1High -frequency broadband matched field processing in the 8 -16 [622548]

1High -frequency broadband matched field processing in the 8 -16
kHz band
Paul Hursky
Science Applications International Corporation
10260 Campus Point Drive
San Diego, CA 92121 USA
[anonimizat] S iderius
Science Applications International Corporation
10260 Campus Point Drive
San Diego, CA 92121 USA
[anonimizat]
Michael B. Porter
Science Applications International Corporati on
10260 Campus Point Drive
San Diego, CA 92121 USA
[anonimizat] Keyko McDonald
Space and Naval Warfare Systems Center, San Diego
53560 Hull Street
San Diego, CA 92152 -5001
keyko.mcdonald@ navy.mil
Abstract – We will show model -based
localization results at 8 -16 kHz using a single
hydrophone in several shallow water environments, with
successful tracking out to 3 km. It is very difficult to
produce accurate replicas of the field at thes e high
frequencies, due to sensitivity to small bathymetric
features, surface motion (waves), and water column
fluctuations. To reduce this sensitivity, we match the
envelope of the field in the time domain, using the
Bellhop ray tracing model to calculat e replicas. At these
high frequencies, ray tracing is a viable approach.
SignalEx tests have been conducted in a variety of
shallow water coastal environments to relate acoustic
communications performance to oceanographic
conditions. A fixed receiver and a transmitter drifting out
to minimum detectable ranges were used. Waveforms to
probe the channel in the 8 to 16 kHz band were
transmitted at regular intervals. These signals were
initially used to study the channel and subsequently to
test our source local ization algorithms. Working in the
time domain enables the fluctuations to be directly
observed as changes in the times of arrival. After
aligning a sequence of probe pulses on the stabler initial
arrivals, the pattern of fluctuations in the amplitudes and
arrival times of the later arrivals can be observed. These
fluctuations cause mismatch between the data and the
replicas with which the data is being correlated, unless
they are incorporated into the model of the signal. We
will present measurements of th e time -varying channel
response and source localization results from two
shallow water sites: the New England Front area, and a
site off the coast of La Jolla in San Diego, California.
I. INTRODUCTION
Over the last 20 years there has been a
great deal of r esearch on using or embedding
acoustic models in signal processing algorithms. An
example application is for vertical or horizontal line
arrays in which the spatial and temporal multipath
structure is used to determine the location of a source
in the ocean waveguide.
The terminology for this work is not
standardized. We use the term 'model -based'
processing to refer to any technique that uses a
computer model of acoustic propagation in the ocean
waveguide. This term encompasses 1) matched -field
processing, which exploits the phase -amplitude
structure of some small set of narrowband signals (see [1], [2], and [3]), 2) back -propagation or time –
reversal techniques which use a computer model to
propagate the field observed on the receive array and
(under certain conditions) refocus it at the source
location (see [4], [5], [6], and [7]), 3) single -phone
correlation processing, which exploits the temporal
multipath structure (see [8], [9], [10], [11], [12], [13],
and [14]). These techniques are all closely related and
in some cases actually identical. However, they
provide a different jumping off point and sometimes
lead to different insights about how to exploit the
space -time structure of the acoustic field.
Our interest here is in extending these
techniques to si gnificantly higher frequencies
(previously, [15] demonstrated source localization at a
mid-frequency range). Higher frequency arrays can be
attractive because they can provide high spatial
resolution in a small space. Alternatively, work at this
band is mo tivated by interest in sources such as
dolphins or AUVs with a signature in this band.
Finally, further incentive to explore applications in this
band is due to the ambient noise background being
significantly lower at high frequencies than in lower
bands (where the clutter is dominated by surface
shipping).
The first issue that arises is that of
understanding qualitatively the propagation physics in
this band. Should we expect distinct echoes from the
surface and bottom? Might the combined effects of
surfa ce and bottom roughness; small -scale ocean
variability; source/receiver motion; and near -surface
bubbles yield a diffuse smear of acoustic energy? The
answers to these questions are partially contained in
the literature, although most of the studies have b een
devoted to single boundary interactions and/or the
back -scattered field. As we will show, our experiments
at a variety of typical shallow water sites reveals a
clear set of surface and bottom echoes rising well
above the reverberant haze.

