Ajustamento de linha poligonal no elipsóide

Abstract

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.