CN110542406B - Improved gyroscope signal denoising method based on EMD-MPF - Google Patents

Improved gyroscope signal denoising method based on EMD-MPF Download PDF

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CN110542406B
CN110542406B CN201910826514.5A CN201910826514A CN110542406B CN 110542406 B CN110542406 B CN 110542406B CN 201910826514 A CN201910826514 A CN 201910826514A CN 110542406 B CN110542406 B CN 110542406B
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intrinsic mode
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mode function
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陈光武
刘昊
司涌波
程鉴皓
石建强
邢东峰
杨菊花
李文元
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Lanzhou Jiaotong University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C9/00—Measuring inclination, e.g. by clinometers, by levels
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/02—Preprocessing
    • G06F2218/04—Denoising
    • G06F2218/06—Denoising by applying a scale-space analysis, e.g. using wavelet analysis

Abstract

The invention discloses an EMD-MPF (empirical mode decomposition-multi-point filter) based improved gyroscope signal denoising method, which comprises the following steps of: decomposing a noisy signal of a gyroscope into an intrinsic mode function and a residual signal; the intrinsic mode function is selected in order through the two determined identification parameters, and the intrinsic mode function is divided into a noise intrinsic mode function, a mixed intrinsic mode function and an information intrinsic mode function; abandoning the noise intrinsic mode function, reserving the information intrinsic mode function, and carrying out noise reduction processing on the mixed intrinsic mode function; and performing signal reconstruction on the mixed intrinsic mode function subjected to noise reduction and the reserved information intrinsic mode function to obtain a denoised gyroscope signal. The method has the advantages of realizing accurate noise signal removal and improving navigation accuracy.

Description

Improved gyroscope signal denoising method based on EMD-MPF
Technical Field
The invention relates to the field of signal denoising, in particular to an improved gyroscope signal denoising method based on EMD-MPF.
Background
Due to the development of Micro-Electro-Mechanical systems (MEMS), accelerometers and gyroscopes with smaller size and cheaper cost can be manufactured to form an Inertial Measurement Unit (IMU) with lower cost, and due to the advantages of small volume, light weight, low power consumption, mass production and the like, the Inertial navigation or positioning and navigation technologies combined with the IMU are rapidly developed and widely applied to various fields such as transportation, Measurement, aerospace and the like. The error magnitude of the MEMS gyroscope can determine the actual performance of the system to a great extent, so that the method has important practical significance for inhibiting various errors of the gyroscope. Errors which may be generated by the gyroscope include installation errors, lever arm errors, scale factor errors and the like; the noise mainly includes two major aspects of system noise and measurement noise. The random drift of the MEMS gyroscope is an important source of noise, the accuracy of the random drift is greatly affected for the gyroscope itself or for the entire navigation system, and the slight drift causes a large error after accumulation or system message fusion due to the long-term operation of the device. Therefore, how to reduce the noise has become one of the most important issues in the signal processing of the MEMS gyroscope.
The denoising method of the signal of the MEMS gyroscope is mainly divided into a modeling denoising method and a non-modeling denoising method: firstly, a mature random drift model or an ARMA is widely adopted for modeling, and then Kalman filtering or various improved Kalman filtering technologies are utilized for filtering noise in a signal; secondly, the wavelet Decomposition or Empirical Mode Decomposition (EMD) method is directly used to analyze the signal and remove the noise therein, so as to extract the effective signal.
Conventional denoising methods typically use low-pass, high-pass, or band-pass filters to eliminate noise. Eliminating high-frequency noise in a strapdown Inertial Navigation System (INS), for example, using a digital low-pass filter; filtering and suppressing the measurement noise of the MEMS sensor by using an FIR low-pass filter; the application of a high pass filter filters the corresponding signal jitter noise for the phenomenon of very high attenuation in the gyroscope jitter band and linear phase response in the pass band. However, the conventional denoising method is based on the classical filtering theory, and is only suitable for the case that the signal and the noise are not overlapped, so that the filtered frequency components of the actual signal still contain white noise. For modern filtering theory, gaussian filtering, wiener filtering, kalman filtering and the like are representative methods thereof, and all the methods need to utilize priori knowledge counted by signals and noise, for example, an adaptive robust kalman filtering method is used, and a weighted covariance of an innovation sequence is used to adjust a measured noise covariance matrix, so as to reduce random noise in a gyroscope; applying an anti-outlier Recursive Least Squares (RLS) adaptive filtering algorithm under a random weighting method to reduce noise components in the output of the MEMS gyroscope; the sideslip angle estimate is compensated using an adaptive extended Kalman filtering method to reduce potentially large drift estimation errors caused by inertial sensor offsets. These methods overcome the disadvantages of classical filtering theory, but in the using process, certain most standard needs to be given, and a priori statistical information of noise needs to be known, and these are usually difficult or impossible to obtain in practice, and can be generally replaced by an optimal estimation. Meanwhile, the methods need to accurately establish a model, and the deviation of the model can also influence the final denoising effect.
On the basis, a non-modeling denoising method is continuously developed. Wavelet Transform (WT) is a new transform analysis method, which inherits and develops the idea of short-time fourier transform localization, and overcomes the disadvantage that the window size does not change with the frequency, so that it has good multi-resolution analysis characteristic, and can subdivide the high-frequency time and the low-frequency time, thereby achieving the effective analysis of signals of different frequency bands and time. Analyzing the error characteristics of the gyroscope by using an improved wavelet transformation method, and establishing a new soft threshold function so as to inhibit the measurement noise of the gyroscope; the second generation wavelet transform is applied to denoising the MEMS gyroscope. However, the wavelet transform analysis method needs to select different decomposition layer numbers and wavelet bases for different situations, and also needs to select a proper threshold value for denoising, which is very inconvenient to use; meanwhile, the WT method is more suitable for linear, steady-state signals. Therefore, the problem of low navigation accuracy caused by the inaccurate removal of the noise information exists.
