Acoustic and Seismic Array Processing in Sensor Network

Kung YaoUCLA

CTW, May 23, 2006

Outline0. Introduction1. Source localization using randomly distrib.

arrays based on TDOA-LS methods2. Source localization of near/far field

sources based on AML method3. Near field seismic source localization using

accelerometric data4. Distributed sensor node localization5. Conclusions6. Challenging Problems

0. Introduction• The purpose of a sensor network is to sense

one or more specific physical phenomena • Often it is necessary to detect, track, localize,

classify these physical sources• We consider three different approaches for

acoustic and seismic source localization• Often it is also necessary to localize the

sensing nodes/arrays relative to the sources • We also consider a distributed Gauss-Newton

iterative node localization method

1. Randomly distributed array processing based on TDOA-LS methods

Sensor 1 delay= 0

Sensor 2 delay= t12

Sensor R delay= t1R

Source

x1(t)

sensor input1

Propagationdelays

R

x2 (t)

xR(t)

+coherentlycombinedoutput y(t)

t1R

t122

sensor output

Sensor 1 delay= 0

Sensor 2 delay= t12

Sensor R delay= t1R

Source

x1(t)

sensor input1

Propagationdelays

R

x2 (t)

xR(t)

+coherentlycombinedoutput y(t)

t1R

t122

sensor output

Coherent Processing for Narrowband Beamforming

Space-Time-Frequency Wideband Beamforming

D

+

+

D

D

+y(t) = filtered array output

w10*

w11*

w20*

w1(L-1)*

D

+

+

D

D

w21*

w2(L-1)*

D

+

+

D

D

w30*

w31*

w3(L-1)*

x1(n) x2(n) x3(n)

Data from D number of sources collected by Nrandomly distributed sensors

Output of the beamformer

td,n - time-delayL - number of FIR tapsw - array weight

1*

1 0( ) ( )

N L

nl nn l

y t w x t l−

= =

= −∑∑

,1

( ) ( ) ( )D

n d d n nd

x t s t t m t=

= − +∑

Sample Auto- and Cross-Correlation Matrices

Array Weight Obtained by Dominant Eigenvector of Cross-Correlation Matrix

(For simplicity, consider N = 3)

Maximizing Beamformer Output

where w3L = [w10, w11,…,w1(L-1),…,w20,…,w2(L-1),…,w30,…,w3(L-1)]T

Time delays td, n est. from the w3L (Yao et al, IEEE JSAC, Oct. 1998)

the eigenvector of largest eigenvalue of R3Lw3L=λ3Lw3L

is

Intuitive & Formal Interpretation of the Beamformer

Intuitive interpretation

Max array output ~ coherently sum the “strongest

part” of the source

Szego asymptotic distribution of eigenvalues (1915)

S S dL

LL

max.

.limmax{ ( )} ( )= ∫ =

− →∞ω ω λ

0 5

0 5

≈ ==

λ LL

wLLH

L Lw R w( ) max { }1

S dL

LLL

L( ).

.lim

( ) ... ( )ω ω λ λ

−∫ =

→∞

+ +

0 5

0 51

for sufficiently large L

Simple Example

• Second order AR source with spectral peak at f = 0.2

• t12 = 3 ; t23 = 2 ; t13 = 5

• Array wL = φ3L (rL : -1 : (r-1)L+1), r = 1, 2, 3.

• Propagation delay information contained in the array weights wL

(r)

• Each array FIR acts as a narrowband filter centered at frequency of Smax

(3L)(r)

0 50 1000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

W eight index

Mag

. of t

hree

arr

ay w

eigh

ts

0 0 .5 10

1

2

3

4

5

6

f

Mag

. of t

rans

fer

func

tion

of a

n ar

ray

chan

nel

n |wL(1)| |wL

(2)| |wL(3)|

1 0.0062 0.0011 0.00022 0.0088 0.0020 0.00053 0.0114 0.0036 0.00114 0.0140 0.0062 0.00205 0.0165 0.0088 0.00366 0.0191 0.0114 0.00627 0.0216 0.0140 0.00888 0.0241 0.0165 0.01149 0.0266 0.0191 0.014010 0.0291 0.0216 0.016511 0.0315 0.0241 0.019112 0.0339 0.0266 0.021613 0.0363 0.0291 0.024114 0.0386 0.0315 0.026615 0.0409 0.0339 0.0291

Mag. of three arrayweights

Mag. of transfer function of any array channel vs. freq

Values of |wL(1)|, |wL

(2)| and |wL(3)|

Continuing

Source Localization from EstimatedTime Difference of Arrival (TDOA)

