Abstract:

Time geographic kernel density estimation is an extension of classical kernel density estimation (KDE) based on time geography. It mainly extends the definition domain of the standard kernel function to the space-time reachable domain of time geography, so as to avoid the problem of non-zero density being assigned outside the reachable domain by enhancing the physical meaning of the definition domain in space-time. The space-time reachable area includes the space-time disc and the potential path area (PPA) compounded by the space-time disc. These two types of reachable domains can be used as the domain of the kernel function to solve the above problems, but they also bring new problems. The kernel function constructed based on the space-time disc can be superimposed into the probability density on the PPA, but it is sensitive to the time point of the disc. Compared with the ideal Brown Bridge model, the kernel function constructed based on PPA lacks bimodal characteristics, and cannot generate the probability density function on the space-time disc. Therefore, the research on the combination of time geography and KDE is still in the stage of theoretical exploration before application. The goal of this article is to sort out this process and elicit future development trends. Focusing on the goal of quantifying the uncertainty of space-time trajectory, this article first reviews the different functions of time geography and KDE, and then elaborates the meaning, framework and mode of the integration of the two. Finally, this article believes that the time-geographic reachable domain instead of the domain of KDE is an important means to improve the uncertainty measurement of space-time trajectory, but there is still a certain distance from the landing of the target.

Key words: kernel density estimation, time geography, potential path area, space-time trajectory