Ideal proportional navigation for exoatmospheric interception

Abstract Ideal proportional navigation (IPN) is a natural choice for exoatmospheric interception for its mighty capture capability and ease of implementation. The closed-form solution of two-dimensional ideal proportional navigation was conducted in previous public literature, whereas the practical interception happens in the three-dimensional space. A novel set of relative dynamic equations is adopted in this paper, which is with the advantage of decoupling relative motion in the instantaneous rotation plane of the line of sight from the rotation of this plane. The dimension-reduced IPN is constructed in this instantaneous plane, which functions as a three-dimensional guidance law. The trajectory features of dimension-reduced IPN are explored, and the capture regions of dimension-reduced IPN with limited acceleration against nonmaneuvering and maneuvering targets are analyzed by using phase plane method. It is proved that the capture capability of IPN is much stronger than true proportional navigation (TPN), no matter the target maneuvers or not. Finally, simulation results indicate that IPN is more effective than TPN in exoatmospheric interception scenarios.

[1]  J. Chern,et al.  Solutions of true proportional navigation for maneuvering and nonmaneuvering targets , 1992 .

[2]  Paul Zarchan,et al.  Tactical and strategic missile guidance , 1990 .

[3]  Analytical Solution of Three-Dimensional Realistic True Proportional Navigation , 1996 .

[4]  E. Duflos,et al.  3D guidance law modeling , 1999 .

[5]  Gordon D. Friedlander.  Retrospective: Ampère: Father of electrodynamics: The master mathematician, teacher, and practitioner of electrical science is celebrated on the 200th anniversary of his birth , 1975, IEEE Spectrum.

[6]  F. Adler.  Missile Guidance by Three‐Dimensional Proportional Navigation , 1956 .

[7]  Chen-Yuan Kuo,et al.  GEOMETRIC APPROACH TO THREE-DIMENSIONAL MISSILE GUIDANCE PROBLEM , 1998 .

[8]  Chaoyong Li,et al.  Gain-Varying Guidance Algorithm using Differential Geometric Guidance Command , 2010, IEEE Transactions on Aerospace and Electronic Systems.

[9]  Debasish Ghose,et al.  Capture region for a realistic TPN guidance law , 1993 .

[10]  Fang-Bo Yeh,et al.  Closed-form solution for a class of guidance laws , 1987 .

[11]  Debasish Ghose.  On the generalization of true proportional navigation , 1994 .

[12]  Zhang Bing,et al.  Novel TPN control algorithm for exoatmospheric intercept , 2012 .

[13]  Stephen A. Murtaugh,et al.  Fundamentals of proportional navigation , 1966, IEEE Spectrum.

[14]  Wang Hui.  Application of the 3D Differential Geometric Guidance Commands , 2007 .

[15]  Lei Chen,et al.  Improved differential geometric guidance commands for endoatmospheric interception of high-speed targets , 2013 .

[16]  Ciann-Dong Yang,et al.  Analytical solution of generalized three-dimensional proportional navigation , 1996 .

[17]  Feng Tyan.  The capture region of a general 3D TPN guidance law for missile and target with limited maneuverability , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[18]  Guo-Jin Tang,et al.  Optimal multi-objective trajectory design based on close-looped control for autonomous rendezvous , 2011 .

[19]  조형석,et al.  호밍미사일이 새로운 유도방식에 관한 연구 ( A New Guidance Law for Homing Missiles ) , 1983 .

[20]  M. Guelman.  The closed-form solution of true proportional navigation , 1976, IEEE Transactions on Aerospace and Electronic Systems.

[21]  Jing Wuxing.  Practical study on 2D differential geometric guidance problem , 2007 .

[22]  Fang-Bo Yeh,et al.  The closed-form solution of generalized proportional navigation , 1987 .

[23]  Pin-Jar Yuan,et al.  Analytic Study of Biased Proportional Navigation , 1992 .

[24]  J. Chern,et al.  Ideal Proportional Navigation , 1992 .

[25]  Debasish Ghose.  True proportional navigation with maneuvering target , 1994 .

[26]  Fei-Bin Hsiao,et al.  Generalized guidance law for homing missiles , 1989 .

[27]  Feng Tyan.  Unified approach to missile guidance laws: a 3D extension , 2005 .

[28]  Chi-Ching Yang,et al.  A unified approach to proportional navigation , 1997 .

[29]  P. R. Mahapatra,et al.  The proportional navigation dilemma-pure or true? , 1990 .

[30]  Feng Tyan.  Capture region of 3D PPN guidance law for intercepting high speed target , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[31]  Guo-Jin Tang,et al.  Research on the strategy of angles-only relative navigation for autonomous rendezvous , 2011 .

[32]  Kebo Li,et al.  Differential geometric modeling of guidance problem for interceptors , 2011 .

[33]  Chi-Ching Yang,et al.  Analytical solution of 3D true proportional navigation , 1996 .