The Bayesian framework for parameter inference provides a basis from which subject-specific reduced-order vocal fold models can be generated. Previously, it has been shown that a particle filter technique is capable of producing estimates and associated credibility intervals of time-varying reduced-order vocal fold model parameters. However, the particle filter approach is difficult to implement and has a high computational cost, which can be barriers to clinical adoption. This work presents an alternative estimation strategy based upon Kalman filtering aimed at reducing the computational cost of subject-specific model development. The robustness of this approach to Gaussian and non-Gaussian noise is discussed. The extended Kalman filter (EKF) approach is found to perform very well in comparison with the particle filter technique at dramatically lower computational cost. Based upon the test cases explored, the EKF is comparable in terms of accuracy to the particle filter technique when greater than 6000 particles are employed; if less particles are employed, the EKF actually performs better. For comparable levels of accuracy, the solution time is reduced by 2 orders of magnitude when employing the EKF. By virtue of the approximations used in the EKF, however, the credibility intervals tend to be slightly underpredicted.
References
1.
B. D.
Erath
, M.
Zañartu
, K. C.
Stewart
, M. W.
Plesniak
, D. E.
Sommer
, and S. D.
Peterson
, “A review of lumped-element models of voiced speech
,” Speech Commun.
55
, 667
–690
(2013
).2.
I.
Steinecke
and H.
Herzel
, “Bifurcations in an asymmetric vocal-fold model
,” J. Acoust. Soc. Am.
97
, 1874
–1884
(1995
).3.
D. D.
Mehta
, M.
Zañartu
, T. F.
Quatieri
, D. D.
Deliyski
, and R. E.
Hillman
, “Investigating acoustic correlates of human vocal fold phase asymmetry through mathematical modeling and laryngeal high-speed videoendoscopy
,” J. Acoust. Soc. Am.
130
, 3999
–4009
(2011
).4.
M.
Zañartu
, L.
Mongeau
, and G. R.
Wodicka
, “Influence of acoustic loading on an effective single mass model of the vocal folds
,” J. Acoust. Soc. Am.
121
, 1119
–1129
(2007
).5.
I. R.
Titze
, “Nonlinear source-filter coupling in phonation: Theory
,” J. Acoust. Soc. Am.
123
, 2733
–2749
(2008
).6.
B. D.
Erath
, S. D.
Peterson
, M.
Zañartu
, G. R.
Wodicka
, and M. W.
Plesniak
, “A theoretical model of the pressure distributions arising from asymmetric intraglottal flows applied to a two-mass model of the vocal folds
,” J. Acoust. Soc. Am.
130
, 389
–403
(2011
).7.
B. D.
Erath
, M.
Zañartu
, S. D.
Peterson
, and M. W.
Plesniak
, “Nonlinear vocal fold dynamics resulting from asymmetric fluid loading on a two-mass model of speech
,” Chaos
21
, 033113
(2011
).8.
B.
Cranen
and J.
Schroeter
, “Modeling a leaky glottis
,” Phonetics
23
, 165
–177
(1995
).9.
J. C.
Ho
, M.
Zañartu
, and G. R.
Wodicka
, “An anatomically based, time-domain acoustic model of the subglottal system for speech production
,” J. Acoust. Soc. Am.
129
, 1531
–1547
(2011
).10.
J.
Lucero
, “A theoretical study of the hysteresis phenomenon at vocal fold oscillation onset-offset
,” J. Acoust. Soc. Am.
105
, 423
–431
(1999
).11.
S. R.
Moisik
and J. H.
Esling
, “Modeling the biomechanical influence of epilaryngeal structure on the vocal folds: A low-dimensional model of vocal-ventricular fold coupling
,” J. Speech, Lang., Hear. Res.
57
, S687
–S704
(2014
).12.
P. H.
Dejonckere
and M.
Kob
, “Pathogenesis of vocal fold nodules: New insights from a modelling approach
,” Folia Phoniatr. Logop.
61
, 171
–179
(2009
).13.
M.
Zañartu
, G. E.
Galindo
, B. D.
Erath
, S. D.
Peterson
, G. R.
Wodicka
, and R. E.
Hillman
, “Modeling the effects of a posterior glottal opening on vocal fold dynamics with implications for vocal hyperfunction
,” J. Acoust. Soc. Am.
136
, 3262
–3271
(2014
).14.
M.
Dollinger
, U.
Hoppe
, F.
Hettlich
, J.
Lohscheller
, S.
Schuberth
, and U.
Eysholdt
, “Vibration parameter extraction from endoscopic image series of the vocal folds
,” IEEE Trans. Biomed. Eng.
49
, 773
–781
(2002
).15.
R.
Schwarz
, M.
Döllinger
, T.
Wurzbacher
, U.
Eysholdt
, and J.
Lohscheller
, “Spatio-temporal quantification of vocal fold vibrations using high-speed videoendoscopy and a biomechanical model
,” J. Acoust. Soc. Am.
