TY - JOUR

T1 - Detecting Weak Physical Signal from Noise

T2 - A Machine-Learning Approach with Applications to Magnetic-Anomaly-Guided Navigation

AU - Zhai, Zheng Meng

AU - Moradi, Mohammadamin

AU - Kong, Ling Wei

AU - Lai, Ying Cheng

N1 - Funding Information:
We thank Dr. Aaron Nielsen and Dr. Arje Nachman for their great insights into and suggestions for this work. This work is supported by AFOSR under Grant No. FA9550-21-1-0438.
Publisher Copyright:
© 2023 American Physical Society.

PY - 2023/3

Y1 - 2023/3

N2 - Detecting a weak physical signal immersed in overwhelming noises entails separating the two, a task for which machine learning is naturally suited. In principle, such a signal is generated by a nonlinear dynamical system of intrinsically high dimension for which a mathematical model is not available, rendering unsuitable traditional linear or nonlinear state-estimation methods that require an accurate system model (e.g., extended Kalman filters). We exploit the architectures of reservoir computing and feed-forward neural networks (FNNs) with time-delayed inputs to solve the weak-signal-detection problem. As a prototypical example, we apply the machine-learning schemes to Earth's magnetic anomaly field-based navigation. In particular, the time series are collected from the interior of the cockpit of a flying aircraft during different maneuvering phases, where the overwhelmingly strong noise background is the result of other components of Earth's magnetic field and the fields generated by the electronic devices in the cockpit. We demonstrate that, when combined with the traditional Tolles-Lawson model for Earth's magnetic field, the articulated machine-learning schemes are effective for accurately detecting the weak anomaly field from the noisy time series. The schemes can be applied to detecting weak signals in other domains of science and engineering.

AB - Detecting a weak physical signal immersed in overwhelming noises entails separating the two, a task for which machine learning is naturally suited. In principle, such a signal is generated by a nonlinear dynamical system of intrinsically high dimension for which a mathematical model is not available, rendering unsuitable traditional linear or nonlinear state-estimation methods that require an accurate system model (e.g., extended Kalman filters). We exploit the architectures of reservoir computing and feed-forward neural networks (FNNs) with time-delayed inputs to solve the weak-signal-detection problem. As a prototypical example, we apply the machine-learning schemes to Earth's magnetic anomaly field-based navigation. In particular, the time series are collected from the interior of the cockpit of a flying aircraft during different maneuvering phases, where the overwhelmingly strong noise background is the result of other components of Earth's magnetic field and the fields generated by the electronic devices in the cockpit. We demonstrate that, when combined with the traditional Tolles-Lawson model for Earth's magnetic field, the articulated machine-learning schemes are effective for accurately detecting the weak anomaly field from the noisy time series. The schemes can be applied to detecting weak signals in other domains of science and engineering.

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U2 - 10.1103/PhysRevApplied.19.034030

DO - 10.1103/PhysRevApplied.19.034030

M3 - Article

AN - SCOPUS:85149697095

SN - 2331-7019

VL - 19

JO - Physical Review Applied

JF - Physical Review Applied

IS - 3

M1 - 034030

ER -