Measurement Noise Research Articles

Adaptive Kalman filter with LSTM network assistance for abnormal measurements

A classic state estimation method, the Kalman filter integrates prior information, system dynamics models, and measurement data to achieve posterior state estimations. However, measurements often encounter various unknown disturbances, leading to abnormal or inaccurate measurements and subsequently impacting the performance of Kalman filtering. In response to this challenge, this paper introduces a novel adaptive Kalman filter approach aided by posterior state estimations using the Long short-term memory (LSTM) networks. The proposed method begins by utilizing prior residuals to construct a chi-square distribution model, which facilitates the detection of abnormal measurements within data. Upon identifying abnormal measurements, an LSTM network is employed to generate alternative predictive measurements, replacing the original inaccurate measurement. This approach enhances the model’s capability to handle complex relationship and measurement uncertainties and improves filtering estimation accuracy. A noise covariance adjustment method is introduced in extreme cases where alternative predictive measurements alone are insufficient for filter requirements. This method mitigates the adverse effects of abnormal measurements on posterior estimation. Throughout the entire adaptive assistance process involving the LSTM network, deep learning maintains a stable structure of the filter while enhancing adaptability. This strategy ensures the filter’s resilience in dynamic environments with unknown factors by providing predicted measurements conforming to the chi-square distribution and corresponding measurement noise covariance. Ultimately, the efficacy of the proposed algorithm is validated through simulations and experiments involving vehicle positioning with inertial sensors.

Assessment and mapping of noise pollution in recreation spaces using geostatistic method after COVID-19 lockdown in Turkey.

Increased use of recreational areas after the lifting of COVID-19 pandemic restrictions has led to increased noise levels. This study aims to determine the level of noise pollution experienced in recreational areas with the increasing domestic and international tourism activities after the lifting of pandemic lockdowns, to produce spatial distribution maps of noise pollution, and to develop strategic planning suggestions for reducing noise pollution in line with the results obtained. Antalya-Konyaaltı Beach Recreation Area, the most important international tourism destination of Turkey, is determined as the study area. To determine the existing noise pollution, 31 measurement points were marked at 100m intervals within the study area. Noise measurements were taken during the daytime (07:00-19:00), evening (19:00-23:00), and nighttime (23:00-07:00) on weekdays (Monday, Wednesday, Friday) and weekends (Sunday) over 2months in the summer when the lockdown was lifted. In addition, the sound level at each measurement point was recorded for 15min, while the number of vehicles passing through the area during the same period was determined. The database created as a result of measurements and observations was analyzed using statistical and geostatistical methods. After the analysis of the data, it was found that the co-kriging-stable model showed superior performance in noise mapping. Additionally, it was revealed that there is a high correlation between traffic density and noise intensity, with the highest equivalent noise level (Leq) on weekdays and weekend evenings due to traffic and user density. In conclusion, regions exposed to intense noise pollution were identified and strategic planning recommendations were developed to prevent/reduce noise sources in these identified regions.

Simultaneous Reconstruction of Multiple Time-Varying Thermal Properties Based on Translucent Materials.

In the realm of high-tech materials and energy applications, accurately measuring the transient heat flow at media boundaries and the internal thermal conductivity of materials in harsh heat exchange environments poses a significant challenge when using conventional direct measurement methods. Consequently, the study of photothermal parameter reconstruction in translucent media, which relies on indirect measurement techniques, has crucial practical value. Current research on reconstructing photothermal properties within participating media typically focuses on single-objective or time-invariant properties. There is a pressing need to develop effective methods for the simultaneous reconstruction of time-varying thermal flow fields and internal thermal conductivity at the boundaries of participating media. This paper introduces a computational model based on the numerical simulation theory of internal heat transfer systems in participating media, stochastic particle swarm optimization algorithms, and Kalman filter technology. The model aims to enable the simultaneous reconstruction of various thermal parameters within the target medium. Our results demonstrate that under varying levels of measurement noise, the inversion results for different target parameters exhibit slight oscillations around the true values, leading to a reduction in reconstruction accuracy. However, overall, the model demonstrates robustness and accuracy in ideal conditions, validating its effectiveness.

