The wavelet method as an alternative for reducing ionospheric effects from single-frequency GPS receivers

The ionospheric effect is one of the major errors in GPS data processing over long baselines. As a dispersive medium, it is possible to compute its influence on the GPS signal with the ionosphere-free linear combination of L1 and L2 observables, requiring dual-frequency receivers. In the case of single-frequency receivers, ionospheric effects are either neglected or reduced by using a model. In this paper, an alternative for single-frequency users is proposed. It involves multiresolution analysis (MRA) using a wavelet analysis of the double-difference observations to remove the short- and medium-scale ionosphere variations and disturbances, as well as some minor tropospheric effects. Experiments were carried out over three baseline lengths from 50 to 450 km, and the results provided by the proposed method were better than those from dual-frequency receivers. The horizontal root mean square was of about 0.28 m (1 sigma).

Análise de wavelets para detecção e correção do multicaminho no posicionamento relativo GNSS estático e cinemático

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A fully adaptive multiresolution scheme for shock computations

The scheme is based on Ami Harten's ideas (Harten, 1994), the main tools coming from wavelet theory, in the framework of multiresolution analysis for cell averages. But instead of evolving cell averages on the finest uniform level, we propose to evolve just the cell averages on the grid determined by the significant wavelet coefficients. Typically, there are few cells in each time step, big cells on smooth regions, and smaller ones close to irregularities of the solution. For the numerical flux, we use a simple uniform central finite difference scheme, adapted to the size of each cell. If any of the required neighboring cell averages is not present, it is interpolated from coarser scales. But we switch to ENO scheme in the finest part of the grids. To show the feasibility and efficiency of the method, it is applied to a system arising in polymer-flooding of an oil reservoir. In terms of CPU time and memory requirements, it outperforms Harten's multiresolution algorithm.The proposed method applies to systems of conservation laws in 1Dpartial derivative(t)u(x, t) + partial derivative(x)f(u(x, t)) = 0, u(x, t) is an element of R-m. (1)In the spirit of finite volume methods, we shall consider the explicit schemeupsilon(mu)(n+1) = upsilon(mu)(n) - Deltat/hmu ((f) over bar (mu) - (f) over bar (mu)-) = [Dupsilon(n)](mu), (2)where mu is a point of an irregular grid Gamma, mu(-) is the left neighbor of A in Gamma, upsilon(mu)(n) approximate to 1/mu-mu(-) integral(mu-)(mu) u(x, t(n))dx are approximated cell averages of the solution, (f) over bar (mu) = (f) over bar (mu)(upsilon(n)) are the numerical fluxes, and D is the numerical evolution operator of the scheme.According to the definition of (f) over bar (mu), several schemes of this type have been proposed and successfully applied (LeVeque, 1990). Godunov, Lax-Wendroff, and ENO are some of the popular names. Godunov scheme resolves well the shocks, but accuracy (of first order) is poor in smooth regions. Lax-Wendroff is of second order, but produces dangerous oscillations close to shocks. ENO schemes are good alternatives, with high order and without serious oscillations. But the price is high computational cost.Ami Harten proposed in (Harten, 1994) a simple strategy to save expensive ENO flux calculations. The basic tools come from multiresolution analysis for cell averages on uniform grids, and the principle is that wavelet coefficients can be used for the characterization of local smoothness.. Typically, only few wavelet coefficients are significant. At the finest level, they indicate discontinuity points, where ENO numerical fluxes are computed exactly. Elsewhere, cheaper fluxes can be safely used, or just interpolated from coarser scales. Different applications of this principle have been explored by several authors, see for example (G-Muller and Muller, 1998).Our scheme also uses Ami Harten's ideas. But instead of evolving the cell averages on the finest uniform level, we propose to evolve the cell averages on sparse grids associated with the significant wavelet coefficients. This means that the total number of cells is small, with big cells in smooth regions and smaller ones close to irregularities. This task requires improved new tools, which are described next.

Multipath reduction from GPS double differences using wavelets: How far can we go?

