EFFECT OF ENVIRONMENTAL VARIABILITY ON
MODEL-BASED SIGNAL PROCESSING: REVIEW OF
EXPERIMENTAL RESULTS IN THE MEDITERRANEAN
JEAN-PIERRE HERMAND
Dept of Optics and Acoustics, Université Libre de Bruxelles,
ave F.-D. Roosevelt 50, CP194/5, B-1050 Brussels, Belgium
E-mail: [email protected]
Over the last decade experiments were conducted in the Mediterranean for localising
controlled sound sources and for deducing bottom geo-acoustic properties from the
measurement of the acoustic-channel impulse response over a broad frequency range.
Inversion of the large time-bandwidth-product signals transmitted to probe the medium
was performed using a coherent receiver, the model-based matched filter. The reference
channels incorporate Green’s function models for partially known or hypothesised environmental conditions and source parameters (range, depth and Doppler). The search
terminated when most of the time-spread energy on single or multiple elements of the
receive array was recombined coherently into a single peak. Although performance limitations were imposed by environmental and modelling uncertainties the model-based
processor was always seen as intrinsically robust to the acoustic-signal variability encountered in our experiments. Substantial processing gains were obtained in most situations depending on the time dispersion, spatial diversity, predictability and coherence
of the specific acoustic channel. Most importantly, correct and stable inversion results
were possible even from a sparse but representative set of hydrologic data.
1 Introduction
Ocean-duct and shallow-water transmission channels are characterised by time dispersion
and frequency-selective fading of the acoustic signal. The performance of a conventional
matched filter (MF) receiver can be drastically improved if the reference channel compensates for the amplitude and phase distortion occurred in the time dispersive medium >dH.
Source-location and environmental parameters were determined by varying the reference
channel of the model-based matched filter (MBMF) receiver >1, nH. It was shown that the
use of large time-bandwidth(TW)-product signals for probing the medium was important
not only to improve resolution performance but also to reduce propagation fading.
This paper focuses on the effects of environmental variability and other modelling uncertainties upon MBMF inversion results and the role of the transmit frequency bandwidth
and spatial receive aperture in limiting these effects.
In Sect. 2 a theory is proposed to explain the robustness of a multichannel MBMF
receiver to environmental and geometric variability, observed in various experiments.
Section 3 reviews source localisation results achieved with a towed source and horizontal
receive array (HRA). Section 4 reviews geo-acoustic inversion results obtained with a
fixed source and single and multiple elements of a vertical receive array (VRA). Section 5
concludes the paper.
155
N.G. Pace and F.B. Jensen (eds.), Impact of Littoral Environmental Variability on Acoustic Predictions and
Sonar Performance, 155-162.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
156
2
J.-P. HERMAND
Uncertainty in model-based matched filter processing
Let us define frequency integrals of the Green’s function G(ω, r) of a stationary medium,
!
!2
!
!
"
"
! 1
!
1
!
!
α(r) ! !
G(ω, r)dω!
and β(r) !
|G(ω, r)|2 dω
(1)
∆ω
! ∆ω
!
Π
Π
where r is the radius vector between the source and a receiver and Π is the frequency
range of radiation. For a signal with centre frequency ω0 and large time-bandwidth
product ∆t∆ω such that ∆t(∆ω)2 /ω0 ! 2π, the coefficients α(r) and β(r) determine
to the output peak signal-to-noise ratio (SNR) ρ(r) of the MF and optimum receivers,
ρmf (r) = 2E/N0 α(r)
<
ρopt (r) = 2E/N0 β(r)
(2)
where E is the source signal energy and N0 is the white noise power spectral density at
the receiver input. The upper bound on α(r) is equal to β(r) and their ratio
γ(r) = α(r)/β(r)
≤
1
(3)
is a measure of the degree of time dispersion in the real propagation channel.
The output peak SNR of a MBMF processor which partially compensates for the
dispersion distortion of the received signal is given by [1]
2
ρmb (r) = 2E/N0 β(r) max |RGGM (ξ, r)|
ξ
<
ρopt (r)
(4)
where RGGM is a measure of the degree of similarity between the real sound field and
the model field GM (ω, r),
#
G(ω, r)G†M (ω, r) exp(jωξ)dω
(5)
RGGM (ξ, r) ! $ Π
%1/2 < 1
#
#
2
2
|G(ω, r)| dω |GM (ω, r)| dω
Π
Π
and ξ is a phase variable which includes the mean travel time.
Since transmission over most ocean channels involves propagation through a random
time-varying medium, the integrands in Eq. (1) must be averaged over an ensemble of
realisations of the channel transfer function,
"
""
1
1
α(r) =
Re
[R
(ω
,
ω
;
r)]
dω
dω
and
β(r)
=
RG (ω, r)dω
G 1
2
1
2
(∆ω)2
∆ω
Π
Π
(6)
where RG ! #G(ω1 , r)G† (ω2 , r)$ is the complex-valued two-frequency correlation
function [4] and #·$ denotes ensemble averaging. RG is a measure of the correlation
between the fading at different frequencies.