2
Figure 1. Telesonar testbed hardware.
The second issue is whether we can predict
the field accurately enough to localize a source using
the echo pattern as a fingerprint of target location. Our
results demonstrate that source localization at high
frequencies is possible out to ranges of several
kilometers using just a single phone. However, special
techniques must be applied to exploit the reliable
features of the propagation.
From 1999 to the present, a series of data –
collection experiments were performed at a number of
shallow water coastal areas. Figure 1 shows a
photograph of the Telesonar Testbed hardware
developed at Spawar Systems Center for transmitting
and recording acoustic waveforms in the 8 -16 kHz
band. Besides transmitting a variety of acoustic
communications sequences during the SignalEx tests,
probe pulses were transmitted on a regular basis to
measure the impulse response of the ocean
waveguide. Although some of the experiments used
fixed-fixed configurations, we will discuss data in
which the transmitter was allowed to drift from short
range out to a range at which the signals were no
longer detectable.
Section II will discuss the impulse response
measurements. Section III will discuss how the
impulse response function was modeled. Section IV
will discuss how the observed impulse response was
used to estimate source location.
II. IMPULSE RESPONSE MEASUREMENTS
Figure 2 shows two views of the waveform
sequence during the SignalEx test off the coast of La
Jolla on May 10, 2002. The upper plot in this figure,
covering 25 minutes, shows different colored
rectangles. The green rectangles represent identical
probe sequences. The other colors represent various
other test sequences, each of which is preceded by a
probe sequence. The lower plot in this figure shows
that a single probe sequence contains repeating
probe waveforms. In the 2002 SignalEx tests to be
discussed in this paper, there were 100 LFM chirps in
each probes interval, each sweeping fr om 8 to 16
kHz, having a duration of 50 milliseconds, and
repeating every 250 milliseconds (4 chirps/second, so
100 chirps emitted in 25 seconds).Figure 3 shows 100 processed chirps
(matched filter outputs), stacke d one on top of each
other. The rows of this image have been aligned by
spacing them according to the known pulse repetition
interval of 250 milliseconds, corrected for a constant
Doppler. Each row of this image contains the
envelope of the matched filter output, calculated using
the known probe waveform as the matched filter
replica. There are significant fluctuations in all arrivals.
Figure 4 shows the same 100 chirps, but with each
row aligned at the offset relati ve to the previous row
where the maximum row -to-row cross -correlation
occurs. In other words, we cross -correlate each pair of
rows and offset the second of the pair to bring the
cross -correlation peak to the zero lag. This method of
aligning one matched fi lter output with respect to its
predecessor is only one of many techniques we
attempted, including peak picking – using a cross –
correlation to align these waveforms turned out to be
the most robust for this and other datasets. Because
the cross -correlation is driven by the higher amplitude
earlier arrivals, the fluctuations are all but removed
from these earlier arrivals by this process. This
enables the fluctuating relative times of arrival
between these earlier and later arrivals to be clearly
seen. The t imes of the later arrivals vary according to
some process that is independent of the process
governing the earliest arrivals.
Given the configuration with the receiver
close to the bottom and the source in the water
column, the 1st and 2nd arrivals are th e direct and
bottom -reflected paths, and the 3rd and 4th arrivals are
surface interacting paths. Although the fluctuations
seen in the 3rd and 4th arrivals (obviously strongly
correlated), could be due to water column
phenomena, they are probably due to th e motion of
the surface. Note that the horizontal scale is only 12
milliseconds. Additional arrivals were observed at later
arrival times, with similarly variable arrival times
(relative to the aligned earliest arrivals) and
amplitudes, although these are not shown here.
Figure 2. Diagram of overall probe schedule (upper plot) and
blowup of the probes only (lower plot).

