A short-time window mean-vmd algorithm-based inertial navigation non-stationary signal denoising method

Abstract

The application provides a short-time window mean-VMD algorithm-based inertial navigation non-stationary signal denoising method, and belongs to the field of positioning and navigation. The method comprises the following steps: (1) short-time window mean processing; (2) signal stationary processing; (3) variational mode decomposition processing; (4) signal reconstruction; and (5) denoising signal acquisition. The method can eliminate the influence of vibration and electromagnetic and other multi-source heterogeneous noise interference on combined inertial navigation positioning detection, can inhibit multi-source heterogeneous noise interference of a coal mine tunneling working face, and can improve the positioning precision of coal mine tunneling equipment.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of positioning and navigation, and particularly relates to a short-time window mean-VMD algorithm-based inertial navigation non-stationary signal denoising method. BACKGROUND

[0002] As the core equipment of the tunneling working face, the tunneling machine is one of the key technologies for realizing automatic and intelligent tunneling. The optical fiber inertial navigation is suitable for application in the precise positioning of the coal mine tunneling equipment due to its high pose detection precision and independence on external information. However, the working space of the coal mine tunneling working face is narrow, the environment is complex and changeable, the electromagnetic interference is serious, and the tunneling equipment is easily disturbed by vibration during cutting, which will affect the pose detection accuracy of the optical fiber inertial navigation. Therefore, it is necessary to deeply study the optical fiber inertial navigation signal denoising method of the tunneling equipment and eliminate the influence of noise interference on the precise positioning of the tunneling equipment.

[0003] At present, the empirical mode decomposition (EMD) denoising and wavelet denoising methods are mainly used for denoising the inertial navigation detection signals. However, the wavelet denoising method is limited by the selection of the wavelet basis and the decomposition layer number, and is not suitable for the colored noise in the data. The EMD denoising method depends on the empirical judgment for the selection of the effective intrinsic mode function and the effective IMF component contains noise, which leads to poor denoising effect. SUMMARY

[0004] The application aims to eliminate the influence of multi-source heterogeneous noise interference such as vibration and electromagnetic interference on the combined inertial navigation positioning detection, and provides a short-time window-VMD algorithm-based inertial navigation non-stationary signal denoising method, which can suppress the multi-source heterogeneous noise interference of the coal mine tunneling working face and improve the positioning precision of the coal mine tunneling equipment.

[0005] In order to achieve the above-mentioned purpose, the application adopts the following technical solutions:

[0006] A short-time window mean-VMD algorithm-based inertial navigation non-stationary signal denoising method, the steps are as follows:

[0007] (1) Short-time window mean processing

[0008] The original signal is differentiated in the time domain, and the signal mean value is calculated in the short-time window;

[0009] (2) Signal stationarization processing

[0010] Each signal after the short-time window mean processing is spliced into a complete signal, and the complete signal after the short-time window mean processing is subtracted from the initial signal to become a stationary signal;

[0011] (3) Variational mode decomposition processing

[0012] The stationary signal is decomposed by variational mode decomposition, and the number of decomposition layers corresponds to the frequency components in the signal;

[0013] (4) signal reconstruction

[0014] According to the energy value of the modal component, the modal component of the useful signal is screened for signal recombination;

[0015] (5) noise reduction signal acquisition

[0016] The stationary signal after VMD noise reduction is added to the short-time window mean signal to obtain the final noise reduction signal.

[0017] Further, in the step (1), the specific implementation steps of the short-time window mean value processing include:

[0018] (1.1) The original signal is divided into several groups, and the window width and the number of repeating units are set according to the original signal. The window width refers to the data length contained in a single window, and the repeating unit refers to the repeating part of the kth window and the k+1 window, i.e. the number of overlapping samples in each segment. The default value is to produce 50% overlap between segments; then the total length of the original signal is:

[0019] n=xW-(x-1)L (1)

[0020] In the above formula, n is the total length of the original signal, which is divided into x windows, each window width is W, and the overlapping length between windows is L;

[0021] (1.2) Calculate the mean value of each short-time window;

[0022]

[0023] In the above formula, F(t,x) is the mean value of each short-time window.

