M.Sc Thesis
M.Sc Student Oren Gutman Proportional Navigation in Target Displacement Scenarios Department of Mechanical Engineering Professor Emeritus Zalman Palmor

Abstract

Proportional Navigation (PN) is a guidance law for homing missiles that has been used successfully for the last 50 years. According to this law, the maneuver of the missile is proportional to the line of sight rate. It is based on the fact that if the target and the missile have constant velocities then on a collision course the line of sight rate is zero . We revisit the basic block diagrams in PN, and study the effect of initial conditions on miss-distance. Using the important case of multiple targets, we compare two PN block diagrams. The first, the ideal PN, applies the true line of sight rate, which is calculated by an analytic derivative of the line of sight angle. The block diagram resulting from this guidance loop is minimal. The second applies an approximated derivative of a LOS angle. The block diagram resulting from this guidance loop is unobservable with respect to target displacement due to zero-pole cancellation at the origin. The consequence is that for the target displacement initial condition the two diagrams do not result in the same miss-distance. A missile-target engagement with a step in target displacement is a basic initial condition scenario in the neighborhood of a collision course. In particular it serves as a model for the multiple targets problem. In multiple targets scenario a missile is guided by PN on the power centroid of two targets flying in close formation. At the moment where the missile seeker can separate the targets, it appears to the missile that the target has instantaneously shifted from the power centroid to the location of the resolved target. Since the separation occurs at a late moment of the engagement, this shift may induce a large miss-distance. In this research we show that target displacement and heading error are interchangeable. By choosing a certain reference line, one may interpret a multiple target scenario as a target displacement. By choosing a different reference line one may interpret it as a heading error. Nevertheless, since miss distance is invariant with respect to the choice of reference line, it follows that heading error and Target displacement must result in the same miss distance. Moreover, we suggest a few solutions that can resolve the above difficulty; One of the solutions is to reset the derivative network with the correct initial conditions. By doing so target displacement and heading error yield the same miss distance again.