Estimating the Optimal State of Charge for Electric Car Batteries Using an Extended Kalman Filter

The efficient management of battery state of charge (SOC) is crucial for maximizing the performance, range, and longevity of electric vehicle (EV) batteries. This paper presents a novel approach for estimating the optimal state of charge of electric car batteries using an Extended Kalman Filter (EKF). The EKF is a recursive algorithm that combines measurements from various sensors with a dynamic battery model to estimate the current SOC and predict future SOC values with high accuracy. The paper provides a detailed explanation of the EKF algorithm and its application to battery SOC estimation, highlighting its ability to handle nonlinearities, uncertainties, and measurement noise inherent in battery systems. Furthermore, this research presents a simulation-based validation of the proposed EKF approach using real-world driving data from electric vehicles. The simulation results demonstrate the effectiveness of the EKF algorithm in accurately estimating the SOC of electric car batteries under various operating conditions, including different driving patterns, temperatures, and battery degradation scenarios.

ANFIS and Takagi–Sugeno interval observers for fault diagnosis in bioprocess system

This paper develops a data-driven approach for incipient fault diagnosis based on ANFIS and Takagi–Sugeno (TS) interval observers. First, the nonlinear bioreactor system is identified using an adaptive neuro-fuzzy inference system (ANFIS), which results in a set of polytopic TS models derived from measurement data. Second, a bank of TS interval observers is deployed to detect sensor and process faults using adaptive thresholds. Unlike other works that require training fault data, only fault-free data is considered for ANFIS learning in this work. Fault insolation is based on residual generation and evaluated on a fault signal matrix (FSM). Parametric uncertainty and measurement noise are considered to guarantee the method’s robustness. The effectiveness of the proposed method is tested on a well-known bioreactor Continuous stirred tank reactor system (CSTR) reference simulator.

Integrated elastic identification and LOS angular rate extraction for slender rockets: A continuous-discrete maximum correntropy Kalman filter approach

Slender rockets experience significant elastic deformation during flight due to aeroelastic forces, impacting their dynamic behavior and posing challenges for traditional line-of-sight (LOS) angular rate estimation methods. This paper addresses this challenge by proposing a novel and highly accurate line-of-sight angular rate extraction model. This model integrates elastic identification with line-of-sight angular rate extraction, employing estimated generalized coordinates to calculate seeker elastic deformation. After elastic decoupling of the seeker, the slender rocket's line-of-sight angular rate can be estimated accurately. Additionally, the model incorporates a continuous-discrete maximum correntropy Kalman filter (CD-MCKF) to effectively handle the non-Gaussian measurement noise and limitations associated with discretizing the continuous model. Simulations demonstrate that the proposed method achieves significantly higher accuracy compared to existing approaches. The improved accuracy of this method can provide more precise calculations for the design of slender rocket guidance and control systems, ultimately improving the flight stability and control accuracy of rockets, and laying a solid foundation for the integrated guidance and control research of slender rockets.

MR imaging of the magnetic fields induced by injected currents can guide improvements of individualized head volume conductor models

Abstract Volume conductor models of the human head are routinely used to estimate the induced electric fields in transcranial brain stimulation (TBS) and for source localization in electro- and magnetoencephalography (EEG and MEG). Magnetic resonance current density imaging (MRCDI) has the potential to act as a non-invasive method for dose control and model validation but requires very sensitive MRI acquisition approaches. A double-echo echo-planar imaging (EPI) method is here introduced. It combines fast and sensitive imaging of the magnetic fields generated by the current flow of transcranial electric stimulation with increased robustness to physiological noise. For validation, noise floor measurements without injected currents were obtained in 5 subjects for an established multi-echo gradient-echo (MGRE) sequence and the new EPI method. In addition, data with current injection was acquired in each subject with a right-left (RL) and anterior-posterior (AP) electrode montage with both sequences to assess the accuracy of subject-specific detailed head models. In line with previous findings, the noise floor measurements showed that the MGRE results suffered from spatial low-frequency noise patterns, which were mostly absent in the EPI data. A recently published approach optimizes the ohmic conductivities of subject-specific head models by minimizing the difference between simulated and measured current-induced magnetic fields. Here, simulations demonstrated that the MGRE noise patterns have a larger negative impact on the optimization results than the EPI noise. For the current injection measurements, a larger discrepancy was found for the RL electrode montage compared with the AP electrode montage consistently for all subjects. This discrepancy remained in part also after optimization of the ohmic conductivities, was similar for the data of the two sequences and larger than the measurement noise and thus demonstrates systematic biases in the volume conductor models. We have shown that EPI-based MRCDI is superior to established techniques by mitigating the effects of previously reported spatial low-frequency noise in MRCDI if limited spatial resolution is acceptable. Additionally, the consistent inter-subject results indicate that MRCDI is capable of picking up inaccuracies in computational head models and will be useful to guide systematic improvements.

