The three-axis active magnetic compensation (TAMC) system is widely used to suppress environmental magnetic disturbances in a magnetically shielded room (MSR), enabling stable ultraweak magnetic measurements with reduced cost. Nonlinear, time-varying, and coupled behaviors induced by the shielding material's magnetic properties pose challenges to accurate modeling and disturbance suppression. A composite control strategy combining linear extended state observer (LESO) with integral sliding mode control (ISMC) is proposed. The LESO is implemented for each axis to provide real-time estimates of external disturbances, model uncertainties, and interaxis coupling. Based on the LESO estimates, the ISMCs are designed to enhance robustness against parameter variations and nonlinearity while compensating for disturbances. Experimental results on a TAMC platform demonstrate that the proposed method effectively suppresses magnetic disturbances, which significantly reduces magnetic fluctuations inside the MSR and ensures reliable conditions for high-precision biomagnetic measurements.

The availability and distribution of isolated X-ray pulsars suitable for navigation are limited in space. In contrast, there is a considerable number of binary pulsars available for navigation, albeit with the added complexity of accounting for the orbit of the binary pulsar system. Directly utilizing binary pulsars for spacecraft navigation has significant systematic biases. Therefore, to establish a measurement model applicable to both binary pulsars and isolated pulsars, effectively suppressing time-varying systematic biases and enhancing navigation accuracy, this paper introduces a pulsar navigation method based on the phase and Doppler frequency shift of binary pulsars. Initially, we formulated a navigation measurement model considering systematic biases, leveraging the phase and Doppler frequency shift of binary pulsars. Subsequently, a detailed analysis of systematic biases was conducted. Recognizing the characteristics of systematic biases, we further established a binary pulsar navigation measurement model with sequential difference. For deep space spacecraft, the time-varying system bias amplitude is large, but it changes slowly during the filtering period. Therefore, the proposed binary pulsar navigation measurement model with sequential difference effectively suppresses the majority of systematic bias effects. The effectiveness of the proposed method is demonstrated through 100 Monte Carlo simulation trials based on the Tianwen-1 Mars mission trajectory. The results show that the proposed method achieves a position error of approximately 824 m and a velocity estimation accuracy better than 1 m/s. Further analysis indicates that the remaining errors are primarily influenced by measurement noise and process noise, suggesting that reducing noise levels or incorporating more accurate models could further improve navigation performance.

This study addresses the challenge of predicting magnetic fields within magnetically shielded room for magnetocardiography (MCG) and magnetoencephalography (MEG). Traditional dense sensor arrays are prohibitively expensive, while single-point scanning introduces systematic errors. We propose a method utilizing a second-order spherical harmonic function to reconstruct the magnetic field. Six fluxgate sensors are symmetrically positioned around the target area, enabling the computation of spherical harmonic coefficients via regularized least-squares fitting to capture dipole and quadrupole modes. Experimental results demonstrate average prediction errors of 0.49 nT (5.23%), 0.33 nT (6.17%), and 0.15 nT (4.89%) for the X-, Y-, and Z-axis components, respectively. Compared to traditional methods, this method reduces the required sensor count by 77% and measurement time by 96% when predicting the magnetic field of 27 points in the target area. The key innovation lies in enabling high-precision field prediction with sparse measurements, thereby overcoming the limitations of point measurements. This technique surpasses prior art by achieving sub-nano Tesla accuracy while significantly reducing both cost and measurement time, providing an efficient solution for MCG and MEG systems.

Improving the signal-to-noise ratio (SNR) of magnetocardiography (MCG) signals holds significant clinical application value. In actual environments, the presence of multi-source magnetic disturbances can decrease the SNR of MCG signals, thereby affecting the SNR of MCG measurements. To tackle this issue, this paper innovatively proposes an improved extended state observer (ESO) with embedded repetitive control (RCIESO) for application in active magnetic compensation. The improved method includes two key steps: (1) enhancing the disturbance observation capability by incorporating correction terms into the traditional ESO structure; (2) embedding the internal model of repetitive control into the improved ESO framework to achieve excellent harmonic disturbance observation. Experimental results show that the proposed PI-RCIESO method effectively suppresses various types of magnetic disturbances and leads to an improvement in the SNR of MCG signals.

