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Linear estimation for data with error ellipsesAmen, Sally Kathleen 21 August 2012 (has links)
When scientists collect data to be analyzed, regardless of what quantities are being measured, there are inevitably errors in the measurements. In cases where two independent variables are measured with errors, many existing techniques can produce an estimated least-squares linear fit to the data, taking into consideration the size of the errors in both variables. Yet some experiments yield data that do not only contain errors in both variables, but also a non-zero covariance between the errors. In such situations, the experiment results in measurements with error ellipses with tilts specified by the covariance terms.
Following an approach suggested by Dr. Edward Robinson, Professor of Astronomy at the University of Texas at Austin, this report describes a methodology that finds the estimates of linear regression parameters, as well as an estimated covariance matrix, for a dataset with tilted error ellipses. Contained in an appendix is the R code for a program that produces these estimates according to the methodology. This report describes the results of the program run on a dataset of measurements of the surface brightness and Sérsic index of galaxies in the Virgo cluster. / text
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Přesnost evropského GNSS pro civilní letectví / Accuracy of the European GNSS for the Civil AviationBittner, Jan January 2012 (has links)
This diploma thesis deals with a positioning accuracy of global positioning system GPS and satellite augmentation system EGNOS. My thesis describes the procedure for investigation of the errors in previously mentioned global navigation satellite systems according to L10 regulation and further on an elaboration is worked out in more detail far beyond the requirements of this regulation. In the practical part, an assessment of errors on a real data sample is done, the errors are measured with using a static observation, and later a discussion is carried out on the achieved results.
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AJUSTAMENTO DE LINHA POLIGONAL NO ELIPSÓIDE / TRAVERSE ADJUSTMENT IN THE ELLIPSOIDBisognin, Márcio Giovane Trentin 26 April 2006 (has links)
Traverses Adjustment in the surface of the ellipsoid with the objectives to guarantee
the solution unicity in the transport of curvilinear geodesic coordinates (latitude and
longitude) and in the azimuth transport and to get the estimates of quality. It deduces
the coordinate transport and the azimuth transport by mean Legendre s series of the
geodesic line. This series is based on the Taylor s series, where the argument is the
length of the geodesic line. For the practical applications, it has the necessity to
effect the truncation of the series and to calculate the function error for the latitude,
the function error for the longitude and the function error for the azimuth. In this
research, these series are truncated in the derivative third and calculates the express
functions error in derivative fourth. It is described the adjustment models based on
the least-squares method: combined model with weighted parameters, combined
model or mixed model, parametric model or observations equations and correlates
model or condition equations model. The practical application is the adjustment by
mean parametric model of a traverse measured by the Instituto Brasileiro de
Geografia e Estatística (IBGE), constituted of 8 vertices and the 129.661 km length.
The localization of errors in the observations is calculated by the Baarda s data
snooping test in the last iteration of the adjustment that showed some observations
with error. The estimates of quality are in the variance-covariance matrices and
calculate the semiaxes of the error ellipse or standard ellipse of each point by means
of the spectral decomposition (or Jordan s decomposition) of the submatrices of the
variance-covariance matrix of the adjusted parameters (the coordinates). It is
important to note that the application of the Legendre s series is satisfactory for short
distances until 40km length. The convergence of the series is fast for the adjusted
coordinates, where the stopped criterion of the iterations is four decimals in the
sexagesimal second arc, where it is obtained from interation second of the
adjustment. / Ajustamento de linhas poligonais na superfície do elipsóide com os objetivos de
garantir a unicidade de solução no transporte de coordenadas geodésicas
curvilíneas (latitude ϕ e longitude λ ) e no transporte de azimute e de obter as
estimativas de qualidade. Deduz o transporte de coordenadas e o transporte de
azimute pelas séries de Legendre da linha geodésica. Essa série se fundamenta na
série de Taylor, em que o argumento é o comprimento da linha geodésica. Para as
aplicações práticas, há a necessidade de efetuar o truncamento da série e calcular a
função erro para a latitude, função erro para a longitude e função erro para o
azimute. Nesta pesquisa, trunca-se a série na derivada terceira e calculam-se as
funções erro expressas em derivada quarta. Expõe os modelos de ajustamento
fundamentados no método dos mínimos quadrados (MMQ): modelo combinado com
ponderação aos parâmetros, modelo combinado ou implícito, modelo paramétrico ou
das equações de observação e modelo dos correlatos ou das equações de
condição. A aplicação prática é o ajustamento pelo modelo paramétrico de uma linha
poligonal medida pelo Instituto Brasileiro de Geografia e Estatística (IBGE),
constituída de 8 vértices e de comprimento igual a 129,661 km. A localização de
erros nas observações é efetuada pelo teste data snooping de Baarda na última
etapa do ajustamento que mostrou algumas observações com erro. As estimativas
de qualidade estão nas matrizes variância-covariância (MVC) e calcula-se os semieixos
da elipse dos erros (ou elipse padrão) de cada ponto mediante a
decomposição espectral (ou decomposição de Jordan) das submatrizes da MVC dos
parâmetros (as coordenadas) ajustados. Mostra-se que a aplicação das séries de
Legendre é satisfatória para distâncias curtas até 40km. A convergência da série é
rápida para as coordenadas ajustadas, onde o critério de parada das iterações seja
quatro decimais do segundo de arco em que se atingiu na segunda etapa do
ajustamento.
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