3
Figure 3. Stacked impulse responses, aligned according to a
constant Doppler correcti on.
Figure 4. Stacked impulse responses, aligned by cross –
correlating consecutive pairs of responses.
Figure 4 shows a single probes interval (of
25 seconds, with 100 probes, each probe a n LFM
chirp). Such probes intervals were repeated every two
minutes for roughly six hours, while the transmitter
drifted from a range of 400 to 6000 meters (as shown
in Figure 6). Each of the 25 -second intervals was
Doppler corrected (as in Figure 3), aligned (chirp -to-
chirp, as in Figure 4), and summed to form a single
average impulse response function estimate. Figure 5
show s the result of stacking 90 such averages (three
hours of the drift). These are the measurements that
will be used to form the source location estimate.
Figure 5. Measured channel impulse response as a function
of range (receive r depth of 71 meters and source depth of 24
meters).
Figure 6. SignalEx La Jolla 2002 experiment configuration.
III. MODELING
Figure 6 shows the bathymetry off the coast
of La Jolla where the experiment was performed. The
bathymetry between the receiver (indicated by the
circle) and the drifting source (whose track is marked
by dots) is reasonably flat, at least for the first 3 -4
kilometers, before the source veers to the right. A
single radia l from the fixed receiver was used to set
the bathymetry that was used in the model. Figure 7
shows the measured sound speed profile and the
depths of the source (24 meters) and receiver (71
meters).

4
Figure 7. SignaleEx La Jolla 2002 environment.
Figure 8. Modeled channel impulse response as a function of
range (receiver depth of 71 meters and source depth of 24
meters).
To reproduce the range -dependent impulse
response function shown in Figure 5, the broadband
channel impulse response function was modeled
using the Bellhop ray/beam tracing program (see [18],
[19], and [20]). This model calculates magnitudes,
phases (although only envelopes are shown in the
plots of modeling calculations below), and times of
travel of all multipath components for a particular
source and receiver geometry (source depth, source –
to-receiver range, and receiver depth), given a sound
speed profile, properties of the surface and bottom,
and a potentially range -dependent bathymetry. A
band -limited impulse response function is synthesized
from these multipath arrival parameters.
Figure 8 shows the multipath structure
calculated by Bellhop for the ex periment configuration
during the La Jolla SignalEx test (relative time of
arrival is shown along the horizontal axis, and range
along the vertical axis, range being calculated from
GPS measurements). The agreement between the
coarse features of Figure 5 and Figure 8 is excellent,
which bodes well for our model -based source
localization. However, the later arrivals in the measured
data, whose relative time of arrival exhibit s the
fluctuations seen in Figure 3 and Figure 4, have been
smeared out by the averaging process, resulting in the
amplitudes of the later arrivals in Figure 5 being
underestimated, compared to the modeled amplitudes
of the later arrivals in Figure 8.
Figure 9 and Figure 10 show blowups of the
measured and modeled data (seen in Figures Figure 5
and Figure 8), showing what happens to the impulse
response over ranges from 400 to 1600 meters. Note
that from 1000 to 1400 meters there is a pair of
earliest arrivals that is not predicted by the ray model.
Note too that from 600 to 1200 meters, the later set of
arrivals (at 10 and 20 milliseconds in Figure 9) show
significant fading that is not predicted by the ray
model. These d ifferences between the measured and
modeled data can be expected to cause problems for
any source localization based on matching this
measured and modeled data.
The dropouts seen along some of the later
arrivals in the modeled data are due to the range –
dependent bathymetry. These were duplicated by a
broadband parabolic equation calculation, run as a
check on the ray tracing results. Because the
measured data is the result of averaging over 25
seconds of drift, these dropouts are not observed in
the measure d data.
Comparing the measured and modeled
impulse response functions, and given the fluctuations
in the times of arrival and amplitudes and how they
vary among the different multipath arrivals, it is not
obvious what form the optimal source location
estim ate should take.

