State-of-the-art approaches to magnetic anomaly detection rely on the generalized likelihood ratio test (GLRT). These approaches are based on the formulation of a parametric model of the source to be detected, expressed in a suitable functional basis. One of the primary objectives of this study is to demonstrate that, for a given measurement configuration, the signal is constrained to evolve within a restricted subset of the space generated by these functional bases. The parametric representation of the signal is identified as a semi-algebraic space which, for the dipole model used in this article, turns out to be a cone outside of which the estimated signal does not satisfy the physical equations. Thus, a second objective is to exploit this property to constrain the signal parameters in the GLRT to belong to the semi-algebraic space, in order to improve detection performance. The performance gain of the proposed algorithm is compared to the one of conventional approaches; numerical simulations show that the proposed approach not only outperforms state-of-the-art methods but can even provide results close to those of the clear-seeing (optimal) receiver.

翻译：当前最先进的磁异常检测方法依赖于广义似然比检验（GLRT）。这些方法基于对目标源参数化模型的构建，该模型以合适的函数基组表达。本研究的主要目标之一在于证明：对于给定的测量配置，信号被约束在由这些函数基组生成空间的一个受限子集中演化。信号的参数化表示被识别为一种半代数空间，对于本文采用的偶极子模型而言，该空间表现为一个锥体，超出此范围的估计信号无法满足物理方程。因此，本研究的第二个目标是利用这一特性，将GLRT中的信号参数约束在半代数空间内，从而提升检测性能。将所提算法的性能增益与传统方法进行对比；数值模拟表明，本文方法不仅优于现有最先进方法，甚至能获得接近理想观测（最优）接收机的检测结果。