Spatio-Temporal Dynamic Fields Estimating and Modeling of Missing Points in Data Sets Using a Flexible State-Space Model

Abstract

Modelling and estimating spatio-temporal dynamic field are common challenges in much applied research. Most existing spatio-temporal interpolation methods require massive prior calculations and consistent observational data, resulting in low interpolation efficiency. This paper presents a flexible state-space model for iteratively fitting time-series from random missing points in data sets, namely Flexible Universal Kriging state-space model(FUKSS). In this work, a recursive method similar to Kalman filter is used to estimate the time-series, avoiding the problem of increasing data caused by Kriging space-time extension. Based on the statistical characteristics of Kriging, this method introduces a spatial selection matrix to make the different observation data and state vectors identical at different times, which solves the problem of missing data and reduces the calculation complexity. In addition, a dynamic linear autoregressive model is introduced to solve the problem that the universal Kriging state-space model cannot predict. We have demonstrated the superiority of our method by comparing it with different methods through experiments, and verified the effectiveness of this method through practical cases.