Aiaa.paperOne-Step Aeroacoustics Simulation Using Lattice Boltzmann Method
Sensor Networks, Aeroacoustics, and Signal...
Transcript of Sensor Networks, Aeroacoustics, and Signal...
17 May 2004 ICASSP Tutorial II-1
Sensor Networks, Aeroacoustics,
and Signal Processing
Part II: Aeroacoustic Sensor Networks
Brian M. SadlerRichard J. Kozick
17 May 2004
17 May 2004 ICASSP Tutorial II-2
Heterogeneous Network of Acoustic Sensors
CentralNode?
Source
One mic.
Sensorarray
10’s to 100’s of mrangeIssues:
•Centralized versusdistributed processing
•Minimize comms., energy•Triangulation, TDOA?•Effects of acoustic prop.•(Node localization, sensor layout & density,Classification, tracking)
17 May 2004 ICASSP Tutorial II-3
Acoustic Source & Propagation
SPECTROGRAM OF SENSOR 1 (dB)
TIME (sec)
FREQ
UEN
CY
(Hz)
120 125 130 135 140 145 150 155
0
50
100
150
200
250
Source Turbulence scatters wavefronts
Signalat sensor(mic.)
Source:•Loud•Spectral lines
One sensor:•Detection•Doppler estimation•Harmonic signature
DSP
17 May 2004 ICASSP Tutorial II-4
More Sophisticated Node:Sensor Array
DSP1 m apertureor (much) less
Issues:•Array size/baseline
Coherence decreases with larger spacing•AOA estimation accuracy with turbulent scattering•What can we do with a hockey-puck sensor?
Small, covert, easily deployablePerformance?
17 May 2004 ICASSP Tutorial II-5
Why Acoustics?• Advantages:
– Mature sensor technology (microphones)– Low data bandwidth: ~[30, 250] Hz
Sophisticated, real-time signal proc.– Loud sources, difficult to hide: vehicles, aircraft, ballistics
• Challenges:– Ultra-wideband regime: 157% fractional BW– λ in [1.3, 11] m Small array baselines– Propagation: turbulence, weather, (multipath)– Minimize network communications
• We bound the space of useful system design and performance [Kozick2004a]
– with respect to SNR, range, frequency, bandwidth, observation time, propagation conditions (weather), sensor layout, source motion/track
– evaluate performance of algorithms (simulated & measured data)
Distinct fromRF arrays
17 May 2004 ICASSP Tutorial II-6
Brief History of Acoustics in Military [Namorato2000]
• Trumpeting down walls of Jericho• Chinese, Roman (B.C.)• Civil War: Generals used guns to
signal attacks• World War 1:
– Science of acoustics developed– Air & underwater acoustic systems
• World War 2: Mine actuating, submarine detection
• Many developments …• Army Research Laboratory, 1991-
present [Srour1995]– Hardware and software for
detection, localization, tracking, and classification
– Extensive field testing in various environments with many vehicle types
17 May 2004 ICASSP Tutorial II-7
• A little more background:– Source characteristics– Sound propagation through turbulent atmosphere
• Detection of sources (Saturation, Ω)• Array processing
– Coherence loss from turbulence (Coherence, γ)– Array size: 2 sensors source AOA– Array of arrays source localization
Distributed processing? Data to transmit?Triangulation/TDOA Minimize comms.
