The Theory of Geodetic Observations

The primary goal of this dissertation is an examination of the mathematical model of geodetic observations. This examination accomplishes two basic objectives, understanding the statistical nature of the model and appreciation of the effects of various hypotheses on the parameter and variance-covari...

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Bibliographic Details
Main Author: Stukhart, George, Jr
Format: Report
Language:English
Subjects:
CORRELATION TECHNIQUES
DECISION THEORY
Geodesy
LEAST SQUARES METHOD
MATHEMATICAL MODELS
MULTIVARIATE ANALYSIS
SEQUENTIAL ANALYSIS
SEQUENTIAL ESTIMATION
STATISTICAL ANALYSIS
STATISTICAL DISTRIBUTIONS
STATISTICAL INFERENCE
Statistics and Probability
SURVEYING(GEOGRAPHIC)
THESES
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Summary:The primary goal of this dissertation is an examination of the mathematical model of geodetic observations. This examination accomplishes two basic objectives, understanding the statistical nature of the model and appreciation of the effects of various hypotheses on the parameter and variance-covariance estimates. Only the linear observation equations with constant coefficients is treated, the model being classified into four fundamental categories according to the error distribution: normal, independent and homoscedatic, nonhomiscedatic, and correlated. Each of these is related through weighting and orthogonality principles, and effects due to correlation, singularity, nonnormality and improper weighting are discussed. The observation errors are random variables, there is a discussion of statistical modelling, as well as other basic concepts which the geodesist may need to know in order to evaluate adjustment results. (Author)