Communication Group CourseMultidimensional DSP
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Title:
AcousticDirection of Arrival and Source Localization
Estimation Methods Overview
Presented by:
Pejman Taslimi MScDepartment of Electrical Engineering, Amirkabir University of Technology,
Tehran, Iran, [email protected]; [email protected]
Presented to:
Professor Moghaddamjoo (Ali M. Reza)
Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran, [email protected]; [email protected]
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
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 responsesThe length of the modeling filters is very long (thousands of samples are not uncommon).
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 2
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Direction of Arrival,Time Difference of Arrival (TDOA)
Source Localisation
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 3
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Single-SourceFree-Field Model
Linear and Equispaced Array
Multiple SourceFree-Field Model
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 4
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Single-SourceReverberant Model
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 5
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Multiple-SourceReverberant Model
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 6
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Cross CorrelationMost simple and straightforward Method
Single SourceFree-FieldTwo Sensors
Time-averaged EstimateBiased (lower estimation variance and is asymptotically unbiased)Unbiased
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 7
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Performance affected by:Signal self-correlationReverberation
Spatial Aliasing
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 8
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Generalised Cross Correlation Method
DTFT
Cross-spectrum
Frequency-domain weighting
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 9
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Generalised Cross Correlation Method
Classical Cross-Correlation-degenerates to Cross-Correlation Method
Fast FT let efficient implementation
Depends on source signal statistics
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 10
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
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
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 11
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Generalised Cross Correlation Method
Phase Transform (PHAT)TDOA information in phase rather than amplitude (of the cross-spectrum)
Better than CC and SCOT
GCC generally:very short decision delays (good tracking capability)moderately noisynon-reverberant (fundamental weakness to reverberation)
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 12
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Spatial Linear Prediction Method
More than two sensorsSingle-source Free-field
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 13
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Spatial Linear Prediction
SNR = {10(upper),-5(lower)}Sampling frequency = 16 kHzIncident angle = 75.5 degTrue TDOA = 0.0625 ms
Data frame = 128 msULA, d = 8 cm
Backward Predictionor Interpolationcan also be used
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 14
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Multi-channel Cross-Correlation Coefficient
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 15
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
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 oneif two or more signals perfectly correlated = 1if all signals completely uncorrelated = 0
if one signal completely uncorrelated with others,MCCC measures correlation among N-1 remaining
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 16
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
MCCC
for FSLP
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 17
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Narrowband-MUSIC
Output Covariance Matrix
for n>2
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 18
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Broadband-MUSIC
Alignment signal vector
Spatial correlation matrix
Source signal covariance matrix
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 19
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
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
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 20
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Broadband-MUSIC
if p = true TDOA for n > 2
Compare to narrowband:--eigenvalue decomposition for all spatial correlation matrices (has a paramemter of p) are computed.
--peak of the cost function isIn contrast to narrowband which is infinity
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 21
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Minimum Entropy Method
For non-Gaussian signal, employs Higher order statistics
Entropy is defined as
Joint Entropy for multivariate random variable
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 22
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Minimum Entropy Method
for Gaussian, zero mean sourcein absence of noiseJoint PDF of aligned sensor output is
Joint Entropy
equivalent to MCCC
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 23
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Minimum Entropy Method
if model signal by Laplace Distributionunivariate, zero mean
multivariate, zero mean
modified Bessel function of third kind
Joint Entropy
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 24
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Minimum Entropy Method
if all processes are ergodic:ensemble average replaced by time averageThe 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
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 25
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Adaptive Eigenvalue Decomposition Algorithm
Single-source, two sensorsReverberant 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
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 26
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Adaptive Eigenvalue Decomposition Algorithm
w vector is in null space of covariance matrixIf:-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
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 27
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Adaptive Eigenvalue Decomposition Algorithm
Misjudgement in the case of resonated multipathwill be discussed!
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 28
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Adaptive Blind Multichannel Identification Based Methods
The generalisation of blind SIMO identification from two channels to multiple (> 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
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 29
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Adaptive Blind Multichannel Identification Based Methods
Multichannel LMS updates the estimate of the channel IR
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 30
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
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
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 31
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
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 noiseCCF becomes sum of two correlation functions
Two large peak at each TDOA
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 32
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
TDOA Estimation of Multiple Sources
Incident angles (deg) = {75.5, 41.4}
Plot of CCF using PHAT algorithm
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 33
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
TDOA Estimation of Multiple Sources
Incident angles (deg) = {75.5, 41.4}
Plot of MCCC
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 34
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
TDOA Estimation of Multiple Sources
For narrowband-MUSIC
Covariance Matrix is:
Narrowband-MUSIC not useful for non-stationary
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 35
DoA Estimation Methods
Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ
Thank you for your attention
•Introduction
•Problem / Model
•Cross-Correlation
•GCC
•Prediction
•MCCC
•Eigenvector
•Entropy
•Adaptive ED
•Adaptive Multichannel
•Multiple Sources
Page 36