Efficient array design algorithm for wide-band application of the MUltiple SIgnal Classification algorithm
This paper analyzes the error in MUSIC results due to the effect of finite precision arithmetic. Thus, relation of this error to sources correlation level and array and sources configuration parameters is clearly identified. As a result efficient array design algorithm suitable for acoustic environm...
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| Published in | Acoustical Science and Technology Vol. 30; no. 3; pp. 187 - 198 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Tokyo
ACOUSTICAL SOCIETY OF JAPAN
01.01.2009
Acoustical Society of Japan Japan Science and Technology Agency |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1346-3969 1347-5177 2186-859X 2432-2040 0369-4232 1347-5177 |
| DOI | 10.1250/ast.30.187 |
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| Abstract | This paper analyzes the error in MUSIC results due to the effect of finite precision arithmetic. Thus, relation of this error to sources correlation level and array and sources configuration parameters is clearly identified. As a result efficient array design algorithm suitable for acoustic environments is derived. This algorithm is efficient in the sense that it can determine minimum number of sensors. This algorithm is quite general as it includes the effect of all parameters such as number of sources, sources correlation level, maximum resolution, maximum source angle, number of sensors, sensor spacing and arithmetic precision. Also this algorithm is shown to be seamlessly applicable in realistic environments where many additional effects and sources of error often exist. During this paper it is shown that this algorithm is indispensable for DOA estimation in wide-band and reverberant environments. |
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| AbstractList | This paper analyzes the error in MUSIC results due to the effect of finite precision arithmetic. Thus, relation of this error to sources correlation level and array and sources configuration parameters is clearly identified. As a result efficient array design algorithm suitable for acoustic environments is derived. This algorithm is efficient in the sense that it can determine minimum number of sensors. This algorithm is quite general as it includes the effect of all parameters such as number of sources, sources correlation level, maximum resolution, maximum source angle, number of sensors, sensor spacing and arithmetic precision. Also this algorithm is shown to be seamlessly applicable in realistic environments where many additional effects and sources of error often exist. During this paper it is shown that this algorithm is indispensable for DOA estimation in wide-band and reverberant environments. |
| Author | Hagiwara, Ichiro Desoki, Ahmed Takada, Jun-ichi |
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| Cites_doi | 10.1109/29.32276 10.1137/0707001 10.1109/7.32085 10.1007/978-1-4612-3632-0 10.1109/TASSP.1986.1164815 10.1109/78.91162 10.1250/ast.30.417 10.1109/TASSP.1985.1164667 10.1137/1015095 10.1109/TASSP.1983.1164233 10.1109/78.212735 10.1109/ICASSP.1987.1169373 10.1109/29.103073 10.1109/TSP.1993.193167 10.1109/ICASSP.1989.267050 10.1109/29.1617 10.1109/TAES.1983.309427 |
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| Keywords | Acoustic reverberation MUSIC Quantization: 43.60.Gk Target tracking Wide-band Acoustics Spacing Sensor spacing Array design Wide band Signal quantization Precision Arrival angle Classification Signal processing System identification Resolution |