Enhancing USVs navigation based on minimum error entropy of GPS vector tracking

In recent years, unmanned surface Vessels (USVs) have increasingly been used for river monitoring and hydrological surveys. USVs rely on global navigation satellite systems (GNSS) for navigation. However, signal blocking can cause the traditional GNSS vector tracking (VT) loop to increase the code phase and carrier frequency errors, leading to higher positioning errors that do not meet USVs’ requirements. To address this problem, we propose a VT method based on the minimum error entropy (MEE) in the signal tracking module. The MEE Kalman filter is adopted as the loop filter to mitigate code phase and carrier frequency errors, reduce non-Gaussian noise and random errors generated by signal blocking, and enhance the positioning accuracy and robustness of USV navigation. The measurement noise covariance of the loop filter was adjusted adaptively using the signal carrier-to-noise ratio. A field experiment was conducted using a commercial GNSS receiver as reference. The results demonstrate a 19.3% improvement in positioning accuracy compared with the traditional method in an open environment. Moreover, the proposed method maintains stable operation and achieves a 79.4% improvement in positioning accuracy during signal blocking. This novel algorithm offers a new concept for USV navigation systems to cope with signal blocking.

Assessment of Site Effects and Numerical Modeling of Seismic Ground Motion to Support Seismic Microzonation of Dushanbe City, Tajikistan

In the territory of Dushanbe city, the capital of Tajikistan, detailed geological and geophysical data were collected during geophysical surveys in 2019–2020. The data comprise 5 microtremor array measurements, 9 seismic refraction tomography profiles, seismological data from 5 temporary seismic stations for standard spectral ratio calculations, 60 borehole datasets, and 175 ambient noise measurements. The complete dataset for Dushanbe was used to build a consistent 3D geologic model of the city with a size of 12 × 12 km2. The results of the seismological and geophysical surveys were compared and calibrated with borehole data to define the boundaries of each layer in the study area. The Leapfrog Works software was utilized to create a 3D geomodel. From the 3D geomodel, we extracted six 12 km long 2D geological cross-sections. These 2D geological cross-sections were used for 2D dynamic numerical modeling with the Universal Distinct Element Code software to calculate the local seismic response. Finally, the dynamic numerical modeling results were compared with the amplification functions obtained from the seismological and ambient noise data analysis. The 2D dynamic numerical modeling results allowed a better assessment of the site effects in the study area to support seismic microzonation and the determination of local peak ground acceleration changes in combination with regional seismic hazard maps. In addition, our results confirm the strong seismic amplification effects noted in some previous studies, which are attributed to the influence of local topographic and subsurface characteristics on seismic ground motions.

Multi-interest adaptive unscented Kalman filter based on improved matrix decomposition methods for lithium-ion battery state of charge estimation

Accurately predicting the state of charge (SOC) is crucial to improving Li-ion battery performance. However, available model-based estimation approaches still face challenges in handling model uncertainty and measurement noise effects on parameter identification. Besides, the widely used unscented Kalman filter (UKF) algorithm has limitations in electric vehicles as it requires the error covariance matrix to maintain positive definiteness, limiting its applicability under certain conditions. This study introduces the bias-compensated forgetting factor recursive least squares (BCFFRLS) method for parameter estimation within the second-order RC equivalent circuit model specific to the INR18650-20R battery. Furthermore, we propose a novel algorithm named the optimization multi-interest adaptive unscented Kalman filter (O-MIAUKF). This algorithm is designed to address stability and robustness issues with traditional UKF encounters in dynamic environments. Experimental validation demonstrates that the O-MIAUKF algorithm excels in maintaining strong stability and robustness in various working conditions, accurately estimating SOC even with a non-positive covariance matrix. The SOC estimation error remains stable at 0.8 %, which is lower than that of the current Extended Kalman Filter (EKF), UKF, and Dual Extended Kalman Filter (DEKF).

