Author(s)

Xuanyu Chang, Wenzheng Wang

Corresponding Author

Xuanyu Chang

Abstract

This study aims to accurately pinpoint the landing point of rocket debris by establishing mathematical models and applying optimization algorithms. Initially, we constructed a model to determine the positional coordinates of rocket debris at the moment of the sonic boom. By analyzing the collected data from various monitoring devices using multi-source localization methods, we concluded using our established model. During the model construction, we transformed the Earth's geographical coordinates into a Cartesian coordinate system, simplifying the distance calculations. We employed the least squares method and gradient optimization algorithms to solve the equations, thereby minimizing errors and ultimately determining the positional coordinates and the time of the sonic boom of the rocket debris. Although the results of the gradient descent algorithm were almost unusable, we adopted a method based on nonlinear least squares. Furthermore, we explored the problem of multi-debris sound source identification and localization, utilizing the Hungarian algorithm for matching, defining a cost matrix function, and optimizing with the linear assignment function. By validating the model with data recorded from monitoring devices, we analyzed the sound source localization of rocket debris. Ultimately, we proposed a single-point localization model for rocket debris, based on multi-source localization and least squares optimization, solving the problem of landing points for multiple debris in a short period. This study not only provides a new method for the localization of rocket debris but also lays the foundation for future related research.

Keywords

Rocket Debris Localization, Multi-source Localization, Least Squares Method, Hungarian Algorithm, Sonic Source Identification