Accurately estimating and suppressing magnetic noise within magnetocardiography (MCG) devices is of great significance for improving the accuracy of MCG measurements. However, the calculation of magnetic noise inside a single-ended open magnetic shielding cylinder (MSC) lacks an accurate magnetic noise model. This paper analyzes and reconstructs the magnetic noise model (R-MN model) based on the variable-parameter magnetic loss separation model to address this issue. By incorporating appropriate penalty terms into the objective function, the variable-parameter magnetic loss separation model achieves high-precision loss separation utilizing the Artificial Hummingbird Algorithm. Compared with the conventional magnetic noise calculation method, the proposed R-MN model can reduce the root mean square error of noise prediction by 96.8%. The permalloy-nanocrystalline MSC composite structure designed based on the R-MN-model reduces the intrinsic average magnetic noise of the conventional MSC within the frequency range of 1-40 Hz from 11.77 fT/Hz(1/2) to 4.41 fT/Hz(1/2). This study provides theoretical foundations and technical support for designing low-noise, large-scale, and asymmetrically structured magnetic shielding devices.

To improve the accuracy and stability of X-ray pulsar time-delay estimation for multi-scenario celestial remote sensing and navigation, this paper proposes a time-delay estimation method based on a waterfall-plot multi-criteria framework and develops an end-to-end simulation framework for multi-scenario applications. First, a pulsar profile waterfall-plot model is built, and principal component analysis is performed to characterize candidate periodic structures. The contribution rate of the principal eigenvalue is used to describe the overall significance of the candidate period, and the projection variance of the first principal component is used to measure the prominence of the candidate pattern in the principal subspace. Second, support vector regression is used to fit the peak track of the waterfall plot, and a regression slope is used to describe the geometric stability of the candidate period. These three indicators are fused for pulsar period and time-delay estimation. Tests based on Insight-HXMT satellite observation data show that, compared with the χ2 and Z2 test methods, our method improves time-delay estimation accuracy by 68.68% and 50.43%, respectively. Multi-scenario navigation simulations indicate positioning improvements of approximately 0.83 km, 3.04 km, and 1.05 km in the Earth-orbiting, Earth–Moon transfer, and Mars approach scenarios, respectively. These results suggest that the proposed framework can improve pulsar time-delay estimation and may provide useful measurement support for celestial remote sensing and navigation.

To further improve the accuracy and speed of real-time dynamic estimation of X-ray pulsar periods, this paper proposes a pulsar period estimation model based on the interlayer phase difference (IPD) of the fast folding algorithm (FFA) and the weighted Z2 (WZ) test. This paper adopts a staged estimation strategy and divides the pulsar period estimation into a fast initial estimation stage and a local refinement search stage. First, in the fast initial estimation stage, an FFA IPD model based on the relationship among phase, time, and period is established. The interlayer phase is used to directly perform a single initial estimation of a large range of periods, thereby improving the period estimation speed. Second, in the local refinement search stage, the response coverage index is proposed for the Z2 test function. The WZ test function is constructed to perform a refinement test on the local candidate period to improve the period estimation accuracy. Meanwhile, for the PSR B0531+21 source, we conducted ablation tests, analyzed influencing factors and simulation performance of the proposed method, and validated its practical application performance using Neutron Star Interior Composition Explorer observation data. We also performed generalization performance tests on other sources such as PSR B0540-69 and SMC X-1. The results show that our method has significant advantages compared to several existing estimation methods. Specifically, for the PSR B0531+21 source, compared to the integrated chi 2 test method, our method improves estimation accuracy by 50.21% and reduces computational time by 73.47%.

