Dynamics-Based Attitude Determination Using the Global Positioning System

We present an algorithm for attitude determination using Global Positioning System (GPS) phase die erence measurements. The problem is formulated as an optimization problem on the group of rotation matrices subject to the system’ skinematicand dynamicequations of motion. We e rst formulate an objectivefunction whose update at each time step requires the integration of the dynamic equations and employs a forgetting factor to weight the history of accumulated GPS measurements. In the event that angular velocity measurements are not available, a cubicsplineinterpolationalgorithmontherotationgroupisusedtoestimatetheangularvelocityfromtheavailable 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.