Nonlinear processing of n-dimensional phase signals

Many measurement principles in physics and engineering deliver a set of ambiguous phase signals, from which the unknown quantity, e.g. a distance or angle, has to be calculated. In this paper a novel nonlinear algorithm is introduced, in order to achieve an optimized determination of this unknown quantity from phase measurements. This algorithm is based on a generalization of the well-known nonius principle and applies nonlinear signal processing. The main advantages compared to known methods are an enormous reduction of measurement errors and a significant increase of robustness against large input errors. Furthermore, this approach can be implemented very effectively on digital systems. Examples show the usefulness and easy implementation of the proposed algorithm.