A powerful kinematic model for proportional navigation of guided weapons against maneuvering targets

An accurate solution is presented of the nonlinear differential equations describing the pursuer motion under the PN (proportional navigation) law in the general case when the target is laterally maneuvering. A quasilinearization (QL) approach is used, followed by a perturbation technique to obtain analytical solutions to the trajectory parameters. An explicit expression for the pursuer lateral acceleration is derived and is shown to contain contributions due to initial heading error and target maneuver, with a coupling between the two effects. The solution is shown to be a substantial and consistent generalization of the classical linear solution for maneuvering targets. The generalized QL solution presented provides very accurate estimates of pursuer lateral acceleration over a much broader range of engagement geometries and target maneuvers than other presently available analytical solutions.<
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