1 |
Adaptive iterative filtering methods for nonlinear signal analysis and applicationsLiu, Jingfang 27 August 2014 (has links)
Time-frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture the changes in these types of signals, it is necessary for the analysis methods to be local, adaptive and stable. In recent years, decomposition based analysis methods were developed by different researchers to deal with non-linear and non-stationary signals. These methods share the feature that a signal is decomposed into finite number of components on which the time-frequency analysis can be applied. Differences lie in the strategies to extract these components: by iteration or by optimization. However, considering the requirements of being local, adaptive and stable, neither of these decompositions are perfectly satisfactory. Motivated to find a local, adaptive and stable decomposition of a signal, this thesis presents Adaptive Local Iterative Filtering (ALIF) algorithm. The adaptivity is obtained having the filter lengths being determined by the signal itself. The locality is ensured by the filter we designed based on a PDE model. The stability of this algorithm is shown and the convergence is proved. Moreover, we also propose a local definition for the instantaneous frequency in order to achieve a completely local analysis for non-linear and non-stationary signals. Examples show that this decomposition
really helps in both simulated data analysis and real world application.
|
2 |
Parameter Estimation for Nonlinear State Space ModelsWong, Jessica 23 April 2012 (has links)
This thesis explores the methodology of state, and in particular, parameter estimation for time
series datasets. Various approaches are investigated that are suitable for nonlinear models
and non-Gaussian observations using state space models. The methodologies are applied to a
dataset consisting of the historical lynx and hare populations, typically modeled by the Lotka-
Volterra equations. With this model and the observed dataset, particle filtering and parameter
estimation methods are implemented as a way to better predict the state of the system.
Methods for parameter estimation considered include: maximum likelihood estimation, state
augmented particle filtering, multiple iterative filtering and particle Markov chain Monte
Carlo (PMCMC) methods. The specific advantages and disadvantages for each technique
are discussed. However, in most cases, PMCMC is the preferred parameter estimation
solution. It has the advantage over other approaches in that it can well approximate any
posterior distribution from which inference can be made. / Master's thesis
|
Page generated in 0.0946 seconds