Deformation Detection in the GPS Real-Time Series by the Multiple Kalman Filters Model

Global Positioning System (GPS) is widely used for monitoring some natural phenomena and man-made structures. The detection of the deformation epoch in real time is of great importance in these applications. This study is concerned with designing algorithms to detect the deformation epoch in order to improve the quality of GPS measurements for the real-time deformation applications. In this regard, the multiple Kalman filters model based on the idea of model selection is proposed to improve the reliability of the detection of the deformation epoch. For the model selection, the proposed model makes use of the statistical criterion comparison in each case instead of the hypothesis test. The model with the lower value of the statistical criterion is to be preferred. According to the statistical criterion, the optimal Kalman filter model can be selected to describe the time series and to identify the deformation epoch at each epoch. The simulated data and the GPS kinematic time series are used to verify the e...

[1]  Steffen Schön,et al.  Affine distortion of small GPS networks with large height differences , 2007 .

[2]  Ch. Hajiyev,et al.  Kalman Filter Innovation Sequence Based Fault Detection in LEO Satellite Attitude Determination and Control System , 2007, 2007 3rd International Conference on Recent Advances in Space Technologies.

[3]  Alan S. Willsky,et al.  A survey of design methods for failure detection in dynamic systems , 1976, Autom..

[4]  Greg Welch,et al.  An Introduction to Kalman Filter , 1995, SIGGRAPH 2001.

[5]  Richard B. Langley,et al.  Local deformation monitoring using GPS in an open pit mine: initial study , 2003 .

[6]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .

[7]  Chris Rizos,et al.  On-line detection of abrupt changes in the carrier-phase measurements of GPS , 1997 .

[8]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[9]  Yuanxi Yang,et al.  Adaptively robust filtering for kinematic geodetic positioning , 2001 .

[10]  G. Strang,et al.  Linear Algebra, Geodesy, and GPS , 1997 .

[11]  Muhammed Sahin,et al.  Real-time deformation monitoring with GPS and Kalman Filter , 2000 .

[12]  Erik W. Grafarend,et al.  Horizontal Deformation Rate Analysis Based on Multiepoch GPS Measurements in Shanghai , 2008 .

[13]  Edward M. Mikhail,et al.  Observations And Least Squares , 1983 .

[14]  J. Rissanen.  A UNIVERSAL PRIOR FOR INTEGERS AND ESTIMATION BY MINIMUM DESCRIPTION LENGTH , 1983 .

[15]  P.J.G. Teunissen,et al.  Quality control in integrated navigation systems , 1990, IEEE Aerospace and Electronic Systems Magazine.

[16]  Stelios P. Mertikas.  Automatic and Online Detection of Small but Persistent Shifts in GPS Station Coordinates by Statistical Process Control , 2001, GPS Solutions.

[17]  Mohinder S. Grewal,et al.  Kalman Filtering: Theory and Practice Using MATLAB , 2001 .

[18]  Richard A. Brown,et al.  Introduction to random signals and applied kalman filtering (3rd ed , 2012 .