Communication Group Course

1
Communication Group Course Multidimensional DSP
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources

Title Acoustic Direction of Arrival and Source
Localization Estimation Methods
Overview Presented by Pejman Taslimi
MSc Department of Electrical Engineering,
Amirkabir University of Technology, Tehran, Iran,
pejman_at_ieee.org taslimi_at_aut.ac.ir Presented
to Professor Moghaddamjoo (Ali M.
Reza) Department of Electrical Engineering,
Amirkabir University of Technology, Tehran, Iran,
reza_at_uwm.edu moghaddamjoo_at_aut.ac.ir
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
2
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 2

Microphone Arrays Microphone arrays work
differently than antenna arrays - speech is a
wideband signal, - reverberation of the room (or
multipath) is high - environments and signals are
highly non-stationary - noise have the same
spectral characteristics as the desired speech
signal - the system must employ an extremely wide
dynamic range (as much as 120 dB) and it must be
very sensitive to weak tails of the channel
impulse responses The length of the modeling
filters is very long (thousands of samples are
not uncommon).
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
3
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 3

Direction of Arrival, Time Difference of Arrival
(TDOA) Source Localisation
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
4
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 4

Single-Source Free-Field Model Linear and
Equispaced Array Multiple Source Free-Field
Model
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
5
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 5

Single-Source Reverberant Model
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
6
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 6

Multiple-Source Reverberant Model
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
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DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 7

Cross Correlation Most simple and straightforward
Method Single Source Free-Field Two
Sensors Time-averaged Estimate Biased (lower
estimation variance and is asymptotically
unbiased) Unbiased
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
8
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 8

Performance affected by Signal
self-correlation Reverberation Spatial Aliasing
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
9
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 9

Generalised Cross Correlation Method DTFT Cros
s-spectrum Frequency-domain weighting
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
10
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 10

Generalised Cross Correlation Method Classical
Cross-Correlation -degenerates to
Cross-Correlation Method Fast FT let
efficient implementation Depends on source
signal statistics
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
11
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 11

Generalised Cross Correlation Method Smoothed
Coherence Transform (SCOT) Pre-whitening before
cross-spectrum For equal SNR at both
sensors Better than CC method, needs
enough SNR
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
12
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 12

Generalised Cross Correlation Method Phase
Transform (PHAT) TDOA information in phase rather
than amplitude (of the cross-spectrum) Bett
er than CC and SCOT GCC generally very short
decision delays (good tracking capability) moderat
ely noisy non-reverberant (fundamental weakness
to reverberation)
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
13
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 13

Spatial Linear Prediction Method More than two
sensors Single-source Free-field
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
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DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 14

Spatial Linear Prediction SNR
10(upper),-5(lower) Sampling frequency 16
kHz Incident angle 75.5 deg True TDOA 0.0625
ms Data frame 128 ms ULA, d 8 cm Backward
Prediction or Interpolation can also be used
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
15
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 15

Multi-channel Cross-Correlation Coefficient
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
16
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 16

Multi-channel Cross-Correlation
Coefficient normalised spatial correlation
matrix (nscm) symmetric, positive
semi-definite, all diagonal elements equals
one, squared correlation coefficient is
between zero and one if two or more signals
perfectly correlated 1 if all signals
completely uncorrelated 0 if one signal
completely uncorrelated with others, MCCC
measures correlation among N-1 remaining
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
17
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 17

MCCC for FSLP
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
18
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 18

Narrowband-MUSIC Output Covariance
Matrix for ngt2
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
19
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 19

Broadband-MUSIC Alignment signal
vector Spatial correlation matrix Source
signal covariance matrix
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
20
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 20

Broadband-MUSIC if p true TDOA if not,
depends on source signals characteristics --if
white process, diagonal matrix of covariance
full rank --in general, positive semi-definite
rank greater than one Performing eigenvalue
decomposition
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
21
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 21

Broadband-MUSIC if p true TDOA for n gt
2 Compare to narrowband --eigenvalue
decomposition for all spatial correlation
matrices (has a paramemter of p) are
computed. --peak of the cost function is In
contrast to narrowband which is infinity
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
22
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 22

Minimum Entropy Method For non-Gaussian signal,
employs Higher order statistics Entropy is
defined as Joint Entropy for multivariate
random variable
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
23
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 23

Minimum Entropy Method for Gaussian, zero mean
source in absence of noise Joint PDF of aligned
sensor output is Joint Entropy equivalent
to MCCC
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
24
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 24

Minimum Entropy Method if model signal by
Laplace Distribution univariate, zero
mean multivariate, zero mean modified
Bessel function of third kind Joint Entropy
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
25
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 25

Minimum Entropy Method if all processes are
ergodic ensemble average replaced by time
average The following estimators are
proposed In general, ME algorithm performs
comparably to or better than the MCCC
algorithm. ME algorithm is computationally
intensive The idea of using entropy expands our
knowledge in pursuit of new TDOA estimation
algorithms
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
26
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 26

Adaptive Eigenvalue Decomposition
Algorithm Single-source, two sensors Reverberant
Model First identify two impulse response (from
source to sensor) Then measure TDOA by detecting
direct path In absence of additive
noise Covariance matrix of two sensors
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
27
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 27

Adaptive Eigenvalue Decomposition Algorithm w
vector is in null space of covariance
matrix If -g1 and g2 polynomials are co-prime
share no common zero -source autocorrelation is
full ranked (SIMO fully excited) Then w is
blindly identifiable In presence of
noise sensor covariance matrix is positive
semi-definite
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
28
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 28

Adaptive Eigenvalue Decomposition
Algorithm Misjudgement in the case
of resonated multipath will be discussed!
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
29
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 29

Adaptive Blind Multichannel Identification Based
Methods The generalisation of blind SIMO
identification from two channels to multiple (gt
2) channels is not straightforward The
model filters are normalized in order to avoid a
trivial solution whose elements are all
zeros. Based on the error signal defined here, a
cost function at time k 1 is given by
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
30
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 30

Adaptive Blind Multichannel Identification Based
Methods Multichannel LMS updates the estimate of
the channel IR
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
31
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 31

Adaptive Blind Multichannel Identification Based
Methods If model filters are always normalised
after each update, MCLMS is -Identify Q
strongest elements (in impulse response) -Choose
the one with smallest delay
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
32
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 32

TDOA Estimation of Multiple Sources -number of
source determination -estimating the TDOA due to
each source For CC Method, in case of two
sources, CCF is All signals mutually
independent and uncorrelated noise CCF becomes
sum of two correlation functions Two large peak
at each TDOA
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
33
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 33

TDOA Estimation of Multiple Sources Incident
angles (deg) 75.5, 41.4 Plot of CCF using
PHAT algorithm
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
34
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 34

TDOA Estimation of Multiple Sources Incident
angles (deg) 75.5, 41.4 Plot of MCCC
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
35
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 35

TDOA Estimation of Multiple Sources For
narrowband-MUSIC Covariance Matrix
is Narrowband-MUSIC not useful for
non-stationary
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
36
DoA Estimation Methods

• Introduction
• Problem / Model
• Cross-Correlation
• GCC
• Prediction
• MCCC
• Eigenvector
• Entropy
• Adaptive ED
• Adaptive Multichannel
• Multiple Sources
• Page 36

Thank you for your attention
Pejman Taslimi Spring 2009 Course Presentation
Amirkabir Univ
37
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