Processing Superposed Measurement Data By Regression Algorithms
Hartmut Moeck · WIT transactions on modelling and simulation · 1970
The structure of physical phenomena usually results from interrelated influences. Assuming a corresponding decomposition model is known, the problem of measurement data analysis will often be reduced to fitting the data by superposed single influence functions with respect to a fixed period of time or a common spatial region. But since in many cases the influences have unknown shifts of time and position, additional relations with respect to the domain have to be taken into account. We present a modular system for fitting one or two-dimensional measurement data, using arbitrarily superposed model functions. The desired intrinsic shape parameters of the model functions and as the parameters of the transition of time and position are determined by special constraint minimisation procedures. There are many applications of such regression models, but because of its nonconvex basic structure the efficiency of the approach strongly depends on the availability of suitable start estimations. We present a fitting approach that is in a certain sense universal. However, a satisfactory solution can be found only if good conditions prevail for the application. We giveexamples of time series processing and a particular case of surface measurement. Transactions on Modelling and Simulation vol 10, © 1995 WIT Press, www.witpress.com, ISSN 1743-355X