Fundamentals of Proportional Navigation and Its Application to an Antisatellite Interceptor

Proportional navigation is an interception guidance technique in which interceptor maneuvers are commanded which are proportional to the measured rate of rotation of the line of sight between an interceptor and its target. The maneuvers are directed to provide control of the rotational rate of the line of sight so that the interceptor converges on the target. This paper, which is tutorial in nature, presents and discusses the basic kinematics of proportional navigation and several of its variations under ideal conditions (i.e. no noise, no time lags, and no target acceleration). The discussions are directed, by example, to the case of exoatmospheric interception of a satellite; however, the guidance theory presented is applicable to the general intercept problem involving a constant speed interceptor and a nonmaneuvering airborne target. The analysis presented is restricted to a two-dimensional end game which is initiated when the interceptor seeker acquires a target satellite. It is assumed that prior to target acquisition the interceptor has been launched from the ground and guided toward a predicted intercept point on the basis of ephemeris data obtained from satellite tracking stations. Subsequent to target acquisition, the end game consists of nulling the projected miss distance produced by ephemeris uncertainties and midcourse guidance errors. Emphasis is given to the time-varying behavior of the basic parameters, including line-of-sight rotational rate, miss distance, acceleration, and velocity increase.