Author(s)

Zhengyuan Li, Ling Wang

Corresponding Author

Zhengyuan Li

Abstract

In order to accurately determine the position and time of a sonic boom generated by rocket debris, this study initially converts the geographical coordinates of observation equipment into a Cartesian coordinate system for mathematical modeling. Subsequently, a multi-lateration technique is utilized to construct an optimization model, aiming to minimize the sum of squared differences between the predicted and actual observed arrival times of the sonic boom. To address this optimization challenge, the paper employs the BFGS algorithm, an effective numerical optimization method capable of identifying parameter values that minimize the objective function. Through iterative computation, the algorithm predicts the three-dimensional coordinates and specific timing of the sonic boom occurrence. Finally, the study demonstrates the accuracy of the model's predictions through three-dimensional visualization results, laying the groundwork for subsequent processing of more complex multi-debris localization issues.

Keywords

Sonic Boom Localization, Rocket Debris, Multi-lateration, BFGS Algorithm, Three-dimensional Visualization