Generalized Guidance Law for Homing Missiles

The utmost purpose of using a guidance law for a homing missile is to turn the heading of the missile toward some desired direction as rapidly as possible by commanding the acceleration of the missile proportional to the angular rate of such direction. Such a direction may be simply along the line of sight, the missile collision course, or any other appropriate direction. The generalized guidance law presented here covers a wide variety of guidance laws; some have appeared in the literature, while most of them are totally new. Based on the exact nonlinear equations of motion, general analytical expressions for capture area, missile commanded acceleration, and homing time duration are derived in closed forms. An optimal nonlinear guidance law originating from this generalized guidance law, which minimizes a weighted linear combination of the time of capture and energy expenditure, is also derived. The efficiency and mechanization of the generalized guidance law and the comparisons with various existing guidance laws are demonstrated in a simulation study. The miss distance due to seeker/autopilot dynamics, maneuvering targets, acceleration saturation, and measurement bias is also investigated.