Convergence of discrete-time Kalman filter estimate to continuous-time estimate for systems with unbounded observation

in Mathematics of Control, Signals & Systems (2018), 30(3), 9

In this article, we complement recent results on the convergence of the state estimate obtained by applying the discrete-time Kalman filter on a time-sampled continuous-time system. As the temporal ... [more ▼]

In this article, we complement recent results on the convergence of the state estimate obtained by applying the discrete-time Kalman filter on a time-sampled continuous-time system. As the temporal discretization is re fined, the estimate converges to the continuous-time estimate given by the Kalman-Bucy fi lter. We shall give bounds for the convergence rates for the variance of the discrepancy between these two estimates. The contribution of this article is to generalize the convergence results to systems with unbounded observation operators under di fferent sets of assumptions, including systems with diagonalizable generators, systems with admissible observation operators, and systems with analytic semigroups. The proofs are based on applying the discrete-time Kalman fi lter on a dense, numerable subset on the time interval [0,T] and bounding the increments obtained. These bounds are obtained by studying the regularity of the underlying semigroup and the noise-free output. [less ▲]

Modal Locking Between Vocal Fold Oscillations and Vocal Tract Acoustics

in Acta Acustica United with Acustica (2018), 104(2), 323-337

During voiced speech, vocal folds interact with the vocal tract acoustics. The resulting glottal source–resonator coupling has been observed using mathematical and physical models as well as in in vivo ... [more ▼]

During voiced speech, vocal folds interact with the vocal tract acoustics. The resulting glottal source–resonator coupling has been observed using mathematical and physical models as well as in in vivo phonation. We propose a computational time-domain model of the full speech apparatus that contains a feedback mechanism from the vocal tract acoustics to the vocal fold oscillations. It is based on numerical solution of ordinary and partial differential equations defined on vocal tract geometries that have been obtained by magnetic resonance imaging. The model is used to simulate rising and falling pitch glides of [α, i] in the fundamental frequency (fo ) interval [145 Hz, 315 Hz]. The interval contains the first vocal tract resonance fR 1 and the first formant F 1 of [i] as well as the fractions of the first resonance fR 1 /5, fR 1 /4, and fR 1 /3 of [α]. The glide simulations reveal a locking pattern in the fo trajectory approximately at fR 1 of [i]. The resonance fractions of [α] produce perturbations in the pressure signal at the lips but no locking. [less ▲]

Continuous time Gaussian process dynamical models in gene regulatory network inference

E-print/Working paper (2018)

One of the focus areas of modern scientific research is to reveal mysteries related to genes and their interactions. The dynamic interactions between genes can be encoded into a gene regulatory network ... [more ▼]

One of the focus areas of modern scientific research is to reveal mysteries related to genes and their interactions. The dynamic interactions between genes can be encoded into a gene regulatory network (GRN), which can be used to gain understanding on the genetic mechanisms behind observable phenotypes. GRN inference from time series data has recently been a focus area of systems biology. Due to low sampling frequency of the data, this is a notoriously difficult problem. We tackle the challenge by introducing the so-called continuous-time Gaussian process dynamical model (GPDM), based on Gaussian process framework that has gained popularity in nonlinear regression problems arising in machine learning. The model dynamics are governed by a stochastic differential equation, where the dynamics function is modelled as a Gaussian process. We prove the existence and uniqueness of solutions of the stochastic differential equation. We derive the probability distribution for the Euler discretised trajectories and establish the convergence of the discretisation. We develop a GRN inference method based on the developed framework. The method is based on MCMC sampling of trajectories of the GPDM and estimating the hyperparameters of the covariance function of the Gaussian process. Using benchmark data examples, we show that our method is computationally feasible and superior in dealing with poor time resolution. [less ▲]

Output error minimizing back and forth nudging method for initial state recovery

in Systems & Control Letters (2016), 94

Acoustic wave guides as infinite-dimensional dynamical systems

in ESAIM: Control, Optimisation and Calculus of Variations (2015), 21(2), 324-347

Interaction of vocal fold and vocal tract oscillations

in Proceedings of the 24th Nordic Seminar on Computational Mechanics (2011)

We study the mechanical feedback coupling between the human vocal folds and vocal tract (VT) by simulating fundamental frequency glides over the lowest VT resonance. In the classical source–filter theory ... [more ▼]

We study the mechanical feedback coupling between the human vocal folds and vocal tract (VT) by simulating fundamental frequency glides over the lowest VT resonance. In the classical source–filter theory of speech production, the vocal folds produce a signal which is filtered by the resonator, vocal tract without any feedback. We have developed a computational model of the vocal folds and the VT that also includes a counter pressure from the VT to the vocal folds. This coupling gives rise to new computational observations (such as modal locking) that can be established experimentally. [less ▲]

A LF-pulse from a simple glottal flow model

in Proceedings of the 6th International Workshop on Models and Analysis of Vocal Emissions for Biomedical Applications (2009)