We investigated a Gaussian conditional geostatistical spatio-temporal model (CGSTM) aiming to fit data observed at non-fixed locations over discrete times, based only on the observed locations. The model specifies the process state at the current time conditioning on the process state in the recent past. Particularly, the process mean uses a weighting function governing the spatio-temporal model evolution and handling the interaction between space and time. The CGSTM provides attractive features, such as it belongs to the dynamic linear model framework, models non-fixed locations over time and easily provides forecasting maps k-steps ahead. Likelihood estimation and inference are based on a Kalman filter-based algorithm. Equivalent closed form of a covariance and precision matrices of the spatio-temporal joint-distribution was obtained. We performed a simulation study considering locations of a real data example, which presents data locations varying over time. A second simulation study was ran using various scenarios for parameter values and number of observations in time and space, observing consistency and unbiasedness of model estimators. Thirdly, The model was fitted to the average monthly rainfall dataset, with 678 temporal registers at 32 stations located in western Paraná, Brazil. The rainfall station locations suffered geographical changes from 1961 to 2017. In this modelling, we used explanatory variables and provided forecasting maps.

我们研究了高斯条件地统计时空模型（CGSTM），旨在仅基于观察到的位置来拟合离散时间在非固定位置观察到的数据。该模型以最近的过程状态为条件指定当前时间的过程状态。特别地，过程均值使用权重函数来控制时空模型的演化并处理时空之间的相互作用。CGSTM提供了吸引人的功能，例如它属于动态线性模型框架，随着时间的推移对非固定位置进行建模并轻松提供了预测图k前进。可能性估计和推断基于基于卡尔曼滤波器的算法。获得了时空联合分布的协方差和精确矩阵的等价闭合形式。我们进行了一次模拟研究，考虑了实际数据示例的位置，该示例显示了随时间变化的数据位置。进行了第二次模拟研究，使用了各种方案来进行参数值和时空观测的数量，观察模型估计量的一致性和无偏性。第三，该模型适合于平均月降雨量数据集，位于巴西巴拉那州西部的32个站点上有678个临时记录。从1961年到2017年，降雨站的位置发生了地理变化。在此建模中，我们使用了解释变量并提供了预测图。