The phase and amplitude gradient estimator (PAGE) method [Thomas, Christensen, and Gee, J. Acoust. Soc. Am. 137, 3366–3376 (2015)] has been developed as an alternative to the traditional p-p method for calculating energy-based acoustic measures such as active acoustic intensity. While this method shows many marked improvements over the traditional method, such as a wider valid frequency bandwidth for broadband sources, contaminating noise can lead to inaccurate results. Contaminating noise degrades performance for both the traditional and PAGE methods and causes probe microphone pairs to exhibit low coherence. When coherence is low, better estimates of the pressure magnitude and gradient can be obtained by using a coherence-based approach, which yields a more accurate intensity estimate. This coherence-based approach to the PAGE method, known as the CPAGE method, employs two main coherence-based adjustments. The pressure magnitude adjustment mitigates the negative impact of uncorrelated contaminating noise and improves intensity magnitude calculation. The phase gradient adjustment uses coherence as a weighting to calculate the phase gradient for the probe and improves primarily the calculation of intensity direction. Though requiring a greater computation time than the PAGE method, the CPAGE method is shown to improve intensity calculations, both in magnitude and direction.

1.
D. K.
Wilson
and
R. J.
Greenfield
, “
Spatial structure of low-frequency wind noise
,”
J. Acoust. Soc. Am.
122
,
EL223
EL228
(
2007
).
2.
M. E.
Weber
, “
Wideband, frequency-domain beamforming for coherent signal processing
,”
J. Acoust. Soc. Am.
74
,
S76
(
1983
).
3.
A. I.
Malekhanov
and
A. G.
Sazontov
, “
Large-array acoustic signal processing in random deep-water channels: Effects of coherence
,”
J. Acoust. Soc. Am.
97
,
3294
(
1995
).
4.
J. A.
Clark
, “
Measurement of coherence with a vector acoustic intensity probe
,”
J. Acoust. Soc. Am.
81
,
S43
(
1987
).
5.
J. S.
Bendat
and
A. G.
Piersol
,
Random Data: Analysis and Measurement Procedures
(
Wiley
,
Hoboken, NJ
,
2010
).
6.
D.
Mirabilii
,
K. K.
Lakshminarayana
,
W.
Mack
, and
E. A. P.
Habets
, “
Data-driven wind speed estimation using multiple microphones
,” in
ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
(IEEE, Piscataway,
NJ
,
2020
), pp.
576
580
.
7.
M. R.
Cook
,
K. L.
Gee
,
T. B.
Neilsen
, and
S. D.
Sommerfeldt
, “
The effects of contaminating noise on the calculation of active acoustic intensity for pressure gradient methods
,”
J. Acoust. Soc. Am.
145
,
173
214
(
2019
).
8.
J.
Hald
, “
Denoising of cross-spectral matrices using canonical coherence
,”
J. Acoust. Soc. Am.
146
,
399
408
(
2019
).
9.
K. T.
Walker
and
M. A.
Hedlin
(
2010
). “
A review of wind-noise reduction methodologies
,” in
Infrasound Monitoring for Atmospheric Studies
, edited by
A. Le
Pichon
,
E.
Blanc
, and
A.
Hauchecorne
(
Springer
,
Dordrecht
,
2010
).
10.
C. M.
Nelke
and
P.
Vary
, “
Dual microphone wind noise reduction by exploiting the complex coherence
,” in
Speech Communications 11 ITG Symposium VDE
(VDE Verlag, Berlin,
2014
).
11.
J. Y.
Chung
, “
Cross-spectral method of measuring acoustic intensity without error caused by instrument phase mismatch
,”
J. Acoust. Soc. Am.
64
,
1613
1616
(
1978
).
12.
D. C.
Thomas
,
B. Y.
Christensen
, and
K. L.
Gee
, “
Phase and amplitude gradient method for the estimation of acoustic vector quantities
,”
J. Acoust. Soc. Am.
137
,
3366
3376
(
2015
).
13.
E. B.
Whiting
,
J. S.
Lawrence
,
K. L.
Gee
,
T. B.
Neilsen
, and
S. D.
Sommerfeldt
, “
Bias error analysis for phase and amplitude gradient estimation of acoustic intensity and specific acoustic impedance
,”
J. Acoust. Soc. Am.
142
,
2208
2218
(
2017
).
14.
M. R.
Cook
,
K. L.
Gee
,
S. D.
Sommerfeldt
, and
T. B.
Neilsen
, “
Coherence-based phase unwrapping for broadband acoustic signals
,”
Proc. Mtgs. Acoust.
30
,
055005
(
2017
).
15.
R.
Hickling
and
A. W.
Brown
, “
Determining the direction to a sound source in air using vector sound-intensity probes
,”
J. Acoust. Soc. Am.
129
,
219
224
(
2011
).
16.
Northrup Grumman
, SLS FSB-1 Mission Page, https://www.northropgrumman.com/space/sls-fsb-1-mission-page/ (June 22,
2021
) (Last viewed January 17, 2022).
17.
F. J.
Irarrazabal
, “
Relative infrasound calibration of microphones with applications to outdoor vector intensity measurements
,” MS thesis, BYU, Provo, UT (
2021
), https://scholarsarchive.byu.edu/etd/9191 (Last viewed January 17, 2022).
18.
R. J.
Kozick
and
B. M.
Sadler
, “
Source localization with distributed sensor arrays and partial spatial coherence
,”
IEEE Trans. Signal Process.
52
(
3
),
601
616
(
2004
).
19.
O.
Besson
,
P.
Stoica
, and
A. B.
Gershman
, “
Simple and accurate direction of arrival estimator in the case of imperfect spatial coherence
,”
IEEE Trans. Signal Process.
49
(
4
),
730
737
(
2001
).
20.
A.
Paulraj
and
T.
Kailath
, “
Direction of arrival estimation by eigenstructure methods with imperfect spatial coherence of wave fronts
,”
J. Acoust. Soc. Am.
83
,
1034
1040
(
1988
).
21.
K. L.
Gee
,
F. J.
Irarrazabal
,
M. R.
Cook
,
S. D.
Sommerfeldt
,
T. B.
Neilsen
,
M. C.
Mortenson
, and
P.
Nelson
, “
Overview of the phase and amplitude gradient estimator method for acoustic intensity
,” in
INTER-NOISE and NOISE-CON Congress and Conference Proceedings
, Institute of Noise Control Engineering (
2019
).
22.
K. L.
Gee
,
T. B.
Neilsen
, and
S. D.
Sommerfeldt
, “
Experimental validation of acoustic intensity bandwidth extension by phase unwrapping
,”
J. Acoust. Soc. Am.
141
,
EL357
EL362
(
2017
).
23.
F. J.
Irarrazabal
,
M. R.
Cook
, and
K. L.
Gee
, “
Initial infrasound source characterization using the phase and amplitude gradient estimator method
,”
Proc. Mtgs. Acoust.
36
,
045004
(
2019
).
24.
B. O.
Reichman
,
B. M.
Harker
,
T. B.
Neilsen
, and
K. L.
Gee
, “
Acoustic measurements in the far field during QM-2 solid rocket motor static firing
,”
Proc. Mtgs. Acoust.
29
,
045008
(
2016
).
You do not currently have access to this content.