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Methods for Frequency Domain Estimation of Continuous-Time Models

Author: J. Gillberg
Published: Licentiate Thesis no. 1133, Dec 2004.
Research area: Identification
Keywords: identification continuous-time frequency domain

Thesis as PDF (943 kbytes)

Approaching parameter estimation from the discrete-time domain is the dominating paradigm in system identification. Identification of continuous-time models on the other hand is motivated by the fact that modelling of physical systems often take place in continuous-time. For many practical applications there is also a genuine interest in the parameters connected to these physical models. In the black-box discrete-time modelling framework however, the identified parameters often lack a physical interpretation.

Uniform sampling has also been a standard assumption. A single sensor delivering measurements at a constant rate has been considered as the ideal situation. With the advent of networked asynchronous sensors the validity of this assumption has however changed. In fields such as economics and finance, uniform sampling might not be practically possible. This indicates a need for methods coping with non-uniform sampling

In the first part of this thesis the problem of estimation of irregularly sampled continuous-time ARMA models in the frequency domain is treated. In this process, the model output is assumed to be piecewise constant or piecewise linear, and an approximation of the continuous-time spectral density is calculated. Maximum Likelihood estimation in the frequency domain is then used to obtain parameter estimates. Rules of thumb concerning the model bias and variance are derived and used in order to select the frequencies to be used in estimation. Finally, the methods are applied to a tire pressure estimation problem.

The second part of the thesis treats frequency domain identification of continuous-time ARMA and OE models for uniformly sampled data. Here the end objective is to inspire improved interpolation schemes which excel over the piecewise-linear and piecewise-constant approximations used in the first part. The result is a method which estimates the continuous-time spectrum/Fourier transform from its discrete-time counterpart


    author = "Gillberg, Jonas",
    title = "Methods for Frequency Domain Estimation of Continuous-Time Models",
    school = "Department of Electrical Engineering, Link{\"{o}}ping University",
    year = "2004",
    month = Dec,
    address = "SE-581 83 Linköping, Sweden",
    type = "Licentiate Thesis no.  1133",