Multivariate denoising using wavelets and principal component analysis

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

“…General overview of wavelets and wavelet analysis are found in Bakshi (1998), Chui (1992), and Aminghafaria et al (2006). For the most practical applications to measure data, the wavelet dilation and translation parameters are discretized dynamically, and the family of wavelets is represented as follows:…”

“…Lilong et al (2010) mitigated the GPS systematic errors using wavelet de-noise method; this study used the db4 mother wavelet and the denoise method is soft-threshold de-noise method, the double differential observation forming to decompose double difference with the aim of mitigating systematic errors and recovering double difference observation after that used the de-noising bias elimination outlier detection data compression then GPS observation reconstruction is determined. Finally, Yu et al (2006) and Aminghafaria et al (2006) summarized the methods of wavelet analysis eliminating noises as follows. First, one is a compulsive that the high-frequency coefficients are processed to be zero in the decomposed signal constructions of wavelet analysis, and some scale or different scale signal components with these coefficients in the data time series are all eliminated.…”

Real time angular velocity measure using median filter

“…That fact justify the need for better algorithms to filter the measured value aiming to get as close as possible to the true signal, one that carry the desired information, in this case the velocity of a motor. There are several works about signal denoising [12][13][14][15] but most of them uses sophisticated techniques that some times are hard to implement in real time. The most common approach for denoising in real time (or some times designated as on-line) is to use linear filters designed based on some knowledge of the signal (for instance the band of the signal) [8].…”

Adaptive Blind Multiuser Detection Under Impulsive Noise Using Principal Components

“…However, the batch algorithm [2] requires singular value decomposition (SVD), which is inconvenient for adaptive implementation. Further, it requires accurate rank estimation of the correlation matrix, which is not easy in an inherently noisy environment [4]- [9].…”

“…These detectors employ the PCA algorithm [9] at the outputs of a bank of matched filters. Main purpose is to retrive the original sequence from the received signal that is corrupted by other users and MAI, without the help of training sequences and a priori knowledge of the channel.…”