Communication Group Course Multidimensional DSP DoA Estimation Methods Pejman Taslimi – Spring...

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



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


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 2



Direction of Arrival,Time Difference of Arrival (TDOA)

Source Localisation

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 3



Single-SourceFree-Field Model

Linear and Equispaced Array

Multiple SourceFree-Field Model

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 4



Single-SourceReverberant Model

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 5



Multiple-SourceReverberant Model

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 6



Cross CorrelationMost simple and straightforward Method

Single SourceFree-FieldTwo Sensors

Time-averaged EstimateBiased (lower estimation variance and is asymptotically unbiased)Unbiased

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 7



Performance affected by:Signal self-correlationReverberation

Spatial Aliasing

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 8



Generalised Cross Correlation Method

DTFT

Cross-spectrum

Frequency-domain weighting

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 9




Classical Cross-Correlation-degenerates to Cross-Correlation Method

Fast FT let efficient implementation

Depends on source signal statistics

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 10




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


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 11




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


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 12



Spatial Linear Prediction Method

More than two sensorsSingle-source Free-field

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 13



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


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 14



Multi-channel Cross-Correlation Coefficient

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 15



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


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 16



MCCC

for FSLP

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 17



Narrowband-MUSIC

Output Covariance Matrix

for n>2

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 18



Broadband-MUSIC

Alignment signal vector

Spatial correlation matrix

Source signal covariance matrix

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 19



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


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 20



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


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 21



Minimum Entropy Method

For non-Gaussian signal, employs Higher order statistics

Entropy is defined as

Joint Entropy for multivariate random variable

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 22




for Gaussian, zero mean sourcein absence of noiseJoint PDF of aligned sensor output is

Joint Entropy

equivalent to MCCC

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 23




if model signal by Laplace Distributionunivariate, zero mean

multivariate, zero mean

modified Bessel function of third kind

Joint Entropy

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 24




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


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 25



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


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 26




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


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 27




Misjudgement in the case of resonated multipathwill be discussed!

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 28



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


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 29




Multichannel LMS updates the estimate of the channel IR

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 30




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


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 31



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


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 32




Incident angles (deg) = {75.5, 41.4}

Plot of CCF using PHAT algorithm

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 33




Incident angles (deg) = {75.5, 41.4}

Plot of MCCC

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 34




For narrowband-MUSIC

Covariance Matrix is:

Narrowband-MUSIC not useful for non-stationary

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 35



Thank you for your attention

•Introduction

•Problem / Model


•GCC

•Prediction

•MCCC

•Eigenvector

•Entropy

•Adaptive ED


•Multiple Sources

Page 36

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