Precise Localization of Single Rocket Debris Sonic Boom Sources Using TDOA and Particle Swarm Optimization

School of Mechanical Engineering and Automation, Shenyang Institute of Technology, Fushun, 113122, China,

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Abstract

This paper addresses the precise localization of airborne sonic boom sources from rocket debris. A mathematical model utilizing Time Difference of Arrival (TDOA) technology is constructed to determine the exact location (longitude, latitude, altitude) and time of sonic boom occurrence. The model first defines the relative time difference between the shockwave reception at monitoring devices and reference devices, converting it into distance difference using the speed of sound. For distance calculation, the model employs the cosecant formula to compute the great circle distance between two points on the Earth’s surface, incorporating a proportional correction method to estimate the elevation’s impact on distance. The objective function is defined as minimizing the sum of squared deviations between predicted propagation time and actual observation time. Analysis of the four unknowns (three-dimensional coordinates and time) indicates that at least four monitoring devices are required for solution. Ultimately, the study employs a particle swarm optimization (PSO) algorithm to solve the multivariate optimization problem. Simulation results show that the objective function value decreases significantly during the initial phase and rapidly approaches 0, indicating the algorithm is converging toward a global optimum. The calculated sonic boom source coordinates and timing are: longitude 110.631°, latitude 27.145°, elevation 960.1 meters, time offset −8.944 seconds.