3D RECONSTRUCTION OF THE FORT SANTIAGO DUNGEONS USING HANDHELD LASER SCANNING METHOD

Abstract. The preservation of Cultural Heritage sites is an inherent responsibility of the citizens of a country. To this end, developments in digitization serve as a permanent way of preserving a site at its optimum state, and the creation of accurate 3D models becomes a repository of measurements for future reconstruction. Thus, in this study, the Fort Santiago Dungeons, a popular Cultural Heritage site in the Philippines, was 3D-reconstructed using the GeoSLAM ZEB Revo RT, a handheld Light Detection and Ranging (LiDAR) scanner that uses a Simultaneous Localization and Mapping (SLAM) Algorithm. With it, dense point clouds were produced with acceptable results in terms of colorization using the ZEB-CAM accessory, completeness, and measurement noise. This trend extended to quantitative evaluations of the dense point clouds of different formats (LAS and PLY) and colorization settings, as the Root Mean Square Errors (RMSE) against corresponding ground measurements were 0.734cm and 0.739cm for the Non-colorized, and 1.308cm and 1.312cm for Colorized, respectively. Likewise, the derived mesh files gave similar RMSEs with the Non-colorized at 1.044cm (LAS) and 0.999cm (PLY); and with the Colorized at 1.339cm (LAS) and 1.326cm (PLY). Overall, results showed that the mesh file derived from PLY dense point cloud exceeded the other format - as the dungeon's interior was better represented. Nonetheless, even though there were differences in the RMSEs of the measurements, due to factors such as the number of points and the processing itself, all are within the 5cm threshold to be considered useful in the event of reconstruction.

Experimental Research on an Afterburner System Fueled with Hydrogen–Methane Mixtures

A new afterburner installation is proposed, fueled with pure hydrogen (100%H2) or hydrogen–methane mixtures (60% H2 + 40% CH4, 80% H2 + 20% CH4) for use in cogeneration applications. Two prototypes (P1 and P2) with the same expansion angle (45 degrees) were developed and tested. P1 was manufactured by the classic method and P2 by additive manufacturing. Both prototypes were manufactured from Inconel 625. During the tests, analysis of flue gas (CO2, CO, and NO concentration), PIV measurements, and noise measurements were conducted. The flue gas analysis emphasizes that the behavior of the two tested prototypes was very similar. For all three fuels used, the CO2 concentration levels were slightly lower in the case of the additive-manufactured prototype P2. The CO concentration levels were significantly higher in the case of the additive-manufactured prototype P2 when 60% H2/40% CH4 and 80% H2/20% CH4 mixtures were used as fuel. When pure H2 was used as fuel, the measured data suggest that no additional CO was produced during the combustion process, and the level of CO was similar to that from the Garrett micro gas turbine in all five measuring points. The NO emissions gradually decreased as the percentage of H2 in the fuel mixture increased. The NO concentration was significantly lower in the case of the additive-manufactured prototype (P2) in comparison with the classic manufactured prototype (P1). Examining the data obtained from the PIV measurements of the flow within the mixing region shows that the highest axial velocity component value on the centerline was measured for the P1 prototype. The acoustic measurements showed that a higher H2 concentration led to a reduction in noise of approximately 1.5 dB for both afterburner prototypes. The outcomes reveal that the examined V-gutter flame holder prototype flow was smooth, without any perpendicular oscillations, without chaotic motions or turbulent oscillations to the flow direction, across all tested conditions, keeping constant thermal power.

A Robust Interacting Multi-Model Multi-Bernoulli Mixture Filter for Maneuvering Multitarget Tracking under Glint Noise.

In practical radar systems, changes in the target aspect toward the radar will result in glint noise disturbances in the measurement data. The glint noise has heavy-tailed characteristics and cannot be perfectly modeled by the Gaussian distribution widely used in conventional tracking algorithms. In this article, we investigate the challenging problem of tracking a time-varying number of maneuvering targets in the context of glint noise with unknown statistics. By assuming a set of models for the possible motion modes of each single-target hypothesis and leveraging the multivariate Laplace distribution to model measurement noise, we propose a robust interacting multi-model multi-Bernoulli mixture filter based on the variational Bayesian method. Within this filter, the unknown noise statistics are adaptively learned while filtering and the predictive likelihood is approximately calculated by means of the variational lower bound. The effectiveness and superiority of our proposed filter is verified via computer simulations.

