[G05-P] Poster

[G05-P-06] Multiplicative random error models: Parameter estimation and error analysis

^○Yun Shi, Jing Zhang, Peng Chen, Jie Lv, Chao Li (Xi'an University of Science and Technology)

Conventional geodetic adjustment theory has been almost always developed on the linear and/or linearized model of measurements. The most important feature of these conventional adjustment methods and theory are that the random errors of measurements are added to the functional models. In other words, the sizes or magnitudes of random errors are independent of the true values of measured quantities. However, in geodetic practice, we know that this assumption is not necessarily always true. For example, we know that the accuracy of an EDM, GPS and/or VLBI baseline is proportional to the length of the baseline itself, which clearly indicates that the random errors of this type are proportional to the measured quantities. From the statistical point of view, such random errors should be multiplied to the functional models and are not additive any more. In this talk, we will extend the conventional model of geodetic adjustment to account for multiplicative errors and/or mixed additive-multiplicative errors. We will address the parameter estimation and error analysis in the linear/linearized model of measurements with mixed additive-multiplicative random errors. More specifically, we will first discuss three least-squares-based methods to estimate the model parameters, namely, least squares, weighted least squares (LS) and bias-corrected weighted least squares. We will then analyze these three methods from the statistical point of view. We construct five estimators of the variance of unit weight in association with the three LS-based methods and compare them, statistically and through numerical simulations. Although LiDAR data have been proved to be of multiplicative nature, they have been treated as if they were of additive random errors. Thus, as a final part, we will simulate a landslide example, which is supposed to be surveyed with LiDAR, to demonstrate how the methods discussed here works and how they can be applied to DEM construction for disaster monitoring.