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. We present even order explicit symplectic geometric algorithms to solve the QKDE via a four-step strategy. Firstly, the Padè-Cayley lemma is proved and used to simplify the symplectic Padè approximation for the linear Hamiltonian system with infinitesimal symplectic structure. Secondly, both parallel and alternative iterative methods are proposed to construct the symplectic difference schemes with even order accuracy. Thirdly, the symplecity, orthogonality and invertibility of the single-step transition matrices are proved rigorously. Finally, the explicit symplectic geometric algorithms are designed for both the linear time-invariant and time-varying QKDE. The maximum absolute error for solving the QKDE is O(τ2l)$ where τ is the time step and l 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 real-time applications. The performance of the proposed algorithms are verified and validated by mathematical analysis and numerical simulation.