Efficient, Accurate, and Non-Gaussian Statistical Error Propagation Through Nonlinear, Closed-Form, Analytical System Models

Uncertainty analysis is an important part of system design. The formula for error propagation through a system model that is most-often cited in literature is based on a first-order Taylor series. This formula makes several important assumptions and has several important limitations that are often ignored. This thesis explores these assumptions and addresses two of the major limitations. First, the results obtained from propagating error through nonlinear systems can be wrong by one or more orders of magnitude, due to the linearization inherent in a first-order Taylor series. This thesis presents a method for over-coming that inaccuracy that is capable of achieving fourth-order accuracy without significant additional computational cost. Second, system designers using a Taylor series to propagate error typically only propagate a mean and variance and ignore all higher-order statistics