Determination of an appropriate mother wavelet for de-noising of weak GPS correlation signals based on similarity measurements

The Wavelet Transform (WT) is one of the most widely used tools for de-noising of Global Positioning System (GPS) signals which is a method for enhancing the sensitivity of GPS receivers in the acquisition of weak signals. The appropriate selection of mother wavelet which results in concentration of the major part of the power of a signal on a few numbers of wavelet coefficients is one of the most determinative factors in the efficiency of the de-noising process. Considering the importance of this issue, for the first time, in this paper, we introduce a quantitative method for selecting an appropriate mother wavelet for decomposing weak GPS correlation signals. Our proposed method uses the similarity measurements to choose the fittest mother wavelet. We use P, Q, and Magnitude-Shape (MS) criteria which are three individual remodeling factors, to evaluate the capability of different mother wavelets in the proper decomposition of weak GPS correlation signals. Eventually, the mother wavelet is selected based on our introduced Figure of Merit (FOM) which increases the reliability of the method. Our suggested method improves the sensitivity of GPS receivers in the acquisition of weak signals by enhancing the quality of the de-noising process using WT.