Comparative Methods for Wavelet Domain Matrix Weighting, Scalar Weighting, and Modified Weighting

In this paper, we conduct a comparative study of wavelet domain matrix weighting, scalar weighting, and modified weighting methods. The implementation involves multi-resolution analysis through wavelet decomposition using algorithms like discrete wavelet transform (DWT) with db4 wavelets, Kalman filtering for state estimation with optimized covariance matrices, and information fusion techniques combining multiple sensor data through weighted averaging. Our research also includes quantitative evaluation metrics such as mean squared error (MSE) and peak signal-to-noise ratio (PSNR) for performance comparison. The proposed methods demonstrate improved signal processing capabilities through MATLAB code implementations featuring wavelet decomposition functions (wavedec/waverec), Kalman filter loops with prediction-correction cycles, and fusion algorithms using weighted summation operations. This work has been accepted by an IEEE journal, contributing significant advancements to the field and providing valuable references for future research. We hope this paper offers readers deep insights and inspiration to promote further developments in signal processing and data fusion technologies.