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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.

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