Launch Point and Impact Point Estimation Using Automatic Differentiation on Inverse Problems

초록

This paper presents an advanced method for estimating the launch and impact points of rockets through the use of automatic differentiation. The central challenge of this research is the precise estimation of a rocket's initial conditions, such as launch points and initial flight path angles, along with specific parameters like booster burn time, based on sparse radar measurements. To address this, we have formulated an inverse problem designed to infer these critical parameters from the available measurement data. The inverse problem is defined by incorporating a dynamic model of a rocket and an appropriate cost function that evaluates the fitness of the launch parameters in relation to the measured radar data, hence solving the inverse problem can identify the launch parameters that most accurately reflect the observed radar measurements. Automatic differentiation is employed to compute the gradient information, which is crucial for the optimization algorithms used in our methodology. The integration of automatic differentiation significantly enhances the robustness and efficiency of the model optimization process, enabling more precise and reliable estimation of rocket trajectories. The effectiveness of this estimation process for launch and impact points was rigorously evaluated through numerical simulations, demonstrating the potential of our approach to substantially improve the accuracy of determining the launch and impact points of inbound rockets.