ABSTRACT
This chapter focuses on various grid/sample-based methods, and the application to the orbital uncertainty propagation problem. Uncertainty propagation through dynamic systems widely exists and is often an essential need in many science and engineering disciplines, such as biology, computational physics, and aerospace engineering. Orbital uncertainty propagation is one of important applications of uncertainty propagation in space situational awareness, which concerns space surveillance and tracking. In order to predict the uncertainty of the dynamic system accurately, the high-precision numerical integrator for solving the ordinary differential equation is required. Consider the orbital uncertainty propagation problem as an example using the Gaussian mixture. Different from the Gaussian quadrature based uncertainty propagation method, the polynomial chaos has the ability to represent the high order moments information of the Probability Density Function. The conventional generalized polynomial chaos requires the given description of the initial uncertainty distribution. MapReduce is a programming model, and widely used in processing big data.
