Dynamics-based attitude determination using the global positioning system

We present an algorithm for attitude determination using Global Positioning System (GPS) phase difference measurements. The problem is formulated as a n optimization problem on the group of rotation matrices subject to the sys tem's kinematic and dynamic equations of motion. We first formulate an obje ctive function ir:hose update at each time step requires the integration of the dynamic equations and employs a forgetting factor to weight the histor y of accumulated CPS measurements. In the event that angular velocity measu rements are not available, a cubic spline interpolation algorithm on the ro tation group is used to estimate the angular, velocity from the available a ttitude measurements. A geometric version of Newton's algorithm on the rota tion group is also employed for the optimization, together with a method fo r rapidly calculating a suboptimal solution to be used as the initial point in the iteration. Simulation results comparing the performance of the prop osed algorithm with those that neglect the dynamics are given.