Remainder of Tutorial
Experimentallyvalidatedmodels
17 May 2004 ICASSP Tutorial II-8
Source Characteristics• Ground vehicles (tanks, trucks), aircraft (rotary,
jet), commercial vehicles, elephant herdsLOUD
• Main contributors to source sound:– Rotating machinery: Engines, aircraft blades– Tires and “tread slap” (spectral lines)– Vibrating surfaces
• Internal combustion engines: Sum-of-harmonics due to cylinder firing
• Turbine engines: Broadband “whine”• Key features: Spectral lines and high SNR
Distinct fromunderwater
17 May 2004 ICASSP Tutorial II-9
+/- 350 m from Closest Point of Approach (CPA)
TIME (sec)
HighSNR
17 May 2004 ICASSP Tutorial II-10
SPECTROGRAM OF SENSOR 1 (dB)
TIME (sec)
FRE
QU
EN
CY
(Hz)
60 65 70 75 80 85 90 95
0
50
100
150
200
250
+/- 85 m from CPA
CPA = 5 m15 km/hr
Time
Freq
uenc
y
-20 -15 -10 -5 0 5 10 15 2013
13.5
14
14.5
15
15.5
16Gv2c1007: FUNDAMENTAL FREQUENCY ESTIMATE
FRE
Q. (
Hz)
BLOCK FROM CPA
Doppler shift:0.5 Hz @ 14.5 Hz
3 Hz @ 87 Hz
Harmonic lines
17 May 2004 ICASSP Tutorial II-11
Overview of Propagation Issues• “Long” propagation time: 1 s per 330 m• Additive noise: Thermal, Gaussian
(also wind and directional interference)• Scattering from random inhomogeneities
(turbulence) temporal & spatial correl.– Random fluctuations in amplitude: Ω– Spatial coherence loss (>1 sensor): γ
• Transmission loss: Attenuation by spherical spreading and other factors
17 May 2004 ICASSP Tutorial II-12
Transmission Loss• Energy is diminished from Sref (at 1 m
from source) to S at sensor:– Spherical spreading– Refraction (wind, temp. gradients)– Ground interactions– Molecular absorption
• We model S as a deterministic parameter:
Average signal energy
LowPassFilter
0
5
10
15
0
5
10
15
20
25
1300
1400
1500
easting (km)northing (km)
he
igh
t (m
)
Tra
nsm
issi
on
Lo
ss (
dB
)
50
60
70
80
90
100
110
120
NumericalSolution[Wilson2002]
+/- 125 m from CPA
[Embleton1996]
17 May 2004 ICASSP Tutorial II-13
Measured Aeroacoustic Data
17 May 2004 ICASSP Tutorial II-14
Fluctuations due to turbulence
Measured SNR vs. Range & Frequency
Aspect dependence
SNR ~ 50 dBat CPA
Time
dB
17 May 2004 ICASSP Tutorial II-15
Outline
• Detection of sources– Saturation, Ω– Detection performance
• Array processing – Coherence loss from
turbulence, γ– Array size: 2 sensors
Source AOA– Array of arrays:
Source localization
Triangulation/TDOA, minimize comms.
Sinusoidal signal emitted by moving source:
( )χπ += tfSts o2cos)( refref
)()()( twtstz +−= τSignal at the sensor:
1. Propagation delay, τ2. Additive noise 3. Transmission loss4. Turbulent scattering
17 May 2004 ICASSP Tutorial II-16
Sensor Signal: No Scattering• Sensor signal with transmission
loss,propagation delay, and AWG noise:
• Complex envelope at frequency fo– Spectrum at fo shifted to 0 Hz– FFT amplitude at fo
( )( ) n timepropagatio ,2cos)(
),()(
=+=
+≤≤+−=
τχπ
τ
tfSts
Tttttwtstz
o
oo
( )[ ][ ] )(~exp
)(~exp)(~
twjS
twjStz o
+=
+−=
θ
τωχ
17 May 2004 ICASSP Tutorial II-17
Sensor Signal: With Scattering• A fraction, Ω, of the signal energy is scattered
from a pure sinusoid into a zero-mean, narrowband, Gaussian random process, :
• Saturation parameter, Ω in [0, 1] – Varies w/ source range, frequency, and
meteorological conditions (sunny, windy)– Based on physical modeling of sound propagation
through random, inhomogeneous medium• Easier to see scattering effect with a picture:
( ) [ ] [ ] )(~exp)(~exp1)(~ twjtvSjStz +Ω+Ω−= θθ
)(~ tv
[Norris2001, Wilson2002a]
17 May 2004 ICASSP Tutorial II-18
AWGN, 2No
-B/2 B/20
(1- Ω)S
Bv
Area= ΩS
-B/2 B/20
(1- Ω)S
Bv
ΩS
• Study detection of source, w/ respect to– Saturation, Ω (analogous to Rayleigh/Rician fading in comms.)– Processing bandwidth, B, and observation time, T– SNR = S / (2 No B)– Scattering bandwidth, Bv < 1 Hz (correlation time ~ 1/Bv > 1 sec)– Number of independent samples ~ (T Bv) often small
• Scattering (Ω > 0) causes signal energy fluctuations
Weak Scattering: Ω ~ 0 Strong Scattering: Ω ~ 1
Freq.
Power SpectralDensity (PSD)
17 May 2004 ICASSP Tutorial II-19
Probability Distributions• Complex amplitude
has complex Gaussian PDF with non-zero mean:
• Energy has non-central χ-squared PDF with 2 d.o.f.
