A vector-sensor consisting of a monopole sensor collocated with orthogonally oriented dipole sensors is used for direction of arrival (DOA) estimation in the presence of an isotropic noise-field or internal device noise. A maximum likelihood (ML) DOA estimator is derived and subsequently shown to be a special case of DOA estimation by means of a search for the direction of maximum steered response power (SRP). The problem of SRP maximization with respect to a vector-sensor can be solved with a computationally inexpensive algorithm. The ML estimator achieves asymptotic efficiency and thus outperforms existing estimators with respect to the mean square angular error (MSAE) measure. The beampattern associated with the ML estimator is shown to be identical to that used by the minimum power distortionless response beamformer for the purpose of signal enhancement.
REFERENCES
1.
D.
Levin
, E. A. P.
Habets
, and S.
Gannot
, “On the angular error of intensity vector based direction of arrival estimation in reverberant sound fields
,” J. Acoust. Soc. Am.
128
, 1800
–1811
(2010
). 2.
D.
Levin
, E. A. P.
Habets
, and S.
Gannot
, “Impact of source signal coloration on intensity vector based DOA estimation
,” in Proceedings of the International Workshop on Acoustic Echo and Noise Control (IWAENC)
, Tel-Aviv
, Israel
(2010
). 3.
H.-E.
de Bree
, P.
Leussink
, I. T.
Korthorst
, D. H.
Jansen
, D. T.
Lammerink
, and P. M.
Elwenspoek
, “The microflown, a novel device measuring acoustical flows
,” in 8th International Conference on Solid-State Sensors and Actuators, and Eurosensors IX
(1995
), Vol. 1
, pp. 536
–539
. 4.
H. F.
Olson
, “Gradient microphones
,” J. Acoust. Soc. Am.
17
, 192
–198
(1946
). 5.
G.
Elko
and A.-T. N.
Pong
, “A steerable and variable first-order differential microphone array
,” in IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)
(1997
), Vol. 1
, pp. 223
–226
. 6.
G.
Elko
and A.-T. N.
Pong
, “A simple adaptive first-order differential microphone
,” in IEEE Workshop on Applications of Signal Processing to Audio and Acoustics
(1995
), pp. 169
–172
. 7.
R.
Derkx
and K.
Janse
, “Theoretical analysis of a first-order azimuth-steerable superdirective microphone array
,” IEEE Trans. Audio, Speech, Lang. Process.
17
, 150
–162
(2009
). 8.
B. A.
Cray
and A. H.
Nuttall
, “Directivity factors for linear arrays of velocity sensors
,” J. Acoust. Soc. Am.
110
, 324
–331
(2001
). 9.
G. L.
D’Spain
, J. C.
Luby
, G. R.
Wilson
, and R. A.
Gramann
, “Vector sensors and vector sensor line arrays: Comments on optimal array gain and detection
,” J. Acoust. Soc. Am.
120
, 171
–185
(2006
). 10.
A.
Nehorai
and E.
Paldi
, “Acoustic vector-sensor array processing
,” IEEE Trans. Signal Process.
42
, 2481
–2491
(1994
). 11.
P.
Tichavsky
, K.
Wong
, and M.
Zoltowski
, “Near-field/far-field azimuth and elevation angle estimation using a single vector hydrophone
,” IEEE Trans. Signal Process.
49
, 2498
–2510
(2001
). 12.
P.
Tam
and K.
Wong
, “Cramér-Rao bounds for direction finding by an acoustic vector sensor under nonideal gain-phase responses, noncollocation, or nonorthogonal orientation
,” IEEE Sens. J.
9
, 969
–982
(2009
). 13.
D. P.
Jarrett
, E. A. P.
Habets
, and P. A.
Naylor
, “3D source localization in the spherical harmonic domain using a pseudointensity vector
,” in European Signal Processing Conference (EUSIPCO)
, Aalborg, Denmark
(2010
). 14.
D. P.
Jarrett
, E. A. P.
Habets
, and P. A.
Naylor
, “Eigenbeam-based acoustic source tracking in noisy reverberant environments
,” in Conference Record of the 44th Asilomar Conference on Signals, Systems and Computers (ASILO-MAR)
, Pacific Grove, CA
(2010
), pp. 576
–580
. 15.
K.
Wong
and H.
Chu
, “Beam patterns of an underwater acoustic vector hydrophone located away from any reflecting boundary
,” IEEE J. Ocean. Eng.
27
, 628
–637
(2002
). 16.
H.
Cox
, “Super-directivity revisited
,” in Proceedings of the 21st IEEE Instrumentation and Measurement Technology Conference, IMTC 04
(2004
), Vol. 2
, pp. 877
–880
. 17.
