Wegener, M.; Grasso Toro, F.; Schnieder, E.:
Enhancement of the GUM method to dynamical systems: A straightforward approach.
ADM 2014 - 8th Workshop on Analysis of Dynamic Measurements, Turin, Italien, May 2014.


Evaluation of the measurement uncertainty is essential for all kinds of professional measurements. The GUM framework represents a well-accepted guideline for the evaluation of measurement uncertainties. In the GUM, time-independent quantities and static measuring systems are presupposed. Measurements with time-varying quantity values and dynamical systems are not yet covered by the GUM method. This kind of measurement, however, is the basis for technical applications where measured values are directly processed in real-time by subsequent systems, e.g., filter algorithms and decision-making processes. In particular for safety-relevant applications in transport, uncertainty information concerning time-variant quantities in line with existing standards is required for safety cases (ISO 26262, IEC 61508). Standard compliant evaluation of measurement data will make sophisticated future applications in transport possible, e.g., lane-selective vehicle localisation and toll collection as well as automatic merging of traffic flows. The algorithm for calculating a time-varying measurement uncertainty has to be of low complexity for a real-time data evaluation with limited on board computing power. Thus, mathematically extensive approaches like Monte Carlo simulations are not appropriate for such applications. This issue has not been considered satisfyingly in current metrological research. Therefore, this contribution presents a straightforward application of the existing GUM standard to the class of dynamical systems described by linear state-space-models. A state-space model that characterizes the evolution of the time-variant uncertainty matrix is analytically derived from the measurement model. The stability property of such “uncertainty systems” is analysed with methods known from the theory of LTI systems and is illustrated by means of two examples: a first-order low-pass filter and the indirect distance measurement of a vehicle straight ahead motion.