• has Rice PDF
( )( )2,-1CN~~ σθ +ΩΩ SSez j
-20 -15 -10 -5 0 5 100
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
ENERGY, 10 log10(P) (dB)
PR
OB
AB
ILIT
Y D
EN
SIT
Y
PDF OF RECEIVED ENERGY (S=1, SNR = 30 dB)
Ω = 0.02
0.04
0.08
0.20
0.50
1.00
2~zP =
( )( )2,-1CN~~ σθ +ΩΩ SSez j
P
(Experimental validation in[Daigle1983, Bass1991, Norris2001])
17 May 2004 ICASSP Tutorial II-20
Saturation vs. Frequency & Range• Saturation depends on [Ostashev2000]:
– Weather conditions (sunny/cloudy), but varies little with wind speed
– Source frequency ω and range do
( )
( )
( ) 21
27
27
weather
Hz]500,30[2
,cloudymostly ,
21042.1
sunnymostly ,2
1003.4
2exp1(rad/sec)frequency (m), source of range
ωκ
πω
πωπ
ω
ωµ
µω
⋅=
∈
×
×
≈
−−=Ω==
−
−
o
o
dd
Theoretical forms
Constants from numerical evaluation of particular conditions
17 May 2004 ICASSP Tutorial II-21
50 100 150 200 250 300 350 400 450 5000
0.5
1SA
TUR
ATI
ON
, ΩMOSTLY SUNNY
do = 10 m50 m
100 m
200 m500 m
50 100 150 200 250 300 350 400 450 5000.2
0.4
0.6
0.8
1
FREQUENCY (Hz)
SATU
RA
TIO
N, Ω
MOSTLY SUNNY
1 km2 km
5 km
10 km
50 100 150 200 250 300 350 400 450 5000
0.5
1
SATU
RA
TIO
N, Ω
MOSTLY CLOUDY
do = 10 m
50 m100 m200 m500 m
50 100 150 200 250 300 350 400 450 5000.2
0.4
0.6
0.8
1
FREQUENCY (Hz)
SATU
RA
TIO
N, Ω
MOSTLY CLOUDY
1 km
2 km
5 km
10 km
Turbulence effects are small only for very short range and low frequency
Fully scattered
Saturation variesover entire range[0, 1] for typicalrange & freq.values
17 May 2004 ICASSP Tutorial II-22
Detection Performance
-5 0 5 10 15 20 25 300
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR (dB)
P D
PROBABILITY OF DETECTION, PFA = 0.01
Ω = 0Ω = 0.1Ω = 0.3Ω = 1
PD = probability of detectionPFA = probability of false alarm
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.985
0.99
0.995
1
P D
PROBABILITY OF DETECTION, PFA = 0.01
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0.7
0.8
0.9
1
SATURATION, Ω
P D
SNR = 20 dBSNR = 15 dBSNR = 10 dB
SNR = 30 dBSNR = 25 dB
Noscattering
Fullscattering
Scattering beginsto limit performance
17 May 2004 ICASSP Tutorial II-23
102 103 1040
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RANGE (m)P D
PROB. OF DETECTION WITH SNR α 1/RANGE2
CLOUDY, 40 Hz SUNNY, 40 HzCLOUDY, 200 Hz SUNNY, 200 Hz
101 102 103 1040
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RANGE (m)
SATU
RA
TIO
N, Ω
SATURATION VARIATION WITH WEATHER AND FREQUENCY
CLOUDY, 40 Hz SUNNY, 40 HzCLOUDY, 200 Hz SUNNY, 200 Hz
200 Hz40 Hz
Lower frequenciesdetected at largerranges
Detection Performance with Range
SNR = 50 dB at 10 m rangeSNR ~ 1/(range)2
Saturation increases with•Range•Frequency•Temperature (sunny)
1 km
17 May 2004 ICASSP Tutorial II-24
Detection Extensions• Sensor networks: Detection queuing
(wake-up) of more sophisticated sensors• Multiple snapshots & frequencies
– Source motion & nonstationarities– Coherence time of scattering
• Multiple sensors with different SNR and Ω– Distributed detection, what to communicate?– Required sensor density for reliable detection– Source localization based on energy level at the
sensors [Pham2003]
Physical models for cross-freq coherenceand coherence timeare in preliminary stage[Norris2001, Havelock1998]
17 May 2004 ICASSP Tutorial II-25
Outline
• Detection of sources– Saturation, Ω– Detection performance
• Array processing – Coherence loss from
turbulence, γ– Array size: 2 sensors
Source AOA– Array of arrays:
Source localization
Triangulation/TDOA, minimize comms.
