Data Quantisation and Closed-Loop System Identification

In the development of a rigorous and complete procedure for automating the performance of data-driven process identification, there is a need to consider data quantisation. Such an issue can arise when the sensors have not been properly calibrated for the range of values experienced in the actual process. Through a detailed mathematical analysis of the problem, it is shown that the ratio between the variance of the signal and the gap between quantisation levels strongly influences the ability to identify a process. Using this criterion, a data quantisation index is proposed that allows for the effect of data quantisation on the data system to be quantified. Monte Carlo simulations of a closed-loop system with different system properties is examined to show that the proposed index can accurately distinguish between good and bad data quantisation.