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There are many practical applications based on the Least Square Error (LSE)or Total Least Square Error (TLSE) methods. Usually the standard least squareerror is used due to its simplicity, but it is not an optimal solution, as itdoes not optimize distance, but square of a distance. The TLSE method,respecting the orthogonality of a distance measurement, is computed ind-dimensional space, i.e. for points given in E2 a line p in E2, resp. forpoints given in E3 a plane in rho in E3, fitting the TLSE criteria are found.However, some tasks in physical sciences lead to a slightly different problem.In this paper, a new TSLE method is introduced for solving a problem when dataare given in E3 and a line p in E3 is to be found fitting the TLSE criterion.The presented approach is applicable for a general -dimensional case, i.e. whenpoints are given in E^d a line E^d is to be found. This formulation isdifferent from the TLSE formulation.

A New Formulation for Total Least Square Error Method in d-dimensional Space with Mapping to a Parametric Line