Centre for Research on Environmental Systems and Statistics Captain Toolbox

CAPTAIN Toolbox website

Overview & availability

User interface & examples

Time variable parameter subset

Multivariable transfer function subset

Download CAPTAIN Toolbox


Lancaster University
Systems and Control
Environmental Science

Transfer Function analysis of simulated data with noise.

The Refined Instrumental Variable (RIV) algorithm allows for robust unbiased estimation of multivariable discrete and continuous time transfer function models. In this example, we employ the Captain Toolbox to analyse a multiple-input system based on a second order transfer function. Coloured noise is added to the system output with the introduction of a first order filter, through which a white noise signal is passed. The system is put through a series of input steps from which output data are collected as illustrated below.

Inputs 1 (top) and 2 (middle), together with the simulated output (bottom).

The structure of the transfer function is identified with a straightforward call to the Captain Toolbox function rivid, which also returns the parameter estimates. The model fit is compared with the noisey simulation data below. Note that the fitted data are not the 1 step-ahead-predictions, rather, they are obtained by feeding the input signals through the estimated transfer function.

Estimated model output and simulated data (circles).

Despite the large amount of noise seen in the figure above, the parameter estimates are within 1 percent of their actual values. Finally, the estimated and actual noise signals are illustrated below: the two variables are almost indistinguishable.

Estimated (red) and actual noise.

previous example  

To the Top

c.taylor@lancaster.ac.uk 23-FEB-2011