then, the TOAs are determined
using the Recurrence Plot Analysis (RPA) method. The method
is applied for each response of a fixed length and the result
is stored in a detection map which contains the time bins
of the responses and the time distributed recurrences (TDR)
computed for each time bin. Next, the TOAs of each response
are determined relative to the first one and a comparison with
the classical signal envelope approach is done.
The paper is organized as follows: in section II, the RPA
method will be presented; section III will describe the exper-
imental setup and in section IV, the results are highlighted.
Then, in section V, the most important ideas and future work
aspects are presented.
II. RECURRENCE PLOT ANALYSIS METHOD
The Recurrence Plot Analysis (RPA) is derived from the
dynamical systems theory and it considers the evolution of a
measurement in its phase space [4], [5]. Therefore, we firstly
consider a received signal as the time series [6], [7] expressed
in (2):
x = {x[1],x[2], ..., x[N ]} (1)
where N is the length of the received signal.
Then, the time series is represented in a m dimensional
phase space. The vectors that describe the trajectory of the
dynamical system have as coordinates m values of the time
series which equally spaced:
v
i
=
m
k=1
x[i +(k - 1)d] · e
k
,i = 1,M (2)
where v
i
are the vectors from the phase space corresponding
to a state of the system, m is the embedding dimension, d is
the the delay (lag) between the samples of the received signal,
M = N - (m - 1)d and e
k
are the axis unit vectors.
Afterwards, the next step of the RPA method is to compute
the distance/ recurrence matrix. The distance matrix determines
the pointwise distance between the points of the phase space.
These points are given by the position vectors expressed in
(2):
D
i,j
= Δ(v
i
,v
j
) (3)
R
i,j
= Θ(ε - Δ(v
i
,v
j
)) (4)
where Δ(v
i
,v
j
) from (3) is a distance considered between
the points from the phase space (the Euclidean distance, the
L
1
norm, the angular distance [7], etc.). The operator Θ(·)
from (4) is the Heaviside step function and ε(·) is the chosen
threshold that discriminates if one distance is a states of
recurrence or not (usually is value is constant).
The most important parameters of the RPA method are the
delay, d and the embedding dimension, m. The choice of the
delay [8] is critical for the ”quality” of the trajectory in the
phase space. If the delay is chosen too small, then the trajectory
is over folded around the main diagonal of the phase space,
hereby the representation is redundant. But, if the delay is
978-0-933957-43-5 ©2015 MTS