Noise Intrinsic Mode Functions Research Articles

A hybrid denoising method for gyroscopes based on multiple screening

To reduce the random error of microelectromechanical system (MEMS) gyroscope, a hybrid method combining improved empirical mode decomposition (EMD) and least squares algorithm (LS) is proposed. Firstly, based on the multiple screening mechanism, intrinsic mode functions (IMFs) from the first decomposition are divided into noise IMFs, strong noise mixed IMFs, weak noise mixed IMFs and signal IMFs. Secondly, according to their characteristics, they are processed again. IMFs from the second decomposition are divided into noise IMFs and signal IMFs. Finally, useful signal is gathered to obtain the final denoising signal. Compared with some other denoising methods proposed in recent years, the experimental results show that the proposed method has obvious advantages in suppressing random error, greatly improving the signal quality and improving the accuracy of inertial navigation.

A method for compensating random errors in MEMS gyroscopes based on interval empirical mode decomposition and ARMA

The random error in micro-electro-mechanical systems (MEMS) gyroscopes is one of the major aspects that limit measurement accuracy. In order to address the inaccurate extraction of noise and trend during the signal preprocessing, as well as the subjectivity in autoregressive moving average (ARMA) model ordering, this paper proposes a method based on interval empirical mode decomposition and ARMA model. In the proposed method, the original signal is decomposed into a series of intrinsic mode functions (IMFs) and a residual through empirical mode decomposition (EMD). Based on the Hellinger distance and autocorrelation function, IMFs are then classified into noise IMFs, hybrid IMFs, and signal IMFs. The improved sand cat swarm optimization is utilized to optimize the ordering process of the ARMA model. The improved adaptive filter is adopted to compensate the random error, and the compensated signal is reconstructed with the signal IMFs and residual to obtain the final output. Experiments show that under static conditions, the proposed method could reduce the root mean square error (RMSE) by 52.6% and 33.3%, respectively, compared with the traditional EMD and ARMA methods. Under dynamic conditions, the proposed method could reduce the RMSE by 51.1% and 37.1%, respectively, compared with the traditional EMD and ARMA methods. The proposed method could effectively compensate the random error and improve the measurement accuracy of MEMS gyroscopes.

SVMD coupled with dual-threshold criteria of correlation coefficient: A self-adaptive denoising method for ship-radiated noise signal

Due to the complexity of the marine environment, ship-radiated noise signal (SRNS) often contains harsh marine background noise. Hence extracting the features of SRNS becomes very difficult. Aim to eliminate the interference of background noise, this paper proposes a self-adaptive denoising method for SRNS, called SVMD-Dual-CC-WST, which not only uses the successive variational mode decomposition (SVMD) as a theoretical basis but also combines with the dual-threshold screening of the correlation coefficient (Dual-CC) criterion and wavelet soft threshold (WST). Firstly, different original signals are decomposed into several intrinsic mode functions (IMFs) by SVMD. Then, the CC of the IMFs is calculated, and the IMFs are adaptively divided into three categories using the Dual-CC criterion, including signal IMFs, noisy IMFs, and noise IMFs. Finally, the noise IMFs are discarded, and the noisy IMFs are denoised with WST and then reconstructed with the signal IMFs to obtain the denoising signals. Simulated signals and SRNS experiments prove the effectiveness of the proposed method.

Underwater acoustic signal denoising model based on secondary variational mode decomposition

Due to the complexity of marine environment, underwater acoustic signal will be affected by complex background noise during transmission. Underwater acoustic signal denoising is always a difficult problem in underwater acoustic signal processing. To obtain a better denoising effect, a new denoising method of underwater acoustic signal based on optimized variational mode decomposition by black widow optimization algorithm (BVMD), fluctuation-based dispersion entropy threshold improved by Otsu method (OFDE), cosine similarity stationary threshold (CSST), BVMD, fluctuation-based dispersion entropy (FDE), named BVMD-OFDE-CSST-BVMD-FDE, is proposed. In the first place, decompose the original signal into a series of intrinsic mode functions (IMFs) by BVMD. Afterwards, distinguish pure IMFs, mixed IMFs and noise IMFs by OFDE and CSST, and reconstruct pure IMFs and mixed IMFs to obtain primary denoised signal. In the end, decompose primary denoising signal into IMFs by BVMD again, use the FDE value to distinguish noise IMFs and pure IMFs, and reconstruct pure IMFs to obtain the final denoised signal. The proposed mothod has three advantages: (i) BVMD can adaptively select the decomposition layer and penalty factor of VMD. (ii) FDE and CS are used as double criteria to distinguish noise IMFs from useful IMFs, and Otsu algorithm and CSST algorithm can effectively avoid the error caused by manually selecting thresholds. (iii) Secondary decomposition can make up for the deficiency of primary decomposition and further remove a small amount of noise. The chaotic signal and real ship signal are denoised. The experiment result shows that the proposed method can effectively denoise. It improves the denoising effect after primary decomposition, and has good practical value.

