Research On Spatio-Temporal Uncertainty Propagation

Uncertainty propagation of spatio-temporal data is one of the most major problems, and also a focus of research in time geography. Space-time prism is an important geographic entity used to describe the range of potential accessible area determined by individual mobility. To date, the classical first-order Taylor series expansion method, Monte Carlo simulation and moment-design method are frequently used to analyze the spatio-temporal uncertainty propagation on the model. However, they need too much pro-information of system which restricts the application in some degree. In particular, the precision of traditional methods is relatively low and we can not get the analytical expression when the system is of high degree of nonlinearity and non-differential or the error distribution is unknown, while nonlinear situation is common. Thus, a further study of an analytical method of spatio-temporal uncertainty propagation, especially for the nonlinear propagation cases, is of theoretical significance and high practical application value.In order to further improve the basic theoretical foundation of spatio-temporal uncertainty propagation, enhance the precision of spatio-temporal uncertainty propagation, and discuss the analytical algorithms, in this paper, we start with improving the approachability of Taylor-series expansions, and focus on the study of analytical uncertainty propagation algorithm on the base of the second-order Taylor series expansion. Then the validity of the model is verified by comparing with Monte Carlo simulations through several simulation experiments. The main research work of this paper are as follows:1. We analyze the existing basic theories and methods of spatio-temporal uncertainty propagation, summarize and compare these methods so as to provide the required guidance for practical applications in time geography.2. In order to further improve the uncertainty propagation theory of spatio-temporal data in time geography, the strict definitions of the spatio-temporal models of mobile target is given from the viewpoint of set theory. Then, the strict mathematical expression of uncertain space-time prisms under uncertain time, uncertain space and uncertain speed parameters are given.3. In view of low accuracy of the first-order Taylor series expansion method, this paper puts forward the analytical method of spatio-temporal uncertainty propagation on the base of second-order Taylor series expansion method which provides strict theoretical support to thespatio-temporal uncertainty propagation problems. At the same time, the simulation experiments and example analysis are carried out to verify the stability and effectiveness of the method in comparison with Monte Carlo stochastic simulation method.