IEEE Robotics & Automation Magazine - September 2013 - 43

the problem, and the remote sensing was incorporated as a
Dirichlet boundary condition. The approach resulted in reliable estimations of the volumetric variability of the underwater thermal field in a small coastal area off the coast of Latvia
(Baltic Sea), where an AUV recorded temperature data while
performing a mission to search for sea mines. This field
experiment, conducted by the North Atlantic Treaty Organization (NATO) Undersea Research Centre (NURC) in April
2009, provided a valuable data set to test and compare different procedures to integrate data from remote sensing and
underwater robots into a unified environmental picture.
Unfortunately, the small size of the area of operations and the
use of a single robotic platform limited the scientific exploitation of this field experiment. A more comprehensive field
experiment was carried out by the same institution a year
later in the western Mediterranean to further investigate the
capability of a fleet of gliders to characterize a spatially
extended restricted area when supported by remote sensing
data. Based on this field experiment, this article compares the
environmental assessments obtained from 1) the spline models and 2) a traditional modeling approach in their ability to
represent the temperature field.

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La
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Corsica
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The Rapid Environmental Picture
2010 Field Experiment
A field experiment named Rapid Environmental Picture 2010
(REP10) was conducted by the NURC with the NATO
Research Vessel Alliance during August 2010 in an ocean
region off of La Spezia, Italy, in the Ligurian Sea. A nearly
rectangular and access-restricted area was defined with
dimensions of approximately 60 km × 80 km, as illustrated in

changes, their hydrodynamic shape, and small wings to carry
out undulatory motions between the surface and a predetermined depth with a net horizontal displacement. This propulsion procedure requires very low energy consumption and
provides gliders with up to several months of autonomy at
sea. This capability has raised a growing interest in glider
technology of naval forces. For example, the U.S. Navy
recently awarded a contract to the glider manufacturer Webb
Research Corporation-Teledyne Brown Engineering Inc. to
provide a fleet of up to 150 glider vehicles. The fleet would be
operated for persistent surveillance and monitoring from the
T-AGS60 Pathfinder survey ships [5].
The advent of glider technology to assess environmental
conditions creates new scientific and technological demands,
e.g., the proper exploitation of the information content of the
data collected by this kind of platform. The oceanographic
data is often exploited by representing the sampled field on a
regular grid to facilitate the extraction of dynamic information
from the data. The two most common interpolation methods
found in oceanographic and meteorological literature are the
best linear prediction scheme [(BLP), "kriging," or "objective
analysis"] [6], [7] and spline interpolation [8]. The former
scheme is commonly used in different scientific disciplines to
assign, from the data gathered at arbitrary locations, the best
values at grid points of a regular grid [6]. This approach relies
on a priori knowledge of the mean and covariance of the sampled field to provide the best linear estimation of the average
and variance of the field at given unsampled locations. Unfortunately, knowledge of a covariance model is problematic in
regions such as coastal areas, where historical data may be
sparse or even nonexistent [9], [10]. Moreover, gliders generate
spatially dense measurements, which may cause this approach
to be computationally unfeasible.
Spline models are found in meteorological literature as an
alternative to the estimation scheme discussed above [8].
From a stochastic point of view, the spline model technique
provides the maximum-likelihood estimate from the data and
a priori information that the first (membrane model) or second derivatives (plate model) are zero everywhere and the
result of random errors, i.e., white noise. In other words, it
provides the most probable continuous (membrane model)
or differentiable (plate model) field compatible with observations. BLP and spline interpolation methods are reviewed and
compared in [11]. It is also concluded in [11] that spline
methods are preferred over BLP schemes when the underlying statistics of the spatiotemporal variability of the area are
poorly known, which is the case of the marine region considered in this article. In addition to the above schemes, a review
of other data interpolation methods less common in oceanography can be found in [12].
Spline models have recently been proposed to reconstruct
underwater thermal fields from sparse spatially biased data
gathered by an autonomous underwater vehicle (AUV) and
remote sensing [12]. Specifically, the variational formulation
underlying the spline procedure was solved using a finite element technique to substantially reduce the dimensionality of

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50
200

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Figure 1. Geographical location of the REP10 field experiment.
This experiment aimed to characterize a prescribed accessrestricted area (gray polygon) by using observations from three
Slocum gliders (thick black lines) and remote sensing SST
(colored field in °C, here for 21 August 2010). A second data set
was collected by a towed ScanFish for validation proposes (red
lines). The brown dashed arrow represents the main stream of
the NC in the region. Finally, contours of the 50-, 200-, 500-,
1,000-, and 2,000-m isobaths are illustrated by the white lines.
The inset shows the position of the experimental area in the
Western Mediterranean basin.

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