Model updating of a shear‐wall tall building using various vibration monitoring data: Accuracy and robustness

SummaryAcceleration measurements are often used for model updating of civil engineering structures, especially in the case of seismic monitoring. It is yet unclear if accelerations alone would generate an accurate and robust finite‐element (FE) model. This study examines this notion and analyzes the possibility of using other vibration monitoring data for model updating of shear‐wall tall buildings. This study compares the accuracy and robustness of the FE models being optimized via accelerations, roof displacement, wall rotations, interstory drift ratios, and the linear combination of these measurements. A numerical case study is analyzed using Timoshenko beams for modeling the lateral vibration of a benchmark 42‐story building under seismic excitations. Results show that the acceleration response of the examined building is mostly governed by its higher vibration modes. Depending on the characteristics of ground motions, using accelerations alone may generate an FE model biased towards higher‐order modes without effectively capturing the lower‐order modes. For instance, the first modal frequency of the updated FE model could be 12.0% lower than the true value, and the reconstructed displacement and rotation responses are noticeably inaccurate. Employing multi‐source monitoring data for model updating, for example, the combinations of roof displacement and acceleration measurements, could reduce the normalized root‐mean‐square errors in displacements by more than 70%. This study also quantifies the robustness of the FE model under various measurement noise levels and 50 pairs of earthquake records. Finally, the effects of multi‐source data on FE model updating are validated via experiments on a 7‐story shear wall building. Analysis reveals that a more accurate and robust FE model can be determined via a combination of accelerations and top displacement than via acceleration alone.

Finite‐horizon estimation for 2‐D systems with time‐correlated multiplicative noises: A recursive iterative coupled estimator design

AbstractThis paper addresses the state estimation problem for a class of two‐dimensional shift‐varying systems with time‐correlated multiplicative measurement noises and additive noises. The time‐correlated multiplicative noises can be described as a linear system model corrupted by white noise. The main objective of this paper is to propose a recursive iterative coupled new‐type estimators and design the estimated gain reasonably to guarantee the minimum error covariance at each step. First, two new‐type coupling estimators are designed by introducing a new term. The unbiasedness of the two estimators are guaranteed by resorting to the mathematical inductive approach. Subsequently, an effective estimation is proposed given initial conditions. Moreover, the boundedness performance is investigated of the error covariance, and an upper bound is given based on the spectral norm. Finally, two numerical example are presented as an example to show the effectiveness of the estimation algorithm.

Contact-point response reconstruction for indirect bridge monitoring via Bayesian expectation-maximization based augmented Kalman filter

The drive-by bridge dynamic measurement using an instrumented vehicle during its passage over the bridge can be an indirect bridge structural health monitoring system. The identification of the contact-point (CP) responses between vehicle wheels and bridge structure from vehicle responses offers an efficient and economical way for the modal identification and condition assessment of short- to mid-span road bridges. This paper proposes a novel method for the contact-point displacement response reconstruction of the vehicle-bridge interaction (VBI) system in a joint input-state estimation manner based on Bayesian Expectation-Maximization (BEM). An analytical model of VBI including the road approach in front of a simply-supported bridge is presented firstly. Then the augmented state-space model of the vehicle with the contact-point responses included as variables along with vehicle states is established. A new method by integrating the augmented Kalman filter (AKF) with a BEM strategy is proposed to solve the state estimation problem without knowing the vehicle axle responses. The vehicle states and CP displacement responses are identified simultaneously. The effects of the measurement noise, road surface roughness and vehicle speed on the identified results are investigated using numerical simulations. The experimental tests are used to further verify the feasibility and accuracy of the proposed method. The results show that the proposed method has potential for drive-by bridge condition assessment using on-board vehicle response measurements for a large population of short- to mid-span bridges.

Real-time estimation of fuel injection rate and injection volume in high-pressure common rail systems

The injection rate and injection volume are essential parameters for the combustion process, which greatly affect the engine efficiency and emission performance. However, at the current time the injection information cannot be obtained in real time during the actual operation of engine. This paper presents a novel real-time estimation method for the injection rate and injection volume based on the measurable rail pressure. A comprehensive dynamic model is derived by considering both the effect of fuel injection and supply process on the pressure fluctuation. Then a linear time-varying state space model is constructed by choosing three appropriate state variables. On this basis, considering the measurement noise and model uncertainty, a Kalman filter-based estimation method of the injection information is investigated. And the noise covariance matrix Q is optimally designed to adapt to a wide range of operating conditions. The proposed estimation method is validated on the different conditions, and the results show the injection rate estimation errors are within 4.5 %, the injection volume estimation errors are within 4 %. And on the situation with overlap of injection and supply process, the injection rate and injection volume estimation errors are all within 4.5 %.

Evaluating the relationship between magnetic resonance image quality metrics and deep learning-based segmentation accuracy of brain tumors.

