2019
DOI: 10.1061/(asce)su.1943-5428.0000286
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M split Estimation Based on L 1 Norm Condition

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Cited by 21 publications
(29 citation statements)
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“…There are several variants of M split estimation that differ from one another in the objective function or assumed parameters [19,22,29]. So far, the most popular is the squared M split estimation for which ρfalse(1false)false(yi;Xfalse(1false)false)=pivifalse(1false)2 and ρfalse(2false)false(yi;Xfalse(2false)false)=pivifalse(2false)2.…”
Section: Theoretical Foundationsmentioning
confidence: 99%
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“…There are several variants of M split estimation that differ from one another in the objective function or assumed parameters [19,22,29]. So far, the most popular is the squared M split estimation for which ρfalse(1false)false(yi;Xfalse(1false)false)=pivifalse(1false)2 and ρfalse(2false)false(yi;Xfalse(2false)false)=pivifalse(2false)2.…”
Section: Theoretical Foundationsmentioning
confidence: 99%
“…The process stops when for each l=1,2, it holds that gfalse(lfalse)false(trueX^false(1false),trueX^false(2false)false)=0 and hence trueX^false(lfalse)=Xfalse(lfalse)m=Xfalse(lfalse)m1. Note that other iterative processes that use both the gradients and the Hessians of φfalse(Xfalse(1false),Xfalse(2false)false), namely Newton’s method, can be found in [19,20,29].…”
Section: Theoretical Foundationsmentioning
confidence: 99%
“…Applications of M split estimation concerned so far not only processing of TLS data (presented in [1,15,22,31]) but also deformation analyses [29,30,[32][33][34][35][36], direct identification of gross errors [37], linear regression analyses [30,34], robust coordinate transformation [38], S-transformation [39] and marine navigation [40]. Most of these applications applied only the squared M split estimation (SMS), of which the objective functions stem from the assumption that observation errors are normally distributed.…”
Section: Introductionmentioning
confidence: 99%
“…However, there is also an alternative variant of M split estimation in which objective functions are based on the L 1 norm condition, which refers to the minimization of L 1 norm of error vector [41,42]. Such a variant is called the absolute M split estimation (AMS) [34,43], and it has not been used in laser scanning data analysis so far. Due to that fact, it seems interesting to apply this method in such a context, especially since some previous papers proved that AMS estimation is generally less sensitive to outliers than SMS estimation [34,35].…”
Section: Introductionmentioning
confidence: 99%
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