1
ECE 194C Acoustic Target Tracking in Sensor
Networks
www.ece.ucsb.edu/Faculty/Iltis/ece194c
• Methods for acoustic target tracking.
– Near Field
• Signal-strength ratios.
• Cross-correlation with broadcast acoustic signal
• Sum cross-correlations (no prior signal knowledge)
– Far-field
• Maximum-likelihood (single source)
• MUSIC (multiple sources)
• Alternating maximization (multiple sources.)
2
Cell-Based LocalizationRef: D. Li, K. Wong, Y. Hu and A. Sayeed “Detection, classification…” IEEE Sig.
Proc. Mag. 2002
3
Localization of Acoustic Targets
Time-of-arrival (line-of-bearing) obtained via beamforming in direction of
strongest acoustic signature.
Figure, Ref: Wang and Chandrakasan, IEEE Sig. Proc. Mag. July 2002.
4
Woodpecker Localization
Ref: H. Wang et. al. “Acoustic Sensor Networks for Woodpecker Localization,” SPIE
Conference Proc. 2005, also “Platform for collaborative Acoustic Signal Processing.”
5
Near-Field vs. Far Field
Plane-wave
Approximation.
Wavefront
curvature
6
Near-Field Propagation Model
Source
α|||| 1
1xx −
=s
Tsr
α|||| 2
2xx −
=s
Tsr
22 )()(|||| isisis yyxx −+−=− xx
222 ),( x=yx
x
y
111 ),( x=yx
),( sss yx=x
7
Acoustic Tracking using Energy Ratios
Problem: Source power ST is unknown
Solution: Use received energy ratios at different sensors
(Ref: Li, Wong, Hu Sayeed IEEE Sig. Proc. Magazine 2002)
α
α
ααρ
||||
||||
||||/
||||,
is
js
js
T
is
T
j
iji
ss
r
r
xx
xx
xxxx
−
−=
−−==
22
,
2
,
||||||||
||||||||
isjijs
isjijs
xxxx
xxxx
−=−⇒
−=−
α
αα
ρ
ρ
8
Energy Ratio – Target Localization
For each pair of sensors, candidate target position lies on a circle
[ ]
−
+−+−
−
−+−=
−
−=
−
−=
=−+−
⇒
−+−=−+−
−=−
ρ
ρ
ρ
ρρ
ρ
ρ
ρ
ρ
ρ
ρ
αα
α
α
1
)(
)1(
)()(
)1(
)(,
)1(
)(
)()(
)()()()(
||||||||
2222
2
22
2
22
2
,
22
222
,
22
22
,
2
iijjijij
ij
iijj
c
iijj
c
jicscs
isisjijsjs
isjijs
yxyxyyxxr
yyy
xxx
ryyxx
yyxxyyxx
xxxx
9
Example – 3 Sensors
Form circles 1,2 1,3 2,3
0 100 200 300 400 500 600 700 800 900 10000
100
200
300
400
500
600
700
800
900
1000
x-pos (meters)
y-p
os (
mete
rs)
x2
x1
x3
||x1 - x||2 = ρ1,2
||x2 - x||2
10
Least-Squares Solution
Model for measured ratios with additive noise
ji
is
js
ji n ,,||||
||||+
−
−=
xx
xxρ
Nonlinear least-squares solution (exhaustive search.)
2
1 1
,||||
||||minarg ∑∑
= +=
−
−−=
s sN
i
N
ij i
j
jisxx
xx
xx ρ
1=α
11
Example – 4 Sensors/Least-Square
Solution
0 100 200 300 400 500 600 700 800 900 10000
100
200
300
400
500
600
700
800
900
1000
x-pos (meters)
y-p
os (
mete
rs)
12
Coherent Correlation
Example acoustic signature (truck)
13
Autocorrelation
∑−
=
−=1
0
)()()(N
n
knxnxkρ
14
Sensor Network Coherent CorrelationRef: Q. Wang, W. Chen, R. Zheng, K. Lee and L. Sha “Acoustic target tracking
using tiny wireless sensor devices,” ISPN 2003
Use Reference Beacon Synchronization (RBS) to map sensor clocks to global time.
Clusterhead transmits beacon to sensors, sensors reply with their individual clock
readings. Clusterhead computes correction factor.
Clusterhead
Beacon
Beacon
Bea
con
Clock 2
Clock 1
Clo
ck 3
15
Coherent CorrelationAll sensors record circular buffer of sound.
Clusterhead determines when a signal-of-interest is present.
Clusterhead transmits its received waveform to sensors.
Sensors cross-correlate their recorded sound with broadcast packet.
16
Coherent Correlation
[ ]
1
1
0
1
1
0
11
1
0
11
)()(
)()()(
)()()(
vknxdnx
knxnndnx
knxnrk
N
n
N
n
N
n
+−−
=−+−
−=
∑
∑
∑
−
=
−
=
−
=
ρ
)()()(
)()()(
2
1
0
2
1
0
22
nvknxdnx
knxnrk
N
n
N
n
+−−
−=
∑
∑−
=
−
=
ρ
d1
d2
sfd /11 ≈τDelay estimate in sec.
