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 an optimization problem on the group of rotation matrices subject to the system's kinematic and dynamic equations of motion. We first formulate an objective function ir:hose update at each time step requires the integration of the dynamic equations and employs a forgetting factor to weight the history of accumulated CPS measurements. In the event that angular velocity measurements are not available, a cubic spline interpolation algorithm on the rotation group is used to estimate the angular, velocity from the available attitude measurements. A geometric version of Newton's algorithm on the rotation group is also employed for the optimization, together with a method for rapidly calculating a suboptimal solution to be used as the initial point in the iteration. Simulation results comparing the performance of the proposed algorithm with those that neglect the dynamics are given.