To quantify the overall effect of environmental and modelling uncertainties on MBMF
performance, Eq. (5) is replaced by the combined correlation coefficient [5]
# #
# GG†M exp(jωξ)dω$ dQ
Q Π
KGGM (Ω, R, τ ) ! &
'1/2
# #
# #
# |G|2 dω$ dQ # |GM |2 dω$ dQ
Q Π
Q Π
≤
1
(7)
MODEL-BASED SIGNAL PROCESSING IN THE MEDITERRANEAN
157
where G ! G(ω, r, t), GM ! GM (ω + Ω, r + R, t + τ ) and dQ = drdt. The function
combines averaging of the channel transfer functions over a certain space-time domain Q
and ensemble averaging. The intervals along the coordinate axes Ωdet , ρdet and τdet that
characterise a high degree of determinacy (predictability) of a specific acoustic channel
are determined from the condition that the above quantity decays to 1/2.
An important property of Eq. (7) is that the intervals of deterministic behaviour can
be greater than the corresponding correlation radii of the acoustic field itself [6, 7]. The
frequency band Ωdet can be much larger than the coherence band Ωcoh of the field. Also the
time τdet can be much larger than the characteristic fluctuation time of the environmental
parameters that affect the acoustic transmission. Consequently, the MBMF processing
technique can be less sensitive to uncertainty in knowledge about the environmental
conditions, and about the source and receiver configuration, than expected when the
above intervals are considered separately. Therefore, as will be demonstrated by the
experimental results in the next sections, compensation of distortion in the received signal
can remain effective even in a randomly inhomogeneous dispersive channel for which
Ωdet ⊃ Π ⊃ Ωcoh . Moreover, a MBMF receiver implemented as a bank of filters matched
to a number of anticipated channels is expected to be robust, to some extent, to the
uncertainty upon the environment. From Eqs. (3), (4) and (7), the MBMF processing
gain relative to the MF equals the degree of time dispersion in the real channel [1/γ(r)]
weighted by the degree of determinacy between the real and model fields,
Γ(r) ! max KGGM (Ω, R, τ )/γ(r).
ξ,Q
3
(8)
Source localisation in ocean ducts
The WEST SARDINIA 89-90 sea trials took place under winter conditions at a 2.8-km
deep water site west of Sardinia. Doppler-resolvent, large TW-product, linearly frequency
modulated (LFM) signals were transmitted from a controlled source to a 64-element HRA,
towed at constant depths. The signal bandwidth was varied over one decade 50–500 Hz
around a centre frequency 590 Hz. The medium Green’s function was modelled using
a range-independent (RI), generalised ray theory model. The environmental input was a
single sound speed profile (SSP) calculated from a measured near-surface temperature
profile (XBT), a deeper depth archival temperature data and salinity winter mean data.
In the fixed range experiment the source and receiver were towed near the axis of a
refractive duct [1]. Amplitude and phase scintillations of the transmitted signals caused a
structural change in the duct multipath-arrival structure from one signal to the next with
deep fading occurring occasionally for the smaller signal bandwidths. This was due to
small variations in range and tow depths and to slow spatial and temporal fluctuations
in duct sound speed. Figure 1(a) compares the MBMF gain [Γ, Eq. (8)] to the estimated
energy spreading loss (ESL) [γ, Eq. (3)] for each of the received transmission. Most importantly, for every transmission, the MBMF consistently gathered the time-spread signal
energy back into a single output peak. The gain, varying from 0.5 dB to 3 dB, was proportional to the time- and bandwidth-dependent ESL measured at the MF output. These
calculations included only the time-dispersed, ducted R-path arrivals through eigenray
filtering. Moreover, it was also possible to isolate in depth and range the source that
emitted the acoustic signal and the depth of the receive array [Fig. 1(b)]. The overall
158
J.-P. HERMAND
300 Hz
200
100
250
150
50
(a)
500
(b)
4
Range (km)
35
(dB)
3
2
30
25
200
Re
1
cei
0
0
10
20
30
40
50
Geotime (min)
60
ver
150
dep
th (
70
m)
100
(c)
50
70
90
110
pth
ce de
Sour
130
(d)
Range (km)
20
32
22
24
26
150
(m)
28
30
250 Hz
4
3
31
(dB)
Range (km)
31.5
30.5
30
160
Re 155
ce
ive 150
rd
ep
th 145
(m
)
2
1
110
105
100
(m)
epth
d
e
ourc
95
140
90
S
0
0
10
20
30
Geotime (min)
40
50
Figure 1. Effect of environmental variability upon MBMF source localisation. (a) Time history
of MBMF processing gain relative to the MF (dark grey) and ESL (light grey) over 1.2-h period.
