用于从三维远场数据跟踪移动目标的贝叶斯优化方法
Bayesian optimization approach for tracking a moving target from far-field data in three dimensions
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中文总结 AI 辅助
研究从三维远场数据跟踪移动目标的逆散射问题，通过开发贝叶斯优化框架，结合解析公式设计优化程序，建立后验一致性，未知形状时用神经网络识别，经数值实验验证该框架有效。
中文摘要 AI 辅助
我们研究了一个三维逆散射问题，即从单个入射场产生的远场数据中跟踪刚性移动目标。扩展我们最近的二维研究，我们开发了一个贝叶斯优化框架，用于在连续时间步长上同时跟踪目标的位置和方向，将平移和旋转运动建模为独立随机过程。我们推导了平移和旋转下远场模式的解析公式，并用于设计针对跟踪问题的贝叶斯优化程序。我们还为基础概率模型建立了后验一致性。当目标形状未知时，在初始时刻使用在预计算数据集上训练的全连接神经网络识别其形状。数值实验验证了所提框架的有效性。
英文摘要
We investigate a three-dimensional inverse scattering problem for tracking a rigidly moving target from far-field data generated by a single incident field. Extending our recent two-dimensional study, we develop a Bayesian optimization framework for simultaneously tracking the target's location and orientation over successive time steps, with the translational and rotational motions modeled as independent stochastic processes. We derive analytical formulas for the far-field pattern under translations and rotations and use them to design a Bayesian optimization procedure tailored to the tracking problem. We further establish posterior consistency for the underlying probabilistic model. When the target shape is unknown, its shape is identified at the initial time using a fully connected neural network trained on a precomputed dataset. Numerical experiments validate the effectiveness of the proposed framework.
