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Abstract

The present paper consists of two parts. The first part presents theoretical foundations of Msplit, estimation with reference to the previous author's paper (Wiśniewski, 2009). This time, some probabilistic assumptions are described in detail. A new quantity called f-information is also introduced to formulate the split potential in more general way. The main aim of this part of the paper is to generalize the target function of Msplit estimation that is the basis for a new formulation of the optimization problem. Such problem itself as well as its solution are presented in this part of the paper. The second part of the paper presents some special case of Mspli, estimation called squared Mspli, estimation (also with reference to the mentioned above paper of the author). That part presents a new solution and development in the theory of this version of M,plit estimation and some numerical examples that show properties of the method and its application scope.
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Authors and Affiliations

Zbigniew Wiśniewski
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Abstract

This part of the paper presents particular case of Msplit estimation called a squared Msplit estimation whose target function is based on convex squared functions. One can find here theoretical foundations and algorithm of the squared Msplit estimation as well as some numerical examples.
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Authors and Affiliations

Zbigniew Wiśniewski
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Abstract

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.
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Authors and Affiliations

Robert Duchnowski
1
ORCID: ORCID
Patrycja Wyszkowska
1
ORCID: ORCID

  1. University of Warmia and Mazury, Olsztyn, Poland
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Abstract

M-estimators are widely used in active noise control (ANC) systems in order to update the adaptive FIR filter taps. ANC systems reduce the noise level by generating anti-noise signals. Up to now, the evaluation of M-estimators capabilities has shown that there exists a need for further improvements in this area. In this paper, a new improved M-estimator is proposed. The sensitivity of the proposed algorithm to the variations of its constant parameter is checked in feedforward control. The effectiveness of the algorithm in both types is proved by comparing it with previous studies. Simulation results show the steady performance and fast initial convergence of the proposed algorithm.
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Bibliography

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Authors and Affiliations

Seyed Amir Hoseini Sabzevari
1
Seyed Iman Hoseini Sabzevari
2

  1. Department of Mechanical Engineering, University of Gonabad, Gonabad, 9691957678, Iran
  2. Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, 9177948974, Iran

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