Coherence, γ, depends on
•Sensor separation, ρ•Source frequency, ω•Source range, do•Weather conditions:sunny/cloudy, wind speed
17 May 2004 ICASSP Tutorial II-26
Signal Model forTwo Sensors
( ) ( ) ( )( )
( )( )( )
[0,1] Coherence ,1
1[0,1] Saturation
sin)/(phasearcsinAOA
,exp
1
,-1CN~~~
~ 2
2
1
∈=
=
∈=Ω
====
=
+ΩΩ
=
γγ
γ
θρωφωρφθ
φ
σχ
Γ
a
IaaΓaz
o
o
Hj
cc
j
SSezz
o
ρ= sensor spacing < λ/2
θ = AOA
Turbulence effects
Perfect plane wave:Ω = 0 or 1γ = 1
17 May 2004 ICASSP Tutorial II-27
Model for Coherence, γ• Assume AOA θ = 0,
freq. in [30, 500] Hz• Recall saturation model:
• Coherence model [Ostashev2000]:
ρ= sensor spacing
θdo = range
( )[ ]od21 weather2exp1 ωκ−−=Ω
( )[ ] ( )
( )
+=
≤≤
<<Ω
Ω−−−=
2
2
2
2
22
3/522
322137.0weather
10
,1weatherexp
o
v
o
T
o
effo
cC
TC
c
Ld
κ
γ
ρρωκγ
Velocityfluctuations (wind)
Temperaturefluctuations
γ 0 with freq., sensorspacing, and range
17 May 2004 ICASSP Tutorial II-28
( )[ ] ( )
( )
+=
≤≤
<<Ω
Ω−−−=
2
2
2
2
22
3/522
322137.0weather
10
,1weatherexp
o
v
o
T
o
effo
cC
TC
c
Ld
κ
γ
ρρωκγ
Velocityfluctuations (wind)
Temperaturefluctuations
Depends on wind leveland sunny/cloudy
(From [Kozick2004a], based on[Ostashev2000, Wilson2000])
17 May 2004 ICASSP Tutorial II-29
Assumptions for Model Validity [Kozick2004a]• Line of sight propagation (no multipath)
appropriate for flat, open terrain• AWGN is independent from sensor to sensor
ignores wind noise, directional interference• Scattered process is complex, circular, Gaussian
[Daigle1983, Bass1991, Norris2001]• Wavefronts arrive at array aperture with near-normal incidence • Sensor spacing, ρ, resides in the inertial subrange of the
turbulence:
smallest turbulent eddies << ρ << largest turbulent eddies = Leff
( )[ ] ( )
( )[ ] ( ) effo
effo
Ld
Ld
>>Ω−→−
>>→Ω
Ω−−−=
ρρωκ
ρρωκγ
for 1weatherexp
for 01weatherexp
3/522
3/522
17 May 2004 ICASSP Tutorial II-30
50 100 150 200 250 300 350 400 450 5000.97
0.98
0.99
1
CO
HER
ENC
E, γ
MOSTLY SUNNY, MODERATE WIND
50 m100 m
200 m
500 m
50 100 150 200 250 300 350 400 450 5000.5
0.6
0.7
0.8
0.9
FREQUENCY (Hz)C
OH
EREN
CE,
γ
MOSTLY SUNNY, MODERATE WIND
do = 10 m
1 km2 km
5 km
10 km
50 100 150 200 250 300 350 400 450 5000.97
0.98
0.99
1
CO
HER
ENC
E, γ
MOSTLY CLOUDY, MODERATE WIND50 m
100 m200 m
500 m
50 100 150 200 250 300 350 400 450 500
0.7
0.8
0.9
1
FREQUENCY (Hz)
CO
HER
ENC
E, γ
MOSTLY CLOUDY, MODERATE WIND
do = 10 m
1 km2 km
5 km
10 km
Coherence, γ, versus frequencyand range forsensor spacingρ = 12 inches
γ> 0.99 for range < 100 m.Is this “good”?
Curves shiftup w/ less wind,down w/ more wind
17 May 2004 ICASSP Tutorial II-31
Outline
• Detection of sources– Saturation, Ω– Detection performance
• Array processing – Coherence loss from
turbulence, γ– Array size: 2 sensors
Source AOA– Array of arrays:
Source localization
Triangulation/TDOA, minimize comms.
