Analytical solution of field-of-view limited guidance with constrained impact and capturability analysis

An analytical missile guidance law is derived to meet both the impact time and angle constraints as well as the limit of reduced seeker field-of-view that is required to maintain the lock-on condition for a strap-down seeker. Specifically, an auxiliary variable related to the seeker look angle is introduced as an independent variable to design the relative range and line-of-sight (LOS) angle polynomial profiles. The first-order derivative of the LOS profile is designated positive to guarantee that the seeker's look angle decreases monotonically from its initial value to zero at the collision point. By transforming the guidance equations in terms of the auxiliary variable and integrating them with boundary constraints, an analytical impact time and angle guidance law is obtained and presented in the open-loop and closed-loop forms that are similar to the well-known proportional navigation guidance law with a time-varying gain. Moreover, the achievable impact time and angle sets are analytically determined for capturability analysis based on the initial engagement conditions. This technique is user/designer friendly in that it involves no heuristic tuning of guidance design parameters and error-prone estimate of time-to-go. Numerical simulations with comparisons under different terminal constraints are conducted to validate the effectiveness and advantages of the proposed guidance law.