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Error Propagation and Linearization
The Concept of Adjustment
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according to Eq accuracy adjusted observations adjustment of indirect adjustment of observations applying azimuth calculated Chapter chi-square distribution coefficient matrix cofactor matrix computed condition equations confidence interval corresponding covariance matrix degrees of freedom density function determine diagonal diagonal matrix distributed random variables distribution function elements example expressed given by Eq indirect observations inverse Jacobian matrix known Lagrange multipliers law of propagation least squares adjustment least squares estimates matrix form nonlinear normal distribution normal equations number of observations observations are uncorrelated observed values obtained partial derivatives plane triangle position probability distribution problem procedure propagation of variances quantity radians random errors random vector redundancy reference variance relative frequencies represented residuals respectively sample mean semimajor axis shown in Fig significant figures standard deviation standard error ellipse survey measurement survey station symmetric matrix systematic error Table theodolite weight matrix weighted mean zero