1. Communication Group Course Multidimensional DSP DoA Estimation Methods Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ 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@ieee.org; taslimi@aut.ac.ir Presented to: Professor Moghaddamjoo (Ali M. Reza) Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran, reza@uwm.edu; moghaddamjoo@aut.ac.ir Introduction Problem / Model Cross-Correlation GCC Prediction MCCC Eigenvector Entropy Adaptive ED Adaptive Multichannel Multiple Sources

2. 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 responses The 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

3. 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

4. DoA Estimation Methods Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ Single-Source Free-Field Model Linear and Equispaced Array Multiple Source Free-Field Model Introduction Problem / Model Cross-Correlation GCC Prediction MCCC Eigenvector Entropy Adaptive ED Adaptive Multichannel Multiple Sources Page 4

5. DoA Estimation Methods Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ Single-Source Reverberant Model Introduction Problem / Model Cross-Correlation GCC Prediction MCCC Eigenvector Entropy Adaptive ED Adaptive Multichannel Multiple Sources Page 5

6. DoA Estimation Methods Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ Multiple-Source Reverberant Model Introduction Problem / Model Cross-Correlation GCC Prediction MCCC Eigenvector Entropy Adaptive ED Adaptive Multichannel Multiple Sources Page 6

7. DoA Estimation Methods Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ 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 Introduction Problem / Model Cross-Correlation GCC Prediction MCCC Eigenvector Entropy Adaptive ED Adaptive Multichannel Multiple Sources Page 7

8. DoA Estimation Methods Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ Performance affected by: Signal self-correlation Reverberation Spatial Aliasing Introduction Problem / Model Cross-Correlation GCC Prediction MCCC Eigenvector Entropy Adaptive ED Adaptive Multichannel Multiple Sources Page 8

9. 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

10. 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

11. 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

12. 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 noisy non-reverberant (fundamental weakness to reverberation) Introduction Problem / Model Cross-Correlation GCC Prediction MCCC Eigenvector Entropy Adaptive ED Adaptive Multichannel Multiple Sources Page 12

13. DoA Estimation Methods Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ Spatial Linear Prediction Method More than two sensors Single-source Free-field Introduction Problem / Model Cross-Correlation GCC Prediction MCCC Eigenvector Entropy Adaptive ED Adaptive Multichannel Multiple Sources Page 13

14. DoA Estimation Methods Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ 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 Introduction Problem / Model Cross-Correlation GCC Prediction MCCC Eigenvector Entropy Adaptive ED Adaptive Multichannel Multiple Sources Page 14

15. 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

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

17. 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

18. 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

19. 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

20. 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

21. 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 is In contrast to narrowband which is infinity Introduction Problem / Model Cross-Correlation GCC Prediction MCCC Eigenvector Entropy Adaptive ED Adaptive Multichannel Multiple Sources Page 21

22. 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

23. DoA Estimation Methods Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ Minimum Entropy Method for Gaussian, zero mean source in absence of noise Joint 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

24. DoA Estimation Methods Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ Minimum Entropy Method if model signal by Laplace Distribution univariate, 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

25. DoA Estimation Methods Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ 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 Introduction Problem / Model Cross-Correlation GCC Prediction MCCC Eigenvector Entropy Adaptive ED Adaptive Multichannel Multiple Sources Page 25

26. DoA Estimation Methods Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ 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 Introduction Problem / Model Cross-Correlation GCC Prediction MCCC Eigenvector Entropy Adaptive ED Adaptive Multichannel Multiple Sources Page 26

27. DoA Estimation Methods Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ 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 Introduction Problem / Model Cross-Correlation GCC Prediction MCCC Eigenvector Entropy Adaptive ED Adaptive Multichannel Multiple Sources Page 27

28. DoA Estimation Methods Pejman Taslimi – Spring 2009 Course Presentation – Amirkabir Univ Adaptive Eigenvalue Decomposition Algorithm Misjudgement in the case of resonated multipath will be discussed! Introduction Problem / Model Cross-Correlation GCC Prediction MCCC Eigenvector Entropy Adaptive ED Adaptive Multichannel Multiple Sources Page 28

29. 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

30. 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

31. 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

32. 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 noise CCF 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

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 CCF using PHAT algorithm Introduction Problem / Model Cross-Correlation GCC Prediction MCCC Eigenvector Entropy Adaptive ED Adaptive Multichannel Multiple Sources Page 33

34. 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

35. 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

36. 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