TI-LMD-based multi-path effect extraction for GNSS coordinate time series

Abstract A modified LMD (TI-LMD) method is proposed for the problems of endpoint effects, sliding average step size taking and modal confounding in the multipath effect extraction of GNSS coordinate time series applied by the local mean decomposition (LMD) method. Three main improvements are included: For the LMD endpoint effect, a matching delayed endpoint effect method based on similar triangular waveforms (MEBSTW) is proposed to find the best matching waveform from within the signal to the endpoint for endpoint delay. To address the problem of taking the sliding average step size, a method of taking the sliding average step size based on the sample skewness of the adjacent extreme point spacing (MSDAEP) is proposed to reduce the number of smoothing iterations while ensuring the smoothing accuracy as much as possible in order to improve the computational efficiency. For the LMD modal mixing problem, a Complementary Ensemble Local Mean Decomposition method based on alignment entropy detection (MCELMD) is proposed to combine alignment entropy detection, CELMD and LMD to solve the modal mixing in the decomposition process. Finally, the method is applied to the extraction of multi-path effects in actual GNSS coordinate time series, and it is verified that the method can extract multi-path effects in GNSS coordinate time series more effectively than the traditional LMD method, which has important practical significance for GNSS coordinate time series processing