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

Abstract

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.

Noise jamming suppression using stretch processing and BEMD filtering

“…Some methods [11,12] have been proposed to calculate s k on the premise of a particular noise class. Here we employ a method [13] based on cross-validation [14] to adaptively calculate s k , since this method has no restriction to the noise type. The procedure is as follows.…”

De-noising of GPS structural monitoring observation error using wavelet analysis

“…Global Positioning System (GPS) has been successfully applied in the short-or longtime structural health monitoring (SHM) of the long-and short-period domains of large-scale civil engineering structures (Meng 2002;Zhong et al 2008;Im et al 2011). Yu et al (2006) summarized the advantages of GPS to monitor the deformation of civil structures.…”

“…Solutions to filtering (Ko & Fox 2009) and smoothing (Godsill et al 2004) in linear dynamic systems are well known, and numerous approximations for non-linear systems have been proposed, for both filtering (Ko & Fox 2009) and smoothing (Godsill et al 2004). Some researchers choose the filtration and smoothed models to mitigate the GPS errors as references (Meng 2002;Yu et al 2006;Psimoulis et al 2008;Zhong et al 2008;Kaloop 2012), and others used multiple antennae to reduce the multipath error and then used filtrations of observation also as references (Meng 2002;Roberts et al 2002;Danskin et al 2009;Oluropo et al 2014).…”

“…This study used the translation invariant threshold wavelet noise reduction method to reduce threshold to the signals with noise after translating, and then reverse translation of de-noised signals and get the processed signals. Zhong et al (2008) applied a method based on the technique of cross validation for automatically identifying wavelet signal layers, which is developed and used for separating noise from signals in data series. This study used the method of cross-validation filter after the dyadic wavelet decomposition to automatically identify the wavelet-decomposed signal levels, and then the filtered values of the observational series are reconstructed based on the wavelet coefficients which obtained from the signal levels determined.…”

Denoising GPS‐Based Structure Monitoring Data Using Hybrid EMD and Wavelet Packet

“…Dai et al [20] found that the period of the multipath effect is proportional to the distance between the antenna and refactor, and this relation is very sensitive to the distance change and appeared to be periodical. Other papers [21,22] also indicated that multipath effect caused by close distance reflection appeared to be in low frequency and periodical and recommended various filtering methods to weaken multipath.…”