Reducing Carrier Phase Errors with EMD-Wavelet for Precise GPS Positioning

Jian Wang, Jinling Wang, and Craig Roberts

Abstract:	High-precision GPS baseline calculation is feasible only when very precise carrier-phase observations are available. Unfortunately, these observations are usually affected by systematic errors (such as multipath, ionospheric and tropospheric effects, orbit bias etc). In this paper, a new EMD-Wavelet trend extraction model is presented and integrated into a baseline calculation model for systematic error mitigation. The pre-divided frequency of the wavelet transform seriously affects its ability to extract trends of an input signal. The Empirical Mode Decomposition (EMD) technique is a new signal processing method for analysing non-linear time series, which decomposes a time series into a finite and often small number of Intrinsic Mode Functions (IMFs). The decomposition procedure is adaptive and data-driven. The IMFs are stationary which are more suitable for wavelet analysis. Therefore the merits of both the EMD and Wavelets can be combined for systematic error extraction in double-difference (DD) carrier-phase observations. Initial results from processing a simulated, mixed, nonlinear signal also shows the advantages and disadvantages of EMD and wavelets respectively. These are used to produce an improved EMD-Wavelet trend extraction model using the following process. Firstly, the non-linear series are decomposed into stationary IMFs and residual components. Secondly, the selected high frequency IMFs are de-noised with the wavelet model and finally, the EMD reconstruction gives the extracted system error series. Signal-to-noise ratio (SNR) and root mean square error (RMSE) are used to quantitatively evaluate the trend extraction effect. Based on the proposed trend extraction model, the baseline resolution procedure is shown and experimental results demonstrate: [EMD-Wavelet model is more suitable for systematic error extraction], [ High frequency IMFs are identified using Standardized Empirical Mean (SEM) of fine-to-coarse EMD reconstruction], and [Baseline calculation stability and the DD residual series are greatly improved with the suggested procedure]. The proposed systematic error extraction model can even be applied to baselines with more complicated system errors (eg strong sunspot activity) and other potential applications for similar time series analysis.
Published in:	Proceedings of the 2007 National Technical Meeting of The Institute of Navigation January 22 - 24, 2007 The Catamaran Resort Hotel San Diego, CA
Pages:	919 - 928
Cite this article:	Wang, Jian, Wang, Jinling, Roberts, Craig, "Reducing Carrier Phase Errors with EMD-Wavelet for Precise GPS Positioning," Proceedings of the 2007 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2007, pp. 919-928.
Full Paper:	ION Members/Non-Members: 1 Download Credit Sign In