Capture regions of GIPN guidance laws: a least square SVM approach

In this paper, the expression of capture region of the general ideal proportional navigation (GIPN) missile guidance law is determined by a powerful classifier, least square support vector machine (LSSVM). To reduce the computational burden, an approximation of the Gaussian radial basis function is adopted to obtain the corresponding nonlinear feature mapping function. Through numerous numerical examples, it shows that the proposed technique is adequate for the determination of capture region. All the analysis of the relative dynamics between missile and target are performed in a line of sight (LOS) fixed natural coordinate. To have the capture region ready for LSSVM, all the state variables are transformed into the modified polar variables form. In addition, to reduce the number of independent variables, these modified polar variables are further non-dimensionalized. For simplicity, we assume that target's input acceleration is subject to independent saturation, while missile's input acceleration is subject to magnitude saturation