A representation of the seeker gimbal kinematics is analysed for the roll-pitch seeker. A geometrical closed-form angle increment solution has beem proposed based on the Paden-Kahan sub-problems. Using this method

the angle increment solution of the seeker is decomposed into two canonical Paden-Kahan subproblems. The subproblems lead to solution of inverse kinematics which consists of simple rigid motions

the complexity of the inverse kinematics problem is reduced. Because inverse kinematics of the seeker has not an exclusive solution

the minimum angle increment criteria is introduced in optimizing the inverse kinematics problem. The semi-physics tracking experiments using the angle increment algrithom for circle track target are provided to demonstrate the effectiveness of the proposed inverse kinematics in solving roll-pitch angle increment.