Magnetic resonance imaging (MRI) scans are known to suffer from a variety of acquisition artifacts as well as equipment-based variations that impact image appearance and segmentation performance. It is still unclear whether a direct relationship exists between magnetic resonance (MR) image quality metrics (IQMs) (e.g., signal-to-noise, contrast-to-noise) and segmentation accuracy. Deep learning (DL) approaches have shown significant promise for automated segmentation of brain tumors on MRI but depend on the quality of input training images. We sought to evaluate the relationship between IQMs of input training images and DL-based brain tumor segmentation accuracy toward developing more generalizable models for multi-institutional data. We trained a 3D DenseNet model on the BraTS 2020 cohorts for segmentation of tumor subregions enhancing tumor (ET), peritumoral edematous, and necrotic and non-ET on MRI; with performance quantified via a 5-fold cross-validated Dice coefficient. MRI scans were evaluated through the open-source quality control tool MRQy, to yield 13 IQMs per scan. The Pearson correlation coefficient was computed between whole tumor (WT) dice values and IQM measures in the training cohorts to identify quality measures most correlated with segmentation performance. Each selected IQM was used to group MRI scans as "better" quality (BQ) or "worse" quality (WQ), via relative thresholding. Segmentation performance was re-evaluated for the DenseNet model when (i) training on BQ MRI images with validation on WQ images, as well as (ii) training on WQ images, and validation on BQ images. Trends were further validated on independent test sets derived from the BraTS 2021 training cohorts. For this study, multimodal MRI scans from the BraTS 2020 training cohorts were used to train the segmentation model and validated on independent test sets derived from the BraTS 2021 cohort. Among the selected IQMs, models trained on BQ images based on inhomogeneity measurements (coefficient of variance, coefficient of joint variation, coefficient of variation of the foreground patch) and the models trained on WQ images based on noise measurement peak signal-to-noise ratio (SNR) yielded significantly improved tumor segmentation accuracy compared to their inverse models. Our results suggest that a significant correlation may exist between specific MR IQMs and DenseNet-based brain tumor segmentation performance. The selection of MRI scans for model training based on IQMs may yield more accurate and generalizable models in unseen validation.

Uncertain damage identification methods based on residual force vector under the influence of measurement noise

This paper proposes probabilistic and interval methods, grounded in the residual force vector technique, to quantify measurement uncertainties and effectively integrate them into the identification process. In the probabilistic method, the measurement noise is assumed to be a zero-mean normal distribution, while the stiffness parameters of structural elements are assumed to follow a normal distribution, represented by mean values and standard deviations. In the interval method, the measurement noise is modelled as interval numbers, and the interval perturbation technique is employed to derive interval bounds for elemental stiffness parameters. A two-step model updating strategy is implemented, separately addressing pristine and damaged structures, to mitigate modeling errors. By using the results of probabilistic damage identification, a novel damage index termed damage expectation capable of capturing both the extent and probability of damage is introduced. Furthermore, an interval damage index is introduced to quantify the damage based on interval damage identification results. The impact of noise levels on the statistical properties of uncertain damage indices is also investigated. Numerical examples reveal that deterministic indexes exhibit a monotonic increase in average values with increasing noise levels. Particularly, as noise levels rise, the standard deviation of the combination index initially surpasses the deterministic damage index but eventually diminishes. Through the proposed methodology, structural damage can be identified even in the presence of uncertainties. The efficacy of the proposed damage identification technique is also validated by experimental data.

Analysis and measurement of magnetic noise in multilayer magnetic shielding system combined with mu-metal and ferrite for atomic sensors

The multilayer magnetic shielding system is widely used in atomic sensors. However, for miniaturized atomic sensors with volume limitations, such as spin-exchange relaxation-free (SERF) gyroscopes, the remaining environmental magnetic interference and mu-metal magnetic noise will affect the sensitivity of atomic sensors. In this study, we establish a comprehensive magnetic noise calculation model for the magnetic shielding system of a SERF gyroscope, which considers the influence of the environmental magnetic noise on the magnetic shielding and the coupling effect between different layers. For suppressing magnetic noise of the magnetic shielding system, the property of different ferrites was measured and compared, then the particle swarm optimization is applied to design the magnetic shielding structure. Finally, the experimental device is established for measuring performances of the magnetic shielding system per and post optimization. By comparison, radial and axial magnetic noise post optimization are decreased by 37% and 22%, respectively.