The robust method for selenophysical parameters estimations

Abstract

© SGEM2019. This work focuses on the practical results of determining selenophysical parameters obtained using 2 different approaches to the problem of assessing parameters – the classic Ordinary Least Squares (OLS) and the interference-resistant analysis (method of M-estimation). In this work geliometrical observations were obtained and analyzed using the method. It should be noted the modern robust methods of reducing observations allows for the elimination of wrong measurements that may distort the values of estimations when the classic OLS is used. One of the most efficient robust methods suitable for the solution of such problems is the one of maximum plausibility. Initially, the method of M-estimations was introduced by Huber P.J. Huber called the estimations with this method “M-estimations” for their similarity to the estimations of maximum plausibility. Currently, the method is widely used in a series of works on the analysis of time series observations. The M-estimations method is relatively simple compared to the other robust ones. When using that, one may apply the standard computational procedures of the usual OLS. That is why it is widely applied during the processing of various measurements containing significant errors. At the moment, the method of M-estimations is used when analyzing GNSS measurements. In theory, the M-estimations and the ones obtained with the classic OLS should coincide in case of a sample obeying the normal distribution. In our case, the estimations appeared to be different from each other. Therefore, the ejection of the hypothesis on the equal accuracy of the measurements seems justified. However, it is reasonably assumed that there are some deviations from the normal model of the measurement errors, in particular anomalous ones. Thus, the method of maximum plausibility allows for the elimination of the anomalous measurements in a sample taken for processing, which is necessary during reducing both selenophysical positional observations and similar time series.