[0024] Further, in the step (2), the specific implementation steps of the signal stationary processing include:

[0025] (2.1) Reassemble each short-time window to obtain a complete mean value signal;

[0026] aver (t)=F(t,1)+F(t,2)+…+F(t,x) (3)

[0027] In the above formula, F aver (t) is the mean value signal;

[0028] (2.2) After subtracting the mean value signal from the original signal, the stationary signal is obtained. Subtracting the mean value can reduce the bias noise and also reduce the random walk noise;

[0029] sta ​​(t) = f(t) - F aver (t) (4)

[0030] In the above formula, F sta (t) is a stationary signal, and f(t) is an original signal.

[0031] Further, in the step (3), the multi-source heterogeneous noise of the coal mining working face mainly includes two components of vibration and electromagnetic interference, and considering the working frequency of the inertial navigation, the electromagnetic interference is mainly concentrated in the power frequency 50Hz and the harmonic 100Hz, so the decomposition layer is 4.

[0032] The variational mode decomposition method is to solve the variational model by iteration, and use the optimal parameter combination [K, a] to effectively decompose the noise into intrinsic mode components IMF with limited bandwidth.

[0033] Further, in the step (3), the specific implementation steps of the variational mode decomposition include:

[0034] Suppose that a multi-component signal is composed of K modal components u k (t) with limited bandwidth, and the center frequency of each IMF is ω(t), and the constraint condition is that the modal sum is equal to the input signal, and the specific construction steps are as follows:

[0035] (3.1) The analytic signal of u k (t) is obtained by Hilbert transform, and its one-sided spectrum is calculated, and by multiplying the operator, the center band of u k (t) is modulated to the corresponding base band

[0036] (3.2) Calculate the square norm L 2 of the demodulation gradient, and estimate the bandwidth of each modal component, and the VMD constrained variational model is as follows:

[0037]

[0038] In the above formula, {u k}={u1,…,u k} represents each IMF modal function after decomposition, and {ω k}={ω1,…,ω k} represents the center frequency of each modal; in order to find the optimal solution of the constrained variational problem, first introduce the Lagrange multiplier λ and the second-order penalty factor α, wherein the second-order penalty factor α can ensure the accuracy of signal reconstruction in a Gaussian noise environment, and the Lagrange multiplier λ can ensure the strictness of the constraint condition, and the extended Lagrange expression is as follows:

[0039]

[0040] The weight of the penalty factor is inversely proportional to the complexity of data noise, which ensures the fidelity of data, and under the influence of the Lagrange operator with the weight of the penalty factor and strict constraints, the constraint problem has good convergence.

[0041] (3.3) The alternating direction multiplier method (ADMM) is used to continuously update each component and the center frequency, and finally the saddle point of the unconstrained model is obtained, that is, the optimal solution of the original problem, and the functional is updated for all ω≥0

[0042]

[0043] In the above formula, ω represents the frequency, respectively, are the Fourier transforms of f(t), λ(t);

[0044] (3.4) is The residual quantity after Wiener filtering, the algorithm re-estimates the center frequency according to the power spectrum center of each component, and the specific process is as follows:

[0045] 1) initialization and n;

[0046] 2) execute cycle: n = n + 1;

[0047] 3) when ω>0, update

[0048] 4) update the functional ω k ;

[0049]

[0050] 5) update

[0051]

[0052] In the above formula, γ represents the noise tolerance, when the signal contains strong noise, γ can be set to 0 to achieve better denoising effect;

[0053] 6) repeat steps (3.4.2) to (3.4.5) until the iteration condition is met to stop;

[0054]

[0055] For all ω≥0, the one-sided spectrum of the analytical signal only contains non-negative frequencies.

[0056] Further, in the step (4), the signal reconstruction specifically implements the steps comprising:

[0057] The energy value of each component after VMD decomposition is calculated, and the expression is

[0058]

[0059] In the above formula, E k is the energy value of the kth component, μ k is the kth component, T max,k and T min,k are the upper and lower time limits of the kth component, respectively.