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| References | 6) G. Su and M. Morf, “Signal subspace approach for multiple wide-band emitter location,” IEEE Trans. Acoust. Speech Signal Process., 31, 1502–1522 (1983). 3) R. O. Schmidt, “Multiple emitter location and signal parameter estimation,” Proc. RADC Spectral Est. Workshop 1979, pp. 243–258 (1979). 20) I. S. Dhillon and B. Parlett, “Orthogonal eigenvectors and relative gaps,” SIAM J. Matrix Anal. Appl., 25, 858–899 (2004). 9) B. Friedlander and A. J. Weiss, “Direction finding for wide-band signals using an interpolated array,” IEEE Trans. Signal Process., 41, 1618–1634 (1993). 12) A. Desoki, J. Takada and I. Hagiwara, “Improved finite samples resampling for unbiased wide-band direction of arrival estimation,” submitted to Acoust. Sci. & Tech. 22) S. Leach, “Singular value decomposition—A primer,” Unpublished Manuscript, Department of Computer science, Brown University, Providence, RI 02912. 17) C. Davis and W. Kahan, “The rotation of eigenvectors by a perturbation III,” SIAM J. Numer. Anal., 7, 1–46 (1970). 11) K. M. Buckley and L. J. Griffiths, “Broad-band signal-subspace spatial-spectrum (BASS-ALE) estimation,” IEEE Trans. Acoust. Speech Signal Process., 36, 953–964 (1988). 23) O. T. Anderson and N. J. Jacobsen, “New technology increases the dynamic ranges of data acquisition systems based on 24-bit technology,” Sound Vib., 39(4), pp. 8–14 (2005). 7) H. Wang and M. Kaveh, “Coherent signal-subspace processing for the detection and estimation of angles of arrival of multiple wide-band sources,” IEEE Trans. Acoust. Speech Signal Process., 33, 823–831 (1985). 10) M. Doron, E. Doron and H. Weiss, “Coherent wide-band processing for arbitrary array geometry,” IEEE Trans. Signal Process., 41, 414–417 (1993). 26) H. Wang, C. C. Li and J. X. Zhu, “High–resolution direction finding in the presence of multipath: A frequency–domain smoothing approach,” Proc. ICASSP 87, pp. 2276–2279 (1987). 16) G. B. Parlett, The Symmetric Eigenvalue Problem (Prentice-Hall Inc., Englewood Cliffs, 1980). 8) J. Krolik and D. Swingler, “Focused wide-band array processing by spatial resampling,” IEEE Trans. Acoust. Speech Signal Process., 38, 356–360 (1990). 14) S. W. Smith, The Scientist’s and Engineer’s Guide to Digital Signal Processing (California Technical Publishing, San Diego, Calif., 1999). 15) G. H. Gloub and C. F. Van Loan, Matrix Computations (The John Hopkins University Press, Baltimore, 1996). 19) E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov and D. Sorensen, “Further details: Error bounds for the symmetric eigenproblem” in LAPACK Users’ Guide (SIAM, Philadelphia, 1999). 2) G. C. Carter, Coherence and Time Delay Estimation (IEEE Press, Piscataway, N.J., 1993). 18) G. W. Stewart, “Error and perturbation bounds for subspaces associated with certain eigenvalue problems,” SIAM Rev., 15, 727–764 (1973). 5) R. Kumaresan and D. W. Tufts, “Estimating the angles of arrival of multiple plane waves,” IEEE Trans. Aerosp. Electron. Syst., AES-19, 134–139 (1983). 21) A. S. Deif, Advanced Matrix Theory for Scientists and Engineers (Abacus/Gordon & Breach, London, 1991). 1) V. S. U. Pillai, Array Signal Processing (Springer Verlag, New York, 1989). 4) R. Roy and T. Kailath, “ESPRIT — Estimation of signal parameters via rotational invariance techniques,” IEEE Trans. Acoust. Speech Signal Proc., 37, 984–995 (1989). 24) IEEE, IEEE Standard for Binary Floating-Point Arithmetic. (ANSI/IEEE Std 754-1985) (Institute of Electrical and Electronics Engineers, New York, 1985). 28) J. Krolik and D. Swingler, “The performance of minimax spatial resampling filters for focusing wide-band arrays,” IEEE Trans. Acoust. Speech Signal Process., 39, 1899–1903 (1991). 25) G. Bienvenu, P. Fuerxer, G. Vezzosi, L. Kopp and F. Florin, “Coherent wide band high resolution processing for linear array,” Proc. Signal Proc., ICASSP 89, pp. 2799–2802 (1989). 27) J. X. Zhu and H. Wang, “A comparison of smoothing approaches for angle measurement,” IEEE Trans. Aerosp. Electron. Syst., 25, 529–535 (1989). 