RDTS Noise Reduction Method Based on ICEEMDAN-FE-WSTD

Aiming at the problem of temperature measurement error caused by the noise signal on the Raman-based distributed optical fiber temperature sensor (RDTS), a noise reduction method based on the improved complete ensemble empirical mode decomposition with adaptive noise, fuzzy entropy, and the wavelet soft threshold denoising (ICEEMDAN-FE-WSTD) is proposed. First, ICEEMDAN is used to decompose the input signal, and noise intrinsic mode functions (IMFs) are determined by calculating the FE value of each IMF. Then, noise IMFs are denoised by the WSTD method. Finally, the noise reduction results are obtained by combining the denoised IMFs with the remaining useful signal IMFs for reconstruction. The advantages of the proposed method in terms of denoising and character extraction are verified by the simulation signal experiment with different signal-to-noise ratios (SNRs). The temperature measurement experiments are carried out with heating areas set at 40 °C, 45 °C, 50 °C, 55 °C, and 60 °C. Taking the 40 °C temperature measurement experiment as an example, after the temperature measurement signal is denoised by the proposed method, the maximum temperature measurement error in the heating area is reduced by 1.07 °C, the SNR is increased by 4.83 dB, and the root-mean-square error (RMSE) is reduced by 0.77. The temperature drift of RDTS signals after noise reduction by the proposed method is also effectively suppressed, and the maximum temperature measurement error at 2.28 km is reduced by 1.43 °C. The denoising results of the proposed method are compared with the other six noise reduction methods in this article, and the proposed method has the best performance.

A Denoising Method of Micro-Turbine Acoustic Pressure Signal Based on CEEMDAN and Improved Variable Step-Size NLMS Algorithm

The acoustic pressure signal generated by blades is one of the key indicators for condition monitoring and fault diagnosis in the field of turbines. Generally, the working conditions of the turbine are harsh, resulting in a large amount of interference and noise in the measured acoustic pressure signal. Therefore, denoising the acoustic pressure signal is the basis of the subsequent research. In this paper, a denoising method of micro-turbine acoustic pressure signal based on the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and Variable step-size Normalized Least Mean Square (VSS-NLMS) algorithms is proposed. Firstly, the CEEMDAN algorithm is used to decompose the original signal into multiple intrinsic mode functions (IMFs), based on the cross-correlation coefficient and continuous mean square error (CMSE) criterion; the obtained IMFs are divided into clear IMFs, noise-dominated IMFs, and noise IMFs. Finally, the improved VSS-NLMS algorithm is adopted to denoise the noise-dominated IMFs and combined with the clear IMF for reconstruction to obtain the final denoised signal. Adopting the above principles, the acoustic pressure signals generated by a micro-turbine with different rotation speeds and different states (normal turbine and fractured turbine) are denoised, respectively, and the results are compared with the axial flow fan test (ideal interference-free signal). The results show that the denoising method proposed in this paper has a good denoising effect, and the denoised signal is smooth and the important features are well preserved, which is conducive to the extraction of acoustic pressure signal characteristics.

