Modified Command to Line-of-Sight Intercept Guidance for Aircraft Defense

Abstract

P ROTECTING an aircraft from missile attack is a challenging issue. Most missile guidance algorithms [1–11] use information basically about the missile and the target but not that of the protected system. Considering only the kinematics with the aid of the collision triangle, Boyell [12] calculated a minimum range to intercept the attacking missile over a specified distance to protect a moving aircraft/torpedo and obtained a closed-form expression of the range for the missile to be successful against attacking missiles. Shneydor [13] developed conditions for the applicability of Boyell’s technique and simplified the expression for the operational range for the defense missile. However, those analyses were based on an ideal guidance assuming a perfect collision course. Rusnak [14] applied the differential game theory (DGT) to such a three-player game, a protected aircraft, an attacking missile, and a defense missile, by changing the three-player game into a two-team game by way of grouping the same cooperative players: a protected aircraft and a defensivemissile. Rusnak [14] showed that the resulting expression of the guidance lawwas represented by two line-of-sight (LOS) rate terms multiplied by variable gains derived from the differential game theory. One of the two LOS rates is the LOS rate of the aircraft with respect to the attacking missile, and the other is the LOS rate of the attacking missile with respect to the defense missile. The Rusnak method demands the recursive backward computations from the end. Perelman et al. [15] further modified Rusnak’s method to represent the two LOS rate terms in a closed form instead of using the recursive solution. Both simulation studies showed that the required acceleration could be reduced as compared with that of the conventional two-player differential game theory. Further recent work on such DGT can be found in [16]. Shima [17] proposed an optimal guidance methodology for a defense missile assuming prior knowledge of an attacking missile’s guidance law. Shaferman and Shima [18] applied a multiple model adaptive estimator algorithm with the multiple model adaptive control for such a three-player game to estimate the attacking missile’s guidance law. The proposed work here takes a basic approach to the three-player guidance law, similar to the proportional navigation (PN), in the way that it uses geometrical information of the moving object, that is, the protected aircraft’s LOS and the LOS rate. This type of guidance law can be classified as a three-point guidance [19–21]; examples are the beam rider (BR) guidance [2,19–21] and the command to LOS (CLOS) guidance [2,19–21]. The “three points” in the three-point guidance usually means amissile, a target, and a reference point from which the target LOS is drawn or the target is observed. In this study, the protected aircraft is selected as one of the three points instead of the reference point. Ratnoo and Shima [22] applied the CLOS guidance for aircraft protection. Their analysis shows that the defense missile requires less lateral acceleration (latax) than that of the attacking missile. They also proposed a guidance law for the protected aircraft that would help the defense missile against the target. However, the problem is that as the range of the target becomes larger, the resolution of the target LOS angle at a tracking pointwill be lower. This fact degrades the system performance or demands a highresolution radar to track a moving target from a distance. This Note proposes a different approach as compared with the BR or the CLOS guidance though it falls under the three-point guidance classification. The proposed approach manipulates two LOS rates associated with three vehicles and has benefits over the conventional three-point guidance law in two major aspects: 1) a simple form with one gain for two LOS rates, and 2) high sensitivity to an attacking missile’smaneuvers in the proximity of the attackingmissile, but low sensitivity to the attacking missile’s maneuvers in the proximity of the protected aircraft. This novel guidance law, called the airborneCLOS guidance (A-CLOSG) law, is derived using optimal control theory.