Nonlinear least squares and SVD based algorithms for the estimation of a coordinate transformation.

A typical problem in movement analysis is to determine, with the maximum accuracy, the coordinate transformation that allows to pass from one reference system to another, when the coordinates of N points embedded to the rigid body, and expressed both in a local reference system (SL) and in a global reference system (SG), are known. The aim of this work is the implementation of a recursive nonlinear least-squares algorithm (LSA) [1] to estimate the seven parameters of the coordinate transformation, assuming that the global coordinates are affected both by additive random noise and by systematic error. The results have been compared with those obtain through a well known algorithm, based on the Singular Value Decomposition (SVD) [2]. Methods: The coordinate transformation taken in account is