A Novel Noise Reduction Method of UAV Magnetic Survey Data Based on CEEMDAN, Permutation Entropy, Correlation Coefficient and Wavelet Threshold Denoising

Despite the increased attention that has been given to the unmanned aerial vehicle (UAV)-based magnetic survey systems in the past decade, the processing of UAV magnetic data is still a tough task. In this paper, we propose a novel noise reduction method of UAV magnetic data based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), permutation entropy (PE), correlation coefficient and wavelet threshold denoising. The original signal is first decomposed into several intrinsic mode functions (IMFs) by CEEMDAN, and the PE of each IMF is calculated. Second, IMFs are divided into four categories according to the quartiles of PE, namely, noise IMFs, noise-dominant IMFs, signal-dominant IMFs, and signal IMFs. Then the noise IMFs are removed, and correlation coefficients are used to identify the real signal-dominant IMFs. Finally, the wavelet threshold denoising is applied to the real signal-dominant IMFs, the denoised signal can be obtained by combining the signal IMFs and the denoised IMFs. Both synthetic and field experiments are conducted to verify the effectiveness of the proposed method. The results show that the proposed method can eliminate the interference to a great extent, which lays a foundation for the further interpretation of UAV magnetic data.

Residual Current Detection Method Based on Variational Modal Decomposition and Dynamic Fuzzy Neural Network

To further improve the detection ability of residual current in low-voltage distribution networks, an adaptive residual current detection method based on variational mode decomposition (VMD) and dynamic fuzzy neural network (DFNN) is proposed. First, using the general <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -value selection method of VMD proposed in this study, the residual current signal is decomposed into <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> intrinsic mode functions (IMFs). By introducing the cross-correlation coefficient <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R$ </tex-math></inline-formula> and the time-domain energy entropy ratio <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$E$ </tex-math></inline-formula> as two classification indexes, IMFs are divided into three categories: effective IMFs, noise IMFs and aliasing IMFs. Then, the aliasing IMFs are denoised by recursive least squares (RLS), and the denoised IMFs are superimposed with the effective IMFs to obtain the reconstructed signal. Finally, the dynamic fuzzy neural network (DFNN) is adjusted by the minimum output method to achieve the detection of the reconstructed residual current signal, and the network is used to predict the residual current according to the detection results. The detection results of the simulation and measured data show that the proposed algorithm has high detection accuracy and is superior to the wavelet neural network, empirical mode decomposition-thresholding, and wavelet entropy-auto encoder-back propagation neural network methods in terms of mean square error, goodness of fit and running time. This method provides a reference for further research on new adaptive residual current protection devices.

A New Joint Denoising Algorithm for High‐G Calibration of MEMS Accelerometer Based on VMD‐PE‐Wavelet Threshold

Recently, the High‐G MEMS accelerometer (HGMA) has been used in navigation, mechanical property detection, consumer electronics, and other fields widely. As the core component of a measuring system, it is very crucial to enhance the calibration accuracy of the accelerometer. In order to remove the noises in the accelerometer output signals to enhance its calibration accuracy, a combined denoising method which combines variational mode decomposition (VMD) with permutation entropy (PE) and wavelet threshold is given in this article. For the sake of overcoming the defect of signal distortion caused by the traditional denoising methods, this joint denoising method combines the good decomposition characteristics of VMD and the good denoising ability of wavelet threshold and introduces PE as a judgment criterion to achieve a good balance between denoising effect and signal fidelity. The combination of PE and VMD not only avoids the phenomenon of mode aliasing but also improves the ability to identify the noise components, which makes the wavelet threshold denoising more specific. Firstly, some intrinsic mode functions (IMFs) are obtained by using VMD to decompose the complex signal containing noise which is outputted from the accelerometer. Secondly, the IMF components can be divided into noise IMF components, mixed IMF components, and useful IMF components by PE algorithm. Thirdly, the noise IMF components can be discarded directly, and then the mixed IMF components can be denoised by wavelet threshold to obtain the noiseless IMF components; in addition, the useful IMF components need to be retained. Finally, the final denoising signal can be obtained by reconstructing the IMF components which have been denoised by the wavelet threshold and the useful IMF components retained before denoising. The experimental results prove that the combined denoising algorithm combines the merits of VMD, PE, and wavelet threshold, and this new algorithm has a good performance in the calibration denoising of accelerometer. Compared with the serious signal distortion caused by using only EMD or wavelet threshold, this method not only has a good denoising effect (the noises in the static part are eliminated by 99.97% and the SNR of the dynamic part is raised to 18.56) but also can maintain a good signal fidelity (the error of shock peak amplitude is 3.4%, the error of vibration peak amplitude is 0.4%, and the correlation coefficient between the denoising signals and dynamic part is as high as 0.982).

