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Sensor Networks, Aeroacoustics, and Signal Processing Part II: Aeroacoustic Sensor Networks Brian M. Sadler Richard J. Kozick 17 May 2004. Central Node?. Heterogeneous Network of Acoustic Sensors. One mic. Sensor array. Source. 10’s to 100’s of m range. Issues:

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Heterogeneous network of acoustic sensors
Sensor Networks, Aeroacoustics,and Signal ProcessingPart II: Aeroacoustic Sensor NetworksBrian M. SadlerRichard J. Kozick17 May 2004

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Heterogeneous network of acoustic sensors



Heterogeneous Network of Acoustic Sensors

One mic.



10’s to 100’s of mrange

  • Issues:

  • Centralized versus distributed processing

  • Minimize comms., energy

  • Triangulation, TDOA?

  • Effects of acoustic prop.

  • (Node localization, sensor layout & density, Classification, tracking)

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Acoustic source propagation


Acoustic Source & Propagation

Signalat sensor



Turbulence scatters wavefronts

  • Source:

  • Loud

  • Spectral lines

  • One sensor:

  • Detection

  • Doppler estimation

  • Harmonic signature

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More sophisticated node sensor array


More Sophisticated Node:Sensor Array

1 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 deployable

    • Performance? Wavelength ~ 1 to 10 m

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Why acoustics
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

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Brief history of acoustics in military namorato2000
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

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Remainder of tutorial
Remainder of Tutorial

  • A little more background:

    • Source characteristics

    • Sound propagation through turbulent atmosphere

  • Detection of sources (Saturation, W)

  • Array processing

    • Coherence loss from turbulence (Coherence, g)

    • Array size: 2 sensors  source AOA

    • Array of arrays  source localizationDistributed processing? Data to transmit?Triangulation/TDOA Minimize comms.


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Source characteristics
Source Characteristics

  • Ground vehicles (tanks, trucks), aircraft (rotary, jet), commercial vehicles, elephant herds LOUD

  • 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

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Heterogeneous network of acoustic sensors



TIME (sec)

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

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Heterogeneous network of acoustic sensors


Harmonic lines

Doppler shift:

0.5 Hz @ 14.5 Hz

 3 Hz @ 87 Hz


+/- 85 m from CPA

CPA = 5 m

15 km/hr

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Overview of propagation issues
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: W

    • Spatial coherence loss (>1 sensor): g

  • Transmission loss: Attenuation by spherical spreading and other factors

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Transmission loss



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





+/- 125 m from CPA

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Measured snr vs range frequency
Measured SNR vs. Range & Frequency



Aspect dependence

SNR ~ 50 dB

at CPA

Fluctuations due to


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Sinusoidal signal emitted by moving source:

  • Detection of sources

    • Saturation, W

    • Detection performance

  • Array processing

    • Coherence loss from turbulence, g

    • Array size: 2 sensors  Source AOA

    • Array of arrays: Source localizationTriangulation/TDOA, minimize comms.

  • Propagation delay, t

  • Additive noise

  • Transmission loss

  • Turbulent scattering

Signal at the sensor:

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Sensor signal no 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

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Sensor signal with scattering
Sensor Signal: With Scattering

  • A fraction, W, of the signal energy is scattered from a pure sinusoid into a zero-mean, narrowband, Gaussian random process, :

  • Saturation parameter, W 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:

[Norris2001, Wilson2002a]

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Heterogeneous network of acoustic sensors

Weak Scattering: W ~ 0

Strong Scattering: W ~ 1

(1- W)S

Power Spectral

Density (PSD)


Area= WS


(1- W)S










  • Study detection of source, w/ respect to

    • Saturation, W (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 (W > 0) causes signal energy fluctuations

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Probability distributions
Probability Distributions

  • Complex amplitude has complex Gaussian PDF with non-zero mean:

  • Energy has non-central c-squared PDF with 2 d.o.f.