SenTech HE01 acoustic sensor [Prado2002]
• Freq. in [30, 250] Hz λ in [1.3, 11] m
• Angle of arrival (AOA) accuracy w.r.t.– Array aperture size– Turbulence (Ω, γ)
• Small aperture:– Easier to deploy– More covert– Better coherence– How small can we go?
17 May 2004 ICASSP Tutorial II-32
Impact on AOA Estimation
• How does the turbulence (Ω, γ) affect AOA estimation accuracy? [Sadler2004]
– Cramer-Rao lower bound (CRB), simulated RMSE– Achievable accuracy with small arrays?
( ) ( ) ( )
( )[ ]( )( )[ ] 1-2
2
2
22
SNR-1SNR2-1-1SNR2
-1SNR2SNR1-1SNR2
12
ˆCRBˆCRB,1ˆCRB
+⋅Ω+⋅ΩΩΩ⋅⋅+
⋅Ω+⋅Ω+Ω⋅=
−
==
γγ
γ
φρωλ
πρ
φθφ
φφ
φφ
J
cJoLarger sensor
spacing, ρ:DESIRABLE
BAD!
( )( )( )
phasearcsinAOA
exp1
===
=
φωρφθ
φ
ocj
a
17 May 2004 ICASSP Tutorial II-33
Special Cases of CRB• No scattering (ideal plane wave model):
• High SNR, with scattering:
SNR2 ⋅=φφJ
( )( )( )
SNR21 and 1 SNRfor -1
1-1
2
-1-1-12
-1SNR2-12
22
2
2
2
22
−<>>+
Ω⋅→
⋅ΩΩ⋅+
⋅Ω+ΩΩ⋅=
γγ
γ
γγ
γφφJ
SNR-limitedperformance
Coherence-limitedperformance
If SNR = 30 dB, then γ < 0.9989995 limits performance!
17 May 2004 ICASSP Tutorial II-34
Phase CRB with Scattering ( Ω, γ)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
2
2.5
3
COHERENCE, γ
sqrt
[CR
B( φ
)] (r
ad)
SNR = 30 dB
Ω = 00.05
0.25
0.5
0.75
0.9
0.95
1.0
Idealplanewave
Coherence lossγ < 1 is significantwhen saturationΩ > 0.1
17 May 2004 ICASSP Tutorial II-35
50 100 150 200 250 300 350 400 450 5000
5
10
15
20
25
30
35
40
FREQUENCY (Hz)
sqrt
[CR
B( θ
)] (d
eg)
MOSTLY SUNNY, STRONG WIND
do = 10 m100 m
500 m
1 km
2 km
5 km
10 km
CRB on AOA EstimationSNR = 30 dB for all ranges
Sensor spacing ρ = 12 in.
Increasingrange (fixed SNR)
Aperture-limitedat low frequency
Ideal plane wave modelis accurate for very shortranges ~ 10 m
Coherence-limited at larger ranges
17 May 2004 ICASSP Tutorial II-36
50 100 150 200 250 300 350 400 450 5000
2
4
6
8
10
12
14
16
18
20
FREQUENCY (Hz)
sqrt
[CR
B( θ
)] (d
eg)
MOSTLY CLOUDY, LIGHT WIND
do = 10 m 100 m500 m1 km
2 km
5 km
10 km
Cloudy and Less WindSNR = 30 dB for all ranges
Sensor spacing ρ = 12 in.
Aperture-limitedat low frequency
Atmospheric conditionshave a large impact onAOA CRBs
Plane wave model isaccurate to 100 m range
17 May 2004 ICASSP Tutorial II-37
Coherence vs. Sensor Spacing
100 101 1020.995
0.9955
0.996
0.9965
0.997
0.9975
0.998
0.9985
0.999
0.9995
1
SENSOR SPACING, ρ (in.)
CO
HER
ENC
E, γ
SOURCE FREQ. = 100 Hz, RANGE = 200 m, SNR = 30 dB
Omega = 0.80, SUNNY
Omega = 0.43, CLOUDY
MOSTLY SUNNY, LIGHT WIND MOSTLY SUNNY, MODERATE WIND MOSTLY SUNNY, STRONG WIND MOSTLY CLOUDY, LIGHT WIND MOSTLY CLOUDY, MODERATE WINDMOSTLY CLOUDY, STRONG WIND
Lightwind
Strongwind
γ = 0 for ρ ~ 1,000 in = 25 m
17 May 2004 ICASSP Tutorial II-38
CRB on AOA vs. Sensor Spacing
101 1020
5
10
15
SENSOR SPACING, ρ (in.)
sqrt
[CR
B( θ
)] (d
eg)
SOURCE FREQ. = 100 Hz, RANGE = 200 m, SNR = 30 dB
MOSTLY SUNNY, LIGHT WIND MOSTLY SUNNY, STRONG WIND MOSTLY CLOUDY, LIGHT WIND MOSTLY CLOUDY, STRONG WIND IDEAL PLANE WAVE (Ω = 0, γ = 1)
ρ = 5 inches
17 May 2004 ICASSP Tutorial II-39
Coherence vs. Sensor Spacing
100 101 102 1030.8
0.82
0.84
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
SENSOR SPACING, ρ (in.)
