Datum Deformation Analysis and Dynamic Stochastic Simulation for GPS Monitoring System

It is a very important work to analyze the working datum marks' stability for GPS deformation monitoring system.After the system working some period of time,a large amount of deformation observation data can be obtained,and these data can be described as one time series.If the datum marks is steady-going during this period of time,the time series of the observed data should be an ergodic stochastic series and cohere with the condition and nature of a stationary stochastic process. The autocorrelation function is one of eigenvalues of the stochastic process,it reflects the relativity of observations in different time.If the stochastic functions are not correlative,the estimation of their standard autocorrelation function should tend to zero when the time tends to infinity.Hereby,we can identify whether the studied time series is ergodic or not.In addition,if the stationary stochastic process contains periodical components,its autocorrelation function has periodical components as well,and the periodicity of both is same. FK(W20。40ZQ Generally speaking,the observed data of GPS deformation monitoring system is very difficult to be equally spaced,occasionally missing data within quite a length time,by reason of the influence of various factors (subjective and objective).The frequency spectral analysis is a quite efficient method to analyze periodical signals,but its prominent limitation is that the data must be equally spaced.For this reason,in this paper the spectral analysis is only applied to identify whether the time series has periodical components or not.If it contains periodical components,a higher order polynomial is used to approach the data series by the leasts-quares method.The practice testifies that this method is grealy effective which is applied for describing the long periodical alteration of the time series. Taking GPS automatic monitoring system of outside deformation for Geheyan dam on the Qingjiang river as example,this paper analyzes the deformation characteristics of tow working datum marks for this system.Results show that in vertical component,there is a small linear displacement trend with yearly 1.64mm,and a long periodical deformation trend with about one year;in horizontal directin,the linear displacement trend is not distinct,but there are also the deformation characteristics of a long periodical trend.In order to test and verify above results,the random data generator is employed to simulate the random data series,the end results are coincident.The research indicates that the small linear displacement trend included in the time series'errors can be identified by the time series' data of large sample quantity.