Guidance Algorithm Design: A Nonlinear Inverse Approach

Abstract

The design of a missile guidance algorithm valid for any initial missile and target orientation is described. The limitations of proportional navigation- (PN-) or line-of-sight rate-based guidance for this problem are pointed out. Design heuristics are explained, and general guidelines for the synthesis of guidance algorithms are stated. It is shown thatthedesign of an algorithm valid forany initial missileand target orientation leadsto a nonlinearinverse problem. Standard geometric methods for solving nonlinear inverse problems are adapted to derive a new class of algorithms based on the relative heading error angle (RHEA). Examples of RHEA algorithms are then discussed and compared with PN guidance for different engagement scenarios. am = missile acceleration at = target acceleration Vm = missile speed Vt = target speed Xm, Ym = dimensional missile coordinates Xt, Yt = dimensional target coordinates xm, ym = nondimensional missile coordinates xt, yt = nondimensional target coordinates ®m = nondimensional missile acceleration ®t = nondimensional target acceleration µ = line of sight (LOS) angle µ 0 = LOS rate o = target to missile velocity ratio Ω = nondimensional distance to go ? = nondimensional time Âm = missile heading angle Ât = target heading angle A = relative heading error angle