Sensor Networks, Aeroacoustics, and Signal Processingkozick/acoustic/ic04/SadlerKozickPart2.pdfSensor Networks, Aeroacoustics, and Signal Processing Part II: Aeroacoustic Sensor Networks

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


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)


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


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?


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


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


• 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


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


+/- 350 m from Closest Point of Approach (CPA)

TIME (sec)

HighSNR


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


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


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]


Measured Aeroacoustic Data


Fluctuations due to turbulence

Measured SNR vs. Range & Frequency

Aspect dependence

SNR ~ 50 dBat CPA

Time

dB


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


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


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]


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)


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])


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


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


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


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


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]


Outline





Source localization


Coherence, γ, depends on

•Sensor separation, ρ•Source frequency, ω•Source range, do•Weather conditions:sunny/cloudy, wind speed


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


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


( )[ ] ( )

( )

+=

≤≤

<<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])


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


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


Outline





Source localization


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?


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


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!


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


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


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


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


CRB on AOA vs. Sensor Spacing

101 1020

5

10

15


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


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


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


CRB on AOA vs. Sensor Spacing

101 102 1030

5

10

15

20

25

30


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


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


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


Turbulence Conditions for Three-Harmonic Example

Coherence is ~ 1,but still limits performance.

Strongscattering


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]


Outline





Source localization


• 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


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


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


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


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


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


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)


TDE Experiment – Wideband Source


TDE Experiment – Wideband Source

Measured coherenceexceeds thresholdcoherence ~ 0.8 for this case

Accurate localization from TDEs


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


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


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?


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.

Documents

Sensor Networks, Aeroacoustics, and Signal Processingkozick/acoustic/ic04/SadlerKozickPart2.pdfSensor Networks, Aeroacoustics, and Signal Processing Part II: Aeroacoustic Sensor Networks