非平稳随机信号下的空间滤波与推估正成为热点，其空间自相关性建模是关键。最小二乘配置和克立金等只适于有平稳协方差函数的空间过程的滤波与推估；已导出的描述加性非平稳随机信号空间自相关性的各种非平稳协方差函数由于缺少遍历性而具有主观性。本项目引入乘性非平稳随机信号，与加性非平稳随机信号一道来描述空间过程的随机变化，提出用偏随机游动和变系数自回归模型这样的新思路来构成空间自相关模型，与非平稳协方差函数形成互补，并改善其主观性。在正态假设下将非平稳随机信号作为缺失数据，并根据自相关模型来构建完整的空间数据似然密度，用EM算法、加权最小二乘法、偏差改正最小二乘法等获取连续光滑期望函数模型参数估计，预测随机信号并评价精度等，进一步扩展到粗差污染和无全局连续光滑期望函数情况。将获得的理论成果在GPS电离层数据分析中展开应用。项目完成后不仅促进大地测量数据处理理论发展，也是对空间统计学的贡献，具有科学意义。

The spatial filtering and predication for nonstationary random signal process with nonstationary covariance function has been becoming a hot spot, and its key is to model the spatial autocorrelation. The least squares collocation and kriging method can only be used for filtering and predication of spatial process with stationary covariance function.The already derived a wide variety of nonstationary covariance function for characterizing spatial autocorrelation of nonstationary random signal are subjective due to the absence of erogity. This project will introduce the multiplicative nonstationary random signal, together with the additive nonstationary random signal, to characterize the nonstationary random part of spatial data set. The partial random walk and the autogression with varying coefficients as new models are proposed to model the spatial autoucorrelation, and thus form the complementary of nonstationary covariance and improve the subjectivety.The nonstationary random signal data, under the assumption of being normally distributed, are regarded as missing values, and used for constructing the complete data likelihood density depending on the coreesponding spatial autuocorrelation. The EM algorithm, weighted least squares method and bias-corrected least squares method are used to estimate the continuous smoothing expectation function model parameters, predicate the random signal and assess precision. And further, the research is extended to cases with gross errors and/or no global continuous smoothing expectation function. The obtained theoretical result and tool will be used to analyize the GPS technology-derived total electronic content(TEC).After completing this project, the relatively systematic theroy and methodology of filtering and predication for processing nonstationary random signal process with nonstationary spatial correlation will be formed, this will not only promote geodetic surveying data processing, but also make a contribution to spatial statistics.