Model of laser radar signatures of ballistic missile warheads

Ballistic missiles can separate in mid-course flight producing several components that include the warhead, control modules, booster segments, and debris. Since many warheads are spin-stabilized, laser radar range-Doppler imaging may provide signatures for identifying the warhead. Discrimination algorithms are most effective when they are based on the signatures expected from the target, however, an analytical model that relates the geometric and physical parameters of the target to its range-Doppler signature has not been available. This study developed a closed-form analytical formulation that models the range-Doppler signatures of a spinning conic warhead as a function of its parameters such as, angular velocity, half-cone angle height, and aspect angle. Using the 3-D conic surface equation, the angle-of-incidence at an arbitrary point is expressed in terms of the geometric parameters of the target. A relationship that links the Doppler shift to the cross-range coordinate of the target is used to complete the formulation of a point return as a function of range and Doppler. The model predictions match the experimental data well and suggest that this closed-form analytical solution can be used for parameter identification and discrimination in ballistic missile defense.