-20 -15 -10 -5 0 5 10 15 20-20

-15

-10

-5

0

5

10

15

20

+1 +2

+3

x-coordinate

y-co

ordi

nate

sensor #1 at (0,0)

sensor #2 at (10,0)

sensor #3 at (9,7)

constant contour of time delay t13=5

constant contour of time delay t12=3

constant contour of time delay t23=2

• Least-squares solution is then given as follows after algebraic manipulation

Aw b=

TDOA - Least-Squares

=

=

−

−−

=

2

23

22

212

1

213

212

1

13333

12222

21,,

2/

2/2/

n

t

t

t

nnnnn r

rr

b

v

vszyx

w

t

tt

tzyx

tzyxtzyx

A

We write , where

w A b= + A A A AT T+ −= ( ) 1, where the pseudoinverse

An overdetermined solution of the source location and speed of propagation can be given from the sensor data as follows

-20 -10 0 10 20 30 40 50-10

-5

0

5

10

15

X (feet)

Y (fe

et)

Fig.4(a)

0 5 10 15 200

2000

4000

6000

8000

10000

Time slot

velo

city

(ft/s

ec)

Fig.4(b)

Source Localization and Speed of PropagationResults Using Seismic Array Sensors

2. Approx. ML Estimation Method

• ML method is a well-known statistical est. tool

• We formulated an approx. ML (AML) method for wideband signal for DOA, source localization, and optimal sensor placement in the freq. domain (Chen-Hudson-Yao, IEEE Trans. SP, Aug. 2002)

• AML method generally outperforms many suboptimal techniques such as closed-form least squares and wideband MUSIC solutions

• Has relative high complexity

AML Metric Plot

Near-field case Far-field case

• Peak at source location in near-field case• Broad “lobe” along source direction in far-field

case• Sampling frequency fs = 1KHz, SNR = 20dB

− sensor locations

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Y-a

xis

(met

er)

X-axis (meter)-5 0 5 10 15

-5

0

5

10

15

Semi-Anechoic Room at Xerox Parc

-2 -1 0 1 2 3 4

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

X-axis (meter)

Y-a

xis

(met

er)

Sensor locations Actual source location Source location estimates

-2 -1 0 1 2 3 4

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

X-axis (meter)

Y-a

xis

(met

er)

Sensor locations Actual source location Source location estimates

Indoor Convex Hull Exp. Results

AML LS

• Semi-anechoic room, SNR = 12dB• Direct localization of an omni-directional loud speaker

playing the LAV (light wheeled vehicle) sound• AML RMS error of 73 cm, TOA-LS RMS error of 127cm

Outdoor Testing at Xerox -Parc

-4 -2 0 2 4 6 8 10 12 140

5

10

15

A B

C

X-axis (meter)

Y-a

xis

(met

er)

Sensor locations Source location estimatesActual traveled path

-4 -2 0 2 4 6 8 10 12 140

5

10

15

A B

C

X-axis (meter)

Y-a

xis

(met

er)

Sensor locations Source location estimatesActual traveled path

Outdoor Moving Source Exp. Results

AML LS

• Omni-directional loud speaker playing the LAV sound while moving from north to south

• Far-field situation: cross-bearing of DOAs from three subarrays

Optimum Sensor Placement via CRB Approach

−1

0

1

2

3

4

CRB of source localization in log scale

−20 −10 0 10 20 30 40

−20

−10

0

10

20

30

40

Source should be inside the convex hull of the sensors

Low CRB value

High CRB value

Sensor Network at 29 Palms

-150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150-100

-75

-50

-25

0

25

50

75

100

Node 1

Node 61

X-axis (meter)

Y-a

xis

(met

er)

Sensor locations Source location estimates

29 Palms Field Measurement• Single Armored Amphibious Vehicle (AAV) traveling at

15mph• Far-field situation: cross-bearing of DOAs from two

subarrays (square array of four microphones, 1ft spacing)

Outdoor Experimentusing iPAQ testbed

One and Two Source AML Localization

Space-Frequency Classification of Targets

• Previous discussions show that AML is able to estimate the DOAs of multiple targets

• Then the targets are spatially separated, detected, and located

• Since the AML algorithm not only estimates the DOA spatially, but also can yield the dominant spectral contents of each target

• The spectral signature of the target at a given DOA can provide information for classification

Spectra of Two Targets Used in Simulation for AML DOA Estimation

Tracked vehicle data Simple sound dataOne FFT index no. = 14 Hz

Excellent estimation of spectrum of source 1 at subarray 1

Excellent estimation of spectrum of source 2 at subarray 1

Other Use of AML Algorithm

• We are using the AML algorithm to detect, localize, and classify woodpeckers in collaboration with bio-complexity researchers

