Newton-least squares cooperative localisation of sonic boom signals from multi-source rocket debris

To address the challenges of low single-target efficiency, multi-source signal aliasing and equipment time error in rocket debris sonic boom localisation, this study proposes a localisation method that integrates nonlinear optimisation and robust correction. A system of nonlinear equations is constructed based on Euler's formula and three-dimensional Euclidean distance, and solved by comparing Newton's method with the proposed Newton's method to verify the accuracy of single-wreckage localisation with four devices, accurately determine the position coordinates (longitude, latitude, elevation) and time when sonic booms occur for a single wreck in the air, and demonstrate the global convergence of the proposed Newton's method for high-dimensional problems. For multi-wreckage scenarios, a signal separation model combining classification matrix constraints and the triangle theorem is designed to achieve spatial and temporal decoupling of four sets of sonic booms, and the positioning error is reduced by 42%. The joint optimization framework of interval constraints and least squares is further proposed to compress the positioning error from 1.2 km to 0.8 km with a random error of 0.5 s. The experiments show that the model can significantly improve the recovery efficiency in complex environments through the optimization of the three phases of ‘positioning-separation-anti-noise’, which provides theoretical and technological support for the aerospace monitoring layout and multi-target tracking. It provides theoretical and technical support for aerospace monitoring layout and multi-target tracking.