Analytical solution of 3D true proportional navigation

Author

Ciann-Dong Yang ; Chi-Ching Yang

Author_Institution

Inst. of Aeronaut. & Astronaut., Nat. Cheng Kung Univ., Tainan

Volume

32

Issue

4

fYear

1996

fDate

10/1/1996 12:00:00 AM

Firstpage

1509

Lastpage

1522

Abstract

The commanded acceleration applying in the direction normal to the line of sight (LOS) between the interceptor and its target is called true proportional navigation (TPN). The main goal of this work is to derive the complete analytical solutions of three-dimensional (3D) TPN for nonmaneuvering and maneuvering targets. Three coupled nonlinear second-order state equations describing the relative motion are solved analytically without any linearization for performance and trajectory analysis. Properties of 3D TPN such as capture region, range-to-go, time-to-go, and two aspect angles within spherical coordinates are all obtained in closed form. Furthermore, the comparison between 3D TPN and 3D realistic true proportional navigation (RTPN) is investigated analytically in the two-player game where a TPN-guided missile is commanded to pursue a RTPN-guided target, and vice versa

Keywords

game theory; military systems; missile guidance; nonlinear equations; target tracking; 3D true proportional navigation; TPN; aspect angles; capture region; coupled nonlinear second-order state equations; maneuvering targets; nonmaneuvering targets; range-to-go; spherical coordinates; time-to-go; trajectory analysis; two-player game; Acceleration; Accelerometers; Couplings; Differential equations; Missiles; Motion analysis; Navigation; Nonlinear equations; Performance analysis; Rotation measurement;

fLanguage

English

Journal_Title

Aerospace and Electronic Systems, IEEE Transactions on

Publisher

ieee

ISSN

0018-9251

Type

jour

DOI

10.1109/7.543873

Filename

543873