Even Order Explicit Symplectic Geometric Algorithms for Quaternion
Kinematical Differential Equation in Guidance Navigation and Control via
Diagonal Pad\`{e} Approximation and Cayley Transform
The Quaternion kinematical differential equation (QKDE) plays a key role in
navigation, control and guidance systems. Although explicit symplectic
geometric algorithms (ESGA) for this problem are available, there is a lack of
a unified way for constructing high order symplectic difference schemes with
configurable order parameter. We present even order explicit symplectic
geometric algorithms to solve the QKDE with diagonal Pad\`{e} approximation and
Cayley transform. The maximum absolute error for solving the QKDE is
O(Ο2β) where Ο is the time step and β is the
order parameter. The linear time complexity and constant space complexity of
computation as well as the simple algorithmic structure show that our
algorithms are appropriate for realtime applications in aeronautics,
astronautics, robotics, visual-inertial odemetry and so on. The performance of
the proposed algorithms are verified and validated by mathematical analysis and
numerical simulation