Partial linearization of one class of the nonlinear total least squares problem by using the inverse model function

In this paper we consider a special nonlinear total least squares problem, where the model function is of the form \(f(x;a,b)=\phi^{-1}(ax+b)\). Using the fact that after an appropriate substitution, the model function becomes linear in parameters, and that the symmetry preserves the distances, this nonlinear total least squares problem can be greatly simplified. In this paper we give the existence theorem, propose an efficient algorithm for searching the parameters and give some numerical examples.