A nonlinear 3-D navigation algorithm based on a generalization of the classical law by Adler is developed. In the development of the engagement kinematics it is shown that choosing two opposite directions of the unit normal to the lead angle plane formed by the missile velocity and the line of sight (LOS), and two different roots of a quadratic equation associated with the true collision velocity, one arrives at four different scenarios which give rise to distinct missile trajectories and distinct interception times. Through numerical simulation, it is shown that one of the choices leads to a missile trajectory that deviates from the target, while the other three result in interception of the target. The generalization of Adler's proportional navigation comprises two equations, a linear one and a nonlinear relation that possesses the turning rates of the LOS, the navigation gain, the lead angle, the range, and a velocity correction that brings the instantaneous collision-course velocity vector on the locus of the missile velocity. Numerical tests based on the generalized 3-D navigation scheme and Adler's proportional navigation law are compared and discussed. The generalized law is found to require less acceleration for intercept.
Generalization of Adler's Three-Dimensional Proportional Navigation Law
IEEE Transactions on Aerospace and Electronic Systems ; 61 , 2 ; 4719-4728
2025-04-01
1516209 byte
Article (Journal)
Electronic Resource
English
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