Accurate positioning of multiple rocket debris

This paper aims to accurately determine the position and time of sonic explosions in the air by analyzing data from single and multiple debris cases. It focuses on identifying the minimum number of monitoring devices needed, considering random recording time errors, and correcting models to improve positioning accuracy. Additionally, it explores precise positioning strategies when time errors can't be effectively reduced, enhancing airspace debris management. Problem 1: Understanding sound wave propagation, we used a three-ball positioning method. Since both the detection point and the sonic explosion debris are high in the air, the fourth point was used for accuracy. Using least squares method with randomly selected data, we determined the position (longitude: 110.4989, latitude: 27.3105, height: 857.4884m) and time (19.3128s). Problem 2: Theoretically, 44 devices are needed, but four can classify unknown time data groups. Calculations are based on extending the first problem's theoretical basis, introducing relative time and position error solutions. Problem 3: Using actual data, four devices calculate correct locations, but time uncertainty causes larger errors. Introducing additional equipment for secondary screening or multiple data exclusion improves accuracy. Problem 4: Random perturbations of time data (ranging from -0.5 to 0.5) tested the model's anti-interference capabilities. Adjustments included adding an error function and repeating data perturbations until the solution met error range criteria. This significantly reduced time and position errors, with position errors within 1km. This study enhances the efficiency and safety of airspace debris management by improving the accuracy of sonic explosion positioning.