Joint Input-Output Identification of a Closed-Loop Process

The third and final method for closed-loop process identification is called the joint input-output identification method, which uses all three signals, y and in order to identify a model of the system in a two-step procedure. In the first step, a model between r, and m, is fit to give 

the reference signal, r is filtered using the resulting g-polynomial to obtain an uncorrelated with noise, input signal, The process model can be identified by fitting the following relationship 

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