三维理想比例导引律的捕获区域分析

Is Capture Region of 3D Ideal Proportional Navigation (IPN) also the Biggest?

在基于球体坐标系内建立的弹-目相对运动方程基础上,对几种典型的比例导引律在三维空间内进行了统一描述。通过引入相对运动的单位角动量,将传统的“捕获区域”描述转化为“捕获长度”的描述,求出了三维空间内理想比例导引律(IPN)的捕获区域,并将之与真比例导引(TPN)、现实真比例导引(RTPN)的捕获区域进行了比较和分析。结果表明,在导航比大于2的情况下对于任何初始攻击布局IPN的捕获条件几乎都成立,而且其捕获区域不受导航比的限制,这和二维平面内的结果相同。

It is well known that 2D IPN＇s capture region is bigger than that of any other existing PN. We now present our research results concerning whether this is also true for 3D IPN. In the full paper ,we explain our research results in detail; in this abstract, we just add some pertinent remarks to listing the three topics of explanation： （1） the establishment of missile-target relative motion equations, （2） the unified description of 3D PN laws, （3） the analysis of 3D IPN＇s capture region; in topic 1, eqs. （6）, （7）, and （8） in the full paper, taken from the open literature, form the system of missile-target relative motion equations; in topic 2, we utilize Ref. 3, written by Yang and Yang, to describe the command accelerations of a missile under various PN laws; in topic 3, we introduce the well-known transformation of ＂capture region＂ into ＂capture length＂; also in topic 3, we derive eq. （28） in the full paper needed for calculating the capture length of IPN and give eqs. （29） and （30） in the full paper, taken from the open literature and needed for calculating respectively the capture lengths of RTPN and TPN ; still in topic 3, the comparison of eqs. （28）, （20） and （30） shows preliminarily that the capture length or capture region of IPN is the biggest among the three capture lengths or capture regions of IPN, RTPN, and TPN. The formulas for calculating capture lengths of other 3D PNs need to be derived before the question of whether the capture region of 3D IPN is the biggest can be finally answered.