System Identification Toolbox

Delays

The selection of the delay nk in the model structure is a very important step in obtaining good identification results. You can get an idea about the delays in the system by the impulse response estimate from impulse.

Incorrect delays are also visible in parametric models. Underestimated delays (nk too small) show up as small values of leading estimates, compared to their standard deviations. Overestimated delays (nk too large) are usually visible as a significant correlation between the residuals and the input at the lags corresponding to the missing terms in the resid plot.

A good procedure is to start by using arxstruc to test all feasible delays together with a second-order model. Use the delay that gives the best fit for further modeling. When you have found an otherwise satisfactory structure, vary nk around the nominal value within the structure, and evaluate the results.

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Recursive Parameter Estimation