Abstract: An air to air homing missile guidance algorithm based on a state-dependent Riccati equation solution of a spherical-based nonlinear intercept representation of the intercept kinematics problem. The achieved algorithm also provides characteristics asymptotically stabilizing the intercept kinematics achieved with the classic proportional navigation or PRONAV intercept algorithm but provides reduced hunting instability and other fuel-consuming and time consuming missile maneuvers. The disclosed algorithm is in the form of four state equations, two equations for an angular acceleration embodiment and two for a linear acceleration embodiment. Each such embodiment includes seven state variables each having a gain coefficient of complex fraction form; each embodiment is additionally refined for differing cross-channel couplings.

Abstract: Two new homing guidance laws, designated as proportional Guidance (PROGUIDE) and Augmented Proportional Guidance (Augmented PROGUIDE), have been developed for use against non-maneuvering and maneuvering targets, respectively. These guidance laws are the solutions of linear-quadratic regulator control problems and minimize deviations from the collision triangle over the entire period of homing flight, thereby indirectly minimizing miss distance. In contrast to proportional navigation (PRONAV), these algorithms command the achievement of angular acceleration instead of linear acceleration and there is a significant advantage in doing so.

Abstract: Two new adaptive homing guidance laws are developed which are variants of Augmented Proportional Navigation (PRONAV). The first guidance law commands flight path angle rate and is referred to as adaptive matched augmented PRONAV (AMAAP). The second guidance law commands linear acceleration and is referred to as adaptive matched augmented linear PRONAV (AMALP). The major attributes of these guidance laws are (1) they are the solutions of a linear quadratic control problem, (2) they do not require an estimate of time-to-go (tgo), (3) they are matched to a nonlinear model of the target's motion, (4) they adapt in real time to provide optimal guidance over each small segment of the intercept trajectory, and (5) they optimally account for missile deceleration.