Disclosure of Invention
The invention aims to provide a gyroscope signal denoising method based on EMD-MPF improvement to realize the advantage of accurately removing noise signals and further improving navigation accuracy.
In order to achieve the purpose, the embodiment of the invention adopts the technical scheme that:
an EMD-MPF improved gyroscope signal denoising method comprises the following steps:
decomposing a noisy signal of a gyroscope into an intrinsic mode function and a residual signal;
the intrinsic mode function is selected in order through the two determined identification parameters, and the intrinsic mode function is divided into a noise intrinsic mode function, a mixed intrinsic mode function and an information intrinsic mode function;
abandoning the noise intrinsic mode function, reserving the information intrinsic mode function, and carrying out noise reduction processing on the mixed intrinsic mode function;
and performing signal reconstruction on the mixed intrinsic mode function subjected to noise reduction and the reserved information intrinsic mode function to obtain a denoised gyroscope signal.
As a specific implementation manner of the embodiment of the present invention, the decomposition of the noisy signal of the gyroscope into the intrinsic mode function and the residual signal is as follows:
a noisy signal of a gyroscope is decomposed into a plurality of intrinsic mode functions and a residual signal.
As a specific implementation manner of the embodiment of the present invention, a reconstruction formula in signal reconstruction of the noise-reduced mixed eigenmode function and the retained information eigenmode function is as follows:
Figure BDA0002189261260000031
wherein the content of the first and second substances,
Figure BDA0002189261260000032
representing a noise signal; m1And M2Respectively, are the identification parameters of the mobile phone,
Figure BDA0002189261260000033
representing a mixed eigenmode function; h is(i)(t) represents an information eigenmode function; r isL(t) denotes a residual signal, and MPF denotes a modified PF method.
As a specific implementation manner of the embodiment of the present invention, the MPF is an improved PF method, and includes:
let the probability distribution of the predicted particle sample be denoted as p (x)i) I is more than or equal to 1 and less than or equal to N, and weight wi＞w0Particle sample x ofTIs denoted as p1(xi) I is more than or equal to 1 and less than or equal to T, namely p, sampling the rest particles xN-TIs denoted as q (x)i) N-T is more than i and less than or equal to N, namely q and wiIs a weight, w0As weight threshold, both N and T are constants;
the K-L divergence between different particle samples was calculated as follows:
Figure BDA0002189261260000041
for small-weight particle samples, N-T random numbers u are generatedjIn the range uj∈(w0,1]The weight of the particle sample is updated, DKLIs K-L divergence:
Figure BDA0002189261260000042
particle sample x whose weight is to be updatedN-TSorting by weight, i.e. small to large
Figure BDA0002189261260000043
X is to bei+1The distance from the particle with the largest weight is denoted as S, and resampling is performed to generate new particles as follows:
Figure BDA0002189261260000044
Figure BDA0002189261260000045
synthesizing two parts of particles, carrying out weight normalization, and completing the continuous iteration of the PF method, xiDenotes the ith particle, xi+1Denotes the i +1 th particle, xN-T+1Denotes the N-T +1 th particle, xNWhich represents the N-th particle, is,
Figure BDA0002189261260000046
representing new particles resulting from the resampling.
As a specific implementation manner of the embodiment of the present invention, in the two determined identification parameters, the two identification parameters are M respectively1And M2Selecting and determining the identification parameter M1The method comprises the following steps: determining an identification parameter M using an autocorrelation function variance1。
As a specific implementation manner of the embodiment of the present invention, the identification parameter M is determined by using the variance of the autocorrelation function1The method comprises the following steps:
calculating respective corresponding autocorrelation functions according to the intrinsic mode function signals of different orders;
calculating the mean squared error of Euclidean distance between two self-correlation functions according to the self-correlation functions of the continuous intrinsic mode functions to obtain a calculation result MSED;
determining an identification parameter M from MSED1。
As a specific implementation manner of the embodiment of the present invention, the identifier is referred toNumber M1In association with the value k and the value L,
k is more than or equal to 1 and less than or equal to [2L/3 ]]，[2L/3]Represents a maximum integer not exceeding 2L/3, thereby ensuring M1The value of (A) is too large to be L, and k and L are both natural numbers.
As a specific implementation manner of the embodiment of the invention, the identification parameter M is determined2The method comprises the following steps:
calculating the ButaChiya distance between the probability density function of the original signal and the probability density function of each intrinsic mode function, wherein BC is more than or equal to 0 and less than or equal to 1, BD is more than or equal to 0 and less than or equal to infinity, BD is the ButaChiya distance, and BC is the ButaChiya coefficient;
calculating separability of the Bartay-Chiya distance data between the probability density function of the original signal and the probability density function of each eigenmode function under different characteristics based on the power spectral density function;
determining an identification parameter M based on the separability2。
As a specific implementation manner of the embodiment of the present invention, the order selection of the intrinsic mode function through the determined two identification parameters is performed to divide the intrinsic mode function into a noise intrinsic mode function, a mixed intrinsic mode function, and an information intrinsic mode function, and the method includes:
1＜i＜M1time is a noise eigenmode function;
M1＜i＜M2then, is a mixed eigenmode function;
M2when < i < L, the information is an eigenmode function, i represents the order of the eigenmode function
L represents the total order of the eigen-state function.