CO
HER
ENC
E, γ
SOURCE FREQ. = 100 Hz, RANGE = 1,000 m, SNR = 20 dB
Omega = 1.00, SUNNYOmega = 0.94, CLOUDY
MOSTLY SUNNY, LIGHT WIND MOSTLY SUNNY, MODERATE WIND MOSTLY SUNNY, STRONG WIND MOSTLY CLOUDY, LIGHT WIND MOSTLY CLOUDY, MODERATE WINDMOSTLY CLOUDY, STRONG WIND
17 May 2004 ICASSP Tutorial II-40
CRB on AOA vs. Sensor Spacing
101 102 1030
5
10
15
20
25
30
SENSOR SPACING, ρ (in.)
sqrt
[CR
B( θ
)] (d
eg)
SOURCE FREQ. = 100 Hz, RANGE = 1,000 m, SNR = 20 dB
MOSTLY SUNNY, LIGHT WIND MOSTLY SUNNY, STRONG WIND MOSTLY CLOUDY, LIGHT WIND MOSTLY CLOUDY, STRONG WIND IDEAL PLANE WAVE (Ω = 0, γ = 1)
Coherence lossesdegrade AOA perf.for ρ > 8 feet
Ideal planewave modelis optimistic(poor weather)
Plane waveis OK for good weather
(First noted in[Wilson1998],[Wilson1999])
λ/2
17 May 2004 ICASSP Tutorial II-41
CRB Achievability
50 100 150 200 250 300 350 400 450 5000
0.5
1
FREQUENCY (Hz)
SATU
RA
TIO
N, Ω
SNR = 40 dB, ρ = 3 in, RANGE = 50 m
50 100 150 200 250 300 350 400 450 5000.9997
0.9998
0.9999
1
FREQUENCY (Hz)
CO
HER
ENC
E, γ
50 100 150 200 250 300 350 400 450 5000
5
10
15
FREQUENCY (Hz)
RM
SE &
sqr
t[CR
B] O
N A
OA
, θ (d
eg)
SNR = 40 dB, ρ = 3 in, RANGE = 50 m
PD ESTIMATEML ESTIMATECRB
Coherence is high: γ > 0.999
Saturation Ω issignificant for most offrequency range
AOA estimators break away from CRB approx.when Ω > 0.1
Aperture-limited
Phase difference estimator:
=
∠−∠=
PDo
PD
PD
c
zz
φωρ
θ
φ
ˆarcsinˆ :AOA
ˆ :Phase 12
Turbulence prevents performance gain from larger aperture
Scenario:Small Sensor Spacing: ρ = 3 in., SNR = 40 dB, Range = 50 m
17 May 2004 ICASSP Tutorial II-42
AOA Estimation for Harmonic Source
20 40 60 80 100 120 140 160 180 2000
5
10
15
20
25
30
35
AO
A (d
eg)
COMBINED AOA ESTIMATES AT FREQS. 50, 100, 150 Hz
RANGE (m)
RMSE, ρ = 6 insqrt[CRB], ρ = 6 inRMSE, ρ = 3 insqrt[CRB], ρ = 3 in
Equal-strength harmonicsat 50, 100, 150 Hz
SNR = 40 dB at 20 mrange, SNR ~ 1/(range)2
(simple TL)
Sensor spacingρ = 3 in. and 6 in.
Mostly sunny,moderate wind
One snapshot
ρ = 6 in.
ρ = 3 in.
RMSE
CRB
Achievable AOA accuracy ~ 10’s of degrees for this case
17 May 2004 ICASSP Tutorial II-43
Turbulence Conditions for Three-Harmonic Example
Coherence is ~ 1,but still limits performance.
