Convergence of discrete time Kalman filter estimate to continuous time estimate

This article is concerned with the convergence of the state estimate obtained from the discrete time Kalman filter to the continuous time estimate as the temporal discretization is refined. We derive convergence rate estimates for different systems, first finite dimensional and then infinite dimensional with bounded or unbounded observation operators. Finally, we derive the convergence rate in the case where the system dynamics is governed by an analytic semigroup. The proofs are based on applying the discrete time Kalman filter on a dense numerable subset of a certain time interval $[0,T]$.Comment: Author's version of the manuscript accepted for publication in International Journal of Contro

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

We show that for linear dynamical systems with skew-adjoint generators, the initial state estimate given by the back and forth nudging method with colocated feedback, converges to the minimizer of the discrepancy between the measured and simulated outputs - given that the observer gains are chosen suitably and the system is exactly observable. If the system's generator A is essentially skew-adjoint and dissipative (with not too much dissipation), the colocated feedback has to be corrected by the operator e^{At}e^{A*t} in order to obtain such convergence. In some special cases, a feasible approximation for this operator can be found analytically. The case with wave equation with constant dissipation will be demonstrated.Comment: This is the preprint version of the article. The final, published version is available on the journal's websit

Bayesian variable selection in linear dynamical systems

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.Comment: 19 page

Linear system identification from ensemble snapshot observations

Developments in transcriptomics techniques have caused a large demand in tailored computational methods for modelling gene expression dynamics from experimental data. Recently, so-called single-cell experiments have revolutionised genetic studies. These experiments yield gene expression data in single cell resolution for a large number of cells at a time. However, the cells are destroyed in the measurement process, and so the data consist of snapshots of an ensemble evolving over time, instead of time series. The problem studied in this article is how such data can be used in modelling gene regulatory dynamics. Two different paradigms are studied for linear system identification. The first is based on tracking the evolution of the distribution of cells over time. The second is based on the so-called pseudotime concept, identifying a common trajectory through the state space, along which cells propagate with different rates. Therefore, at any given time, the population contains cells in different stages of the trajectory. Resulting methods are compared in numerical experiments

Modal Locking Between Vocal Fold Oscillations and Vocal Tract Acoustics

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 [alpha, i] in the fundamental frequency (f(o)) interval [145 Hz, 315 Hz]. The interval contains the first vocal tract resonance f(R1) and the first formant F-1 of [i] as well as the fractions of the first resonance f(R1)/5, f(R1)/4, and f(R1)/3 of [alpha]. The glide simulations reveal a locking pattern in the f(o) trajectory approximately at f(R1) of [i]. The resonance fractions of [alpha] produce perturbations in the pressure signal at the lips but no locking.Peer reviewe

Economic imperialism : And The Issues Of Explaining Foreign Phenomena Through Neoclassical Methodology – Analyzed In The Work Of Gary S. Becker

Economic imperialism is the phenomenon of scientific imperialism in the science of economics, in which the economic methodology etc. is applied to subject matters that traditionally have been studied by other sciences. The purpose of this thesis is to study to what extent the neoclassical theories of Gary S. Becker can be described as examples of economic imperialism. This is carried out through a review into the literature researching economic imperialism and into the work of Gary S. Becker, with an addition of a descriptive analysis of the economic imperialism present in the work of Gary S. Becker. The analysis reveals fundamental epistemic differences across the theories of Gary S. Becker, with each representing a differing level of scientific imperialism. Furthermore, a review of the literature regarding normativity of scientific imperialism shows that there is no necessary reason to deny the justification of imperialistic research, because it varies case-by-case. The conclusion of the thesis is that the variance in the theories even in a single methodological framework is high enough, that no imperialistic research can be rejected by simply appealing to definition. Additionally, scientific imperialism can be carried out in a way that does not infringe on the sovereignty of other sciences, and if the traditional values of scientific endeavor is accepted, the correct scientific imperialism, including economic imperialism, should be encouraged

Iterative observer-based state and parameter estimation for linear systems

The original publication is available at www.esaim-cocv.orgInternational audienceWe 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