In X-ray pulsar-based navigation, phase and Doppler frequency estimation based on the maximum likelihood estimation and grid search methods is widely used in practical missions and theoretical analysis. However, due to the non-convexity of the objective function and the inefficiency of the grid search method, a key challenge is how to achieve fast estimation of phase and Doppler frequency while maintaining accuracy. To address this issue, the fast and high-precision estimation of phase and Doppler frequency based on prior information and non-convex optimization is proposed in this paper. First, leveraging the prior state information of the spacecraft, an enhanced on-orbit phase model is established by considering a reference time at any given moment. Then, the statistical properties of the parameters to be estimated are analyzed, and the corresponding prior probability model is constructed, using the Bayesian estimation model as the objective function. Finally, incorporating non-convex optimization theory, the Nesterov-adaptive moment estimation is employed to automatically adjust the step size of the quasi-Newton algorithm. Simulation and experimental results demonstrate that the proposed method achieves rapid convergence with high precision, effectively balancing real-time performance and estimation accuracy compared to traditional phase and Doppler frequency estimation methods. Using the Crab pulsar as the primary case study, when the observation duration is 1800 s and the detector area is 30 cm2, the proposed method reduces the running time by 99.91

Active magnetic compensation (AMC) technology contributes to the realization of an extremely weak magnetic environment in magnetic shielding rooms (MSR), which is of great significance for measuring biomagnetic signal using an optically pumped magnetometer (OPM) sensor. However, sensor delay degrades the stability of the AMC system, while random magnetic field disturbances impair control accuracy. An active disturbance rejection control method combined with filtered Smith predictor (ADRC-FSP) is proposed to effectively compensate for sensor delay while suppressing random magnetic field disturbances. First, the structure of the AMC system is analyzed, and a mathematical model is established. Then, considering the action path of random disturbances, an ADRC-FSP is designed. Finally, simulations and experiments verify the effectiveness of proposed method, demonstrating improved system stability and a 34.9% increase in compensation accuracy. It has an important contribution to the measurement of biomagnetic signals.

In order to improve the performance of the x-ray pulsar timing system and further refine the pulsar time series analysis process, we propose a Hankel-singular value decomposition (SVD) principal modal vector energy-fusion based phase delay estimation method for x-ray pulsar. First, the pulsar profile signal is subjected to Hankel embedding and singular value decomposition. The principal modal vector in the structured subspace is extracted from the one-dimensional profile signal, effectively suppressing redundant components such as observation noise. Secondly, cross-spectral analysis is performed on the standard and folded profiles in the main modal domain. Combining the phase ratio method, the phase difference of each frequency component is analytically solved. By utilizing the frequency-domain phase continuity, the resolution limitation caused by discrete search in the time domain is overcome, achieving subsampling level phase delay estimation below the sampling interval. Finally, combining the frequency energy distribution characteristics of each order, we propose a fusion strategy based on cross-spectral energy constraints, using spectral amplitude to construct weights. The phase shifts of each order are weighted and adjusted to further improve estimation accuracy. Meanwhile, we conduct ablation tests, computational complexity analysis, and influencing factor analysis on the proposed method. Furthermore, we perform ground-based experimental tests using actual observation data from the NICER and XPANV-1 satellites. The results show that compared to cross-correlation estimation and maximum likelihood estimation, our method improves estimation accuracy by 26.18% and 42.72%, respectively, and improves estimation stability by 16.91% and 43.88%, respectively. The proposed method has advantages such as high estimation accuracy, strong estimation stability, and subsampling level phase estimation resolution, providing important support for the development of high-precision pulsar timing.

