Estimating 3-D location parameters using dual number quaternions

Abstract

This paper describes a new algorithm for estimating the position and orientation of objects. The problem is formulated as an optimization problem using dual number quaternions. The advantage of using this representation is that the method solves for the location estimate by minimizing a single cost function associated with the sum of the orientation and position errors and thus is expected to have a better performance on the estimation, both in accuracy and in speed. Several forms of sensory information can be used by the algorithm. That is, the measured data can be a combination of measured points on an object's surfaces and measured unit direction vectors located on the object. Simulations have been carried out on a Compaq 386/20 computer and the simulation results are analyzed.