The embodiment of the invention has the following beneficial effects:
in the following, with reference to the drawings and embodiments, a noisy signal is decomposed into an intrinsic mode function and a residual signal, and then the noisy signal is divided into a noise intrinsic mode function, a mixed intrinsic mode function and an information intrinsic mode function by two identification parameter intrinsic mode functions; and then discarding the noise intrinsic mode function, and performing signal reconstruction on the noise-reduced mixed intrinsic mode function and the information intrinsic mode function to accurately remove noise signals and achieve the advantage of improving navigation accuracy.
Drawings
FIG. 1 is a flowchart of an EMD-MPF-based improved gyroscope signal denoising method according to an embodiment of the present invention;
FIG. 2 is a block diagram of an EMD-MPF denoising method according to an embodiment of the present invention;
FIG. 3 is a graph of MEMS gyroscope X-axis static data in accordance with an embodiment of the present invention;
FIG. 4 is an EMD exploded view of X-axis gyro data according to an embodiment of the present invention;
FIG. 5 is a graph illustrating the autocorrelation function of various stages of decomposed signals according to an embodiment of the present invention;
FIG. 6 is a MSED distribution according to an embodiment of the present invention;
FIG. 7 is a graph of probability density functions of decomposed signals according to an embodiment of the present invention;
FIG. 8 is a graph showing the distribution of the Papanicolaou distances according to an embodiment of the present invention;
FIG. 9 shows the filtering result of the hybrid IMF using MPF according to the embodiment of the present invention;
FIG. 10 is a graph comparing the results of X-axis static tests according to embodiments of the present invention;
FIG. 11 shows the results of Allen ANOVA according to an embodiment of the present invention.
Detailed Description
The preferred embodiments of the present invention will be described in conjunction with the accompanying drawings, and it will be understood that they are described herein for the purpose of illustration and explanation and not limitation.
The EMD-MPF denoising method for the MEMS gyro signal is provided by the embodiment. Decomposing an original signal into a plurality of intrinsic mode functions through empirical mode decomposition, dividing IMF into noise IMF, mixed IMF and information IMF through analysis and order selection, and finally obtaining a final de-noising signal through a method of eliminating noise and improving particle filtering.
The EMD method can be used for a self-adaptive signal decomposition algorithm of nonlinear and non-stationary signals, not only breaks through the limitation of Fourier transform, but also does not have the problem that wavelet basis functions are required to be preselected like wavelet transform, and has good time-frequency resolution and self-adaptability. Based on empirical mode decomposition, a complete data driving method is used for reconstructing a signal part, so that the effect of signal filtering is achieved; by applying the time-frequency domain FOG signal denoising method based on empirical mode decomposition and Allan variance, the navigation precision is effectively improved.
As shown in fig. 1, an EMD-MPF-based improved gyroscope signal denoising method includes:
s101: decomposing a noisy signal of a gyroscope into an intrinsic mode function and a residual signal;
s102: the Intrinsic Mode Function (IMF) is selected in order through the two determined identification parameters, and the intrinsic mode function is divided into a noise intrinsic mode function, a mixed intrinsic mode function and an information intrinsic mode function;
s103: abandoning the noise intrinsic mode function, reserving the information intrinsic mode function, and carrying out noise reduction processing on the mixed intrinsic mode function;
s104: and performing signal reconstruction on the mixed intrinsic mode function subjected to noise reduction and the reserved information intrinsic mode function to obtain a denoised gyroscope signal.
As an implementation manner that can be selected by the embodiment of the present invention, the decomposition of the noisy signal of the gyroscope into the intrinsic mode function and the residual signal is as follows:
a noisy signal of a gyroscope is decomposed into a plurality of intrinsic mode functions and a residual signal.
As a specific implementation manner of the embodiment of the present invention, a reconstruction formula in signal reconstruction of the noise-reduced mixed eigenmode function and the retained information eigenmode function is as follows:
Figure BDA0002189261260000071
wherein the content of the first and second substances,
Figure BDA0002189261260000072
representing a noise signal; m1And M2Respectively, are the identification parameters of the mobile phone,
Figure BDA0002189261260000073
representing a mixed eigenmode function; h is(i)(t) represents an information eigenmode function; r isL(t) denotes a residual signal, and MPF denotes a modified PF method.
As an implementation manner that can be selected by the embodiment of the present invention, the MPF is an improved PF method, and includes:
let the probability distribution of the predicted particle sample be denoted as p (x)i) I is more than or equal to 1 and less than or equal to N, and weight wi＞w0Particle sample x ofTIs denoted as p1(xi) I is more than or equal to 1 and less than or equal to T, namely p, sampling the rest particles xN-TIs denoted as q (x)i) N-T < i ≦ N, i.e. q, wiIs a weight, w0As weight threshold, both N and T are constants;
the K-L divergence between different particle samples was calculated as follows:
Figure BDA0002189261260000081
the introduction of the K-L divergence can better ensure the effectiveness and diversity of the particle sample set;
for small-weight particle samples, N-T random numbers u are generatedjIn the range uj∈(w0,1]，ujIs to use random function random in the program in the range (w)0,1]In the production of, DKLFor K-L divergence, the weight of the particle sample is updated:
Figure BDA0002189261260000082
particle sample x whose weight is to be updatedN-TSorting by weight down to large, i.e.
Figure BDA0002189261260000083
X is to bei+1The distance from the particle with the largest weight is denoted as S, and resampling is performed to generate a new particle as follows:
Figure BDA0002189261260000084
Figure BDA0002189261260000085
synthesizing two parts of particles, carrying out weight normalization, and completing the continuous iteration of the PF method, xiDenotes the ith particle, xi+1Denotes the i +1 th particle, xN-T+1Denotes the N-T +1 th particle, xNWhich represents the N-th particle, is,
Figure BDA0002189261260000086
representing new particles resulting from the resampling.