  • has Rice PDF

(Experimental validation in [Daigle1983, Bass1991, Norris2001])

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Saturation vs frequency range
Saturation vs. Frequency & Range

  • Saturation depends on [Ostashev2000]:

    • Weather conditions (sunny/cloudy), but varies little with wind speed

    • Source frequency w and range do

Theoretical forms

Constants from numerical evaluation of particular conditions

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Heterogeneous network of acoustic sensors

Turbulence effects are small only for very short range and low frequency

Saturation variesover entire range[0, 1] for typicalrange & freq.values

Fully scattered

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Detection performance
Detection Performance

PD = probability of detectionPFA = probability of false alarm



Scattering beginsto limit performance

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Detection performance with range
Detection Performance with Range

Lower frequenciesdetected at larger


SNR = 50 dB at 10 m rangeSNR ~ 1/(range)2

1 km

200 Hz

  • Saturation increases with

  • Range

  • Frequency

  • Temperature (sunny)

40 Hz

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Detection extensions
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 W

    • 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]

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  • Detection of sources

    • Saturation, W

    • Detection performance

  • Array processing

    • Coherence loss from turbulence, g

    • Array size: 2 sensors  Source AOA

    • Array of arrays: Source localizationTriangulation/TDOA, minimize comms.

  • Coherence, g, depends on

  • Sensor separation, r

  • Source frequency, w

  • Source range, do

  • Weather conditions: sunny/cloudy, wind speed

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Signal model for two sensors

q = AOA

  • = sensor spacing < l/2

Signal Model forTwo Sensors

Turbulence effects

Perfect plane wave:W = 0 or 1g = 1

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Model for coherence g


do = range

  • = sensor spacing

Model for Coherence, g

  • Assume AOA q = 0, freq. in [30, 500] Hz

  • Recall saturation model:

  • Coherence model [Ostashev2000]:

g 0 with freq., sensorspacing, and range


Velocityfluctuations (wind)

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Heterogeneous network of acoustic sensors

Velocityfluctuations (wind)


Depends on wind leveland sunny/cloudy

(From [Kozick2004a], based on[Ostashev2000, Wilson2000])

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Assumptions for model validity kozick2004a
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, r, resides in the inertial subrange of the turbulence:

    smallest turbulent eddies << r << largest turbulent eddies = Leff

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Heterogeneous network of acoustic sensors

Coherence, g, versus frequencyand range forsensor spacingr = 12 inches

  • > 0.99 for range < 100 m.Is this “good”?

Curves shiftup w/ less wind,down w/ more wind

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SenTech HE01 acoustic sensor [Prado2002]


  • Freq. in [30, 250] Hz  l in [1.3, 11] m

  • Angle of arrival (AOA) accuracy w.r.t.

    • Array aperture size

    • Turbulence (W, g)

  • Small aperture:

    • Easier to deploy

    • More covert

    • Better coherence

    • How small can we go?

  • Detection of sources

    • Saturation, W

    • Detection performance

  • Array processing

    • Coherence loss from turbulence, g

    • Array size: 2 sensors  Source AOA

    • Array of arrays: Source localizationTriangulation/TDOA, minimize comms.

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Impact on aoa estimation
Impact on AOA Estimation

  • How does the turbulence (W, g) affect AOA estimation accuracy? [Sadler2004]

    • Cramer-Rao lower bound (CRB), simulated RMSE

    • Achievable accuracy with small arrays?

Larger sensorspacing, r:



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Special cases of crb
Special Cases of CRB

  • No scattering (ideal plane wave model):

  • High SNR, with scattering:



If SNR = 30 dB, then g < 0.9989995 limits performance!

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Phase crb with scattering w g
Phase CRB with Scattering ( W, g)

Coherence loss

g < 1 is significantwhen saturationW > 0.1


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Crb on aoa estimation
CRB on AOA Estimation

SNR = 30 dB

for all ranges

Sensor spacing

r = 12 in.

Coherence-limited at larger ranges

Increasingrange (fixed SNR)

Aperture-limitedat low frequency

Ideal plane wave modelis accurate for very shortranges ~ 10 m

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Cloudy and less wind
Cloudy and Less Wind

SNR = 30 dB

for all ranges

Sensor spacing

r = 12 in.