[0060] According to the energy value of each component, each component is divided into a trend component, a low-frequency component and a high-frequency component, wherein the trend component and the low-frequency component represent the regularity in the load time series, and the high-frequency component represents the randomness in the load time series. Since the random part cannot be accurately predicted, it is eliminated, and the trend component and the low-frequency component are used as the recombined signal.

[0061] Further, in the step (5), the specific implementation steps of obtaining the noise reduction signal include:

[0062]

[0063] In the above formula, denotes the noise reduction signal after the recombination of the VMD noise reduction stationary signal and the mean signal, which can better restore the signal form and amplitude, denotes the VMD noise reduction stationary signal.

[0064] The inertial navigation non-stationary signal noise reduction method based on the short-time window mean-VMD algorithm of the application eliminates the influence of multi-source heterogeneous noise interference such as vibration and electromagnetic interference on the combined inertial navigation positioning detection, can suppress the multi-source heterogeneous noise interference of the coal mine tunneling working face, and improve the positioning accuracy of the coal mine tunneling equipment. BRIEF DESCRIPTION OF DRAWINGS

[0065] Figure 1 is the flow chart of the method of the application;

[0066] Figure 2 is the short-time window decomposition schematic diagram in the application;

[0067] Figure 3 is the VMD decomposition flow chart in the application;

[0068] Figure 4 is the inertial navigation (accelerometer) signal noise reduction comparison chart, wherein (a) is a noise signal chart, and (b) is a short-time window mean-VMD noise reduction signal chart;

[0069] Figure 5The figure is a spectrum comparison chart for noise reduction of an inertial navigation (accelerometer) signal, wherein (a) is a noise signal spectrum chart, and (b) is a short-time window mean-VMD noise reduction signal spectrum chart;

[0070] Figure 6a The figure is a comparison chart for ideal, pre-noise reduction and post-noise reduction pitch angle positioning results.

[0071] Figure 6b The figure is a comparison chart for ideal, pre-noise reduction and post-noise reduction northward displacement positioning results.

[0072] Figure 6c The figure is a comparison chart for ideal, pre-noise reduction and post-noise reduction roll angle positioning results.

[0073] Figure 6d The figure is a comparison chart for ideal, pre-noise reduction and post-noise reduction eastward displacement positioning results.

[0074] Figure 6e The figure is a comparison chart for ideal, pre-noise reduction and post-noise reduction heading angle positioning results.

[0075] Figure 6f The figure is a comparison chart for ideal, pre-noise reduction and post-noise reduction skyward displacement positioning results. DETAILED DESCRIPTION

[0076] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application will be described in detail below in combination with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor should belong to the protection scope of the present application.

[0077] The present application provides an inertial navigation non-stationary signal noise reduction method based on a short-time window mean-VMD algorithm, which is mainly used to eliminate the influence of multi-source heterogeneous noise interference such as vibration and electromagnetic interference on combined inertial navigation positioning detection, suppress multi-source heterogeneous noise interference in a coal mining working face, and improve the positioning accuracy of coal mining equipment. Since the inertial navigation works in a vibration environment, there are electromagnetic interference and random drift caused by vibration, and there are also sudden values in the signal due to the characteristics of the inertial navigation itself, so the noisy inertial navigation signal belongs to a non-stationary signal. The VMD noise reduction algorithm has better effect on stationary signal noise reduction, so the overall idea of the present application is to obtain a stationary signal by meanizing the noisy signal, and then perform VMD decomposition and noise reduction, and extract low-frequency components from the average signal and recombine them with the mean signal.

[0078] EMBODIMENT

[0079] In combination with Figure 1 The inertial navigation non-stationary signal noise reduction method based on the short-time window mean-VMD algorithm provided in the embodiment has the following specific steps:

[0080] (1) Short-time window mean calculation

[0081] The original signal is differentiated in the time domain by a short time window, and the mean of the signal is calculated within the short time window.

[0082] (2) Signal stabilization processing

[0083] Each segment of the signal after short-time window averaging is reassembled into a complete signal. The complete signal after short-time window averaging is then subtracted from the initial signal to obtain a stationary signal.

[0084] (3) Variational mode decomposition processing

[0085] Variational mode decomposition is performed on a stationary signal, and the number of decomposition levels corresponds to the frequency components in the signal.

