Uncertainty Analysis On Temporal And Spatial Models Of Mobile Objects

The temporal and spatial models of mobile objects in time geography are to describe thetraveling trajectory, the potential path and the law of time-space change, including space-timepath, space-time prism and potential path area et al.. Specially, the space-time prism couldreveal the uncertainty information of objects’ activity. To date, the traditional one orderTaylor series and Monte Carlo simulation are often used to treat the uncertainty propagationon the models, however, too more pro-information of system restricts the application in adifferent degree. Particularly, the precision of traditional methods is low under high degree ofnonlinearity and non-differential. On the other hand, the theory of rough set has been appliedto time geography and then explains the concept of rough space-time prism without thespecific definition of upper and lower approximate. Thus the theory of rough set in timegeography is lack of the foundation of application.To improve the precision of uncertainty propagation and further discuss the theoreticalfoundation of the rough space-time prism, the main research works are as follows:1. In order to improve the measurement theory of time geography, the definitions of thetemporal and spatial models of mobile object on the point of set theory are presented. Thenthe uncertain space-time prisms under different cases are also defined in the form of set.2. Due to the shortages of the error propagation based on the one-order Taylor series, theerror propagation based on the moment design theory is proposed to handle the uncertaintyproblems on the time geography models. The effectiveness and stability of the algorithm arechecked and compared by simulation experiments.3. In order to improve the existing definition of the rough space-time prism, the theory ofcovering approximation spaces is combined with the theory of time geography. Then, theconcept of covering approximation spaces based on the space-time prism is raised and ageneralized lower and upper covering approximation operators are described. Finally, theuncertainty of rough space-time prism is measured by three indexes.