As an implementation manner that can be selected by the embodiment of the present invention, in the two determined identification parameters, the two identification parameters are M respectively1And M2Selecting and determining the identification parameter M1The method comprises the following steps: determining an identification parameter M using an autocorrelation function variance1。
As an optional implementation manner of the embodiment of the present invention, the determining the identification parameter M by using the variance of the autocorrelation function1The method comprises the following steps:
calculating respective corresponding autocorrelation functions according to the intrinsic mode function signals of different orders;
calculating the mean squared error of Euclidean distance between two self-correlation functions according to the self-correlation functions of the continuous intrinsic mode functions to obtain a calculation result MSED;
determining an identification parameter M from MSED1。
As an optional implementation manner of the embodiment of the present invention, the identifier parameter M is1In association with the value k and the value L,
k is more than or equal to 1 and less than or equal to [2L/3 ]]，[2L/3]Represents a maximum integer not exceeding 2L/3, thereby ensuring M1The value of (A) is too large to be L, and k and L are both natural numbers.
As an optional implementation manner of the embodiment of the present invention, the identifier parameter M is determined2The method comprises the following steps:
calculating the ButaChiya distance between the probability density function of the original signal and the probability density function of each intrinsic mode function, wherein BC is more than or equal to 0 and less than or equal to 1, BD is more than or equal to 0 and less than or equal to infinity, BD is the ButaChiya distance, and BC is the ButaChiya coefficient;
calculating separability of the Bartay-Chiya distance data between the probability density function of the original signal and the probability density function of each eigenmode function under different characteristics based on the power spectral density function;
determining an identification parameter M based on the separability2。
As an implementation manner that can be selected by the embodiment of the present invention, the selecting the order of the intrinsic mode function through the determined two identification parameters, and dividing the intrinsic mode function into a noise intrinsic mode function, a mixed intrinsic mode function, and an information intrinsic mode function includes:
1＜i＜M1time is a noise eigenmode function;
M1＜i＜M2then, is a mixed eigenmode function;
M2when i is less than L, the information is an intrinsic mode function, i represents the order of the intrinsic mode function
L represents the total order of the eigen-state function.
In a particular application scenario,
1. improved EMD-MPF method:
EMD is an adaptive spatio-temporal analysis method suitable for processing non-stationary nonlinear sequences. According to the method, through the iterative process of screening, the signals are decomposed into a series of Intrinsic Mode Functions (IMFs) which do not deviate from a time domain, so that the method has good time-frequency resolution and self-adaptability, can perfectly reconstruct the original signals, and has the potential of highlighting fine geological structures which may be ignored in the signals. At present EThe MD method has been successfully applied in the field of reducing signal noise. The eigenmode function must satisfy the following two requirements: (1) the extreme number and the zero-crossing number are equal to or different from each other by one at most; (2) at any point, the average of the envelope defined by the local maxima and the envelope defined by the local minima is zero. For IMF signals h with the quantity L obtained by decomposing the noisy signal x (t)(i)(t) and a residual signal rL(t), it can then be subjected to signal reconstruction of the form:
Figure BDA0002189261260000101
the idea of Particle Filtering (PF) is based on the Monte Carlo method (Monte Carlo methods), which uses a set of particles to represent the probability, and can be used on any form of state space model. The method is a process of approximately representing a probability density function by searching a group of random samples which are transmitted in a state space, and substituting an integral operation by a sample mean value to further obtain the minimum variance estimation of a system state. Because the method adds a layer of importance sampling thought on the basis of the Monte Carlo method, the posterior probability distribution of the system can be approximately represented by a group of samples, and the approximate result can be further used for estimating the state of the nonlinear system. The general procedure for the PF method is as follows:
step 1, initializing state quantity: the initial state is modeled in space by a large number of particles according to a prior probability distribution.
Step 2, a prediction stage: each particle gets a predicted particle according to the state transition equation.
Step 3, a correction stage: the predicted particles are evaluated, and the closer the state is to the actual state, the greater the weight is given to the particles.
Step 4, resampling stage: and screening the particles according to the weight of the particles, wherein the particles with larger weight and a part of the particles with smaller weight are reserved in the screening process.
Step 5, a filtering stage: and substituting the resampled particles into new predicted particles of the state transition equation, namely returning to the step 2 for circulation.
In the traditional EMD method, an original signal is decomposed to obtain a series of IMFs with frequencies distributed from high to low, and generally, noise is considered to exist in a high frequency band basically, so that part of IMFs in the high frequency band can be directly deleted and then recombined to obtain a de-noised signal. Although the PF method is well free from the constraint that the random quantity must satisfy the gaussian distribution when solving the nonlinear filtering problem, the problem is that a large number of samples are required to approximate the posterior probability density of the system well, that is, a large number of effective particles with diversity are required, and the more complicated the actual environment is, the more particles are required, which results in the higher the complexity of the algorithm.
2. Improved IMF order selection method:
the EMD method can decompose a noisy signal into several IMF components of different scales and a residual. Generally, it is known that a noise signal is mainly concentrated in a high frequency part, and the composition of the IMF can be generally divided into three components, i.e., a noise IMF, a hybrid IMF, and an information IMF. Now, for signal denoising rather than pure complete reconstruction, the main problem is how to distinguish correlated IMFs from uncorrelated IMFs, i.e. how to find the demarcation point of different IMF components is the key problem for denoising in this method. From the above, the noise signal is described again as follows:
Figure BDA0002189261260000111
wherein the content of the first and second substances,
Figure BDA0002189261260000112
representing a noise signal; m is a group of1And M2Two demarcation points described below, respectively;
Figure BDA0002189261260000113
represents a mixed IMF portion; h is(i)(t) represents an information IMF part; r isL(t) represents the residual signal.