[0086] (4) Signal reconstruction

[0087] Based on the energy values ​​of the modal components, the modal components of the useful signal are selected for signal reconstruction;

[0088] (5) Noise reduction signal acquisition

[0089] The final denoised signal is obtained by adding the stable signal after VMD denoising to the short-time window mean signal.

[0090] Combination Figure 2 As shown, gyroscope / accelerometer signal errors can be both positive and negative. Averaging these errors can compensate for them to some extent. Subtracting the mean signal from the original signal can transform a non-stationary signal into a stationary one. Since the initial signal data is large and contains abrupt changes, averaging all data is clearly insufficient for signal stabilization. Therefore, the concept of a short-time window is introduced. This involves differentiating the signal in the time domain, dividing it into several groups, and averaging each group. The window width and number of repeating units are set according to the signal, and the signal mean is calculated within the short-time window.

[0091] Specifically, the implementation steps for short-time window averaging include:

[0092] (1.1) Divide the original signal into several groups. Set the window width and the number of repetition units according to the original signal. The window width refers to the data length contained in a single window. The repetition unit refers to the overlapping part between the k-th window and the (k+1)-th window, that is, the number of overlapping samples in each segment. The default value is to produce 50% overlap between segments. Then the total length of the original signal is:

[0093] n=xW-(x-1)L (1)

[0094] In the above formula, n is the total length of the original signal, which is divided into x window segments, each with a width of W and an overlap length of L between windows;

[0095] (1.2) Average each short-time window;

[0096]

[0097] In the above formula, F(t, x) is the signal average of each short-time window.

[0098] Subtract the short-time window average processed complete signal from the initial signal to become a stationary signal, which is convenient for VMD noise reduction.

[0099] Specifically, the specific implementation steps of signal stationary processing include:

[0100] (2.1) Reassemble each short-time window to obtain a complete average signal;

[0101] F aver (t) = F(t, 1) + F(t, 2) + … + F(t, x) (3)

[0102] In the above formula, F aver (t) is the average signal;

[0103] (2.2) After subtracting the average signal from the original signal, a stationary signal is obtained. Subtracting the average can reduce the bias noise and also reduce the random walk noise;

[0104] F sta (t) = f(t) - F aver (t) (4)

[0105] In the above formula, F sta (t) is the stationary signal, and f(t) is the original signal.

[0106] VMD (Variational mode decomposition) is an adaptive, completely non-recursive modal variational and signal processing method. The technology has the advantage of being able to determine the number of modal decompositions, and its adaptability lies in determining the number of modal decompositions of the given sequence according to the actual situation, and adaptively matching the best center frequency and limited bandwidth of each modal in the subsequent search and solution process, and can realize effective separation of intrinsic modal components (IMF), frequency domain division of signals, and then obtain effective decomposition components of the given signal, and finally obtain the optimal solution of the variational problem. It overcomes the problems of end effect and modal component aliasing in EMD method, and has a more solid mathematical theoretical basis, which can reduce the non-stationarity of time series with high complexity and strong nonlinearity, and decompose to obtain sub-sequences containing multiple different frequency scales and relatively stationary. The core idea of VMD is to build and solve the variational problem. The variational mode decomposition method uses iterative solution of variational model to effectively decompose noise into intrinsic modal components (IMF) with limited bandwidth using the optimal parameter combination [K, a]. The overall architecture of the method is the variational mode decomposition problem, and the signal decomposition process of the method is the process of solving the variational function, and the bandwidth of each modal is estimated.

[0107] In the embodiment, the multi-source heterogeneous noise of the coal mine tunneling working face mainly includes two components of vibration and electromagnetic interference, and considering the working frequency of the inertial navigation system, the electromagnetic interference is mainly concentrated at the power frequency of 50 Hz and the harmonic of 100 Hz, so the decomposition layer number is 4.

