Non-uniform Sampling Issues Arrising in Shallow Angle
Wave Profiling Lidar
M.R.Belmont
Status: Accepted
North park Avenue, Exeter University
Exeter , Devon United Kingdom
EX4 4QF
Phone: (0)1392 263622
Email: M.R.Belmont@exeter.ac.uk
Co-Authors:
Non-umiform Sampling Issues Arrising in Shallow Angle Wave Profiling Lidar
M.R.Belmont, J.M.K.Horwood and R.W.F.Thurley
School of Engineering and Computer Science,
University of Exeter.
November 2002
Abstract
The stochastic view of sea-waves developed by Pierson and Neumann, Ref[1,2,3],
has provided the only viable framework for sea state forecasting in the
range hours to days which reflect the operational planning needs of marine
activities. In contrast real time dynamical vessel operations require
deterministic sea profile information. The potential advantages offered
by technologies able to provide predictive wave input in such real time
operations have aroused recent interest in so called deterministic sea-wave
prediction (DSWP), Ref[4 - 11], and consequent vessel motion prediction,
Ref[6]. Given the relationship between the maximum possible prediction
horizon, Ref[5,7,8], and the time factors involved in measurement, data
quality assessment and prediction model building DSWP is effectively restricted
to situations where linear algorithms, Ref[5,8], can be justified.
For fixed site applications typically found in the offshore oil and gas
industry the wave measurements required to build prediction models can
be obtained from developments of existing floating directional wave sensors,
Ref[12]. However for moving vessels involved in activities such as aircraft
recovery remote sensing ship-based sensors are needed. As will be shown
in the full article practical restrictions mean that the radars commonly
used for sea state estimation, i.e., surface roughness statistics and
wave direction measurements, cannot make the required profile measurements
and some form of grazing incidence LIDAR is needed.
In addition to the marine operations the profiling LIDAR can also be used
as a research and monitoring tool in oceanography and in shore environmental
studies. One interesting possibility is its use in measuring the spatial
and temporal behavior of breaking wave systems that are attracting special
attention in coastal erosion investigations.
The grazing incidence requirement stems from a combination of the sensing
range needed, typically 0.5km to 1.0km, and the likely available mast
elevations. The geometry of the resulting metrology problem constitutes
one of the few examples in large scale engineering where spatial non-uniform
sampling becomes critically important. Even if the LIDAR is scanned in
uniform angular increments the sea surface shape means that the interception
sites of the sensing radiation are highly non-uniformly distributed along
the space axis and typical DSWP algorithms, Ref[5,8], require uniformly
sampled data. Given that the optimum DSWP mode of operation requires a
snapshot of the sea surface acquired in the shortest possible time, consistent
with signal to noise ratio considerations, it is vital to require no more
samples than the minimum demanded by the Nyquist criterion. Thus it is
not possible to substantially oversample and use simple interpolation.
The general problem of mapping from a set of non-uniform to uniform samples
is equivalent to transforming from a non-orthogonal to an orthogonal basis.
Given the number of samples involved methods such as direct inversion
or the Gram-Schmidt process are far to computationally demanding for the
time available in DSWP work. Thus specialist techniques are required.
The proposed article examines the aspects of nonuniform sampling relevant
to the DSWP wave profiling application, Ref[13 - 21]. As the distribution
of non-uniform sample locations varies from one set of measurements to
another it is vital to have methods for estimating the computational cost
associated with building a prediction model from any given data. Such
estimating techniques are examined and appropriate algorithms developed.
References in full text
Submitted on November 07, 2002
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