Signal bandwidths and corresponding time intervals of transmission are indicated. January 24,
1989. (b) Scatter of the source-receiver depths and range estimates for all transmissions. The axes
limits correspond to the search intervals. (c) Contour slices of MBMF gain. light grey: 1 dB; grey:
2 dB and black: 3 dB. (d) Same as (a) for opening range over 1-h period. February 6, 1990. West
Sardinia.
effect of environmental, modelling and geometrical uncertainty is represented by the ambiguity volume in Fig. 1(c). The centroid was very close to the nominal range and depths
of the source and receiver: 31.3 km, 100 m and 150 m, respectively.
In the opening range experiment the source and receiver were towed near the surface.
The transmitted signals were strongly time-dispersed by propagation, through a nearsurface duct and were Doppler-shifted (time-expanded). Here, surface interaction and
near-surface variability played an important role. Most of the energy was conveyed by
low-grazing angle paths with narrow dispersion in elevation angle. Hence there was
no significant down Doppler shift and spread. Because of the Lloyd-mirror effect, the
multipath interference structure was highly sensitive to small variation in relative depth
of source and receiver. MBMF processing improved the peak SNR by 1–4 dB in spite of
the moderate sea state (3–4) and the sensitivity to geometry [Fig. 1(d)]. The gain resulted
from phased recombination of a continuum of R-path and RSR-path arrivals which were
not resolved by the MF. Range and relative velocity were correctly determined by a
multichannel MBMF [2]. Comparison with MF cross-ambiguity functions showed that
large spurious peaks built up away from the true time delay and Doppler shift [8] were
suppressed by the MBMF processor. These experimental results demonstrate the relevance
of the combined correlation coefficient Eq. (7) and its properties discussed in Sect. 2.
159
MODEL-BASED SIGNAL PROCESSING IN THE MEDITERRANEAN
1450
0
1470
Sound speed (m/s)
1490
1510
1530
1536
20
Depth (m)
1550
39.2
1526
47.2
151 6
40
1514
55.2
1512
60
S
1510
VRA
63.2
80
100
0
71.2
0.02
110
c=1508.8 m/s ↓
114
ρ=1.5
118
β=0.06 dB/λ
∂zc=3 s−1
122
ρ=1.8
15
↑
c=1470 m/s
c=1650 m/s
↓
c=1530 m/s
β=0.15 dB/λ
9
79.2
6
4.5
87.2
95.2
6
0
6.02
Time (s)
Range (km)
Figure 2. Geometry and RD environmental model of the YELLOW SHARK 94 experiment. Top
panel: Hydrologic variability. Source (S,◦) and VRA positions. Bottom: Geo-acoustic inversion
results [3]. Right: Snapshot of channel impulse responses measured on the 32-element VRA for
the source at 9-km range. Middle: Model-based time reversal mirror. Temporal focus. September
10-11, 1994. Northwest of Formiche di Grosseto islands, off the west coast of Italy.
4
Geo-acoustic inversion in shallow waters
The YELLOW SHARK 94 sea trials were carried out in a shallow water, muddy bottom
site, off the west coast of Italy (Fig. 2). A multitone signal and a LFM signal with the
same frequency band 200–800 Hz were transmitted from a mid-depth acoustic projector
bottom-moored at four ranges to a 32-element VRA [9, 3].
Because of the perfectly static configuration of the acoustic moorings the observed
acoustic variability was due entirely to the ocean volume: essentially, the time-varying
thickness of the mixed layer and fluctuating sound-speed structure in the thermocline. All
frequencies were affected with larger and shorter-term variations at the higher frequencies.
In the experimental setup where both source and VRA were positioned below a welldeveloped thermocline, the depth of the resulting propagation channel and associated
sound-speed gradient were important. For each range, the ocean SSP input to the forward
model was the ensemble average of all profiles measured along the transect during the
acoustic transmissions. The time variation of the effective channel depth were accounted
for by varying both the range-averaged mixed-layer and water depths. The top depth of the
thermocline was controlled by translating the whole SSP in the vertical but maintaining
the bottom-water sound speed constant.
