System Identification and Parameter Estimation – Introduction
The first lecture gives an overview of the course and a general introduction to system identification and parameter estimation.
System identification, in this course, tries to elucidate the dynamic relation between time-signals and to parameterize this relation in a mathematical model (where the model is based on differential equations). In this course emphasis is paid to system identification in frequency domain. Key element of this approach is the Fourier transform. Major advantage of the frequency domain approach is that no a-priori knowledge is required of the type of the model (order of the system). Every recorded time-signal will be contaminated with noise. Noise is, by nature, a random process and consequently measured signals are stochastic. In stochastic theory not the individual realization is important but the statistical properties are, e.g. mean, standard deviation, and also probability density functions. With ergodicity it is thought that one, sufficiently long, realization is representative for many realizations. This implicates that it is sufficient to capture one recording of a signal to assess its (statistical) properties (in stead of multiple recordings). Cross-product and cross-covariance functions are measures to estimate the relation between two (stochastic) signals in time-domain.
Introduction to the course
Readings
Book: Westwick & Kearney
- Chapter 1: all
- Chapter 2: section 2.1 – 2.3.1
Book: Pintelon & Schoukens
Chapter 1: section 1.1 – 1.4 (optional)