The Objective of the Remote Measurements Calibration (RMC) method is to minimize systematic errors through an appropriate scaling procedure. A new method for RMC has been developed. This method solves the problems of observability, multiplicity of solutions, and ambiguity of reference points associated with the method proposed by Adibi et. al. [6-9]. The new algorithm uses the simulated annealing technique together with the matroid method to identify and minimize the number of RTUs (Remote Terminal Units) required to observe the system. After field calibration, these RTUs provide measurements that are used to estimate the whole state of the system. These estimates are then returned as a reference for remotely calibrating the remaining RTUs. The calibration coefficients are estimated by means of highly robust estimator, namely the Least Median of Squares (LMS) estimator. The calibration method is applicable to large systems by means of network tearing and dynamic programming. The number of field calibrations can be decreased further whenever multiple voltage measurements at the same buses are available. The procedure requires that the measurement biases are estimated from recorded metered values when buses, or lines, or transformers are disconnected. It also requires the application of a robust comparative voltage calibration method. To this end, a modified Friedman test has been developed and its robustness characteristics investigated. / Ph. D.

Median in some statistical methods Abstract: This work is focused on utilization of robust properties of median. We propose variety of algorithms with respect to their breakdown point. In addition, other properties are studied such as consistency (strong or weak), equivariance and computational complexity. From practical point of view we are looking for methods balancing good robust properties and computational complexity, be- cause these two properties do not usually correspond to each other. The disser- tation is divided to two parts. In the first part, robust methods similar to the exponential smoothing are suggested. Firstly, the previous results for the exponential smoothing with ab- solute norm are generalized using the regression quantiles. Further, the method based on the classical sign test is introduced, which deals not only with outliers but also detects change points. In the second part we propose new estimators of location. These estimators select a robust set around the geometric median, enlarge it and compute the (iterative) weighted mean from it. In this way we obtain a robust estimator in the sense of the breakdown point which exploits more information from observations than standard estimators. We apply our approach on the concepts of boxplot and bagplot. We work in a general normed vector...