2.1, determination of demarcation point M1:
the current problem is how to determine two demarcation points M1And M2. For the first parameter, the autocorrelation function variance is used for determination. In practical applications, the actual signal component in the noise signal is necessarily unknown. In other words, the noise in the noise signal is never completely known and removed, theoretically or practically. Therefore, the parameters can neither be determined by minimizing the mean square error of the target signal and the noise signal, nor by obtaining the respective signal-to-noise ratio of each component. The reconstructed signal of IMF is as follows:
Figure BDA0002189261260000121
the autocorrelation function can determine the correlation degree of the signal in different time domains, and according to the IMF signals of different orders, the respective corresponding autocorrelation function is calculated as follows:
Figure BDA0002189261260000122
then, the mean squared euclidean distance between the two is calculated according to the autocorrelation function of the continuous IMFs, where Pea is the correlation coefficient, and the calculation result of the last equation (5) is abbreviated as MSED, and is calculated as follows:
Figure BDA0002189261260000123
Figure BDA0002189261260000124
Figure BDA0002189261260000125
according to the statistical property of random noise, the autocorrelation function of the random noise is maximum only at the zero point, and the autocorrelation function of the random noise is quickly attenuated to be close to the zero value at other moments. The Euclidean distance is a common classification basis, and the variance of the autocorrelation function is introduced, so that the dimensionless condition under the autocorrelation function is considered, and the correlation on the time domain among different components is considered by the autocorrelation function, so that the interference of the Euclidean distance under different components under a single characteristic is reduced to a certain extent.
Finally, a first index parameter M is obtained1The following were determined:
Figure BDA0002189261260000126
wherein the value of k is set at 1 and [2L/3 ]]Is [2L/3 ]]Represents a maximum integer not exceeding 2L/3, and is set so as to ensure that M is1Is too large as L.
Through the analysis, according to the autocorrelation characteristic, if the IMF component of the noise body is the IMF component of the noise body, the random noise has a maximum value at a zero point, and can be approximately and rapidly reduced to zero in other time domains; in the case of the IMF component of the mixing information, the random noise will fluctuate significantly in the other time domains. Meanwhile, according to the difference between IMF components of the MSED calculation and description continuous time domain, the smaller the MSED value is, the corresponding h(i)(t) the smaller the specific gravity of the component; whether hybrid or informative IMF, their counterparts h (t) have high energy due to their large amount of useful information for MEMS gyroscopes. In summary, the calculated value of MSED can be used as the first indicative parameter.
2.2, determination of the demarcation point M2:
demarcation point M2The method is mainly used for identifying and distinguishing the information IMF and the hybrid IMF. To determine the second identification parameter, a baryta-curia distance (BD) between the power spectral density function (PDF) of the original signal and the PDF of each IMF is introduced. Bhattacharyya distance and Bhattacharyya coefficient a statistical scientist a.bhattacharyya who worked on the indian statistical institute in the 30's of the 20 th centuryNamed arya. Scholars propose to use euclidean distance as a separation identifier, but euclidean distance is obviously affected by the dimension of the sample; the mahalanobis distance method considers the relationship among various characteristics, eliminates the related interference among variables, is an indirect distinguishing method, and simultaneously has the function of possibly changing a tiny variable in an exaggerated way, thereby reducing the accuracy of the demarcation point. The babbit distance is usually used for probability distribution between two discrete samples, so that the separability between measurement classes is judged, the interference of correlation between variables is eliminated, and the method is a more direct distinguishing method. The barachian distance between the discrete probability distributions p and q is defined as follows:
BD(p,q)＝-ln[BC(p,q)] (9)，
Figure BDA0002189261260000131
wherein BC is called Bhattacharyya coefficient; and BC is more than or equal to 0 and less than or equal to 1 and BD is more than or equal to 0 and less than or equal to infinity.
The power spectral density function defines how the power of a signal or time series is distributed with frequency and is a good description of the data characteristics. Thus, the separability of the barachian distance data between the original signal and the PDF of each IMF under different characteristics is calculated as follows:
Figure BDA0002189261260000141
analyzing the above equation, the more noise is mixed in the IMF, the lower separability is compared with the original signal; in the case of "pure" information IMF, the higher the separability compared to the original signal. Therefore, M2The selection method comprises the following steps:
Figure BDA0002189261260000142
there is a view on the IMF component and the originalThe smaller the baryta-curia distance between the two PDFs of the start signal, the smaller the separability, that is, the more noise contained in the IMF component; conversely, the larger the barachian distance between the two PDFs, the smaller the similarity and the better the separability, i.e., the less noise contained in the IMF component. Therefore, the next point of the maximum value of the barytajiya distance is regarded as a boundary point, and the hybrid IMF component and the information IMF component can be effectively distinguished. In general, the demarcation point M2The determined IMF order is higher than the demarcation point M1The determined order, but there may be a situation where the IMF decomposed by the noisy signal is mostly noisy, resulting in M1At M2Then, the formula (10) is improved as follows, thereby ensuring the identification parameter M2The determined IMF order is higher than M1The determined order is:
Figure BDA0002189261260000143
in summary, M1And M2The IMF component obtained by EMD decomposition is divided into three parts by two identification parameters, wherein i is more than 1 and more than M1Then, the IMF component is discarded as the noise IMF component; m1＜i＜M2Then, considering as a mixed IMF component, further noise reduction processing is performed using the following improved particle filtering; m2If i is less than L, the time information IMF component is considered and retained.
