On the superposition of error contributions

This contribution deals with fundamental considerations on cumulative effects of multiple error contributions in measurement setups and communication links. Generally, any part of a measurement setup bears some uncertainty, such as amplifiers with varying gain, receivers with thermal noise or a communication channel, the characteristics of which can only be specified to a certain amount of accuracy. Usually, such uncertainties described by given standard deviations are combined to an overall uncertainty in terms of error budgets just by root mean squaring (RMS) respective standard deviations. However, in several cases, in particular those of uncertainties due to unknown propagation channel characteristics, the RMS addition cannot be applied and systematically overestimates the overall uncertainty. In this contribution such an error superposition is discussed for the applications of radio navigation systems, where multipath propagation, i.e. reflections on objects, are the major part of error contributions. A superposition of such error contributions is done with a self-developed numerical tool as well as with a laboratory measurement setup. Both methods show the same results. In particular, the latter is necessary for a transparent and litigable visualization and validation of the proposed methods for superposition of error contributions for flight safety authorities.