The problem of geolocating an unknown high-frequency emitter based on the quasi-parabolic ionosphere model with time-difference of arrival measurements of the refracted radio rays is of fundamental importance in various military and civilian applications. Such a problem admits a maximum-likelihood (ML) formulation, which is nonlinear and non-convex. By elucidating the geometry of the feasible set of the ML formulation, we develop a first-order algorithm, which we call Generalized Projected Gradient Descent, to solve it. We prove that every limit point of the iterates generated by our proposed algorithm is a critical point of the ML formulation. Simulation results show that our proposed algorithm can more reliably and accurately geolocate the emitter than a state-of-the-art method in various settings.

中文翻译：

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准抛物线电离层模型下基于TDOA的可证明收敛的投影梯度型算法


基于准抛物线电离层模型以及折射无线电射线到达时间差测量来对未知高频发射器进行地理定位的问题在各种军事和民用应用中具有根本重要性。此类问题采用最​​大似然 (ML) 公式，该公式是非线性且非凸的。通过阐明 ML 公式的可行集的几何形状，我们开发了一种一阶算法（我们称之为广义投影梯度下降）来解决它。我们证明，我们提出的算法生成的迭代的每个极限点都是机器学习公式的关键点。仿真结果表明，在各种设置下，我们提出的算法比最先进的方法能够更可靠、更准确地对发射器进行地理定位。