Denoising Method of MEMS Gyroscope Based on Interval Empirical Mode Decomposition

The microelectromechanical system (MEMS) gyroscope has low measurement accuracy and large output noise; the useful signal is often submerged in the noise. A new denoising method of interval empirical mode decomposition (IEMD) is proposed. Firstly, the traditional EMD algorithm is used to decompose the signal into a finite number of intrinsic mode functions (IMFs). Based on the Bhattacharyya distance analysis and the characteristics of the autocorrelation function, a screening mechanism is proposed to divide IMFs into three categories: noise IMFs, mixed IMFs, and signal IMFs. Then, the traditional modelling filtering method is used to filter the mixed IMFs. Finally, the mixed IMFs after modelling and filtering and signal IMFs are reconstructed to obtain the denoised signal. In the experimental analysis, the static denoising experiment of the turntable, the Allan variance analysis, dynamic denoising experiment, and vehicle experiment are set up in this paper, which fully proves that the method has obvious advantages in denoising and greatly improves the quality of signal and the accuracy of the inertial navigation system solution.

Geomagnetic signal de-noising method based on improved empirical mode decomposition and morphological filtering

To solve the problem that geomagnetic signals are susceptible to random noise and instantaneous pulse interference in geomagnetic navigation, a geomagnetic signal de-noising method based on improved empirical mode decomposition (IEMD) and morphological filtering (MF) is proposed. The instantaneous pulse interference is eliminated by designing different structural elements according to the characteristics of the pulse signal. The signal after filtering the instantaneous pulse interference is decomposed by EMD, and the intrinsic mode functions (IMFs) obtained from the decomposition are determined as two modes (i.e. noise IMFs and mixed IMFs) by the cross-correlation coefficient criterion. The noise IMFs are removed directly, and a normalized least means square filter (NLMS) is designed to remove noise from mixed IMFs, which can adaptively adjust the filtering parameters according to the noise level of different IMF components. The noise-reduced mixed IMFs and residual are reconstructed to obtain the final geomagnetic signal. Experiment results illustrate that the proposed MF-IEMD method can effectively achieve noise reduction. Comparing with the traditional EMD and MF-EMD de-noising methods, the root mean square errors(RMSE) decreased by 49.27% and 24.79%, respectively.

Multiscale Entropy Feature Extraction Method of Running Power Equipment Sound.

The equipment condition monitoring based on computer hearing is a new pattern recognition approach, and the system formed by it has the advantages of noncontact and strong early warning abilities. Extracting effective features from the sound data of the running power equipment help to improve the equipment monitoring accuracy. However, the sound of running equipment often has the characteristics of serious noise, non-linearity and instationary, which makes it difficult to extract features. To solve this problem, a feature extraction method based on the improved complementary ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and multiscale improved permutation entropy (MIPE) is proposed. Firstly, the ICEEMDAN is utilized to obtain a group of intrinsic mode functions (IMFs) from the sound of running power equipment. The noise IMFs are then identified and eliminated through mutual information (MI) and mean mutual information (meanMI) of IMFs. Next, the normalized mutual information (norMI) and MIPE are calculated respectively, and norMI is utilized to weigh the corresponding MIPE result. Finally, based on the separability criterion, the weighted MIPE results are feature-dimensionally reduced to obtain the multiscale entropy feature of the sound. The experimental results show that the classification accuracies of the method under the conditions of no noise and 5 dB reach 96.7% and 89.9%, respectively. In practice, the proposed method has higher reliability and stability for the sound feature extraction of the running power equipment.

A New Feature Extraction Method Based on Improved Variational Mode Decomposition, Normalized Maximal Information Coefficient and Permutation Entropy for Ship-Radiated Noise.

