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The proposed strategy, called finite-time state-dependent Riccati equation (FT-SDRE)-based impact angle guidance, is employed to solve the 3D pursuer/target interception model with fixed lateral accelerations. In this article, we expand its application to a more general scenario where the target experiences changing lateral accelerations. To achieve this, we incorporate a three-point finite difference approach that approximates the second derivatives of the changing azimuth and elevation angles of the maneuvering target in the inertial frame. We develop a high-performance FT-SDRE algorithm with SDAs to simulate the entire interception procedure between the pursuer and the target. For each state of the FT-SDRE, we propose a simplified SDA with adaptive optimal parameter selection. This enables us to solve the Lyapunov equation based on the Newton step of the associated CARE. The numerical results demonstrate that our proposed method is more than twice as fast as using the MATLAB functions icare and lyap to solve the CARE and the Lyapunov equation throughout the entire interception procedure between the pursuer and the target.