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Communication Group Course Multidimensional DSP

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

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Communication Group Course Multidimensional DSP

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  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@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 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

  7. 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 Cross-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) Better than CC and SCOT GCC generally: very short decision delays (good tracking capability) moderately 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

  14. 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 n>2 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 > 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 (> 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 LMSupdates 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

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