3. Improved PF process:
in the traditional resampling process, namely, in each iteration process of the algorithm, particles are resampled according to the weight values of the particles, and the particles with smaller weight values are abandoned and replaced by the particles with larger weight values. The resampling process well solves the original degradation phenomenon in particle filtering, but also brings the problem of sample exhaustion. Therefore, an innovative resampling process is proposed in combination with the improvement of the K-L divergence. Setting weight threshold value of resampling process as w0If the number of particles above the weight threshold is T and the total number of particles is N, the conventional resampling process is to keep the weight higher than w0Of (2)And then generating N-T particles according to the weight resampling. This undermines the usefulness and diversity of the particle sample set. Now, the improved resampling process comprises the following specific steps:
1) let the probability distribution of the predicted particle sample be denoted as p (x)i) I is more than or equal to 1 and less than or equal to N; weighting wi＞w0Particle sample x ofTIs denoted as p1(xi) I is more than or equal to 1 and less than or equal to T; sampling the remaining particles xN-TIs denoted as q (x)i),N-T＜i≤N。
2) The K-L divergence between different particle samples was calculated as follows:
Figure BDA0002189261260000151
3) generating N-T random numbers u for small-weight particle samplesjIn the range uj∈(w0,1]Updating the weight of the particle sample:
Figure BDA0002189261260000152
4) particle sample x whose weight is to be updatedN-TSorting by weight down to large, i.e.
Figure BDA0002189261260000153
X is to bei+1The distance from the particle with the largest weight is denoted as S, and resampling is performed to generate a new particle as follows:
Figure BDA0002189261260000154
Figure BDA0002189261260000155
5) and integrating the two parts of particles, and carrying out weight normalization to complete the continuous iteration operation of the PF method.
The improved re-sampling process not only re-evaluates the weight of partial particles, but also increases the orderliness of the re-evaluation process by utilizing K-L divergence, so that the random distribution difference in the re-sampling process is reduced as much as possible, and the effectiveness and diversity of the particles are kept as much as possible, thereby improving the efficiency of the re-sampling process.
4. The noise reduction system flow of the improved method comprises the following steps:
based on the above improved process, the specific flow of the EMD-MPF denoising method proposed in this embodiment is described in fig. 2, and the execution process is divided into the following steps:
step 1: and decomposing the noisy signal x (t) of the MEMS gyroscope according to an EMD method to obtain a plurality of IMFs and a residual signal.
Step 2: by M1And M2The IMF is selected in order by two identification parameters, and is divided into three parts, namely noise IMF, mixed IMF and information IMF.
And step 3: discarding noise IMF; information IMF is reserved; the hybrid IMF is denoised using a modified PF method.
And 4, step 4: performing signal reconstruction on the mixed IMF and the information IMF after the noise reduction processing to obtain a final complete denoising result, wherein a signal reconstruction formula is as follows:
Figure BDA0002189261260000161
in the gyro signal denoising method based on EMD-MPF improvement, noise in a noise signal cannot be completely known and removed in theory or practice. Therefore, the parameters can neither be determined by minimizing the mean square error of the target signal and the noise signal, nor by obtaining the respective signal-to-noise ratio of each component. Therefore, according to the statistical characteristics of the random noise, only the autocorrelation function of the random noise is maximum at the zero point, and the autocorrelation function of the random noise is rapidly attenuated to be close to the zero value at other times. The Euclidean distance is a common classification basis, and the variance of the autocorrelation function is introduced, so that the dimensionless condition under the autocorrelation function is considered, and the time-domain correlation among different components is considered by the autocorrelation function, so that the interference of the Euclidean distance on different components under a single characteristic is reduced to a certain extent; according to the autocorrelation characteristic, if the IMF component is the noise main body, the random noise has a maximum value at a zero point, and can be approximately and rapidly reduced to zero in other time domains; in the case of the IMF component of the mixing information, the random noise will fluctuate significantly in the other time domains. After modification based on the related content, the IMF component with the main existence of noise and the information IMF can be quickly distinguished without knowing any actual signal component so as to determine the index parameter between the IMF component and the information IMF.
To determine the second identification parameter, a baryta-curia distance (BD) between the power spectral density function (PDF) of the original signal and the PDF of each IMF is introduced. The babbit distance is often used in the probability distribution between two discrete samples to determine separability between measurement classes, not only to exclude interference from correlation between variables, but also to be a more direct method of differentiation. If the smaller the barytajiya distance between the IMF component and the original signal PDF, the smaller the separability, i.e., the more noise contained in the IMF component; conversely, the larger the barytajiya distance between the two PDFs, the smaller the similarity and the more separable, i.e., the less noise contained in the IMF component. Therefore, the next point of the maximum value of the barytajiya distance is regarded as a boundary point, and the hybrid IMF component and the information IMF component can be effectively distinguished.
An innovative resampling process is proposed in combination with the improvement of the K-L divergence. Setting weight threshold value of resampling process as w0If the number of particles above the weight threshold is T and the total number of particles is N, the conventional resampling process is to keep the weight higher than w0And then resampling according to the weights to generate N-T particles. This undermines the usefulness and diversity of the particle sample set.
The implementation was verified experimentally as follows:
the experimental environment is an inertial navigation rotating platform, an inertial measurement unit of the platform is a full-attitude measurement sensing device IMU-300A, and the device consists of three-axis MEMS gyroscopes, three-axis MEMS accelerometers and three-axis magneto-resistance magnetometers. The apparatus is mounted on a two-axis motorized turntable and the system can measure absolute angular velocity and acceleration values on three axes X, Y, Z, respectively.