• We are using the AML metric as the LR function in the recursive formulation of particle filtering approach for real-time tracking of a human speaker in a reverberant room

Tracking Experiment

6 m

9m

2.53 mMic

speaker

Tracking experiments in a reverberant room

Experimental Results

0 2 4 6 8 10 12 141

1.5

2

2.5

3

3.5

4

4.5

5

Time (sec)

Loca

tion

(m)

Tracking results in the x−axis

PFAMLground truth

0 2 4 6 8 10 12 141

2

3

4

5

6

7

8

9

Time (sec)

Loca

tion

(m)

Tracking results in the y−axis

PFAMLGround truth

Tracking Results in x-axis Tracking Results in y-axis

Update rate: 128 ms, # of particles=200

3. Garner Valley, CA Acoustic Array Experiment

• 8 low cost Behringer XM200S microphones

• Each array consists of 4 microphones 1 meter apart in a square

• 2 acoustic arrays• The output of 8 microphones

are sent to the PresonusFirepod 8 channel 94bit/96kb firewire-based recording sys.

• The recording system synchronizes the acoustic signals and sends to a PC for AML-based DOA/loc. algorithm

Garner Valley, CA Seismic Array Experiment

• Episensor tri-axial/bi-axial accelerometer sensors

• Accelerometers have widefrequency/amplitude ranges,and wide dynamic range

• Outputs of accelerometersare fed to the low power, highresolution Quanterra Q330srecording systems

• 9 sensor (6 tri-axial and 3 bi-axial), 8 of them on theperimeter of a 100 feet square, and the last one in the center

Garner Valley Acoustic and Seismic Field Measurements/Results

• Metal hammer struck a heavy metal plate at the two separate locations

Acoustic and Seismic Sensor Map Acoustic Array Map

−50 0 50 100 150−50

0

50

100

150Hammer Strike Experiment A

X (feet)

Y (

feet

)

Seismic SensorsAcoustic ArraysMetal Plate

1 2 3

4 5 6

7 8 9

1

2

−50 0 50 100 150−50

0

50

100

150Hammer Strike Experiment B

X (feet)

Y (

feet

)

Seismic SensorsAcoustic ArraysMetal Plate

2

4

1 3

5

7 9

6

8

1

2

Acoustic Array Localization

• AML-based acoustic DOA/localization using whitening pre-processing yields metal plate at (78.4, 23.8), close to the true location of (75, 25)

• AML-based acoustic DOA/localization using whitening pre-processing yields metal plate at (23.4, 80.1), close to the true location of (25, 75)

Case A Case B

Seismic Event Detection Results• The simple eigen-decomposition procedure can be

performed on sliding time windows through the data record to find signification events of interest

• The data record with 6 significant hammer strikes was selected for analysis

• The eigenvalue plot clearly indicates the 6 peaks above 10-4 is where the 6 significant hammer strikes happened

0 5 10 15 20 25 30 35 40−0.015

−0.01

−0.005

0

0.005

0.01

0.015Original Hammer Strike Signal, Sensor 1 Z Direction

Time (sec)

Sign

al S

treng

th

0 50 100 150 200 250 300 350−11

−10

−9

−8

−7

−6

−5

−4

−3

Window Number

Log

of E

igenv

alues

Eigen Value Progression As a Function of Window Number

Eigenvalue #1Eigenvalue #2Eigenvalue #3

Single-Station Tri-Axial Seismic DOA Est. via Covariance Matrix Analysis

• Use polarization analysis developed for long-range seismic data analysis

• The largest eigenvalue of the covariance matrix corresponds to the average energy of the strongest seismic mode polarized in the direction of the corresponding eigenvector

• Same can be said for the second and the smallest eigenvalues and their corresponding eigenvectors

Single-Station Tri-Axial Seismic DOA Est. via Surface Wave Analysis

• Rayleigh wave is elliptically polarized in two mutually orthogonal directions

• Love wave is rectilinearly polarized in the direction orthogonal to the two Rayleigh directions

• The three-dimensional space can be rotated such that two dimensions only pick up the Rayleigh wave, and the one other, orthogonal dimension picks up only the Love wave

