Space-Time Kalman Filter And Its Application In Deformation Monitoring Data Processing

Abstract:Kalman filter not only dynamically removes the noise of deformation monitoring data, but also predict the deformation. So it has been widely applied in deformation monitoring data processing and analysis. But conventional Kalman filter can only process the monitoring data aiming at the single point and can’t provide the whole analysis of the monitoring areas. Therefore, this paper makes an intensive study of Kalman filter theory, Kriging methods and the combined Space-Time Kalman filter, then introduces the Space-time Kalman filter to the field of deformation monitoring data processing and analysis. The main contents and achievements of this paper are as follows:(1) A weighted regression method based on entropy is proposed to estimate the parameters of variogram model. Kriging and its core and basic tool variogram are important contents of Space-Time Kalman filter, and the choice of variogram models and the parameter estimation are the key to the optimum fitting of variogram models, this is related to the spatial-temporal correlation part of Space-Time Kalman filter and so affects the results of Space-Time Kalman filter. In geostatics, the distances between two adjacent sampling points are the same, that is, unique step sampling, under this circumstances, we can get a relatively precise variogram model using the weighted regression to estimate the model parameters which taking the number of the sampling point pairs as weights. But in deformation monitoring, the distances are usually various, the numbers of sampling point pairs can’t reflect the reliability of the variogram value. So a weighted regression method based on entropy is proposed to estimate the parameters of variogram model.(2) A combined Space-Time Kalman filter is built. Kriging is an optimum linear unbiased local estimation method; it has been widely applied in geostatics. Kalman filter is a dynamic data processing method and is widely used in deformation monitoring. We combine Kriging and Kalman filter into Kriging Kalman filter in which the spatial correlation and temporal correlation are considered separately. The simulation experiment and processing of dam displacement monitoring data show that Kriging Kalman filter make full use of the positions of observation points, and has a more precise filtering result.(3) We make an intensive study of Space-Time Kalman filter put forward by Mardia K V etc. Taking the characteristic of deformation monitoring data into consideration, this paper builds a Space-Time Kalman filter model suitable for deformation analysis. The model builds the Kalman filter state model by dynamic model and estimates the state noise covariance matrix and observation noise covariance matrix by EM algorithm. The simulation experiment and processing of Guangzhou nansha GPS settlement observation data show that Space-Time Kalman filter is able to do spatial-temporal prediction, and the result is rather reliable and has a high precision. It has broad application prospects in deformation analysis.(4) A robust Space-Time Kalman filter model based on IGGIII scheme is built. As it is vulnerable to the external environment and the instrument failure, gross errors are inevitable in deformation monitoring data. Referring to robust Kalman filter put forward by Yang Yuanxi, this paper combines robust estimation with Space-Time Kalman filter to form robust Space-Time Kalman filter using IGGIII robust equivalent weight scheme. The simulation experiment and processing of Tianjin CORS network monitoring data show that besides inheriting the superior properties, robust Space-Time Kalman filter is able to resist the gross error.