17
Cross-Correlation Time-of-Arrival
Estimates
∑−
=
−=1
0
)()(max
argˆN
n
i nxnr ττ
τ
18
TriangulationSensors transmit arrival time estimates to clusterhead.
Clusterhead uses range equations to solve for target position and start time.
Range equations – c = speed of sound approx. 331 m/s.
0
2
3
2
33
0
2
2
2
22
0
2
1
2
11
/)()(
/)()(
/)()(
tcyyxx
tcyyxx
tcyyxx
ss
ss
ss
+−+−=
+−+−=
+−+−=
τ
τ
τ
Time t0 of source transmission is unknown, but we have three equations, three
unknowns (x,y,t).
19
Least-Squares Triangulation
( )∑=
−−+−−=
+=
+−+−=
sN
i
isisi
ss
ss
ii
isisi
tcyyxxtyx
tyx
v
tcyyxx
1
2
0
22
0
0
1
0
22
/)()(ˆ,,
minarg)ˆ,ˆ,ˆ(
ˆ
/)()(
τ
ττ
τ
Assume time-of-arrival measurement errors are i.i.d. Gaussian.
Optimal solution for position/transmission time is nonlinear least-squares
Solutions via modified grid search
20
Coherent Tracking Scenario
21
Tracking a Moving Acoustic Source
22
Noncoherent Acoustic Localization
Correlation-based methods requires knowledge of acoustic waveform.
Alternative approach based on cross-correlation between sensors –
independent of waveform structure. Ref. Chen, Hudson and Yao
“Maximum-likelihood source localization and unknown sensor location
estimation…” IEEE Trans. Sig. Proc. 2002.
Consider cross-correlation between two sensors:
)(nxp
)(nxq
pτ
qτqppq
q
N
n
p
N
n
qppq
c
nsns
nxnxc
τττ
τττ
ττ
−=
−−−=
−=
∑
∑−
=
−
=
)(maxarg
)()(
)()()(
1
0
1
0
23
Sum Cross-CorrelationConsider delay-difference – transmission time t0 cancels.
( )cc
tctc
c
nsnsnxnxc
qspsspq
qspsqp
qppqpq
pqq
N
n
p
N
n
qppqpq
/||||/||||)(
/||||/||||
)(maxarg
)()()()()(
00
1
0
1
0
xxxxx
xxxx
−−−==
+−−+−=−
−=
−−−=−= ∑∑−
=
−
=
τ
ττ
τττ
τττττ
Localize by maximizing sum cross-correlation – Do not need to know s(n)
or start time t0!
∑∑= =
=s sN
p
N
q
spqpqs cJ1 1
))(()( xx τ
24
FFT Implementation of Sum Cross-
Correlation
Nki
qpqq
N
n
Nkni
pp
N
p
N
q
N
n
pqqp
N
p
N
q
spqpqs
pq
s s
s s
ekXnx
enxkX
nxnx
cJ
/2
1
0
/2
1 1
1
0
1 1
)()(
)()(
)()(
))(()(
τπ
π
τ
τ
τ
−
−
=
−
= =
−
=
= =
⇔−
=
−=
=
∑
∑∑∑
∑∑ xx
Recall time-shift
corresponds to linear
phase shift in FFT
)(τpqc
pqττ =
25
FFT Implementation (Cont’d.)
( )
∑
∑∑∑
∑∑∑ ∑
∑∑∑
−
=
=
−−
= =
= =
−
=
−
=
−
= =
−
=
=
=
=
−=
1
0
2
)|,(|
1
*/21
0
),(
1
/2
1 1
1
0
1
0
/2/2
1 1
1
0
|),(|1
)()(1
)(1
)(
)()()(
2
N
k
s
kB
N
p
p
NkiN
k
kB
N
q
q
Nki
N
p
N
q
N
n
N
k
NkniNki
qp
N
p
N
q
N
n
pqqps
kBN
kXekXeN
eekXN
nx
nxnxJ
s
s
p
s
s
q
s s
pq
s s
x
x
xx
444 3444 2144 344 21
τπτπ
πτπ
τ
26
Beamformer Interpretation
)(nxp
n
21
0
2
222
1
)(2
2
1
)(22
2
|)(||)(|)(
|)(||)(|
|)(||),(|
)()(
kSckSNJ
kSNekSe
kXekB
ekSkX
N
k
ss
s
kiN
p
ki
p
N
p
ki
s
ki
p
p
s
sp
s
sp
p
==
==
=
=
∑
∑
∑
−
=
−
=
=
−
x
x
x
x
τπτπ
τπ
τπ
Nki
p
pp
pekSkX
nsnx
/2)()(
)()(
τπ
τ
−=
−=
pτ
27
Example of FFT-Based Noncoherent
Localization
28
Beamformer Magnitude
450500
550600
650700
200
300
400
5000
2
4
6
8
x 108
x-pos (meters)y-pos (meters)
J(x
s)
xs = (588,396)
)()/()()()(
|)(|)(
22
1
0
2
1
)(2
samplescfyyxx
kXeJ
spspssp
N
k
p
N
p
ki
s
s
sp
−+−=
=∑ ∑−
= =
x
xx
τ
τπ
29
Far-Field Direction-of-ArrivalIn the Wang and Chandrakasan scenario (IEEE Sig. Proc. Mag. 2002) isolated clusters of
sensors operate in the far field.
