Wavelet Extended EMD Noise Reduction Model for Signal Trend Extraction

In this paper, the structure of multi-scale decomposition and reconstruction of empirical mode decomposition (EMD) theory is defined. Through the combination of wavelet and EMD theory, a new EMD-wavelet dynamic deformation data de-noising model is proposed. The model is presented to reduce noise of coordinate time series. 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 time series. Compared with the denoising models based on wavelet, Kalman and EMD, the EMD-wavelet model has relatively higher signal-to-noise ratio(SNR) than other models and the lowest root mean-square error (RMSE), E_NAE and E_Bias with respect to the x/y/z coordinate time series. The results show that the EMD-wavelet model has relative advantage.

I. Introduction

Wavelet transform is developed rapidly as a new signal processing tool in recent years. Wavelet noise reduction modeling is one of the most effective techniques with respect to complicated signal analysis. As a signal time-scale(time-frequency) analysis method, Wavelet transform has multi-resolution characteristics, and has the ability of denoting signal characteristics in time and frequency domains. Although wavelet transforms are suitable for noise reduction, in other words, for signal trend extraction, its pre-divided frequency feature limits its ability to decompose the signal into different frequencies according to the inherent characteristics of the signal. Empirical Mode Decomposition (EMD) is a new signal analysis technique showing great promise for signal trend extraction [1]. EMD technique has already been successfully applied to several other scientific problems. It provides an adaptive representation of non-linear signals, which ensure the non-linear signal can be converted into an Intrinsic Mode Function (IMF) more easily for wavelet analysis. Based on EMD and the wavelet shrinkage noise reduction model, a new trend extraction model called the EMD-Wavelet model is presented here.