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2 2022

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Two variants of M split estimation – similarities and differences

Wyszkowska Patrycja, Duchnowski Robert

Advances in Geodesy and Geoinformation

2022

Vol. 71, no. 1

art. no. e22, 2022

M split estimation is a novel method developed to process observation sets that include two (or more) observation aggregations. The main objective of the method is to estimate the location parameters of each aggregation without any preliminary assumption concerning the division of the observation set into respective subsets. Up to now, two different variants of M split estimation have been derived. The first and basic variant is the squared M split estimation, which can be derived from the assumption about the normal distribution of observations. The second variant is the absolute M split estimation, which generally refers to the least absolute deviation method. The main objective of the paper is to compare both variants of M split estimation by showing similarities and differences between the methods. The main dissimilarity stems from the different influence functions, making the absolute M split estimation less sensitive to gross errors of moderate magnitude. The empirical analyses presented confirm that conclusion and show that the accuracy of the methods is similar, in general. The absolute M split estimation is more accurate than the squared M split estimation for less accurate observations. In contrast, the squared M split estimation is more accurate when the number of observations in aggregations differs much. Concerning all advantages and disadvantages of M split estimation variants, we recommend using the absolute M split estimation in most geodetic applications.

Absolute Msplit estimation as an alternative for robust M-estimation

Duchnowski Robert, Wyszkowska Patrycja

Advances in Geodesy and Geoinformation

2022

Vol. 71, no. 1

art. no. e17, 2022

The problem of outlying observations is very well-known in the surveying data processing. Outliers might have several sources, different magnitudes, and shares within the whole observation set. It means that it is not possible to propose one universal method to deal with such observations. There are two general approaches in such a context: data cleaning or robust estimation. For example, the robust M-estimation has found many practical applications. However, there are other options, such as R-estimation or the absolute M split estimation. The latter method was created to be less sensitive to outliers than the squared M split estimation (the basic variant of Msplit estimation). From the theoretical point of view, the absolute M split estimation cannot be classified as a robust method; however, it was proved that it could be used in such a context under certain conditions. The paper presents the primary comparison between that method and a conventional robust M-estimation. The results show that the absolute M split estimation predominates over the classical methods, especially when the percentage of outliers is high. Thus, that method might be used to process LiDAR data, including mismeasured points. Processing synthetic data from terrestrial laser scanning or airborne laser scanning confirms that the absolute M split / estimation can deal with outliers sufficiently.