Strongscattering
17 May 2004 ICASSP Tutorial II-44
Summary of AOA Estimation• CRB analysis of AOA estimation
– Tradeoff: larger aperture vs. coherence loss– Ideal plane wave model is overly optimistic for
longer source ranges– Performance varies significantly with weather cond.– Important to consider turbulence effects
• AOA algorithms do not achieve the CRB in turbulence (Ω > 0.1) with one snapshot
• Similar results obtained for circular arrays with > 2 sensors [Sadler2004]
17 May 2004 ICASSP Tutorial II-45
Outline
• Detection of sources– Saturation, Ω– Detection performance
• Array processing – Coherence loss from
turbulence, γ– Array size: 2 sensors
Source AOA– Array of arrays:
Source localization
Triangulation/TDOA, minimize comms.
• Issues:– Comm. bandwidth– Distributed processing– Exploit long baselines?– Time sync. among arrays
• Model assumptions:– Individual arrays:
* Perfect coherence* Far-field
– Between arrays:* Partial coherence* Different power spectra* Near-field
SOURCE(x_s, y_s)
x
y
ARRAY 1
ARRAY H
(x_1, y_1)
ARRAY 2(x_2, y_2)
(x_H, y_H)
FUSIONCENTER
17 May 2004 ICASSP Tutorial II-46
FusionNode
Source
AOAAOA
AOA
TransmitAOAs
Noncoherenttriangulationof AOAs
FusionNode
Source
Transmitraw data from all sensors
Optimum,coherentprocessing
FusionNode
Source
AOA &TDOA AOA &
TDOA
AOA
TransmitAOAs & TDOAs
Triangulationof AOAs andTDOAs
Transmit raw data from one sensorto other nodes
1) Triangulate AOAs:
•Comms.: Low•Distributed processing•Coarse time sync.
2) Fully centralized
•Comms.: High•Centralized processing•Fine time sync. req’d•Near-field w.r.t. arrays
3) AOAs & TDOAs:
•Comms.: Medium•Distributed processing•Fine time sync. req’d•Alt.: Each array xmitsraw data from 1 sensor
Three Localization Schemes
17 May 2004 ICASSP Tutorial II-47
1. Triangulation of AOAs Minimal comms.2. Fully centralized Maximum comms.3. #1 + time delay estimation (TDE) Raw data from 1 sensor
−50 0 50 100 150 200 250 300 350 400 450
0
50
100
150
200
250
300
350
400
X AXIS (m)
Y A
XIS
(m
)
CRB ELLIPSES FOR COHERENCE 0, 0.5, 1.0 (JOINT PROCESSING)
TARGETARRAY •Schemes 2 & 3 have same CRB!
•Results are coherence sensitive:coherence improves CRB overAOA triangulation
•Are the CRBs achievable?
Localization Cramer-Rao Bounds [Kozick2004b]
140 160 180 200 220 240 260240
260
280
300
320
340
360
X AXIS (m)
Y A
XIS
(m
)
CRB ELLIPSES FOR COHERENCE 0, 0.5, 1.0 (BEARING + TD EST.)
AOAtriangulation
Parameters:3 arrays, 7 elements, 8 ft. diam.Narrowband (49.5 to 50.5 Hz)SNR = 16 dB at each sensor0.5 sec. observation time
17 May 2004 ICASSP Tutorial II-48
Ziv-Zakai Bound on TDEThreshold coherence to attain CRB:
•Function(SNR, % BW, TB product, coherence)•Extends [WeissWeinstein83] to TDE with
partially-coherent signals TB product
Fract BW
SNR
17 May 2004 ICASSP Tutorial II-49
Threshold Coherence Simulation
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
10−4
10−3
10−2
10−1
RMS TDE (WIDEBAND): fo = 100 Hz, ∆ f = 30 Hz
COHERENCE
DE
LAY
(se
c)
THRESHOLD COHERENCE = 0.41
SIMULATIONCRB
0.7 0.75 0.8 0.85 0.9 0.95 1
10−4
10−3
10−2
10−1
RMS TDE (NARROWBAND):, fo = 40 Hz, ∆ f = 2 Hz
COHERENCE
DE
LAY
(se
c)
THRESHOLD COHERENCE > 1.0
Breakaway from CRB is accurately predictedby threshold coherence value
17 May 2004 ICASSP Tutorial II-50
Threshold Coherence
0 10 20 30 40 50 60 70 800.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
BANDWIDTH (Hz), ∆ ω / (2 π)
TH
RE
SH
OLD
CO
HE
RE
NC
E, |
γs |
ω0 = 2 π 100 rad/sec, T = 1 sec
Gs / G
w = 0 dB
Gs / G
w = 10 dB
Gs / G
w → ∞
10−1
100
101
102
103
104
