Two level Differential Evolution algorithms for ARMA parameters estimatio

The problem of determining simultaneously the model order and coefficient of an Autoregressive Moving Average (ARMA) model is examined in this paper. An Evolutionary Algorithm (EA) comprising two-level Differential Evolution (DE) optimization scheme is proposed. The first level searches for the appropriate model order while the second level computes the optimal/sub-optimal corresponding parameters. The performance of the algorithm is evaluated using both simulated ARMA models and practical rotary motion system. The results of both examples show the effectiveness of the proposed algorithm over a well known conventional technique

Graphical Models for Multivariate Time Series

Graphical Models give a graph representation of relations between random variables and processes and they are an important tool for analyzing multivariate data. In this thesis we give a brief introduction to the concept of Graphical Models in static case and then we extend this concept for multivariate data to multivariate time series. We show that conditional independence of components can be represented on a graph where the components are nodes and the lack of arc between two nodes signifies conditional independence. We also present problem to fit an AR model to such a process and show how AR models can be approximated by a low order ARMA model and the benefits of this approximatio

Time-varying Autoregressive Modeling of Nonstationary Signals

Nonstationary signal modeling is a research topic of practical interest. In this thesis, we adopt a time-varying (TV) autoregressive (AR) model using the basis function (BF) parameter estimation method for nonstationary process identification and instantaneous frequency (IF) estimation. The current TVAR model in direct form (DF) with the blockwise least-squares and recursive weighted-least-squares BF methods perform equivalently well in signal modeling, but the large estimation error may cause temporary instabilities of the estimated model. To achieve convenient model stability monitoring and pole tracking, the TVAR model in cascade form (CF) was proposed through the parameterization in terms of TV poles (represented by second order section coefficients, Cartesian coordinates, Polar coordinates), where the time variation of each pole parameter is assumed to be the linear combination of BFs. The nonlinear system equations for the TVAR model in CF are solved iteratively using the Gauss-Newton algorithm. Using the CF, the model stability is easily controlled by constraining the estimated TV poles within the unit circle. The CF model shows similar performance trends to the DF model using the recursive BF method, and the TV pole representation in Cartesian coordinates outperforms all other representations. The individual frequency variation can be finely tracked using the CF model, when several frequency components are present in the signal. Simulations were carried on synthetic sinusoidal signals with different frequency variations for IF estimation. For the TVAR model in DF (blockwise), the basis dimension (BD) is an important factor on frequency estimation accuracy. For the TVAR model in DF (recursive) and CF (Cartesian), the influences of BD are negligible. The additive white noise in the observed signal degrades the estimation performance, and the the noise effects can be reduce by using higher model order. Experiments were carried on the real electromyography (EMG) data for frequency estimation in the analysis of muscle fatigue. The TVAR modeling methods show equivalent performance to the conventional Fourier transform method