Solutions of generalized proportional navigation with maneuvering and nonmaneuvering targets

In this generalized proportional navigation (GPN), the commanded acceleration is applied in a direction with a bias angle to the normal direction of line-of-sight (LOS) and its magnitude is proportional to the product of closing speed and LOS rate between interceptor and its target. Some solutions of GPN were obtained before under the assumption that the magnitude of commanded acceleration is proportional to the LOS rate only. Now in this article, the exact and complete closed-form solutions are derived under this modified guidance scheme for both maneuvering and nonmaneuvering targets. Some related important characteristics, such as capture capability and energy cost, are investigated and discussed. The variation of bias angle will induce the change of capture area and energy cost required. Also, a typical example of target maneuver is introduced to describe the effect of target maneuver easily. It shows that the target maneuver will decrease the capture area and increase the energy cost for effective intercept of target.<>