Continuous-time nonlinear estimation filters using UKF-aided gaussian sum representations

Download

index.pdf

Date

2014

Author

Gökçe, Murat

Metadata

Show full item record

Item Usage Stats

230
views

113
downloads

A nonlinear filtering method is developed for continuous-time nonlinear systems with observations/measurements carried out in discrete-time by means of UKFaided Gaussian sum representations. The time evolution of the probability density function (pdf) of the state variables (or the a priori pdf) is approximated by solving the Fokker-Planck equation numerically using Euler’s method. At every Euler step, the values of the a priori pdf are evaluated at deterministic sample points. These values are used with Gaussian radial basis functions to obtain weighted sum of Gaussian approximation of a priori pdf. The locations of the sample points and mean and covariance values of Gaussian functions are found by the help of the prediction step of an Unscented Kalman Filter (UKF). The weights of the Gaussian functions are calculated using the method of least squares. The pdf of the updated state variables (or a posteriori pdf) is approximated similar to a priori case. This time Bayes rule and the help of the update step of UKF are used. In the developed filter, UKF acts as a one step look ahead mechanism to determine the high likelihood regions of the a priori and a posteriori pdfs and these pdfs are locally approximated around these high likelihood regions. As a second filtering method, particle flow is combined with UKF-aided Gaussian sum representations approach. Both filters are compared with some of the known nonlinear filtering methods by means of computational load and error levels using various scenarios .

Subject Keywords

Continuous-time systems., Fokker-Planck equation., Gaussian sums., Nonlinear filtering.

URI

http://etd.lib.metu.edu.tr/upload/12616894/index.pdf
https://hdl.handle.net/11511/23410

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

QUANTUM-CLASSICAL MIXED-MODE ANALYSIS OF NONLINEARLY COUPLED OSCILLATORS - A TIME-DEPENDENT SELF-CONSISTENT-FIELD APPROACH YURTSEVER, E; BRICKMANN, J (1992-02-01) A two-dimensional vibrational system with a strong nonlinear coupling is studied using a quantum-classical mixed mode self-consistent-field approach. The classical equations of motion as well as the time-dependent Schrodinger equation are solved for respective modes under the influence of the average fields generated by the other modes. This vibrational system was previously shown to be chaotic under classical mechanical treatment but quantum mechanical observations pointed out to highly regular behaviour...
Adaptive Harmonic Balance Methods, A Comparison Sert, Onur; Ciğeroğlu, Ender (2016-01-28) Harmonic balance method (HBM) is one of the most popular and powerful methods, which is used to obtain response of nonlinear vibratory systems in frequency domain. The main idea of the method is to express the response of the system in Fourier series and converting the nonlinear differential equations of motion into a set of nonlinear algebraic equations. System response can be obtained by solving this nonlinear equation set in terms of the unknown Fourier coefficients. The accuracy of the solution is great...
Multiscale Modeling of Thin-Wire Coupling Problems Using Hybridization of Finite Element and Dipole Moment Methods and GPU Acceleration ÖZGÜN, ÖZLEM; Mittra, Raj; Kuzuoğlu, Mustafa (2020-01-01) In this article, a hybrid numerical method, called finite element method (FEM) + dipole moment (DM), is presented for efficient solution of multiscale electromagnetic radiation and scattering problems that involve structures with fine features, such as thin-wire antennas or objects. In this method, the FEM is hybridized with the DM approach to help ease certain computational burdens, such as mesh refinement, ill-conditioning, memory overload, and long computation times, when solving multiscale problems with...
Time series classification with feature covariance matrices Ergezer, Hamza; Leblebicioğlu, Mehmet Kemal (2018-06-01) In this work, a novel approach utilizing feature covariance matrices is proposed for time series classification. In order to adapt the feature covariance matrices into time series classification problem, a feature vector is defined for each point in a time series. The feature vector comprises local and global information such as value, derivative, rank, deviation from the mean, the time index of the point and cumulative sum up to the point. Extracted feature vectors for the time instances are concatenated t...
Moving mesh discontinuous Galerkin methods for PDEs with traveling waves UZUNCA, MURAT; Karasözen, Bülent; Kucukseyhan, T. (2017-01-01) In this paper, a moving mesh discontinuous Galerkin (dG) method is developed for nonlinear partial differential equations (PDEs) with traveling wave solutions. The moving mesh strategy for one dimensional PDEs is based on the rezoning approach which decouples the solution of the PDE from the moving mesh equation. We show that the dG moving mesh method is able to resolve sharp wave fronts and wave speeds accurately for the optimal, arc-length and curvature monitor functions. Numerical results reveal the effi...

Citation Formats

M. Gökçe, “Continuous-time nonlinear estimation filters using UKF-aided gaussian sum representations,” Ph.D. - Doctoral Program, Middle East Technical University, 2014.