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
TIME × BANDWIDTHT
HR
ES
HO
LD C
OH
ER
EN
CE
, | γ
s |
Gs / G
w → ∞
FRAC. BW = 0.1 FRAC. BW = 0.25FRAC. BW = 0.5 FRAC. BW = 1.0
Narrowband sourcerequires perfect coherence
Doubling fractional BWtime-BW product reducedby factor of ~ 10
f0 = 50 Hz, ∆f = 5 Hz T>100 s
17 May 2004 ICASSP Tutorial II-51
TDE Experiment – Harmonic Source
7100 7200 7300 7400 7500 7600 7700 7800 7900 8000 8100
9200
9300
9400
9500
9600
9700
9800
9900
EAST (m)
NO
RT
H (
m)
GROUND VEHICLE PATH AND ARRAY LOCATIONS
1
3
4
5
VEHICLE PATH 10 SEC SEGMENTARRAY 1 ARRAY 3 ARRAY 4 ARRAY 5
0 50 100 150 200 250 3000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
FREQUENCY (Hz)
CO
HE
RE
NC
E |γ
|
MEAN SHORT−TIME SPECTRAL COHERENCE, ARRAYS 1 & 3
0 50 100 150 200 250 300 350 400 450 5000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
FREQUENCY (Hz)C
OH
ER
EN
CE
|γ|
MEAN SHORT−TIME SPECTRAL COHERENCE, ARRAY 1, SENSORS 1 & 5
−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4−1
−0.5
0
0.5
1CROSS−CORRELATION: ARRAYS 1 AND 3
LAG (SEC)
−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4−1
−0.5
0
0.5
1GENERALIZED CROSS−CORRELATION: ARRAYS 1 AND 3
LAG (SEC)−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1CROSS−CORRELATION: ARRAY1, SENSORS 1,5
LAG (SEC)
Moderate coherence,small bandwidth
TDE is not possible between arrays
TDE works within an array(sensor spacing < 8 feet)
17 May 2004 ICASSP Tutorial II-52
TDE Experiment – Wideband Source
17 May 2004 ICASSP Tutorial II-53
TDE Experiment – Wideband Source
Measured coherenceexceeds thresholdcoherence ~ 0.8 for this case
Accurate localization from TDEs
17 May 2004 ICASSP Tutorial II-54
Summary of Array of Arrays• Threshold coherence
analysis tells conditions when joint, coherent processing improves localization accuracy
• Pairwise TDE between arrays captures localization information
reduced comms.• Incoherent triangulation
of AOAs is optimum for narrowband, harmonic sources
SOURCE(x_s, y_s)
x
y
ARRAY 1
ARRAY H
(x_1, y_1)
ARRAY 2(x_2, y_2)
(x_H, y_H)
FUSIONCENTER
17 May 2004 ICASSP Tutorial II-55
Odds & EndsOther Sensing Approaches
• Infrasonics: f < 30 Hz, λ > 11 m [Bedard2000]– Over the horizon propagation via ducting from
temperature gradients– Wind noise is very high– Propagation models may be lacking
• Fuse acoustics with other low-BW sensor modalities
– Seismic has proven useful for heavy, loud vehicles and aircraft (also footsteps)
– Vector magnetic sensors are emerging
17 May 2004 ICASSP Tutorial II-56
Odds & EndsOther Processing
• Doppler estimation: [Kozick2004c]– Localize based on differential Doppler from multiple
sensors (combine with AOAs?)– Not sensitive to coherence– Simple, and exploits spectral lines in source– We have analyzed CRBs and algorithms
• Tracking of moving sources [see Biblio.]• Classification based on harmonic ampls. [see
Biblio.]– Harmonic amplitudes fluctuate– Exploit aspect angle differences of sources?
17 May 2004 ICASSP Tutorial II-57
Summary
• Source characteristics:Spectral lines, ultra-wideband, high SNR
• Propagation: dominated by turbulent scattering
– Amplitude & phase fluctuations (saturation, Ω)
– Spatial coherence loss (coherence, γ)
– Depends on freq., range, weather, sensor spacing
• Signal processing:– Coherence losses limit AOA and
TDE performanceIdeal plane wave is overly
optimistic– Implications for detection and
array aperture size– Sensor network: comms. &
distributed processing
CentralNode?
Source
Provided a detailed case-study ofa particular sensor network.