时空Kalman滤波在变形分析中的应用研究

Research on application of spatio-temporal Kalman filter in deformation analysis

时空Kalman滤波可对变形监测数据进行时空滤波去噪、数据插补和变形预测,本文利用时空Kalman滤波进行变形分析,从模型原理及试验两方面比较分析了Kriged Kalman filter(KKF)、space time Kalman filter(STKF)和spatio-temporal mixed effects(STME)3种典型时空Kalman滤波模型的性能和适用性。结果表明:3种时空Kalman滤波模型均基于空间基函数及动力学模型组合形式描述时空数据的时空相关性,其主要差异在于空间变异的描述形式不同、空间基函数和状态转移矩阵构造过程不同及模型降维方法不同。在适用性方面,KKF模型更适合于稀疏测站的变形分析,STKF模型及STME模型更适合于海量测站的变形分析。在变形分析应用效果方面,3种时空Kalman滤波模型均具有较高精度的时空滤波去噪、数据插补和变形预测性能,其滤波结果相对于普通Kalman滤波结果的平均改善率为21.1%,其缺失数据插补结果相对于Hermite时间插值结果的平均改善率为42.4%,其空间预测结果相对于Kriging空间插值结果的平均改善率为65.3%,其对已知测站未来变形的时空预测结果相对于普通Kalman滤波时间预测结果的平均改善率为20.6%,其对非观测站点未来变形的时空预测结果相对于Kalman滤波+Kriging组合模型预测结果的平均改善率为20.5%。

Spatio-temporal Kalman filter can be used for spatio-temporal data denoising,interpolation and deformation prediction.In order to use the spatio-temporal Kalman filter model for spatio-temporal deformation analysis,the performance and applicability of three typical spatio-temporal Kalman filter models,namely Kriged Kalman filter(KKF),space time Kalman filter(STKF)and spatio-temporal mixed effects(STME),are compared and analyzed from the aspects of principles and experiments.The results show that:in theory,the three spatio-temporal Kalman filter models are based on the combination of spatial basis function and dynamic model to describe the spatio-temporal correlation.The main difference lies in the expression of spatial data,such as trend term,fine-scale variation,observation noise and spatial basis function.In terms of applicability,the KKF model is more suitable for the spatio-temporal deformation analysis of sparse stations,while the STKF model and STME model are more suitable for the spatio-temporal deformation analysis of massive stations.In terms of application effects of spatio-temporal deformation analysis,the three spatio-temporal Kalman filter models have high-precision effect in denoising,data interpolation and deformation prediction performance.The average improvement rate of denoising results compared with ordinary Kalman model is 21.1%,the average improvement rate of interpolation results compared with Hermite time interpolation results is 42.4%,the average improvement rate of its spatio-temporal prediction results relative to Kriging spatial interpolation results is 65.3%,the average improvement rate of its spatio-temporal prediction results for observation stations relative to the time prediction results of ordinary Kalman filter is 20.6%,and the average improvement rate of its spatio-temporal prediction results for non-observation stations relative to the prediction results of Kalman filter+Kriging model is 20.5%.