Control of impact angle using generalized biased proportional navigation against higher-speed targets

In this paper, a generalized biased proportional navigation (PN) guidance law to intercept higher-speed nonmaneuvering targets at a desired impact angle is presented. Inspired by controlling the turn rate of the relative velocity vector, the biased relative PN is introduced to design the relative heading angular rate, which is required to be proportional to the LOS rate as in the case of PN but with an extra bias term. Then the impact angle constrained interception for higher-speed nonmaneuvering targets is controlled through adding a time-varying term to the designed biased relative PN. Analysis of the time-varying term shows that the generalized biased PN has two guidance mode (PN mode and retro-PN mode), so that the useful features of the classical PN and the retro-PN guidance laws can be synthesized in the guidance design. In order to avoid the singularity of the guidance command, the impact angles are divided into two groups. The impact angle can be achieved by selecting appropriate guidance mode to determine the right direction of the trajectory. Extensive simulations are conducted to verify the design features of the algorithm.