Calculations of measurement uncertainty in complex-valued quantities involving 'uncertainty in the uncertainty'

In some measurement uncertainty calculations there is uncertainty in the scale factor of a range of values that may be attributed to a quantity. This poses special problems. For real-valued calculations, international guidelines indicate two possible approaches, one loosely based on classical statistics, the other on Bayesian statistics. Complex-valued extensions of both approaches have been suggested that may be suitable for RF and microwave measurements. This paper presents algorithms for the complex-valued techniques and evaluates them with simulated data sets. We find that there are significant differences between results obtained by the two approaches. This suggests that an objective measure is needed for the performance of an algorithm for calculating measurement uncertainty in a complex-valued quantity.