On moving averages, histograms and time-dependent rates for online measurement

Abstract

Moving averages (MAs) are often used in adaptive systems to monitor the state during operation. Their output is used as input for control purposes. There are multiple methods with different ability, complexity, and parameters. We propose a framework for the definition of MAs and develop performance criteria, e.g., the concept of memory, that allow to parameterize different methods in a comparable way. Moreover, we identify deficiencies of frequently used methods and propose corrections. We extend MAs to moving histograms which facilitate the approximation of timedependent quantiles. We further extend the framework to rate measurement, discuss various approaches, and propose a novel method which reveals excellent properties. The proposed concepts help to visualize time-dependent data and to simplify design, parametrization, and evaluation of technical control systems.