Binary noise, correlation

Stochastic identification techniques, in principle, provide a more reliable method of determining the process transfer function. Most workers have used the Box and Jenkins [59] time-series analysis techniques to develop dynamic models. An introduction to these methods is given by Davies [60]. In stochastic identification, a low amplitude sequence (usually a pseudorandom binary sequence, PRBS) is used to perturb the setting of the manipulated variable. The sequence generally has an implementation period smaller than the process response time. By evaiuating the auto- and cross-correlations of the input series and the corresponding output data, a quantitative model can be constructed. The parameters of the model can be determined by using a least squares analysis on the input and output sequences. Because this identification technique can handle many more parameters than simple first-order plus dead-time models, the process and its related noise can be modeled more accurately. 

In the first experiment, a binary input signal with an amplitude of 1 and switching probability of 0.5 is used. This type of input signal, which has the same spectral characteristics as white noise, was shown by Levin (1960) to be the optimal input signal for the estimation of an FIR model. The correlation matrix associated with the least squares estimates of the FIR model parameters is well-conditioned with a condition number of 10.8. Without any noise added to the process output, the corresponding estimated... 

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