Computational Linearized Least Squares for 2D Positioning Using Mathcad˙ Programming

Abstract

This study involves an application of linearized Least Squares through Taylor series to analyze 2Dpositions. The nonlinear system has mathematical models outnumbered the number of unknowns. Inaddition, this work studies the various effects of geometry of the given coordinates having impacts onconvergence ability and on speed to reach respective solutions. The written Mathcad program is utilized asa study tool which is very easy to use. Moreover, when changing numerical values of parameters, Mathcadprovides instant solutions.

Seven different geometry scenarios of the given coordinates are exampled. The study results showthat when given coordinates are highly distributed around the determined position, the solutions convergefaster than any other cases, with high precision. On the other hand, when given coordinates are highlyclustered or circularly distributed around the determined position, convergence is very problematic. This istrue especially for the case when assumed values for initial solutions (x0, y0) are far away from exactsolutions, thus producing solutions to diverge due mainly to singularity because of very similarity of theobserved mathematical models.

Keywords : Linearized Least Squares / Positioning / Mathcad / Taylor Series