Abstract
In this paper stochastic properties are discussed for the final results of the application of an innovative approach for uncertainty assessment for network computations, which can be characterized as two-step approach: As the first step, raw measuring data and all possible influencing factors were analyzed, applying uncertainty modeling in accordance with GUM (Guide to the Expression of Uncertainty in Measurement). As the second step, Monte Carlo (MC) simulations were set up for the complete processing chain, i.e., for simulating all input data and performing adjustment computations. The input datasets were generated by pseudo random numbers and pre-set probability distribution functions were considered for all these variables. The main extensions here are related to an analysis of the stochastic properties of the final results, which are point clouds for station coordinates. According to Cramer’s central limit theorem and Hagen’s elementary error theory, there are some justifications for why these coordinate variations follow a normal distribution. The applied statistical tests on the normal distribution confirmed this assumption. This result allows us to derive confidence ellipsoids out of these point clouds and to continue with our quality assessment and more detailed analysis of the results, similar to the procedures well-known in classical network theory. This approach and the check on normal distribution is applied to the local tie network of Metsähovi, Finland, where terrestrial geodetic observations are combined with Global Navigation Satellite System (GNSS) data.
Highlights
The quality concepts in geodesy have been based on classical statistical theory and generally accepted assumptions, such as the normal distribution of observations, possible correlation between observations and law of variance propagation
We will participate in this discussion and will study the statistical properties of adjustment results, presenting a new approach in which the variations of the network adjustment results are derived by Monte Carlo simulations, where the quality variability of the input observations is computed in a rigorous procedure based on the rules of GUM
Monte Carlo simulations is recommended to findσ the distribution for the quantity Y
Summary
The quality concepts in geodesy have been based on classical statistical theory and generally accepted assumptions, such as the normal distribution of observations, possible correlation between observations and law of variance propagation. For the here discussed least squares adjustment, the variance–covariance matrix for the unknowns is considered to be the best representation for quality of results. These considerations are the basis for standard quality measures for precision, such as standard deviation, mean square error, error or confidence ellipses and prerequisites for the derivation of reliability measures, as well as for more detailed methods such as congruency analysis. We will participate in this discussion and will study the statistical properties of adjustment results, presenting a new approach in which the variations of the network adjustment results are derived by Monte Carlo simulations, where the quality variability of the input observations is computed in a rigorous procedure based on the rules of GUM
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