System Identification

Noise-Free Simulations

To check whether a model is capable of reproducing the observed output when driven by the actual input, you can run a simulation:

u = Data(:,[],:) % Extracting the input from the data
yh = sim(Model,u)
y = Data(:,:,[]) % extracting the output from the data
plot(y,yh)

The same result is obtained by

compare(Data,Model)

It is a much tougher and revealing test to perform this simulation, as well as the residual tests, on a fresh data set Data that was not used for the estimation of the model Model. This is called cross validation.

Model Error Models

Assessing the Model Uncertainty