Geometric Descent Algorithms for Attitude Determination Using the Global Positioning System

This paper describes a set of numerical optimization algorithms for solving the GPSbased attitude determination problem. We pose the problem as one of minimizing the function tr ( N T Q;2 W) with respect to 2 SO(3), where N, Q, and W are given 3 3 matrices. The method of steepest descent and Newton's method are generalized to SO(3) by taking advantage of its Lie group structure. Analytic solutions to the line search procedure are also derived. Results of numerical experiments for the class of geometric descent algorithms proposed here are presented. 1