An Improved Adaptive IVMD-WPT-Based Noise Reduction Algorithm on GPS Height Time Series

Area of Science:

• Geodesy and Geophysics
• Signal Processing
• Data Analysis

Background:

• Traditional Variational Mode Decomposition (VMD) struggles with adaptive parameter selection (number of intrinsic modal functions and penalty factor) for noise reduction in time series.
• This limitation can lead to suboptimal decomposition, impacting the reliability of Global Positioning System (GPS) signal extraction and analysis.

Purpose of the Study:

• To propose and validate an Improved Variational Mode Decomposition and Wavelet Packet Transform (IVMD-WPT) algorithm for enhanced GPS signal extraction.
• To address the limitations of traditional VMD by adaptively determining decomposition parameters for improved noise reduction.

Main Methods:

• Developed an IVMD-WPT approach utilizing energy entropy mutual information as the objective function.
• Employed a grasshopper optimization algorithm to automatically tune the number of modal decompositions and the penalty factor.
• Evaluated performance using Root Mean Square Error (RMSE), Correlation Coefficient (CC), and Signal-to-Noise Ratio (SNR) on simulated and real GPS data.

Main Results:

• IVMD-WPT demonstrated superior noise reduction compared to traditional Empirical Mode Decomposition (EMD) and VMD methods on simulated data.
• Significant improvements observed in real GPS height time series analysis, with notable reductions in RMSE and increases in CC and SNR.
• The algorithm effectively determined optimal VMD decomposition modal functions and penalty factor combinations.

Conclusions:

• The proposed IVMD-WPT algorithm offers a robust solution for adaptive parameter optimization in VMD for GPS signal processing.
• This method enhances the extraction of effective information for noise reduction while preserving essential data in time series.
• IVMD-WPT proves effective for improving the reliability and accuracy of GPS data analysis.