4.1 Multitone Matched-Field Results
The effect of water-column variability upon acoustic parameter estimation and the importance of signal bandwidth were investigated by inverting separately each of 38 observations of the multitone pressure field of 12-s duration spaced by 2 min. For each of these,
160
J.-P. HERMAND
Z (m)
δZ (m)
C (km/s)
∆Z (m)
111 113 115 −2
0
0
2 1.46 1.48 1.5 1
10
(b)
(c)
(d)
0
0
1
1
∆C (m/s)
1
20 5
30
β (dB/λ)
1
50 .01
.2
C (km/s)
2
.4 1.52 1.57 1.63
Geotime (min)
15
30
45
60
75
1
Frequency (Hz)
0
200
250
315
400
500
630
800
MT
(a)
(e)
(f)
(g)
Figure 3. Effect of water-column variability upon matched-field geo-acoustic inversion. Top panels:
Time history of (a) water depth, (b) thermocline depth, (c) sediment p-wave speed, (d) thickness,
(e) speed gradient, (f) attenuation and (g) basement speed estimates. The curve and symbols are
for inversions based on: 200–800-Hz seven tones (solid line), 250-Hz tone (!), 800-Hz tone (")
and other individual tones (•). The horizontal scales correspond to the search intervals. Middle:
Normalised histograms of multitone (black) and concatenated single-tone (grey) inversion results.
Bottom: Statistics for the single-tone and multitone (MT) inversions. vertical lines of the box:
lower quartile, median, and upper quartile values. horizontal lines: extreme data extent within
1.5× interquartile range. +: outliers.
genetic-algorithm optimisation was performed for each tone individually and for all tones
jointly.
Figure 3 shows the time histories and statistics of two water-column and five bottom
parameters for the 9-km range. The single-tone bottom estimates were widely scattered
over the search intervals with all parameters being highly sensitive to water-column variability. The effect on each parameter was strongly frequency-dependent. In comparison,
the broad-band, multitone (MT) processing provided remarkable stability and correct bottom characterisation. For all parameters, the bias and variance of the MT estimates were
much smaller than the ones of the individual tones. Concatenating single-tone results did
not improve the estimation. Related experimental results are discussed in [9–11].
161
MODEL-BASED SIGNAL PROCESSING IN THE MEDITERRANEAN
(a)
(b)
39.2
1520
3
1500
2
1480
1
C (km/s)
47.2
0
1460
1
55.2
1
Receiver depth (m)
1440
2
63.2
1420
3
1400
71.2
0
2
4
∆Z (m)
6
8
10
(dB)
1
79.2
(c)
5
87.2
0
(dB)
95.2
−5
INC
COH
1.4
1.45
1.5
0
5
−10
10
∆Z1 (m)
C (km/s)
1
1500
10
C 1 (km/s) 1450
1400
(d)
(e)
5
∆Z 1 (m)
0
0.2
0.4
0.1
0.2
0
10
0
10
1500
5
∆Z1 (m)
0
1400
1450 C (km/s)
1
1500
5
∆Z1 (m)
0
1450
1400
C1 (km/s)
Figure 4. Effect of water-column and bottom variability upon MBMF geo-acoustic inversion. (a)
Statistics of sediment-speed and layer-thickness results for each receiver depth, all ranges included
(see Fig. 3 caption). MBMF speed-thickness ambiguity function for the 9-km range: (b) mean
and (c) extreme values. Normalised histograms of (d) concatenated single-depth results and (e)
space-coherent results, all ranges included.
4.2 Model-Based Matched Filter Results
The effects of both water-column and bottom variability upon MBMF processing were
quantified for single and multiple array-signals. All LFM transmissions received at the
4 ranges and 32 depths were included in the analysis (5472 signals). A simplified RI
model of the environment was used where only the two most range-dependent (RD)
bottom parameters were varied: the depth-average sound speed and thickness of the
upper clay layer. The other parameters were fixed to the baseline values obtained with a
six-parameter model [3].
The temporal variability of bottom parameters inverted from single VRA-elements
was remarkably small because of the frequency diversity useage as for the above MT
matched-field results [Fig. 4(a,d)]. Greater variability was observed near the waveguide
boundaries. Space incoherent (INC) and coherent (COH) processing of all VRA signals
further reduced the effect of hydrologic variability by exploiting spatial diversity (a,e).
162
J.-P. HERMAND
COH processing over a few elements, optimally distributed in depth, provided similar stability. Actual RD bottom variability is revealed by prominent histogram peaks (d,e) which
correspond to validated, average values over the different ranges. The two-parameter ambiguity features (b) were stable in spite of the processing gain variations due to acoustic
signal variability (c). Detailed analysis of the depth dependency and sparse array results
are given in [3].
5
Conclusions
The experimental results reviewed in this paper show that model-based matched filter and
matched-field processing over a broad signal-frequency range are effective in reducing
the detrimental effect of environmental and modelling uncertainties. For the encountered
conditions of oceanographic variability, the peak signal-to-noise ratio for the model-based
processor was always larger than the conventional. Correct and stable results of source
localisation and seabed geo-acoustic characterisation were possible even from a sparse
set of hydrologic data.
Acknowledgements
The preparation of this article was supported by the Royal Netherlands Navy. The data
were collected by the SACLANT Undersea Research Centre.
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