Analyses of GPS signals by wavelet algorithms and empirical mode decomposition (EMD) have demonstrated the strength of these techniques in discriminating signals from noise. However, the denoising precision seriously affects the final EMD error, especially for signals containing incremental developments in information. We present a new noise filter and trend extraction model based on the orthogonal wavelet transform and EMD. Simulated and real data are used to evaluate the proposed method. The results suggest that: 1) The orthogonal wavelet transform and EMD method can better mitigate the random errors hidden in periodic signals; 2) For signals with a linear trend, the orthogonal wavelet transform filtering method is superior to EMD. We suggest a method of trend extraction by EMD after noise filtering using the wavelet; 3) For signals with a nonlinear trend, theoretical analysis and simulation results show that the new noise filter and trend extraction model is superior to EMD and the simple combination of wavelets with EMD. The proposed approach not only extracts instantaneous features, but also reduces the number of decomposition layers of the signals and the cumulative errors in later decomposition. This method significantly improves the accuracy of the extracted deformation; 4) After mitigating the influence of multipath and other error effects with the new model, we attain millimeter accuracy for the vertical component position in GPS dynamic deformation.
THEORY OF DIGITAL FILTER BANKS REALIZED VIA MULTIVARIATE EMPIRICAL MODE DECOMPOSITION
