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Convergence of discrete-time Kalman filter estimate to continuous-time estimate for systems with unbounded observation Aalto, Atte 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 ▲] Detailed reference viewed: 34 (4 UL)Spatial discretization error in Kalman filtering for discrete-time infinite dimensional systems Aalto, Atte in IMA Journal of Mathematical Control and Information (2018), 35(suppl_1), 51-72 We derive a reduced-order state estimator for discrete-time infinite dimensional linear systems with finite dimensional Gaussian input and output noise. This state estimator is the optimal one-step ... [more ▼] We derive a reduced-order state estimator for discrete-time infinite dimensional linear systems with finite dimensional Gaussian input and output noise. This state estimator is the optimal one-step estimate that takes values in a fixed finite dimensional subspace of the system’s state space — consider, for example, a Finite Element space. The structure of the obtained state estimator is like the Kalman filter, but with an additional optimal embedding operator mapping from the reduced space to the original state space. We derive a Riccati difference equation for the error covariance and use sensitivity analysis to obtain a bound for the error of the state estimate due to the state space discretization. [less ▲] Detailed reference viewed: 60 (13 UL)Modal Locking Between Vocal Fold Oscillations and Vocal Tract Acoustics ; Aalto, Atte ; et al 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 ▲] Detailed reference viewed: 64 (6 UL)Bayesian variable selection in linear dynamical systems Aalto, Atte ; Goncalves, Jorge E-print/Working paper (2018) We develop a method for reconstructing regulatory interconnection networks between variables evolving according to a linear dynamical system. The work is motivated by the problem of gene regulatory ... [more ▼] We develop a method for reconstructing regulatory interconnection networks between variables evolving according to a linear dynamical system. The work is motivated by the problem of gene regulatory network inference, that is, finding causal effects between genes from gene expression time series data. In biological applications, the typical problem is that the sampling frequency is low, and consequentially the system identification problem is ill-posed. The low sampling frequency also makes it impossible to estimate derivatives directly from the data. We take a Bayesian approach to the problem, as it offers a natural way to incorporate prior information to deal with the ill-posedness, through the introduction of sparsity promoting prior for the underlying dynamics matrix. It also provides a framework for modelling both the process and measurement noises. We develop Markov Chain Monte Carlo samplers for the discrete-valued zero-structure of the dynamics matrix, and for the continuous-time trajectory of the system. [less ▲] Detailed reference viewed: 62 (5 UL)Continuous time Gaussian process dynamical models in gene regulatory network inference Aalto, Atte ; ; et al 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 ▲] Detailed reference viewed: 16 (4 UL)Iterative observer-based state and parameter estimation for linear systems Aalto, Atte in ESAIM: Control, Optimisation and Calculus of Variations (2018), 24(1), 265-288 We propose an iterative method for joint state and parameter estimation using measurements on a time interval [0,T] for systems that are backward output stabilizable. Since this time interval is fixed ... [more ▼] We propose an iterative method for joint state and parameter estimation using measurements on a time interval [0,T] for systems that are backward output stabilizable. Since this time interval is fixed, errors in initial state may have a big impact on the parameter estimate. We propose to use the back and forth nudging (BFN) method for estimating the system’s initial state and a Gauss–Newton step between BFN iterations for estimating the system parameters. Taking advantage of results on the optimality of the BFN method, we show that for systems with skew-adjoint generators, the initial state and parameter estimate minimizing an output error cost functional is an attractive fixed point for the proposed method. We treat both linear source estimation and bilinear parameter estimation problems. [less ▲] Detailed reference viewed: 51 (11 UL)Convergence of discrete time Kalman filter estimate to continuous time estimate Aalto, Atte in International Journal of Control (2016), 89(4), 668-679 Detailed reference viewed: 22 (1 UL)Output error minimizing back and forth nudging method for initial state recovery Aalto, Atte in Systems & Control Letters (2016), 94 Detailed reference viewed: 38 (6 UL)Acoustic wave guides as infinite-dimensional dynamical systems Aalto, Atte ; ; in ESAIM: Control, Optimisation and Calculus of Variations (2015), 21(2), 324-347 Detailed reference viewed: 31 (1 UL)Composition of passive boundary control systems Aalto, Atte ; in Mathematical Control and Related Fields (2013), 3(1), 1-19 Detailed reference viewed: 26 (0 UL)Interaction of vocal fold and vocal tract oscillations Aalto, Atte ; ; et al 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 ▲] Detailed reference viewed: 27 (1 UL)Wave propagation in networks: a system theoretic approach Aalto, Atte ; in Proceedings of the 18th World Congress of the IFAC (2011) Detailed reference viewed: 22 (0 UL)A LF-pulse from a simple glottal flow model Aalto, Atte ; ; in Proceedings of the 6th International Workshop on Models and Analysis of Vocal Emissions for Biomedical Applications (2009) Detailed reference viewed: 23 (0 UL) |
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