5
Figure 9. Measured impulse response to 1600 meters range.
Figure 10. Modeled impulse responses to 1600 meters
range.
IV. LOCALIZATION
The source localization metric or statistic
(also c alled an ambiguity surface) is calculated for
every candidate source location (i.e. we search in
range and depth) by cross -correlating the measured
and modeled impulse response functions and
selecting the maximum cross -correlation peak. A
cross -correlation is necessary, because we do not
have a time reference for the measured data, and as
a result must examine every possible lag or offset
between the measured and modeled impulse
response functions. This calculation produces a value
for every candidate sourc e range and depth, at every
time epoch for which we have measured the impulse
response (as the source drifts in range). Thus a 2D
ambiguity surface is produced for each time epoch,
and the overall output for the entire source drift is a
3D ambiguity volume , indexed on source range,
source depth, and time epoch. Figure 11 shows the
2D slice versus range and time for the known source
depth of 24 meters. The circles indicate the known
source range, calculated from GPS m easurements at
each time epoch. The range track is consistent with
the GPS measurements. Figure 12 shows the slices versus depth that follow the source track in range. A
very strong track is apparent at the known so urce
depth of 24 meters. A persistent track is apparent in
both range and depth.
Our previous experience working with
broadband signatures at lower frequencies showed
that it was significantly more difficult to model the
phases of the multipath components than the
envelopes and times of arrival. We had mixed results
matching on both magnitude and phase, even on low
frequency data. Given reasonably accurate
information about the bottom (enough to predict the
critical angle) and about the sound speed profile in the
water column, it was possible to consistently
reproduce the envelope of the multipath pattern.
However, in the high frequency band being addressed
here, simply matching the modeled and measured
impulse response envelopes only produced a
plausible so urce track for a few short ranges (starting
at 400 meters). There were several reasons for this.
Looking at the measured and modeled data, the
mismatch in the higher amplitude earlier arrivals was
dominating the information provided by the later
arrivals. This was further compounded by the later
arrivals being smeared out by our averaging process,
due to the fluctuations in their time of travel.
Reference [16] used the log envelope of the
measured and modeled waveforms being matched to
emphasize the contrib ution of the later arrivals. With a
similar motivation, the measured and modeled
impulse response waveforms were similarly remapped
prior to matching. The measured waveform was
whitened using a three -pass, split -window moving
average process to estimate bo th the mean and the
standard deviation at each sample. The modeled
waveform was raised to a fractional power (.1) in
order to reduce the disparity between the early and
late arrival amplitudes. These somewhat ad hoc
transforms resulted in the much improved results
shown in Figure 11 and Figure 12.
Note that although we have taken great
pains in the previous sections to align the measured
impulse response functions so that thei r structure
versus range is very apparent, the source localization
algorithm discussed in this section is not sensitive to
this alignment, because it operates on each matched
filter output independently of all others, and seeks the
maximum amplitude in the cross -correlation of the
measured and modeled envelopes (so it checks all
possible lags between the measured and modeled
impulse response functions). The modeled results are
displayed using a reduced time (range/sound speed)
to set the left edge of each i mage row. The measured
response functions are displayed using a detected
early arrival to set the left edge of the first image row,
and the peak cross -correlation (row to row) to set
subsequent rows (as discussed above).

6
Figure 11. Range track at source depth of 24 meters (and
receiver depth of 71 meters).
Figure 12. Depth track for source range track shown in
Figure 11.
V. DISCUSSION AND CONCLUSIONS
The most stri king finding is that there seems
to be a stable, exploitable impulse response of distinct
and predictable multipath arrivals at these high
frequencies. Although we only show results for a
single site, we have seen qualitatively similar results
at a number of sites where SignalEx experiments
were performed.
The measured impulse response can be
reproduced by standard acoustic propagation models
well enough to support source localization using a
single point receiver, although this was much more
difficult tha n we have found at low frequencies (see
[17]).
Admittedly, using a known source waveform
to measure the impulse response would not be
possible with an uncooperative source. However, we
have had no trouble extending similar time -domain
based source localiza tion to a source waveform
unknown scenario (at low frequencies, see [17]) by
matching measured and modeled correlation
waveforms. This requires a reasonably wideband
source signature and pre -whitening if the signature is not smooth in the frequency domain. Figure 13 shows
the cross correlation of two Telesonar Testbed receive
elements, from the SignalEx La Jolla experiment (the
same data we used to demonstrate source
localization in the previous sections), showing a rich
multipath structure. The same model used for the
impulse response above can reproduce this structure.
Note that a correlation waveform has an implicit time
reference, so the matching consists of an inner
product as opposed to a cross -correlation, as w as
needed to match impulse response waveforms.
Note that working in the time -domain
enabled us to deal directly with the fluctuations in the
impulse response caused by surface motion and
bottom bathymetry.
Acknowledgment
The SignalEx experiments were fun ded by
ONR.
Figure 13. Cross -correlation measured from 2 of 4
testbed receive elements, spaced for diversity.

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