Seismic Source LocalizationCovariance Analysis Source Localization

84.8481.2381.4379.7275Hmr. B y-coordinate

13.76 0.39

31.1038.3930.8152.4325Hmr. B x-coordinate

28.5154.4931.8264.1125Hmr. A y-coordinate

74.35 1.71

83.0761.4885.4359.1575Hmr. A x-coordinate

S.D. Range

Wt. L1Unw. L1Wt. TLSUnw. TLS

True SrcLocLocation in Feet

Surface Wave Analysis Source Localization

79.6665.7277.3669.6275Hmr. B y-coordinate

3.170.37

26.9731.1427.5629.8925Hmr. B x-coordinate

26.6734.1527.5932.1925Hmr. A y-coordinate

5.991.66

80.6485.2081.2780.3175Hmr. A x-coordinate

S.D. Range

Wt. L1Unw. L1Wt. TLSUnw. TLS

True SrcLocLocation in Feet

Combined Acoustic/Seismic Localization Case A

• A simple average of the acoustic and seismic coordinates gives the fusion result

−20 0 20 40 60 80 100 120 140

−20

0

20

40

60

80

100

120

140

160

180

X (feet)

Y (

feet

)

Acoustic and Seismic Source Localization Results, Hammer Strike Case A

Seis. Snsr Loc.Acou. Snsr Loc.Metal Plate Loc.Seis. SrcLocAcou. SrcLocFusion SrcLoc

1 2 3

4 5 6

7 8 9

1

2

25.279.5Fusion

26.780.6Seismic

23.878.4Acoustic

2575True

YXLocation in Feet

Combined Acoustic/Seismic Localization Case B

• The fusion result in this case is closer to the true source than either the acoustic or the seismic result

78.725.5Fusion

77.427.6Seismic

80.123.4Acoustic

7525True

YXLocation in Feet

−20 0 20 40 60 80 100 120 140

−20

0

20

40

60

80

100

120

140

160

180

X (feet)

Y (

feet

)

Acoustic and Seismic Source Localization Results, Hammer Strike Case B

Seis. Snsr Loc.Acou. Snsr Loc.Metal Plate Loc.Seis. SrcLocAcou. SrcLocFusion SrcLoc

1 2 3

4 5 6

7 8 9

1

2

4. Sensor Node LocalizationSystem Description

• m anchor nodes (locations known) and n sensor nodes (locations to be estimated)

• Each sensor node has distance measures to all of the sensor and anchor nodes in its neighborhood

Example• 4 anchor nodes at each

corner and 15 sensor nodes in the middle

• Radio range = 0.35• Every link represents a

communication link• Distance measurement dij

available -0.5 0 0.5-0.5

0

0.5sensor nodesanchor nodes

Metric for Minimization2

,

222

,

22)( ∑∑ −−+−−=

kiikki

jiijji daxdxxF x

Centralized Method : • Gauss-Newton (non-linear least squares)• Multi-Dimensional Scaling• SDP

Require communications to a central computer

[ ]TTn

T xx1=x is the i-th sensor location estimate2Rxi ∈is the k-th anchor node location2Rak ∈

1 2ˆ argmin ( , ,..., ), and are known (estimated) range values

n

ij ik

F x x xd d

= xx

Distributed Gauss-Newton Sequential/Parallel Node Localization Methods

Estimation Results

• 10 anchor nodes at each coroner and 100 sensor nodes in the middle

• Radio range = 0.35

-0.8 -0.4 0 0.4 0.8-0.8

-0.4

0

0.4

0.8true locationestimation anchor

Some Average Iteration/ Processing Time Behaviors

• Keep the density of the sensor, the ratio of sensor/anchor and the radio range to be constant

• Each sensor stops the algorithm if

0

5

10

15

20

aver

age

num

ber

of it

erat

ion

40 80 120

160

200

netwrok size (n)

Sequential Parallel

1

10

100

1000

aver

age

proc

essi

ng ti

me

40 80 120

160

200

netwrok size (n)

Sequential Parallel

01.0≤ip

Comparison to Centralized Algorithm

0

50

100

150

200

com

m. e

nerg

y co

nsum

ptio

n

40 80 120

160

200

network size (n)

Sequential Parallel Centralized

5. Conclusions• Considered three source localization methods:

1. TDOA-LS algorithms(centralized processing)2. AML algorithm (distributed processing)3. Seismic localization: covariance method

(centralized processing) and surface wavemethod (distributed processing)

• Distributed Gauss-Newton Node LocalizationMethod (Sequential and Parallel algorithms)

6. Challenging Processing Problems in SN

• Perform distributed computation of eigenvalue/ eigenvector/singular value/singular vector without sending raw data from the sensors to a central proc.

• Theoretical/practical (i.e., low complexity) use of data fusion from different types of sensors (video/acoustic/ seismic) of different quality and sampling rate

• Theoretical (e.g., CRB)/practical issues of placement of sensors of different types

• Using random set theory method for determining number of sources and nearest neighboring nodes

• Real-time/practical (i.e., low complexity) use of particlefiltering methodology for source/sensor node tracking