Abstract The effective way to create uniform magnetic field environment is to use a magnetic shielding room (MSR) combined with uniform compensation coils of active magnetic compensation (AMC) system. The optimization design of the uniform compensation coils located inside the MSR has made positive progress, but coils located outside the MSR is still an open issue. This article focuses on the magnetic field uniformity in the three-axes within the target region after compensating by the external coils of the small-size MSR, while considering the cross-axis coupling magnetic field of the coil. Firstly, the finite element method (FEM) is used to solve the regional shielding factor of the MSR. Then, the target field point (TFP) method is used to optimize the coil design. Finally, the grey wolf optimization (GWO) algorithm is used to obtain the parameters of the optimized coil. Compared with previous edge-mounted compensation coils of AMC system, the maximum remanence of the target region is reduced by about 20 times, achieving higher uniformity. The coil optimization method proposed in this article can provide certain assistance for the design of an external uniform compensation coil for MSR in various applications, creating a high-uniform and extremely weak magnetic field.

In X-ray pulsar navigation, the processing of pulsar photon time-of-arrival (PTOA) data is a key technology, and accurate estimation of the pulsar period is essential for effective PTOA data processing. The speed of period estimation directly affects the real-time performance of the navigation system. To address the low realtime performance of existing pulsar period estimation methods, this paper proposes a fast period estimation method based on phase difference correction. The method establishes a mapping between the phase difference of two folded pulse profiles and the period estimation error. The period is then estimated through an iterative computation process. Compared with the traditional Chi-square search method and the improved Z22-test method, the proposed method significantly reduces the number of epoch-folding operations. Using the Crab pulsar as the primary case study, both simulation and experimental results demonstrate that the proposed method achieves high computational efficiency while maintaining reliable period estimation accuracy. When the observation duration is 1000 s and the detector area is 5000 cm2, the proposed method reduces the CPU time by 99.92% and 99.90% compared to the Chi-square search and improved Z22-test methods, respectively. This substantial improvement in computational efficiency makes the proposed method a promising tool for fast pulsar period estimation, thereby facilitating its practical application in deep space navigation.

A low-noise, near-zero magnetic field environment is essential for the accurate detection of cardiac magnetic signals. In active magnetic field compensation systems, large coil constant causes excessive noise. This study proposes a low-noise compensation coil design based on differential magnetic coupling. In the proposed configuration, the high degree of magnetic field homogeneity of nested saddle coils was combined with the low coil constant characteristic of differential saddle coils. Coupling effects with high-permeability shielding were incorporated by modeling the coil constant as a function of coil-shield distance. A hybrid particle swarm-genetic algorithm and differential magnetic coupling strength was employed to optimize the design. Compared with a conventional saddle coil, the proposed design reduces the coil constant by two orders of magnitude to 84.9 nT/A and improves field uniformity by 41.7%, and reduces magnetic noise (1-30 Hz) by 44.1%.

In X-ray pulsar-based navigation (XNAV), period estimation of pulsar signals is a critical step to obtain navigation measurements. Epoch folding is a classical method for processing pulsar signals. When combined with the χ2 test, it can estimate the signal period. However, its computational efficiency decreases as observation time increases, and its estimation accuracy is inherently limited. This paper presents a novel methodology for constructing two-dimensional point clouds from photon Time of Arrival (TOA) data through folding and rearrangement, and on this basis, achieves pulsar signal period estimation by combining DBSCAN clustering and Principal Component Analysis (PCA). The proposed Time of Arrival Point Cloudification (TPC) method, the χ2 test, and waterfall plot analysis (WFP) were applied to process the simulated data of the PSR B0531-21 (Crab) pulsar. Comparative results demonstrate that under identical simulation conditions, for observation durations between 100–1200 s, TPC achieves an average improvement of 34.93% in estimation accuracy and 99.61% in estimation efficiency over the χ2 test; meanwhile, it yields an average improvement of 27.70% in estimation accuracy and 99.63% in estimation efficiency compared with waterfall plot analysis. Finally, the period estimation performance was compared using real observational data from the Neutron Star Interior Composition Explorer (NICER). The results indicate that while maintaining equivalent estimation accuracy, TPC achieves an average improvement of 83.91% and 97.88% in estimation efficiency compared with the χ2 test and waterfall plot analysis, respectively.

