The presence of complex electromagnetic noise in the ocean significantly impacts the accuracy of ship shaft-rate electric field signal detection, necessitating the development of an effective denoising method to enhance detection precision. Nevertheless, traditional denoising methods encounter issues like low frequency resolution, challenging threshold configuration, and mode mixing. This study introduces a method that integrates variational mode decomposition (VMD) with multi-window spectral subtraction (MSS). The intrinsic mode functions (IMFs) of noisy signals are extracted using VMD, and the noise components within different IMFs are identified. The spectral features of both signal and noise within different IMFs are leveraged to eliminate noise signals via MSS. Subsequently, the denoised components of IMFs are rearranged to derive the denoised ship shaft-rate electric field signals, achieving noise reduction across various frequency bands. Following validation using simulation signals and empirical data, the noise reduction efficacy of VMD-MSS surpasses that of alternative methods, demonstrating robust performance even at low signal-to-noise ratios. The marine electromagnetic noise is effectively suppressed in the empirical data, while preserving the characteristics of ship’s shaft-rate signals, thereby validating the method’s efficacy and demonstrating its practical engineering value.

Aeromagnetic surveys are widely used in geological exploration, mineral resource assessment, environmental monitoring, military reconnaissance, and other areas. It is necessary to perform magnetic compensation for interference in these fields. In recent years, large unmanned aerial vehicles (UAVs) have been more suitable for magnetic detection missions because of the greater loads they can carry. This article proposes some methods for the magnetic compensation of large multiload UAVs. Because of the interference of the large platform and instrument noise, the standard deviations (stds) of the compensation data used in this paper are larger. At the beginning of this article, using the traditional T-L model, we avoid the shortcomings of the anti-magnetic interference ability of triaxial magnetic gate magnetometers. The direction cosine information is obtained by using an inertial navigation system, the global positioning system, and a triaxial magnetic gate magnetometer. Then, we increase the amplitude of the maneuvers in the compensation process; this reduces the multicollinearity problems in the compensation matrix to a certain extent, but it also results in greater magnetic field interference. Lastly, we employ the method of Lasso regularization Newton iteration (LRNM). Compared to the traditional methods of least squares (LS) and singular value decomposition (SVD), LRNM provides improvements of 34% and 27%, respectively. In summary, this series of schemes can be used to perform effective compensation for large multi-load UAVs and improve the actual use of large UAVs, making them more accurate in the measurement of aeromagnetic survey data.

Aeromagnetic detection is a geophysical exploration technology that utilizes aircraft-mounted magnetometers to map variations in the Earth’s magnetic field. As a critical methodology for subsurface investigations, it has been extensively applied in geological mapping, mineral resource prospecting, hydrocarbon exploration, and engineering geological assessments. However, the metallic composition of aircraft platforms inherently generates magnetic interference, which significantly distorts the measurements acquired by onboard magnetometers. Aeromagnetic compensation aims to mitigate these platform-induced magnetic disturbances, thereby enhancing the accuracy of magnetic anomaly detection. Building upon the conventional Tolles-Lawson (T-L) model, this study introduces an enhanced compensation framework that addresses two key limitations: (1) minor deformations that occur due to the non-rigidity of the aircraft fuselage, resulting in additional interfering magnetic fields, and (2) coupled interference between geomagnetic field variations and aircraft maneuvers. The proposed model expands the original 18 compensation coefficients to 57 through dynamic parameterization, achieving a 22.41% improvement in compensation efficacy compared with the traditional T-L model. Furthermore, recognizing the operational challenges of large unmanned aerial vehicles (UAVs) in conventional calibration flights, this work redesigns the flight protocol by eliminating high-risk yaw maneuvers and optimizing the flight path geometry. Experimental validations conducted in the South China Sea demonstrate exceptional performance, with the interference magnetic field reduced to 0.0385 nT (standard deviation) during level flight, achieving an improvement ratio (IR) of 4.1688. The refined methodology not only enhances compensation precision but also substantially improves operational safety for large UAVs, offering a robust solution for modern aeromagnetic surveys.

Harmonics are a common phenomenon widely present in power systems. The presence of harmonics not only increases the energy consumption of equipment but also poses hidden risks to the safety and stealth performance of large ships. Thus, there is an urgent need for a detection method for the harmonic characteristics of time series. We propose a novel harmonic feature estimation method, termed Harmonic Aggregation Entropy (HaAgEn), which effectively discriminates against background noise. The method is based on bispectrum analysis; utilizing the distribution characteristics of harmonic signals in the bispectrum matrix, a new Diagonal Bi-directional Integral Bispectrum (DBIB) method is employed to effectively extract harmonic features within the bispectrum matrix. This approach addresses the issues associated with traditional time–frequency analysis methods, such as the large computational burden and lack of specificity in feature extraction. The integration results, $I_x$ and $I_y$, of DBIB on different frequency axes are calculated using cross-entropy to derive HaAgEn. It is verified that HaAgEn is significantly more sensitive to harmonic components in the signal compared to other types of entropy, thereby better addressing harmonic detection issues and reducing feature redundancy. The detection accuracy of harmonic components in the shaft-rate electromagnetic field signal, as evidenced by sea trial data, reaches 96.8%, which is significantly higher than that of other detection methods. This provides a novel technical approach for addressing the issue of harmonic detection in industrial applications.

Currently, magnetic gradient tensor-based localization methods face challenges such as significant errors in geomagnetic field estimation, susceptibility to local optima in optimization algorithms, and inefficient performance. In addressing these issues, this article propose a two-point localization method under the constraint of overlaying geometric invariants. This method initially establishes the relationship between the target position and the magnetic gradient tensor by substituting an intermediate variable for the magnetic moment. Exploiting the property of the eigenvector corresponding to the minimum absolute eigenvalue being perpendicular to the target position vector, this constraint is superimposed to formulate a nonlinear system of equations of the target’s position. In the process of determining the target position, the Nara method is employed for obtaining the initial values, followed by the utilization of the Levenberg–Marquardt algorithm to derive a precise solution. Experimental validation through both simulations and experiments confirms the effectiveness of the proposed method. The results demonstrate its capability to overcome the challenges faced by a single-point localization method in the presence of some errors in geomagnetic field estimation. In comparison to traditional two-point localization methods, the proposed method exhibits the highest precision. The localization outcomes under different noise conditions underscore the robust noise resistance and resilience of the proposed method.

Addressing the issues of low positioning accuracy and poor robustness in shaft-rate magnetic fields, this study introduces the Improved Exponential Triangular Optimization Algorithm (IETO). By incorporating adaptive attenuation factors, dynamic population reduction, and intelligent boundary contraction strategies, it significantly enhances the global search capability and robustness. A magnetic dipole localization model is developed, and comparative simulations show that IETO achieves reliable accuracy and robustness under low signal-to-noise ratio (SNR) conditions, reducing localization error by 7.82% compared with the conventional Exponential Triangular Optimization Algorithm (ETO). The effects of base station deployment, number of stations, and sea depth on localization performance are further examined, and the capability of IETO for dynamic target tracking is verified. Preliminary sea trial results confirm the practical feasibility and engineering applicability of the proposed method.