A comparative study of several Taylor expansion methods on error propagation

Abstract

In the literature for error propagation, there have been many methods such as Monte Carlo simulations and Taylor expansions. Among them, the Taylor expansion method is popular since it not only gives the propagation relationship, but also can reveal the effects of small perturbations away from the true value. One-order Taylor expansion method, as a linear approximation, has been studied extensively for its simplicity of computation. However, most of the system functions in practice are nonlinear. Aimed at this point, we investigate in this paper the exact error propagation method and higher-order Taylor expansion methods when the random error vectors are distributed independently or dependently, and use Taylor expansion methods to length measurements of linear segments and perimeter measurements of polygons, which are basic operations in GIS. Simulation experiments show that the five-order Taylor expansion method is superior to those used three-order expansions if the accuracy of propagated outputs is the only purpose without considering the computational complexity. This method improves just a little accuracy, but greatly increases the numbers of calculating partial derivatives when it compares with lower-order Taylor expansions. Thus, the three-order Taylor expansion method is generally a more feasible selection in practice.