Y.
Wu
, K.
Wong
, and S.-K.
Lau
, “The acoustic vector-sensor’s near-field array-manifold
,” IEEE Trans. Signal Process.
58
, 3946
–3951
(2010
). 18.
D.
Lubman
, “Antifade sonar employs acoustic field diversity to recover signals from multipath fading
,” AIP Conf. Proc.
368
, 335
–344
(1996
). 19.
A.
Abdi
and H.
Guo
, “A new compact multichannel receiver for underwater wireless communication networks
,” IEEE Trans. Wireless Commun.
8
, 3326
–3329
(2009
). 20.
D.
Levin
, E. A. P.
Habets
, and S.
Gannot
, “Direction-of-arrival estimation using acoustic vector sensors in the presence of noise
,” in IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP)
(2011
). 21.
J.
DiBiase
, H.
Silverman
, and M.
Brandstein
, “Robust localization in reverberant rooms
,” in Microphone Arrays: Signal Processing Techniques and Applications
, edited by M.
Branstein
and D.
Ward
(Springer
, New York
, 2001
), Chap. 8, pp. 157
–180
. 22.
S.
Davies
, “Bearing accuracies for arctan processing of crossed dipole arrays
,” in Proceedings of Oceans’87
(1987
), Vol. 1
, pp. 351
–356
. 23.
F.
Jacobsen
and T.
Roisin
, “The coherence of reverberant sound fields
,” J. Acoust. Soc. Am.
108
, 204
–210
(2000
). 24.
M.
Hawkes
and A.
Nehorai
, “Acoustic vector-sensor correlations in ambient noise
,” IEEE J. Ocean. Eng.
26
, 337
–347
(2001
). 25.
I.
Cohen
and B.
Berdugo
, “Noise estimation by minima controlled recursive averaging for robust speech enhancement
,” IEEE Signal Process. Lett.
9
, 12
–15
(2002
). 26.
R.
Hendriks
, R.
Heusdens
, and J.
Jensen
, “MMSE based noise psd tracking with low complexity
,” in IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP)
(2010
), pp. 4266
–4269
. 27.
A.
Nehorai
and M.
Hawkes
, “Performance bounds for estimating vector systems
,” IEEE Trans. Signal Process.
48
, 1737
–1749
(2000
). 28.
D.
Serre
, Matrices: Theory and Applications, Graduate Texts in Mathematics
, 2nd ed. (Springer
, New York
, 2010
), Chap 3, p. 53
. 29.
M. S.
Bartlett
, “An inverse matrix adjustment arising in discriminant analysis
,” Ann. Math. Stat.
22
, 107
–111
(1951
). 30.
It should be noted that an ambiguity of 180° remains as multiplication of an eigenvector by −1 also produces an eigenvector (or from a different perspective, a dipole possess symmetric geometry with a rear lobe mirroring the main lobe). In Ref. 10, the ambiguity was resolved by assuming that the DOA search is initially constrained to a known half-space. In Ref. 20, the authors have suggested use of to indicate the correct half-space. This approach is natural as it maintains continuity, corresponding to the limiting solution: .
31.
H.
Cox
, R.
Zeskind
, and M.
Owen
, “Robust adaptive beamforming
,” IEEE Trans. Acoust., Speech, Signal Process.
35
, 1365
–1376
(1987
). 32.
S. M.
Kay
, Fundamentals of Statistical Signal Processing: Estimation Theory
(Prentice-Hall
, Upper Saddle River, NJ
, 1993
), Vol. 1
, Chap. 7. 33.
An alternative criterion would be minimum noise, i.e., the target function to be minimized is noise variance wTCew in place of output power wTCw. The solution resulting from this formulation is known as the Capon beamformer or minimum variance distortionless response (MVDR) beamformer. In cases where the DOA is accurately known, as we have assumed, the MPDR and MVDR beamformers are identical.
34.
H.
Cox
, “Resolving power and sensitivity to mismatch of optimum array processors
,” J. Acoust. Soc. Am.
54
, 771
–785
(1973
). 35.
H. L.
Van Trees
, Optimum Array Processing, Detection, Estimation, and Modulation Theory
Vol. 3
(Wiley
, New York
, 2002
), Chap. 6, p. 444
. 36.
R. M.
Mattheij
and G.
Söderlind
, “On inhomogeneous eigenvalue problems. I
,” Linear Algeb. Appl.
88–89
, 507
–531
(1987
). © 2012 Acoustical Society of America.
2012
Acoustical Society of America
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