Due to the existence of marine environmental noise, coupled with the instability of underwater acoustic channel, ship-radiated noise (SRN) signals detected by sensors tend to suffer noise pollution as well as distortion caused by the transmission medium, making the denoising of the raw detected signals the new focus in the field of underwater acoustic target recognition. In view of this, this paper presents a novel hybrid feature extraction scheme integrating improved variational mode decomposition (IVMD), normalized maximal information coefficient (norMIC) and permutation entropy (PE) for SRN signals. Firstly, the IVMD method is employed to decompose the SRN signals into a number of finite intrinsic mode functions (IMFs). The noise IMFs are then filtered out by a denoising method before PE extraction. Next, the MIC between each retained IMF and the raw SRN signal and PE of retained IMFs are calculated, respectively. After this, the norMICs are used to weigh the PE values of the retained IMFs and the sum of the weighted PE results is regarded as the classification parameter. Finally, the feature vectors are fed into the particle swarm optimization-based support vector machine multi-class classifier (PSO-SVM) to identify different types of SRN samples. The experimental results have indicated that the classification accuracy of the proposed method is as high as 99.1667%, which is much higher than that of other currently existing methods. Hence, the method proposed in this paper is more suitable for feature extraction of SRN signals in practical application.

The improved noise reduction method for the vibration signal based on variational mode decomposition

The variational model decomposition (VMD) has a problem that is dificult to determine the number of intrinsic mode functions (IMF).We use the leaked energy to determine the number of IMFs. And we use the energy concentration rate of the IMF?s autocorrelation function and the correlation coefficient between the IMFs and the original signal, define Q as the ratio of the energy concentration and the correlation coefficient, and use Q to determine the noise IMFs in the IMFs. Then, we filter the noise IMFs and use the remaining IMFs to reconstruct signal to achieve noise reduction. Finally, we use the signal-tonoise ratio (SNR) to compare the noise reduction method proposed in this paper and the Empirical Mode Decomposition (EMD) noise reduction method.

MEMS Hydrophone Signal Denoising and Baseline Drift Removal Algorithm Based on Parameter-Optimized Variational Mode Decomposition and Correlation Coefficient.

Underwater acoustic technology is an important means of detecting the ocean. Due to the complex influence of the marine environment, there is a lot of noise and baseline drift in the signals collected by hydrophones. In order to solve this problem, this paper proposes a denoising and baseline drift removal algorithm for MEMS vector hydrophone based on whale-optimized variational mode decomposition (VMD) and correlation coefficient (CC). Firstly, the power spectrum entropy (PSE), which reflects the variation characteristics of the signal frequency is selected as the fitness function of the whale-optimization algorithm to find the parameters (K,α) of the VMD. It is easier to find the global optimal solution of the parameters by combining the whale-optimization algorithm. Then, using the VMD algorithm after obtaining the parameters, the original signal is decomposed to obtain the intrinsic mode functions (IMFs), and calculating the correlation coefficients (CCs) between the IMFs and the original signal. Finally, the CC threshold is used to remove the noise IMFs, and the rest of the useful IMFs are reconstructed to complete the denoising and baseline drift removal process of the original signals. In the simulation experiments, the algorithm proposed in this paper shows better performance by comparing conventional digital signal-processing methods and the related algorithms proposed recently. Applied in the experiments of a MEMS hydrophone, the effectiveness of the proposed algorithm is also verified. This algorithm can provide new ideas for signal denoising and baseline drift removal.

A Noise Suppression Method of Ground Penetrating Radar Based on EEMD and Permutation Entropy

Ensemble empirical mode decomposition (EEMD) is a noise-assisted analysis method, which can overcome the mode mixing problem in empirical mode decomposition (EMD). However, the choice of signal intrinsic mode functions (IMFs) still depends on subjective experience in most cases. In order to solve the problem, a noise suppression method based on EEMD and permutation entropy (PE) is proposed according to the characteristics of ground-penetrating radar (GPR) signal. In the proposed method, first EEMD is used to decompose the GPR signal into a series of IMFs, and the PE of each IMF is calculated; then, the global threshold obtained by the second-order difference of PE of all IMFs is used to distinguish between noise IMFs and target IMFs; finally, the signal is reconstructed with target IMFs to remove the noise. The experimental results for synthetic and practical GPR data show that the proposed method can effectively remove the noise in the GPR signal and improve the resolution of the target.

A New Feature Extraction Method for Ship-Radiated Noise Based on Improved CEEMDAN, Normalized Mutual Information and Multiscale Improved Permutation Entropy.