Wavelets are being extensively used in Geodetic applications. In this paper, the Multi-Resolution Analysis (MRA) using wavelets is applied to pseudorange and carrier phase GPS double differences (DDs) in order to reduce multipath effects. The wavelets were already applied to GPS carrier phase DDs, but some questions remain: How good can be the results, and are all multipath effects reduced? The answers to these questions are discussed in this paper. Thus, the wavelet transform is used to decompose the DD signals, splitting them in lower resolution components. After the decomposition process, the wavelet shrinkage is performed by thresholding to eliminate the components relative to multipath effects. Then, the DD observation can be reconstructed. This new DD signal is used to perform the baseline processing. The daily multipath repeatability was verified. With the application of the proposed approach, the results showed that the reliability of the ambiguity resolution and accuracy of the results improved when compared with the standard procedure. Furthermore, the method showed to be very efficient computationally, because, it is not noticed, at practical level, difference in the time span between the processing with and without application of the proposed method. However, only the high frequency multipath was eliminated.

GPS ambiguity resolution and validation under multipath effects: Improvements using wavelets

Integer carrier phase ambiguity resolution is the key to rapid and high-precision global navigation satellite system (GNSS) positioning and navigation. As important as the integer ambiguity estimation, it is the validation of the solution, because, even when one uses an optimal, or close to optimal, integer ambiguity estimator, unacceptable integer solution can still be obtained. This can happen, for example, when the data are degraded by multipath effects, which affect the real-valued float ambiguity solution, conducting to an incorrect integer (fixed) ambiguity solution. Thus, it is important to use a statistic test that has a correct theoretical and probabilistic base, which has became possible by using the Ratio Test Integer Aperture (RTIA) estimator. The properties and underlying concept of this statistic test are shortly described. An experiment was performed using data with and without multipath. Reflector objects were placed surrounding the receiver antenna aiming to cause multipath. A method based on multiresolution analysis by wavelet transform is used to reduce the multipath of the GPS double difference (DDs) observations. So, the objective of this paper is to compare the ambiguity resolution and validation using data from these two situations: data with multipath and with multipath reduced by wavelets. Additionally, the accuracy of the estimated coordinates is also assessed by comparing with the ground truth coordinates, which were estimated using data without multipath effects. The success and fail probabilities of the RTIA were, in general, coherent and showed the efficiency and the reliability of this statistic test. After multipath mitigation, ambiguity resolution becomes more reliable and the coordinates more precise. © Springer-Verlag Berlin Heidelberg 2007.

Classification of masses in mammographic image using wavelet domain features and polynomial classifier

Breast cancer is the most common cancer among women. In CAD systems, several studies have investigated the use of wavelet transform as a multiresolution analysis tool for texture analysis and could be interpreted as inputs to a classifier. In classification, polynomial classifier has been used due to the advantages of providing only one model for optimal separation of classes and to consider this as the solution of the problem. In this paper, a system is proposed for texture analysis and classification of lesions in mammographic images. Multiresolution analysis features were extracted from the region of interest of a given image. These features were computed based on three different wavelet functions, Daubechies 8, Symlet 8 and bi-orthogonal 3.7. For classification, we used the polynomial classification algorithm to define the mammogram images as normal or abnormal. We also made a comparison with other artificial intelligence algorithms (Decision Tree, SVM, K-NN). A Receiver Operating Characteristics (ROC) curve is used to evaluate the performance of the proposed system. Our system is evaluated using 360 digitized mammograms from DDSM database and the result shows that the algorithm has an area under the ROC curve Az of 0.98 ± 0.03. The performance of the polynomial classifier has proved to be better in comparison to other classification algorithms. © 2013 Elsevier Ltd. All rights reserved.

Classificação de sinais acústicos utilizando a transformada wavelet discreta e a decomposição de modo empírico: aplicações na área de alimentos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Proposta de Algoritmos Inteligentes para Localizar Faltas e Monitorar a Qualidade da Energia em Redes de Distribuição de Energia Elétrica

Pós-graduação em Engenharia Elétrica - FEIS

Análise multiescala de séries temporais do efeito da cintilação ionosférica nos sinais de satélite GPS a partir de wavelets não decimadas

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Deteccão de complexos QRS em eletrocardiogramas baseada na decomposição em valores singulares em multirresolução

Pós-graduação em Engenharia Elétrica - FEIS