[0108] As shown in Figure 3 , the specific implementation steps of VMD noise reduction processing include:

[0109] Suppose that a multi-component signal is composed of K modal components u k (t) with limited bandwidth, and the center frequency of each IMF is ω(t). The constraint condition is that the modal sum is equal to the input signal, and the specific construction steps are as follows:

[0110] (3.1) Obtain the analytic signal of u k (t) by Hilbert transform, and calculate its one-sided spectrum. By multiplying with the operator, the center band of u k (t) is modulated to the corresponding base band

[0111] (3.2) Calculate the square norm L 2 of the demodulation gradient, and estimate the bandwidth of each modal component. The VMD constrained variational model is as follows:

[0112]

[0113] In the above formula, {u k}={u1,…,u k} represent the decomposed IMF modal functions, {ω k} = {ω1, …, ω k} represent the modal center frequencies; To find the optimal solution of the constrained variational problem, first introduce the Lagrange multiplier λ and the second-order penalty factor α, where the second-order penalty factor α can guarantee the accuracy of signal reconstruction in a Gaussian noise environment, and the Lagrange multiplier λ can guarantee the strictness of the constraint condition. The extended Lagrange expression is as follows:

[0114]

[0115] The weight of the penalty factor is inversely proportional to the complexity of the data noise, which ensures the fidelity of the data. Under the joint influence of the weight of the penalty factor and the Lagrange operator under strict constraints, the constrained problem has good convergence.

[0116] (3.3) Use the alternating direction multiplier method (ADMM) to continuously update each component and its center frequency, and finally obtain the saddle point of the unconstrained model, which is the optimal solution of the original problem. For all ω ≥ 0, update the functional

[0117]

[0118] In the above formula, ω represents the frequency, are the Fourier transforms of f(t), λ(t) respectively;

[0119] (3.4) is the residual quantity after Wiener filtering, and the algorithm re-estimates the center frequency according to the power spectrum center of each component. The specific process is as follows: 1) initialization

[0120] and n;

[0121] 2) execute cycle: n = n + 1;

[0122] 3) when ω > 0, update

[0123] 4) update the functional ω k ;

[0124]

[0125] 5) update

[0126]

[0127] In the above formula, γ represents the noise tolerance, which can be set to 0 when the signal contains strong noise to achieve better denoising effect;​​

[0128] 6) Repeat steps (3.4.2) to (3.4.5) until the iteration condition is met to stop;

[0129]

[0130] The one-sided spectrum of all ω≥0 analytical signals only contains non-negative frequencies.

[0131] Specifically, in the step (4), the signal reconstruction specifically comprises the following steps:

[0132] The energy value of each component after VMD decomposition is calculated, and the expression is:

[0133]

[0134] In the above formula, E k is the energy value of the kth component, μ k is the kth component, T max,k and T min,k are the upper and lower time limits of the kth component, respectively;

[0135] According to the energy value of each component, each component is divided into a trend component, a low-frequency component, and a high-frequency component, wherein the trend component and the low-frequency component represent the regularity in the load time series, and the high-frequency component represents the randomness in the load time series. Since the random part cannot be accurately predicted, it is excluded, and the trend component and the low-frequency component are used as the recombined signal.

[0136] Specifically, in the step (5), the specific implementation steps of obtaining the noise reduction signal comprise:

[0137]

[0138] In the above formula, represents the noise reduction signal after the recombination of the VMD noise reduction stationary signal and the mean signal, which can better recover the signal form and amplitude, represents the VMD noise reduction stationary signal.

[0139] Simulation example

[0140] The short-time window mean-VMD algorithm-based inertial navigation non-stationary signal noise reduction method of the above embodiment is simulated.

[0141] The fiber-optic strapdown inertial navigation parameters in the simulation are: the bias stability is 0.05° / h, the random drift is The accelerometer bias stability is 50μg, and the random bias is The sampling frequency is 200 Hz. On the basis of considering the inertial navigation system itself drift, the optical fiber inertial navigation signal is added with multi-source heterogeneous noise under the simulation of the noise condition of the tunneling working face. The noise is composed of electromagnetic interference noise of 50 Hz and second harmonic 100 Hz and vibration interference noise of 10-2000 Hz frequency band range with a maximum amplitude of about 1 / 10.