13) M. Kaveh and A. Barabell, “The statistical performance of the MUSIC and the minimum-norm algorithms in resolving plane waves in noise,” IEEE Trans. Acoust. Speech Signal Process., 34, 331–341 (1986). 22 C. Davis and W. Kahan (17) 1970; 7 24 25 26 27 G. W. Stewart (18) 1973; 15 O. T. Anderson and N. J. Jacobsen (23) 2005; 39 10 12 14 G. Su and M. Morf (6) 1983; 31 15 16 19 K. M. Buckley and L. J. Griffiths (11) 1988; 36 J. Krolik and D. Swingler (28) 1991; 39 1 2 3 R. Kumaresan and D. W. Tufts (5) 1983; AES-19 J. Krolik and D. Swingler (8) 1990; 38 I. S. Dhillon and B. Parlett (20) 2004; 25 4 9 H. Wang and M. Kaveh (7) 1985; 33 M. Kaveh and A. Barabell (13) 1986; 34 21 |
| References_xml | – reference: 21) A. S. Deif, Advanced Matrix Theory for Scientists and Engineers (Abacus/Gordon & Breach, London, 1991). – reference: 19) E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov and D. Sorensen, “Further details: Error bounds for the symmetric eigenproblem” in LAPACK Users’ Guide (SIAM, Philadelphia, 1999). – reference: 12) A. Desoki, J. Takada and I. Hagiwara, “Improved finite samples resampling for unbiased wide-band direction of arrival estimation,” submitted to Acoust. Sci. & Tech. – reference: 27) J. X. Zhu and H. Wang, “A comparison of smoothing approaches for angle measurement,” IEEE Trans. Aerosp. Electron. Syst., 25, 529–535 (1989). – reference: 17) C. Davis and W. Kahan, “The rotation of eigenvectors by a perturbation III,” SIAM J. Numer. Anal., 7, 1–46 (1970). – reference: 11) K. M. Buckley and L. J. Griffiths, “Broad-band signal-subspace spatial-spectrum (BASS-ALE) estimation,” IEEE Trans. Acoust. Speech Signal Process., 36, 953–964 (1988). – reference: 18) G. W. Stewart, “Error and perturbation bounds for subspaces associated with certain eigenvalue problems,” SIAM Rev., 15, 727–764 (1973). – reference: 15) G. H. Gloub and C. F. Van Loan, Matrix Computations (The John Hopkins University Press, Baltimore, 1996). – reference: 2) G. C. Carter, Coherence and Time Delay Estimation (IEEE Press, Piscataway, N.J., 1993). – reference: 10) M. Doron, E. Doron and H. Weiss, “Coherent wide-band processing for arbitrary array geometry,” IEEE Trans. Signal Process., 41, 414–417 (1993). – reference: 6) G. Su and M. Morf, “Signal subspace approach for multiple wide-band emitter location,” IEEE Trans. Acoust. Speech Signal Process., 31, 1502–1522 (1983). – reference: 1) V. S. U. Pillai, Array Signal Processing (Springer Verlag, New York, 1989). – reference: 16) G. B. Parlett, The Symmetric Eigenvalue Problem (Prentice-Hall Inc., Englewood Cliffs, 1980). – reference: 13) M. Kaveh and A. Barabell, “The statistical performance of the MUSIC and the minimum-norm algorithms in resolving plane waves in noise,” IEEE Trans. Acoust. Speech Signal Process., 34, 331–341 (1986). – reference: 20) I. S. Dhillon and B. Parlett, “Orthogonal eigenvectors and relative gaps,” SIAM J. Matrix Anal. Appl., 25, 858–899 (2004). – reference: 8) J. Krolik and D. Swingler, “Focused wide-band array processing by spatial resampling,” IEEE Trans. Acoust. Speech Signal Process., 38, 356–360 (1990). – reference: 28) J. Krolik and D. Swingler, “The performance of minimax spatial resampling filters for focusing wide-band arrays,” IEEE Trans. Acoust. Speech Signal Process., 39, 1899–1903 (1991). – reference: 4) R. Roy and T. Kailath, “ESPRIT — Estimation of signal parameters via rotational invariance techniques,” IEEE Trans. Acoust. Speech Signal Proc., 37, 984–995 (1989). – reference: 23) O. T. Anderson and N. J. Jacobsen, “New technology increases the dynamic ranges of data acquisition systems based on 24-bit technology,” Sound Vib., 39(4), pp. 8–14 (2005). – reference: 24) IEEE, IEEE Standard for Binary Floating-Point Arithmetic. (ANSI/IEEE Std 754-1985) (Institute of Electrical and Electronics Engineers, New York, 1985). – reference: 26) H. Wang, C. C. Li and J. X. Zhu, “High–resolution