THE IMPORTANCE OF ESTIMATION AND APPROXIMATION METHODS IN SYSTEM THEORY
Eugen-Georg Woschni · Cybernetics & Systems · 1992
In several fields of cybernetics—for instance, in measurement—the input signals are not known; that means they are to be supposed using the a priori information of the process. Therefore estimation and approximation methods play an important role. In this paper some typical examples will be treated: First, estimation of the errors caused by violations of die sampling theorem (cutoff and aliasing errors) is treated. It is shown that in particular modern sensors with direct digital output often produce aliasing errors because of the direct coupling of the input of the sensor to die signal source. On the other hand, these errors are dependent on the processing after sampling. The next example concerns problems of optimal filtering. Because in practice the power density of a signal is often not known, approximations are used. Furthermore, it is shown that limitations of the degree of correction arise from changing parameters of the system. This sensitivity of the corrected system is greater as the degree of correction is higher. Here, under extreme conditions adaptive systems—measuring the changing parameters by cross-correlation methods—will be used. Finally, dynamic errors, methods for estimating the correct output, and consequences for the selection of measuring systems using several models of the system behavior are treated.