Developments in Sensor Array Signal Processing

bunkietalentedAI and Robotics

Nov 24, 2013 (3 years and 8 months ago)

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Developments in Sensor
Array Signal Processing
John G McWhirter FRS FREng
Overview of Talk
Sensor array signal processing

historical perspective and overview
Recent developments and current trends

from ABF to BSS

from 2nd order statistics to HOS

convergence with artificial neural networks
Current research and future challenges

Convolutive mixtures

Semi-blind signal separation
Sensor Array Signal Processing
Techniques have recently "come of age"

Enabled by the digital processing revolution

Impressive research results
Wide range of application areas

Key to improving mobile telephone systems

Could revolutionise design of future radars

Medical diagnostic techniques (ECG, EEG)
Adaptive Null Steering
Adaptive Beamforming
Adaptive
algorithm
S
w
1
w
2
wp
w3
w4

Output
signal
Array gain
Complex weights (represent
phase and amplitude)
Output signal
Minimise output power subject
to look-direction constraint

)(cw
H
)()(tte
H
xw
Minimise

subject to
Least squares solution (Gauss normal equations)

where

)(cw
H
)(),()(

cwMnn
Least Squares Solution
wMw)()()(
1
2
ntenE
H
n
t






n
t
jiij
txtxnM
1
*
)()()(
LMS Algorithm
Minimise

where
Stochastic gradient update
Minimal computation
Can be slow to converge
)()()(tytte
H
xw
)()()()1(
*
ttettxww


})(E{
2
te
Canonical Problem and GSLC
0Ac
)()()(tytte
H
xw

wc
H
CANONICAL ADAPTIVE COMBINER
BLOCKING
MATRIX
BEAMFORMER
)(ty
)(tx
…...
….
QRD Processor Array
Direct residual extraction
Systolic array implementation
x
r11
u4
r44
r34
r33
r24
r23
r22
r14
r13
r12
u3
u2
u1
y
x4
x3
x2
x1
1
Residual


Unstabilised Beam Pattern
)()(
)()()(
2/
2/
2
q
H
q
H
q
dhE
wwZww
cww












2/
2/
)()()(



dh
H
ccZ
EknE
2
)(
Penalty Function Method
Penalty function
where
Minimise
Closed form solution
Stabilised Beam Pattern
Sonobuoy Array
Application to Sonar
(sonobuoy trials data)
Conventional (fixed) Beamformer
Adaptive Beamformer (stabilised)
Range
Range
Bearing
Bearing
Blind Signal Separation
Avoids need for array calibration

Foetal heartbeat monitor

HF communications
Independent component analysis (ICA)
Involves use of higher order statistics (HOS)
Requires signals to be non-Gaussian

Typical of man-made signals

Digital communication signals
Signal model (instantaneous)
Data matrix
Unknown mixture matrix A
Unknown signals S
Input signals are non-Gaussian
and statistically independent
Blind Signal Separation
……
st
1
()
st
2
()
st
3
()
xt
1
()
xt
2
()
xt
3
()
xt
p
()
xAsn()()()ttt=+
XASN=+
Signal model
Singular value decomposition (SVD)
Signal subspace
Principal Components Analysis (PCA)
NASX

nnsss
n
s
s
ns
VUVDU
V
V
I
D
UU
UDVX

















0
0
s
H
ss
IVV
XUDV
H
sss
1

By definition
Now define
Then
Can only conclude that
Hidden Rotation Matrix
s
QVS
s
H
ss
IVV
ss
QVV
~
s
H
H
ss
H
ss
IQVQVVV
~~
Independent Component Analysis
Higher Order Statistics
0
0
x
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
x
x
0
0
0
0
0
0
0
0
i
k
j
Fourth order cumulant tensor
Statistically independent signals
Separation tensor diagonalisation
Need for novel mathematical research
}E{
lkjiijkl
xxxxK
otherwise0
if

lkjikK
iijkl
}E{}E{}E{}E{}E{}E{
kjliljkilkji
xxxxxxxxxxxx
HF Communications Array
BLISS Trials Results
HF communications data
FSK signal 30dB stronger than SSB voice signal
BLISS algorithm - 16384 samples
TX1 Mode13454kHzSSBTX2 Mode13454kHzFSKAngularOffsetRelativelevelsSampleRateBFOFreq.Receive
F
BLISS
Voice
Digital
Original
Signal
Foetal Heartbeat Analysis
Input Data








Separated sources
Amplitude
(micro volts)
-200
-100
0
100
200
300
-5
0
5
10
15
20
25
Time (milliseconds)
Triplet 2
Application to triplets
-200
-100
0
100
200
300
-6
-4
-2
0
2
4
6
8
10
12
Time (milliseconds)
Triplet 3
14
Time (milliseconds)
-200
-100
0
100
200
300
-5
0
5
10
15
20
Triplet 1
25
Averaged foetal ECG
Triplet 1
Triplet 2
Triplet 3
Fast ICA (real data)
Find unit norm vector to maximise
Nonlinear adaptive filter (stochastic gradient)
Fixed point ( )
Iterative solution (normalise and repeat)
Deflate/project to find next weight vector
t
4
4
3})E{()kurt(wxwxw
TT
)]()()(3))()()(([)()1(
2
3
tttttttt
T
wwwxwxww


2
3
3})(E{wwxwxw
T
)(3}))((E{)1(
3
nnn
T
wxwxw
Convolutive Mixing
Effects of dispersion, multipath etc

Typical of acoustics in a room

Cocktail party effect
*
*
*
*
)(
2
ts
)(
1
ts
)(
1
tx
)(
2
tx
Channel Model
Weighted sum of delayed samples (convolution)
Express in polynomial form (z-transform)
Convolution becomes simple product
)(.........)1()()(
10
pnshnshnshnx
p

........)(.........)1()0()(
........)(.........)1()0()(
.........)(
1
1
1
10






n
n
p
p
znxzxxzx
znszsszs
zhzhhzh
)()()(zszhzx
Polynomial Matrices
Convolution is product of z-transforms
Two signals and two sensors
Polynomial matrix
Need for new mathematical algorithms
)()()(zszhzx



















)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
zs
zs
zhzh
zhzh
zx
zx
)(zH
Second Order Stage (Convolutive)Strong decorrelation
Whiten or equalise spectra
ij
T
t
iji
tvtv



1
)()()(







)(0
0)(
)/1()(
2
1
z
z
zz
T


VV
ijiji
zzvzv

)()/1()(
Paraconjugation
Paraunitary matrix
Apply a decorrelation and whitening filter (2nd order)
Hidden paraunitary matrix

IHHHHzzzz)(
~
)(
~
)(
Hidden Paraunitary Matrix

z
z
T
1
)(
~
HH
IVV)(
~
)(zz
IHVVH)(
~
)(
~
)()(zzzz
Future Directions
Combine 2nd order and higher order statistics

semi-blind algorithms
Combine PCA and ICA stages

more robust algorithms
Broadband adaptive sensor arrays

broadband subspace identification
Acknowledgements
Colleagues at QinetiQ, Malvern

Dr I J Clarke, Dr C A Speirs, Dr D T Hughes

Dr I K Proudler, Dr T J Shepherd, Mr P Baxter
QinetiQ, Winfrith, Bincleaves, Portsdown
University of Leuven

Dr L De Lathauwer
UK Ministry of Defence

Corporate Research Programme