## System Identification Toolbox

# Tutorial introduction

The toolbox estimates a range of model structures, using a range of estimation methods and can accommodate several different data types

## Data types

The following data types are supported

Multivariable time domain data that is regularly or irregularly sampled;

Multivariable frequency domain data

## Model types

The following model types are supported

Bilinear state space structures

Linear grey box structures

These may be expressed with regard to the shift operator in all cases, with respect to the operator in the transfer function case, and with respect to the continuous time derivative operator in the linear state space case.

## Estimation Methods and Algorithms

The following estimation methods are supported

Prediction Error Estimation (quadratic criterion)

Maximum Likelihood Estimation

Subspace-based estimation

These are implemented via the following algorithms

A range of gradient based search methods including robust Gauss-Newton, Levenberg-Marquardt, and trust region techniques

The expectation-maximisation (EM) algorithm

## Tutorial overviews and examples

The following links provide tutorial examples illustrating the use of the toolbox across the above range of data types, model types and estimation methods.

Estimation of Transfer Function Structures

Estimation of State-Space Structures

Estimation from Frequency Domain Data

Estimation of Hammerstein-Wiener Nonlinear Structures

Estimation from Non regularly sampled Data]