Parameter Estimation in Process Identification

Although for simple models it is possible to estimate the parameters using least-squares, linear regression (see, e.g. (Question 21) in Sect. 3.8.2), for more complex models this is not possible. Instead, more complex methods are required in order to obtain them. One very popular approach is the prediction error method. Parameter estimation using the prediction error method can be summarised as follows  

Select an appropriate (prediction error) model and determine the corresponding one-step ahead optimal predictors (Eq. (6.27)). 

Using the experimental data, compute the prediction values and prediction errors as functions of the unknown parameters 9. 

Obtain the parameter estimates that minimise the sum of all of the prediction errors. Due to the nonlinear nature of the problem, this step is most often performed using a numerical optimisation algorithm. 

In practice, this procedure is greatly simplified, since there exist appropriate computer functions that can perform the required tasks once the general form of the model (orders and time delay) is specified. 

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