Use lines-of-bearing (direction-of-arrival) to triangulate)
Simplifies communication – just transmit LOBs to a central processor for triangulation.
30
Far-Field Uniform Linear Array Model
cd /sinθτ =
cd /sin2 θτ =
−−
−
−
=
)/sin)1((
)/sin2(
)/sin(
)(
)(
cdNns
cdns
cdns
ns
n
θ
θ
θ
M
x
)/sin)1(()( cdpnsnxp θ−−=
d
d
θ
31
ULA Signals – LOB = 0
32
ULA Signals – LOB = 45 deg
cd /)4/sin(π
cd /)4/sin(3 π
33
Cross-Correlation for LOB Estimation
)(max
argˆ
))(()(
/sin)()(max
arg
)/sin)1(()/sin)1((
)()()(
1 1
1
0
1
0
θθ
θ
θτθ
θττ
τθθ
ττ
J
cJ
cdqpc
cdqnscdpns
nxnxc
s sN
p
N
q
pqpq
pqpq
pq
pq
N
n
N
n
pqqppqpq
=
=
−=
−−−−−=
−=
∑∑
∑
∑
= =
−
=
−
=
34
FFT-Based BeamformingUse analysis for noncoherent near-field case
∑∑∑−
= =
−
=
−
==
−−==
1
0
2
1
)(21
1
2
)(2
|)(||),(|)(
)/)sin()1(2exp()()()(
N
k
p
N
p
kiN
k
ki
p
kXekBJ
cdpkikSekSkX
s
p
p
θτπ
θτπ
θθ
θπ
Clusterhead computes line-of-bearing and FFT (Ref. Wang and Chandrakasan)
35
ULA 2 Sensor Scenario
36
Beamformer Outputs
)()/()sin()1()(
|)(||),(|)(
,
1
0
2
,
1
)(21
1
2 ,
samplescfdp
kXekBJ
spi
N
k
pi
N
p
kiN
k
i
s
pi
θθτ
θθθτπ
−=
== ∑∑∑−
= =
−
=
37
Far-Field Multiple Source Localization
(RF)
cd /sinθτ =
cd /sin2 θτ =
)(
))/sin)1((2exp(
))/sin(2exp(
)2exp(
)( t
cdMtfiA
cdtfiA
tfiA
t
c
c
c
vz +
−−
−=
θπ
θπ
π
Response of an antenna array to single RF source, freq. fc.
38
Maximum-Likelihood Solution for RF
Localization
)()()(
))sin)1(exp(
))sinexp()( kk
MiA
iA
A
k vavz +=+
−
= θ
θπ
θπ
M
Discrete-time model after downconversion
2||)()(||min
argˆ θθ
θ az −= kML
Gaussian noise – ML solution (exhaustive search.)
39
Multiple Source Localization
∑∑==
+=+
−
=N
n
nn
N
n
nn
nn
n
kk
MiA
iA
A
k11
)()()(
))sin)1(exp(
))sinexp()( vavz θ
θπ
θπ
M
Array response to N sources
2
121
||)()(||,...,
minargˆ ∑
=
−=N
n
n
N
ML k θθθθ
θ az
“Curse of dimensionality” Complexity is order QN for Q quantization
of angle.
40
ML Solution – 2 Sources
01
23
4
0
1
2
3
4-3
-2.5
-2
-1.5
-1
-0.5
0
x 104
θθ
log
p(z
k | θ
)
8/3,4/ ππθ =
41
Solutions for Multiple Source
Localization
Maximum-likelihood
Exponential complexity in number of sources QN
Alternating Maximization
Requires evaluation of projection matrices, multiple
iterations.
MUSIC (Multiple Source Identification and Classification)
Poor performance at low SNR.
Requires precise array calibration.
42
MUSIC Algorithm
IaazzR2
11
)()()()(1ˆ
v
N
n
H
nnn
k
l
H
z Pllk
σθθ +≈= ∑∑==
][][
.....2
121
H
N
H
sNsz
vMNN
UUUUR Λ=
==>>> + σλλλλλ
)()(
1)(
θθθ
aUUaH
NN
HJ =
NnJn ,...2,1),(maxarg == θθ θ
Compute sample correlation matrix
Perform the SVD to obtain
Compute the MUSIC spectrum
MUSIC direction-of-arrival estimates are
43
MUSIC Algorithm Solution
0 0.5 1 1.5 2 2.5 3 3.50
100
200
300
400
500
600
θ
Mu
sic
Sp
ectr
um
Angles =
σ2 = .1
σ2 = 1
σ2 = 10.
σ2 = 50.
θ = π/4, 3π/8