direction finding in the presence of multipath: A frequency–domain smoothing approach,” Proc. ICASSP 87, pp. 2276–2279 (1987). – reference: 5) R. Kumaresan and D. W. Tufts, “Estimating the angles of arrival of multiple plane waves,” IEEE Trans. Aerosp. Electron. Syst., AES-19, 134–139 (1983). – reference: 7) H. Wang and M. Kaveh, “Coherent signal-subspace processing for the detection and estimation of angles of arrival of multiple wide-band sources,” IEEE Trans. Acoust. Speech Signal Process., 33, 823–831 (1985). – reference: 22) S. Leach, “Singular value decomposition—A primer,” Unpublished Manuscript, Department of Computer science, Brown University, Providence, RI 02912. – reference: 9) B. Friedlander and A. J. Weiss, “Direction finding for wide-band signals using an interpolated array,” IEEE Trans. Signal Process., 41, 1618–1634 (1993). – reference: 3) R. O. Schmidt, “Multiple emitter location and signal parameter estimation,” Proc. RADC Spectral Est. Workshop 1979, pp. 243–258 (1979). – reference: 25) G. Bienvenu, P. Fuerxer, G. Vezzosi, L. Kopp and F. Florin, “Coherent wide band high resolution processing for linear array,” Proc. Signal Proc., ICASSP 89, pp. 2799–2802 (1989). – reference: 14) S. W. Smith, The Scientist’s and Engineer’s Guide to Digital Signal Processing (California Technical Publishing, San Diego, Calif., 1999). – ident: 2 – ident: 4 doi: 10.1109/29.32276 – volume: 7 start-page: 1 issn: 0036-1429 year: 1970 ident: 17 publication-title: SIAM J. Numer. Anal. doi: 10.1137/0707001 – ident: 27 doi: 10.1109/7.32085 – ident: 1 doi: 10.1007/978-1-4612-3632-0 – volume: 34 start-page: 331 year: 1986 ident: 13 publication-title: IEEE Trans. Acoust. Speech Signal Process. doi: 10.1109/TASSP.1986.1164815 – volume: 39 start-page: 1899 year: 1991 ident: 28 publication-title: IEEE Trans. Acoust. Speech Signal Process. doi: 10.1109/78.91162 – ident: 12 doi: 10.1250/ast.30.417 – volume: 39 start-page: 8 year: 2005 ident: 23 publication-title: Sound Vib. – volume: 33 start-page: 823 year: 1985 ident: 7 publication-title: IEEE Trans. Acoust. Speech Signal Process. doi: 10.1109/TASSP.1985.1164667 – ident: 16 – ident: 14 – volume: 15 start-page: 727 issn: 0036-1445 year: 1973 ident: 18 publication-title: SIAM Rev. doi: 10.1137/1015095 – ident: 24 – ident: 22 – ident: 3 – volume: 31 start-page: 1502 year: 1983 ident: 6 publication-title: IEEE Trans. Acoust. Speech Signal Process. doi: 10.1109/TASSP.1983.1164233 – ident: 9 doi: 10.1109/78.212735 – ident: 26 doi: 10.1109/ICASSP.1987.1169373 – volume: 38 start-page: 356 year: 1990 ident: 8 publication-title: IEEE Trans. Acoust. Speech Signal Process. doi: 10.1109/29.103073 – ident: 10 doi: 10.1109/TSP.1993.193167 – ident: 25 doi: 10.1109/ICASSP.1989.267050 – ident: 19 – volume: 36 start-page: 953 year: 1988 ident: 11 publication-title: IEEE Trans. Acoust. Speech Signal Process. doi: 10.1109/29.1617 – ident: 15 – volume: 25 start-page: 858 issn: 0895-4798 year: 2004 ident: 20 publication-title: SIAM J. Matrix Anal. Appl. – volume: AES-19 start-page: 134 issn: 0018-9251 year: 1983 ident: 5 publication-title: IEEE Trans. Aerosp. Electron. Syst. doi: 10.1109/TAES.1983.309427 – ident: 21 |
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| Snippet | This paper analyzes the error in MUSIC results due to the effect of finite precision arithmetic. Thus, relation of this error to sources correlation level and... |
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| SubjectTerms | Acoustic signal processing Acoustics Array design Exact sciences and technology Fundamental areas of phenomenology (including applications) MUSIC Physics Precision Quantization Resolution Sensor spacing Wide-band |
| Title | Efficient array design algorithm for wide-band application of the MUltiple SIgnal Classification algorithm |
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