[0142] In combination Figure 4 As shown in FIG. 6, by comparing the curves of the inertial navigation simulation data before noise reduction and the data after noise reduction by using the method of the present application, it can be seen that the noise reduction effect of the method of the present application is relatively obvious. Through the analysis of the data, the signal-to-noise ratio of the data after noise reduction is 29.6.

[0143] In combination Figure 5 As shown in FIG. 6, in order to better analyze the data, by comparing the spectrum of the original data and the spectrum of the data after noise reduction by using the method of the present application, it can be seen that the present application can effectively eliminate the signals outside the useful frequency band, thereby realizing the noise reduction of the inertial navigation signal and improving the accuracy of the inertial navigation output.

[0144] In combination with FIG. 6, by comparing the positioning results of the original data, the data before noise reduction and the data after noise reduction, it can be seen that the method of the present application can effectively filter out the multi-source heterogeneous noise of the optical fiber inertial navigation signal of the coal mine tunneling equipment, thereby improving the positioning accuracy of the inertial navigation.

Claims

1. A short-time window mean-VMD algorithm-based inertial navigation non-stationary signal denoising method, characterized in that, It comprises the following steps: (1) short-time window mean processing The original signal is differentiated in the time domain in a short-time window, and the signal mean in the short-time window is calculated; (2) signal smoothing processing Each piece of signal after short-time window mean processing is spliced into a complete signal, and the initial signal is subtracted from the complete signal after short-time window mean processing to become a stationary signal; (3) variational mode decomposition processing The stationary signal is subjected to variational mode decomposition, and the number of decomposition layers corresponds to the frequency components in the signal; (4) signal reconstruction According to the energy value of the modal component, the modal component of the useful signal is selected for signal recombination; The specific implementation steps of the signal reconstruction comprise: The energy value of each component after VMD decomposition is calculated, and the expression is: （11） In the above formulae, is an energy value of the kth component, is the kth component, and are the upper and lower time limits, respectively, of the kth component. According to the energy value of each component, each component is divided into a trend component, a low-frequency component and a high-frequency component, wherein the trend component and the low-frequency component represent the regularity in the load time series, and the high-frequency component represents the randomness in the load time series, since the random part cannot be accurately predicted, it is excluded, and the trend component and the low-frequency component are used as the recombined signal; (5) obtaining a denoising signal The stationary signal after VMD denoising is added to the short-time window mean signal to obtain the final denoising signal.

2. The short-time window mean-VMD algorithm-based inertial navigation non-stationary signal denoising method according to claim 1, characterized in that, In the step (1), the specific implementation steps of the short-time window mean processing comprise: (1.1) the original signal is divided into several groups, the window width and the number of repeated units are set according to the original signal, the window width refers to the data length contained in a single window, and the repeated unit refers to the repeated part of the kth window and the k+1th window, i.e. the number of overlapping samples in each segment, the default value is to produce 50% overlap between segments; then the total length of the original signal is: （1） In the formula, n is the total length of the original signal, which is divided into x windows, each window has a width of W, and the overlapping length between windows is L; (1.2) calculate the mean value of each short-time window; （2） In the above formula is the mean value for each short-time window.

3. The short-time window mean-VMD algorithm-based inertial navigation non-stationary signal denoising method according to claim 1, characterized in that, In the step (2), the specific implementation steps of the signal smoothing processing comprise: (2.1) each short-time window is spliced together to obtain a complete mean signal; （3） In the above formulae is the mean signal; (2.2) the stationary signal is obtained by subtracting the mean signal from the original signal; （4） In the above equation is a stationary signal, and f(t) is the original signal.

4. The short-time window mean-VMD algorithm-based inertial navigation non-stationary signal denoising method according to claim 1, characterized in that, In the step (3), the number of decomposition layers is 4.

5. The short-time window mean-VMD algorithm-based inertial navigation non-stationary signal denoising method according to claim 1, characterized in that, In the step (5), the specific implementation steps of obtaining a denoising signal comprise: （12） In the above formula, The VMD denoising signal after the stationary signal and the mean signal are recombined, which can better restore the signal form and amplitude, The VMD denoising signal after the stationary signal and the mean signal are recombined, which can better restore the signal form and amplitude,

Images