Practical interception always happens in three-dimensional region, but it's not easy to study the characteristics of guidance laws in the three-dimensional environment. The main goal of the paper is to derive a practicable method to reduce the dimensions of the guidance problem. The kinematic equations of the line of sight and a new set of relative dynamic equations between missile and target are presented. The decoupling analysis of these dynamic equations indicates that the dimensions of the relative motion could be reduced from three to two. Thus the performance and trajectory analysis of two-dimensional guidance laws presented before could be directly used to solve three-dimensional guidance problem without any linearization and approximation. The dimension-reduction process of three-dimensional true proportional navigation is studied in the paper, and so is the augmented proportional navigation. Furthermore, the capture regions of true proportional navigation and augmented proportional navigation are presented in the phase plane graphically according to the relative dynamic equations.
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