The effective bit of data is confirmed through experiment platform calibration standard in the experiment, and experimental system adopts the biax revolving stage, and the system includes: the navigation attitude reference system and the angle sensor can accurately control the rotation of the rotary table. The system can automatically calibrate, and provides relatively accurate information of the reference attitude angle through the output attitude angle of the navigation attitude reference system.
In order to verify the effectiveness of the method provided by the embodiment more clearly and comprehensively, two parts of experimental contents are set subsequently, wherein the first part adopts static data of the MEMS gyroscope; the second part employs dynamic data. In order to reflect the signal denoising effect of the improved method, the following 4 methods are respectively used for analyzing and comparing results, wherein the method I comprises the following steps: using conventional particle filtering; the second method comprises the following steps: using a traditional EMD method; the third method comprises the following steps: using a modified PF process; the method four comprises the following steps: the MED-MPF-based improved gyroscope denoising method provided by the embodiment is used.
3.1 testing static data of turntable
In the test preparation stage, after the system is powered on, firstly, the test system provided with the gyroscope is subjected to zero returning operation, secondly, preheating is carried out for about 5min, the sampling frequency of data is 100Hz, and the original data output by the gyroscope is collected after the system is stabilized; as shown in fig. 3, the static data of the gyroscope (taking the signal data of the X axis as an example) is acquired, the data length is 49428, and the duration is about 8 min.
First, the noise signal is decomposed by the EMD method, and a 15-order IMF signal and 1 signal residual are obtained as shown in fig. 4.
The autocorrelation function of each IMF signal is calculated according to the 15-order IMF signal and the first-order residual signal obtained by decomposition, and the result is shown in fig. 5. Simply analyzing an autocorrelation function, wherein the autocorrelation function is used for describing the correlation degree of random signals among values at any different time and is used for cross-correlation of the signals; since the autocorrelation coefficient of the random noise at the zero point is the maximum, and meanwhile, the gyro signal has certain correlation at the front and rear moments, the correlation of the random noise cannot be interrupted immediately, and the autocorrelation of the front and rear moments reflects the correlation of the random noise in the time domain to a certain extent, the correlation of the random noise and the useful signal can be judged to a certain extent by using the distance mean square difference between the autocorrelation functions of the continuous IMF signals, so that the purpose of distinguishing the IMF orders mainly containing the random noise is achieved.
The results obtained from fig. 5 and the M1 parameter determination method are shown in fig. 6.
The probability density function gives the probability that the signals have different amplitude values, the distribution condition of the amplitude values of the signals is well described, and the position of a second boundary point can be determined according to the Babbitt distance between the PDF of each-order IMF signal and the PDF of the original signal, so that the mixed IMF and the information IMF are distinguished. The probability density function relationship between each order of IMF and the original signal PDF is shown in fig. 7, and the determination of the M2 identification point is shown in fig. 8.
As shown in the boundary selection results of fig. 7 and fig. 9, it can be known that the IMFs before the 5 th-order IMF signal are basically noise IMFs, and can be directly discarded; a substantially noiseless signal after the 10 th order IMF signal; in the range from 5 th order to 10 th order, that is, the selected mixed IMF part, the improved particle filtering method of this embodiment is used for the part of signals to obtain the comparison result shown in fig. 10, and finally, the filtered result and the IMF signal whose information is dominant are reconstructed to obtain the final processing result.
The filtering result and the information lead the IMF signal to be reconstructed, and the comparison analysis is carried out according to the 4 methods mentioned before, and the result is shown in FIG. 11, so that the method provided by the embodiment has a relatively obvious effect, has a relatively large noise reduction amplitude compared with the original data and the other 3 methods, and is used for carrying out Allen variance analysis subsequently and calculating the signal-to-noise ratio and the mean square error of each method respectively in order to compare the experimental result more intuitively.
The Allen variance is a commonly used method for analyzing the gyro noise, and the method can easily perform detailed characterization and identification on the time domain on the statistical characteristics of various error sources, so that the effectiveness and the applicability of the implementation method to the gyro denoising can be further verified through the quantitative analysis of the Allen variance. By comparing the results in fig. 11, it can be seen that various errors obtained by the Allen analysis of variance are reduced to different degrees by using the method of the present embodiment.
The RMSE can well reflect the fluctuation condition of sample data, and the smaller the numerical value is, the smaller the fluctuation is, and the less noise is contained. The RMSE value of the method provided by the embodiment is reduced by about 91% compared with the original data, about 89% compared with the method 1, about 81% compared with the method 2, about 63% compared with the method 3, and the effect is very obvious. The signal-to-noise ratio reflects the noise content in the signal more directly, and generally, the larger the signal-to-noise ratio is, the smaller the noise mixed in the signal is. The signal-to-noise ratio of the method provided by the embodiment is improved by 20.96dB compared with the original signal, is improved by 19.01dB compared with the method 1, is improved by 14.62dB compared with the method 2, and is improved by 8.67dB compared with the method 3, which shows that the method has an obvious denoising effect on the MEMS gyro signal. The analysis results are shown in table 1.
Figure BDA0002189261260000191
Figure BDA0002189261260000201
Table 1 experimental results error analysis.
The embodiment provides a new denoising method combining EMD and improved PF aiming at the problem of random noise in the output of the MEMS gyroscope. Analyzing a plurality of IMF components obtained by EMD decomposition, calculating two decomposition points to obtain noise IMF, mixed IMF and information IMF, denoising the mixed IMF by using an improved PF method, and reconstructing the denoised mixed IMF and the information IMF to obtain a final denoised signal. In the experimental part, static data and dynamic data are respectively used, results of raw data and 4 denoising methods are compared, and it is found that the method provided by the embodiment has a certain reference value, noise in output signals of the MEMS gyroscope can be effectively removed, and signal quality is greatly improved.