Atmospheric conditionshave a large impact onAOA CRBs

Aperture-limitedat low frequency

Plane wave model isaccurate to 100 m range

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Coherence vs sensor spacing
Coherence vs. Sensor Spacing



g = 0 for r ~ 1,000 in = 25 m

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Crb on aoa vs sensor spacing
CRB on AOA vs. Sensor Spacing

r = 5 inches

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Crb on aoa vs sensor spacing1
CRB on AOA vs. Sensor Spacing

Ideal planewave modelis optimistic

(poor weather)

Coherence lossesdegrade AOA perf.for r > 8 feet

(First noted in[Wilson1998],



Plane waveis OK for good weather

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Crb achievability
CRB Achievability

Phase difference estimator:

Scenario:Small Sensor Spacing: r = 3 in., SNR = 40 dB, Range = 50 m

AOA estimators break away from CRB approx.when W > 0.1

Saturation W issignificant for most offrequency range

Turbulence prevents performance gain from larger aperture

Coherence is high: g > 0.999


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Aoa estimation for harmonic source
AOA Estimation for Harmonic Source

Equal-strength harmonicsat 50, 100, 150 Hz

SNR = 40 dB at 20 mrange, SNR ~ 1/(range)2

(simple TL)

Sensor spacingr = 3 in. and 6 in.

Mostly sunny,moderate wind

One snapshot

r = 3 in.


r = 6 in.


Achievable AOA accuracy ~ 10’s of degrees for this case

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Turbulence conditions for three harmonic example
Turbulence Conditions for Three-Harmonic Example


Coherence is ~ 1,but still limits performance.

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Summary of aoa estimation
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 (W > 0.1) with one snapshot

  • Similar results obtained for circular arrays with > 2 sensors [Sadler2004]

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  • 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

  • Detection of sources

    • Saturation, W

    • Detection performance

  • Array processing

    • Coherence loss from turbulence, g

    • Array size: 2 sensors  Source AOA

    • Array of arrays: Source localizationTriangulation/TDOA, minimize comms.

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Three localization schemes









Three Localization Schemes





Transmit raw data from one sensorto other nodes





Transmitraw data from all sensors

TransmitAOAs & TDOAs

Noncoherenttriangulationof AOAs


Triangulationof AOAs andTDOAs

  • 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 xmits raw data from 1 sensor

  • 1) Triangulate AOAs:

  • Comms.: Low

  • Distributed processing

  • Coarse time sync.

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Heterogeneous network of acoustic sensors

Localization Cramer-Rao Bounds [Kozick2004b]

  • Triangulation of AOAs Minimal comms.

  • Fully centralized Maximum comms.

  • #1 + time delay estimation (TDE) Raw data from 1 sensor

  • Schemes 2 & 3 have same CRB!

  • Results are coherence sensitive: coherence improves CRB over AOA triangulation

  • Are the CRBs achievable?



3 arrays, 7 elements, 8 ft. diam.Narrowband (49.5 to 50.5 Hz)SNR = 16 dB at each sensor0.5 sec. observation time

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Heterogeneous network of acoustic sensors

TB product

Fract BW


Ziv-Zakai Bound on TDE

  • Threshold coherence to attain CRB:

  • Function(SNR, % BW, TB product, coherence)

  • Extends [WeissWeinstein83] to TDE with partially-coherent signals

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Heterogeneous network of acoustic sensors

Threshold Coherence Simulation

Breakaway from CRB is accurately predictedby threshold coherence value

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Heterogeneous network of acoustic sensors

Threshold Coherence

Doubling fractional BW time-BW product reduced by factor of ~ 10

f0 = 50 Hz, Df = 5 Hz  T>100 s

Narrowband sourcerequires perfect coherence

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Heterogeneous network of acoustic sensors

TDE Experiment – Harmonic Source

Moderate coherence,small bandwidth

TDE works within an array(sensor spacing < 8 feet)

TDE is not possible between arrays

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Heterogeneous network of acoustic sensors

TDE Experiment – Wideband Source

Measured coherenceexceeds thresholdcoherence ~ 0.8 for this case Accurate localization from TDEs

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Summary of array of arrays
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

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Odds ends other sensing approaches
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

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Odds ends other processing
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?

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  • Source characteristics:Spectral lines, ultra-wideband, high SNR

  • Propagation: dominated by turbulent scattering

    • Amplitude & phase fluctuations (saturation, W)

    • Spatial coherence loss (coherence, g)

    • Depends on freq., range, weather, sensor spacing

  • Signal processing:

    • Coherence losses limit AOA and TDE performance Ideal plane wave is overly optimistic

    • Implications for detection and array aperture size

    • Sensor network: comms. & distributed processing

Provided a detailed case-study ofa particular sensor network.

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Heterogeneous network of acoustic sensors

Questions?Thanks for attending!

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