Solving nonlinear estimation problems using splines [Lecture Notes

Abstract

We describe the use of splines for solving nonlinear model estimation problems, in which nonlinear functions with unknown shapes and values are involved, by converting the nonlinear estimation problems into linear ones at a higher- dimensional space. This contrasts with the typical use of the splines for function interpolation where the functional values at some input points are given and the values corresponding to other input points are sought for via interpolation. The technique described in this column applies to arbitrary nonlinear estimation problems where one or more one-dimensional nonlinear functions are involved and can be extended to cases where higher-dimensional nonlinear functions are used.