Cardiac source imaging is highly sensitive to sensor array configurations, particularly under multimodal fusion conditions. In this paper, we introduce the singular value decomposition entropy (SVDEn) as a novel metric for optimizing sensor layouts in cardiac source imaging. A greedy optimization method, based on SVDEn, is proposed to systematically evaluate the impact of magnetic sensor layout and number on source imaging performance. Furthermore, three strategies for joint layouts of magnetic and electrical sensors are presented. Among these, the “magnetically-guided joint sensor placement strategy” with a configuration of just 19 magnetic and 19 electrical sensors achieves significantly superior performance compared to traditional 36-magnetic channel layouts, even at lower signal-to-noise ratios (SNRs). This effectively balances cost and performance; for instance, at 15 dB SNR, the average values of distance dipole localization error and spatial dispersion are reduced by 30.93% and 17.60%, respectively. This research provides new insights for developing low-cost, high-performance multimodal cardiac source imaging systems and their wearable applications.

Restoring signals during the cardiac cycle is critical for cardiac imaging. However, recent research on cardiac source imaging, which is based on distributed source models, has focused on spatial accuracy, with less emphasis on temporal sequence accuracy. In particular, comparative studies on the temporal sequence accuracy of different measurement modalities are lacking. In this study, a realistic multitissue human volume conductor model was used, and source signals derived from electrocardiographic signals were employed to compare the temporal sequence accuracy of four measurement modalities across various signal-to-noise ratios. The four measurement modalities compared were magnetocardiography (MCG), electrocardiography, magnetocardiography-electrocardiography combination (MECG), and three-component MCG. The findings indicated that MECG provided the best performance in terms of temporal sequence accuracy. This study validated the effectiveness of multimodal data fusion in cardiac source imaging and offered new insights and methodologies for future studies in cardiac source imaging.

Magnetoencephalography (MEG) measurement, which detects extremely weak magnetic field signals in the brain for studying brain function, is susceptible to external magnetic field noise. Therefore, creating a low-noise and weak magnetic environment is crucial for enhancing MEG measurement accuracy. The active magnetic compensation (AMC) system used for magnetic shielding room (MSR) is an effective approach, yet issues like inaccurate MSR model and system time lag affect compensation precision. To address these issues, this article proposes a high-precision magnetic field noise suppression method based on an improved all-coefficient adaptive control combined with least squares support vector machine (IACAC-LSSVM). It utilizes ACAC to control the inaccurate MSR plant, improves the linear addition of ACAC output through nonlinear state error feedback (NLSEF) to enhance disturbance suppression capability, and combines LSSVM to predict control error and increase bandwidth. Experimental results show that this method improves control accuracy by 36.8% when the model changes, has strong disturbance suppression ability, and increases the noise suppression bandwidth by 1.8 and 1.3 times compared with μ-synthesis control and ACAC. When applied to MEG measurement in a compact MSR, it effectively suppresses low-frequency noise and highlight the alpha rhythm, strongly supporting the clinical diagnosis of brain function.

Magnetic shielding room (MSR) and three-axis magnetic field compensation (TMFC) system are necessary for extremely weak magnetic field measurement. The TMFC system can effectively reduce the impact of magnetic field interference on the extremely weak magnetic field measurement in the MSR, but the coupling effect between different compensation axes reduces the compensation performance. This article proposes an adaptive decoupling control method based on online modified stochastic gradient (MSG) identification. The decoupler is designed to transform the TMFC system into three single-input-single-output (SISO) systems based on the interaction model structure established by frequency-domain identification and the parameters identified online using MSG algorithm. In addition, a feedback controller was designed to ensure that the SISO system has the satisfied dynamic performance and stability. Experimental results indicate that the proposed method realizes dynamic decoupling of TMFC system.