Analytical 3D proportional navigation guidance for field-of-view constrained impact time control

This paper presents a novel 3D proportional navigation guidance (PNG) law with a range-varying gain, which achieves impact time control under the seeker’s restricted field-of-view (FOV) for both stationary and maneuvering targets, even with time-varying missile speeds. Originating from the lead angle-shaping philosophy, this proposed nonlinear guidance method, unlike existing studies, features the novelty that the trajectory-to-go solution, as well as the achievable impact time domain under FOV limit, is formulated as concise and precise analytical expression. Moreover, it circumvents multistage switching logic, linearization procedures, numerical solving guidance parameters, and conservative monotonic decreasing shaping profiles. Additionally, by introducing a 3D relative reference frame, the proposed approach is extended to the scenarios involving maneuvering targets and varying-speed missile model. Notably, the transformed condition for satisfying the FOV constraint within the 3D relative reference frame is rigorously derived in this work, laying a theoretical foundation for addressing the FOV issue through the direct application of 3D relative engagement kinematics. Numerical simulations for different scenarios including a time-varying velocity missile model are performed to validate the effectiveness and superiority of the proposed guidance law.