Adaptive wavelet transform based on cross-validation method and its application to GPS multipath mitigation

Global positioning system (GPS) multipath disturbance is a bottleneck problem that limits the accuracy of precise GPS positioning applications. A method based on the technique of cross-validation for automatically identifying wavelet signal layers is developed and used for separating noise from signals in data series, and applied to mitigate GPS multipath effects. Experiments with both simulated data series and real GPS observations show that the method is a powerful signal decomposer, which can successfully separate noise from signals as long as the noise level is lower than about half of the magnitude of the signals. A multipath correction model is derived based on the proposed method and the sidereal day-to-day repeating property of GPS multipath signals to remove multipath effects on GPS observations and to improve the quality of the GPS measurements.

[1]  Roy Thompson,et al.  An objective method for smoothing palaeomagnetic data , 1978 .

[2]  A. Leick.  GPS satellite surveying , 1990 .

[3]  G. Nason.  Wavelet Shrinkage using Cross-validation , 1996 .

[4]  Wan De.  THE STUDY OF QUASI WAVELETS BASED NUMERICAL METHOD APPLIED TO BURGERS' EQUATIONS , 2000 .

[5]  J. K. Ray,et al.  GPS code and carrier multipath mitigation using a multiantenna system , 2001 .

[6]  Michael S. Braasch,et al.  GPS receiver architectures and measurements , 1999, Proc. IEEE.

[7]  M Schumacher,et al.  Resampling and cross-validation techniques: a tool to reduce bias caused by model building? , 1997, Statistics in medicine.

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

[9]  Chris Rizos,et al.  MULTIPATH MITIGATION BY WAVELET ANALYSIS FOR GPS BASE STATION APPLICATIONS , 2005 .

[10]  Pat Fenton,et al.  Theory and Performance of Narrow Correlator Spacing in a GPS Receiver , 1992 .

[11]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  D. J. Allerton,et al.  Book Review: GPS theory and practice. Second Edition, HOFFMANNWELLENHOFF B., LICHTENEGGER H. and COLLINS J., 1993, 326 pp., Springer, £31.00 pb, ISBN 3-211-82477-4 , 1995 .

[13]  Waldemar Kunysz.  Advanced Pinwheel Compact Controlled Reception Pattern Antenna (AP-CRPA) designed for Interference and Multipath Mitigation , 2001 .

[14]  Xiaoli Ding,et al.  Filtering GPS time-series using a Vondrak filter and cross-validation , 2005 .

[15]  Chris Rizos,et al.  Multipath Mitigation of Continuous GPS Measurements Using an Adaptive Filter , 2000, GPS Solutions.

[16]  Wan-Chi Siu,et al.  Denoising by singularity detection , 1999, IEEE Trans. Signal Process..

[17]  Wan De-cheng,et al.  The study of quasi wavelets based numerical method applied to Burgers' equations , 2000 .

[18]  Paul Cross,et al.  A New Approach to GPS Phase Multipath Mitigation , 2003 .

[19]  Patrick C. Fenton,et al.  A Practical Approach to the Reduction of Pseudorange Multipath Errors in a Ll GPS Receiver , 1994 .

[20]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[21]  Anthonio Teolis,et al.  Computational signal processing with wavelets , 1998, Applied and numerical harmonic analysis.

[22]  P. Y. Georgiadou,et al.  On carrier signal multipath effects in relative GPS positioning , 1988 .

[23]  R.D.J. van Nee,et al.  The Multipath Estimating Delay Lock Loop , 1992 .

[24]  Eniuce Menezes de Souza,et al.  Wavelet Shrinkage: High frequency multipath reduction from GPS relative positioning , 2004 .

[25]  Leo Breiman,et al.  Classification and Regression Trees , 1984 .

[26]  M. Stone.  Cross‐Validatory Choice and Assessment of Statistical Predictions , 1976 .

[27]  Yi Sun,et al.  Wavelet-based compression of terrain , 2003, IGARSS 2003. 2003 IEEE International Geoscience and Remote Sensing Symposium. Proceedings (IEEE Cat. No.03CH37477).

[28]  David L. Donoho,et al.  De-noising by soft-thresholding , 1995, IEEE Trans. Inf. Theory.

[29]  Stéphane Mallat,et al.  Singularity detection and processing with wavelets , 1992, IEEE Trans. Inf. Theory.

[30]  Pedro Elosegui,et al.  Geodesy Using the Global Positioning System: The Effects of Signal Scattering , 1995 .

[31]  M. Pinsky.  Introduction to Fourier analysis and wavelets , 2002 .

[32]  Penina Axelrad,et al.  An Adaptive SNR-Based Carrier Phase Multipath Mitigation Technique , 1996 .