The proportional navigation dilemma-pure or true?

Two generic classes of proportional navigation (PN) laws are compared in detail. One class consists of pursuer-velocity-referenced systems, which include pure proportional navigation (PPN) and its variants; the second category consists of line-of-sight- (LOS-) referenced systems such as true proportional navigation (TPN), generalized true proportional navigation (GTPN), and generalized guidance laws. The existing closed-form solutions are discussed in detail, and the classical linear and quasilinear analytical solutions are summarized. A critical comparison is then made with regard to the definition, implementation, and analytical aspects of the guidance laws, including the method, the nature of solution, and an appraisal of the behavior of the pursuer motion resulting from the laws. It is established that, in spite of some restricted advantages in the solvability of the equations of motion, the LOS-referenced PN schemes suffer from serious limitations in terms of implementation and trajectory behavior. Among the major drawbacks are forward velocity variation requirement, relatively large control effort requirement, restrictions on initial engagement conditions to ensure intercept, lack of robustness, and possibility of unbounded acceleration. It is concluded that PPN is a better guidance law in a practical sense than TPN and its generalizations.<
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