The present embodiment has the following advantages:
1. compared with the traditional EMD method, a more detailed demarcation point selection mode is provided, the hierarchy is divided into three parts, and random noise is more targeted;
2. the second advantage is that the PF algorithm is improved by combining the K-L divergence, and an innovative resampling process is provided, so that the effectiveness and diversity of the particle sample set are kept;
3. the three-dominant empirical mode decomposition decomposes an original signal into a plurality of intrinsic mode functions, then divides IMF into noise IMF, mixed IMF and information IMF through analysis and order selection, and finally obtains a final de-noising signal through a method of eliminating noise and improving particle filtering.
Finally, it should be noted that: although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that changes may be made in the embodiments and/or equivalents thereof without departing from the spirit and scope of the invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (3)

1. An EMD-MPF-based improved gyroscope signal denoising method is characterized by comprising the following steps:
decomposing a noisy signal of a gyroscope into an intrinsic mode function and a residual signal;
the intrinsic mode function is selected in order through the two determined identification parameters, and the intrinsic mode function is divided into a noise intrinsic mode function, a mixed intrinsic mode function and an information intrinsic mode function;
abandoning the noise intrinsic mode function, reserving the information intrinsic mode function, and carrying out noise reduction processing on the mixed intrinsic mode function;
performing signal reconstruction on the mixed intrinsic mode function subjected to noise reduction processing and the retained information intrinsic mode function to obtain a denoised gyroscope signal;
the reconstruction formula for signal reconstruction of the mixed eigenmode function after noise reduction and the reserved information eigenmode function is as follows:
Figure FDA0003472696090000011
wherein the content of the first and second substances,
Figure FDA0003472696090000015
representing a noise signal; m1And M2Respectively, are the identification parameters of the mobile phone,
Figure FDA0003472696090000013
representing a mixed eigenmode function; h is(i)(t) represents an information eigenmode function; r isL(t) denotes a residual signal, MPF denotes a modified PF method;
the MPF is an improved PF process comprising:
let the probability distribution of the predicted particle sample be denoted as p (x)i) I is more than or equal to 1 and less than or equal to N, and weight wi＞w0Particle sample x ofTIs denoted as p1(xi) I is more than or equal to 1 and less than or equal to T, namely p, sampling the rest particles xN-TIs denoted as q (x)i) N-T < i ≦ N, i.e. q, wiIs a weight, w0As weight threshold, both N and T are constants;
the K-L divergence between different particle samples was calculated as follows:
Figure FDA0003472696090000014
generating N-T randoms for a small-weight particle sampleNumber ujIn the range of uj∈(w0,1]The weight of the particle sample is updated, DKLIs K-L divergence:
Figure FDA0003472696090000021
particle sample x whose weight is to be updatedN-TSorting by weight down to large, i.e.
Figure FDA0003472696090000022
X is to bei+1The distance from the particle with the largest weight is denoted as S, and resampling is performed to generate a new particle as follows:
Figure FDA0003472696090000023
Figure FDA0003472696090000024
synthesizing two parts of particles, carrying out weight normalization, and completing the continuous iteration of the PF method, xiDenotes the ith particle, xi+1Denotes the i +1 th particle, xN-T+1Denotes the N-T +1 th particle, xNWhich represents the N-th particle, is,
Figure FDA0003472696090000025
representing new particles resulting from the resampling;
in the two determined identification parameters, the two identification parameters are respectively M1And M2Selecting and determining the identification parameter M1The method comprises the following steps: determining an identification parameter M using an autocorrelation function variance1；
The determining of the identification parameter M using the variance of the autocorrelation function1The method comprises the following steps:
calculating respective corresponding autocorrelation functions according to the intrinsic mode function signals of different orders;
calculating the mean squared error of Euclidean distance between two self-correlation functions according to the self-correlation functions of the continuous intrinsic mode functions to obtain a calculation result MSED;
determining an identification parameter M from MSED1；
The identification parameter M1In association with the value k and the value L,
k is more than or equal to 1 and less than or equal to [2L/3 ]]，[2L/3]Represents a maximum integer not exceeding 2L/3, thereby ensuring that M1The value of (a) is too large to be L, and k and L are both natural numbers;
determining an identification parameter M2The method comprises the following steps:
calculating the ButaChiya distance between the probability density function of the original signal and the probability density function of each intrinsic mode function, wherein BC is more than or equal to 0 and less than or equal to 1, BD is more than or equal to 0 and less than or equal to infinity, BD is the ButaChiya distance, and BC is the ButaChiya coefficient;
calculating separability of the Bartay-Chiya distance data between the probability density function of the original signal and the probability density function of each eigenmode function under different characteristics based on the power spectral density function;
determining an identification parameter M based on the separability2。
2. The method for denoising an EMD-MPF-based improved gyroscope signal according to claim 1, wherein the decomposition of the noisy signal of the gyroscope into an eigenmode function and a residual signal is:
a noisy signal of a gyroscope is decomposed into a plurality of intrinsic mode functions and a residual signal.
3. The method of claim 1, wherein the order selection of the eigenmode functions by the two determined identification parameters is used to divide the eigenmode functions into a noise eigenmode function, a mixed eigenmode function and an information eigenmode function, and comprises:
1＜i＜M1time is a noise eigenmode function;
M1＜i＜M2then, is a mixed eigenmode function;
M2when i is less than L, the information is an intrinsic mode function, i represents the order of the intrinsic mode function
L represents the total order of the eigen-state function.
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