Extracting useful features from ship-radiated noise can improve the performance of passive sonar. The entropy feature is an important supplement to existing technologies for ship classification. However, the existing entropy feature extraction methods for ship-radiated noise are less reliable under noisy conditions because they lack noise reduction procedures or are single-scale based. In order to simultaneously solve these problems, a new feature extraction method is proposed based on improved complementary ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), normalized mutual information (norMI), and multiscale improved permutation entropy (MIPE). Firstly, the ICEEMDAN is utilized to obtain a group of intrinsic mode functions (IMFs) from ship-radiated noise. The noise reduction process is then conducted by identifying and eliminating the noise IMFs. Next, the norMI and MIPE of the signal-dominant IMFs are calculated, respectively; and the norMI is used to weigh the corresponding MIPE result. The multi-scale entropy feature is finally defined as the sum of the weighted MIPE results. Experimental results show that the recognition rate of the proposed method achieves 90.67% and 83%, respectively, under noise free and 5 dB conditions, which is much higher than existing entropy feature extraction algorithms. Hence, the proposed method is more reliable and suitable for feature extraction of ship-radiated noise in practice.

Method for Structural Frequency Extraction from GNSS Displacement Monitoring Signals

Abstract This article focused on the obstacles and the solution of the structural frequency extraction from the global navigation satellite system (GNSS) displacement monitoring signals. Based on the analysis of the signals obtained from a real-time dynamic displacement monitoring system of a compound cable-stayed bridge in Guangzhou, China, it was found that the ultra-low frequency components and the noise in the signal result in the errors and distortion in the structural frequency extraction. Accordingly, a method was proposed. The empirical mode decomposition was firstly carried out to decompose the GNSS signal into a set of intrinsic mode functions (IMFs). A coefficient was used, and the cut-off frequency was set to distinguish effective IMFs, which contain structural oscillation information, from high frequency noise IMFs and trends (including ultra-low frequency IMFs). Then the wavelet was applied to remove the noise of the effective IMFs. A reconstructed signal was obtained by summing up the denoised effective IMFs. The structural frequency was obtained from the reconstructed signal using the fast Fourier transform. The results demonstrate the proposed method can reduce the influence of the ultra-low frequency components and the noise and extract the accurate structure frequency from GNSS displacement monitoring signals.

Mold-Level Prediction for Continuous Casting Using VMD–SVR

In the continuous-casting process, mold-level control is one of the most important factors that ensures the quality of high-efficiency continuous casting slabs. In traditional mold-level prediction control, the mold-level prediction accuracy is low, and the calculation cost is high. In order to improve the prediction accuracy for mold-level prediction, an adaptive hybrid prediction algorithm is proposed. This new algorithm is the combination of empirical mode decomposition (EMD), variational mode decomposition (VMD), and support vector regression (SVR), and it effectively overcomes the impact of noise on the original signal. Firstly, the intrinsic mode functions (IMFs) of the mold-level signal are obtained by the adaptive EMD, and the key parameter of the VMD is obtained by the correlation analysis between the IMFs. VMD is performed based on the key parameter to obtain several IMFs, and the noise IMFs are denoised by wavelet threshold denoising (WTD). Then, SVR is used to predict each denoised component to obtain the predicted IMF. Finally, the predicted mold-level signal is reconstructed by the predicted IMFs. In addition, compared with WTD–SVR and EMD–SVR, VMD–SVR has a competitive advantage against the above three methods in terms of robustness. This new method provides a new idea for mold-level prediction.

An EMD-MRLS de-noising method for fiber optic gyro Signal

In order to reduce the influence of fiber optic gyroscope (FOG) random drift error on inertial navigation systems (INS), a novel de-noising method is proposed in this paper, which based on an improved empirical mode decomposition (EMD) and modified recursive least square (RLS). Referred to as the EMD-MRLS method, it is developed to decompose the FOG outputs into a number of intrinsic mode functions (IMFs) after which mode manipulations are divided into three parts, noise IMFs, mixed IMFs, and information IMFs by two index parameters based on mahalanobis distance (MD). A modified RLS algorithm is then employed to process the mixed IMFs, from which the refined IMFs components are reconstructed to produce the final de-noising results. Other traditional methods, such as RLS, and EMD are investigated to provide a comparison with the proposed one through both simulated signals and experimental FOG outputs. Compared with the EMD method, the results show that the error mean is reduced by 27.01%, and the horizontal position error is reduced by 106.75m, when the INS lasts for 1000s.