123
, 2717
–2732
(2008
).16.
T.
Wurzbacher
, M.
Döllinger
, R.
Schwarz
, U.
Hoppe
, U.
Eysholdt
, and J.
Lohscheller
, “Spatiotemporal classification of vocal fold dynamics by a multimass model comprising time-dependent parameters
,” J. Acoust. Soc. Am.
123
, 2324
–2334
(2008
).17.
C.
Tao
, Y.
Zhang
, and J. J.
Jiang
, “Extracting physiologically relevant parameters of vocal folds from high-speed video image series
,” IEEE Trans. Biomed. Eng.
54
, 794
–801
(2007
).18.
Y.
Zhang
, C.
Tao
, and J. J.
Jiang
, “Parameter estimation of an asymmetric vocal-fold system from glottal area time series using chaos synchronization
,” Chaos
16
, 023118
(2006
).19.
A.
Yang
, M.
Stingl
, D. A.
Berry
, J.
Lohscheller
, D.
Voigt
, U.
Eysholdt
, and M.
Döllinger
, “Computation of physiological human vocal fold parameters by mathematical optimization of a biomechanical model
,” J. Acoust. Soc. Am.
130
, 948
–964
(2011
).20.
A.
Yang
, D. A.
Berry
, M.
Kaltenbacher
, and M.
Döllinger
, “Three-dimensional biomechanical properties of human vocal folds: Parameter optimization of a numerical model to match in vitro dynamics
,” J. Acoust. Soc. Am.
131
, 1378
–1390
(2012
).21.
R.
Schwarz
, U.
Hoppe
, M.
Schuster
, T.
Wurzbacher
, U.
Eysholdt
, and J.
Lohscheller
, “Classification of unilateral vocal fold paralysis by endoscopic digital high-speed recordings and inversion of a biomechanical model
,” IEEE Trans. Biomed. Eng.
53
, 1099
–1108
(2006
).22.
T.
Wurzbacher
, R.
Schwarz
, M.
Döllinger
, U.
Hoppe
, U.
Eysholdt
, and J.
Lohscheller
, “Model-based classification of nonstationary vocal fold vibrations
,” J. Acoust. Soc. Am.
120
, 1012
–1027
(2006
).23.
S. J.
Rupitsch
, J.
Ilg
, A.
Sutor
, R.
Lerch
, and M.
Döllinger
, “Simulation based estimation of dynamic mechanical properties for viscoelastic materials used for vocal fold models
,” J. Sound Vib.
330
, 4447
–4459
(2011
).24.
E.
Cataldo
, C.
Soize
, and R.
Sampaio
, “Uncertainty quantification of voice signal production mechanical model and experimental updating
,” Mech. Syst. Signal Process.
40
, 718
–726
(2013
).25.
J.
Kaipio
and E.
Somersalo
, Statistical and Computational Inverse Problems
(Springer
, New York
, 2005
), pp. 1
–144
.26.
P. J.
Hadwin
, G. E.
Galindo
, K. J.
Daun
, M.
Zañartu
, B. D.
Erath
, E.
Cataldo
, and S. D.
Peterson
, “Non-stationary Bayesian estimation of parameters from a body cover model of the vocal folds
,” J. Acoust. Soc. Am.
139
, 2683
–2696
(2016
).27.
J. L.
Beck
and K.
Yuen
, “Model selection using response measurements: Bayesian probabilistic approach
,” J. Eng. Mech.
130
, 192
–203
(2004
).28.
B. H.
Story
and I. R.
Titze
, “Voice simulation with a body-cover model of the vocal folds
,” J. Acoust. Soc. Am.
97
, 1249
–1260
(1995
).29.
I. R.
Titze
and B. H.
Story
, “Rules for controlling low-dimensional vocal fold models with muscle activation
,” J. Acoust. Soc. Am.
112
, 1064
–1076
(2002
).30.
K.
Ishizaka
and J. L.
Flanagan
, “Synthesis of voiced sounds from a two-mass model of the vocal cords
,” Bell Syst. Tech. J.
51
, 1233
–1268
(1972
).31.
I. R.
Titze
, “Parameterization of the glottal area, glottal flow, and vocal fold contact area
,” J. Acoust. Soc. Am.
75
, 570
–580
(1984
).32.
B. H.
Story
, “Physiologically-based speech simulation using an enhanced wave-reflection model of the vocal tract
,” Ph.D. thesis, University of Iowa
, 1995
.33.
E.
Yumoto
and W. J.
Gould
, “Harmonics-to-noise ratio as an index of the degree of hoarseness
,” J. Acoust. Soc. Am.
71
, 1544
–1550
(1982
).34.
W. S.
Cleveland
and S. J.
Devlin
, “Locally weighted regression: An approach to regression analysis by local fitting
,” J. Am. Statist. Assoc.
83
, 598
–610
(1988
).© 2017 Acoustical Society of America.
2017
Acoustical Society of America
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