Uncertainty propagation on a nonlinear measurement model based on Taylor expansion

Abstract

In this paper, the propagation of uncertainty on a nonlinear measurement model is presented using a higher-order Taylor series. As the derived formula is based on a Taylor series, it is necessary to compute the partial derivatives of the nonlinear measurement model and the correlation among the various products of the input variables. To simplify the approximation of this formula, most previous studies assumed that the input variables follow independent Gaussian distributions. However, in this study, we generate multivariate random variables based on copulas and obtain the covariances among the products of various input variables. By applying the derived formula to various cases regardless of the error distribution, we obtained the results that coincide with those of a Monte-Carlo simulation. To apply high-order Taylor expansion, the nonlinear measurement model should be continuous within the range of the input variables to allow for differentiation, and be an analytic function in order to be represented by a power series. This approach may replace some time-consuming Monte-Carlo simulations by choosing the appropriate order of the Taylor series, and can be used to check the linearity of the uncertainty.