On the propagation of uncertainty in complex-valued quantities

This paper explores a recent suggestion to use a bivariate form of the Gaussian 'error propagation law' to propagate uncertainty in the measurement of complex-valued quantities (Ridler N M and Salter M J 2002 Metrologia 39 295-302). Several alterative formulations of the law are discussed in which the contributions from individual input terms are more explicit. The calculation of complex-valued sensitivity coefficients is discussed and a matrix generalization of the notion of a 'component of uncertainty' in a measurement result is introduced. A form of a 'chain rule' is given for the propagation of uncertainty when several intermediate equations are involved.