Estimation of parameters in a split functional model of geodetic observations (M split estimation)

The paper presents a method of estimating parameters in two competitive functional models. The models considered here are concerned with the same observation set and are based on the assumption that an observation may result from a realization of either of two different random variables. These variables differ from one another at least in the main characteristic (for example, outliers can be realizations of one variable). A quantity that describes the opportunity of identifying a single observation with one random variable is assumed to be known. That quantity, called the elementary split potential, is strictly referred to the amount of information that an observation can provide about two competitive assumptions concerning the observation distribution. Parameter assessments that maximize the global elementary split potential (concerning all observations), are called M (split) estimators. A generalization of M (split) estimation presented in the paper refers to the theoretical foundation of M-estimation.