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CN112800831A - EMD filtering method and system for time-varying gravitational field - Google Patents

EMD filtering method and system for time-varying gravitational field Download PDF

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CN112800831A
CN112800831A CN202011553563.5A CN202011553563A CN112800831A CN 112800831 A CN112800831 A CN 112800831A CN 202011553563 A CN202011553563 A CN 202011553563A CN 112800831 A CN112800831 A CN 112800831A
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water height
equivalent water
height data
latitude
modal
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常克武
艾尚校
肖云
任飞龙
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Xi'an Aerospace Tianhui Data Technology Co ltd
Changan University
61540 Troops of PLA
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Xi'an Aerospace Tianhui Data Technology Co ltd
Changan University
61540 Troops of PLA
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Abstract

本发明公开了一种用于时变重力场的EMD滤波方法及系统。该用于时变重力场的EMD滤波方法包括：获取等效水高数据；等效水高数据是由时变重力场模型数据计算得到的；对等效水高数据按纬度带分别进行经验模态分解，得到有限个固有模态函数分量和一个残余分量；计算等效水高数据与各固有模态函数分量之间的互相关系数；将所有互相关系数中第一个局部极小值点对应的固有模态函数分量确定为混叠模态分量；基于混叠模态分量之后的固有模态函数分量与残余分量进行重构，得到去噪后的等效水高数据。本发明能增强噪声去除能力，提高滤波后的信号信噪比。

Figure 202011553563

The invention discloses an EMD filtering method and system for time-varying gravity field. The EMD filtering method for the time-varying gravity field includes: obtaining equivalent water height data; the equivalent water height data is calculated from the time-varying gravity field model data; state decomposition to obtain a finite number of intrinsic modal function components and a residual component; calculate the cross-correlation coefficient between the equivalent water height data and each intrinsic modal function component; set the first local minimum point in all the cross-correlation coefficients The corresponding natural mode function components are determined as aliased modal components; based on the natural mode function components and residual components after the aliased modal components, the denoised equivalent water height data is obtained. The invention can enhance the noise removal ability and improve the signal-to-noise ratio after filtering.

Figure 202011553563

Description

EMD filtering method and system for time-varying gravitational field
Technical Field
The invention relates to the field of satellite data filtering, in particular to an EMD filtering method and system for a time-varying gravity field.
Background
Due to the influences of instrument measurement errors of low-low tracking gravity measurement satellite loads, satellite orbit errors and the like, obvious north-south stripe noises exist in the result of surface quality change inverted by Level-2 time-varying gravity field model data, and therefore the influence of the stripe noises must be eliminated by filtering the time-varying gravity field model data.
At present, two methods for removing stripe noise aiming at time-varying gravity field model data are mainly used, one method is Gaussian filtering, and the effect of removing the noise is achieved by reducing the weight of a high-order bit coefficient in a spherical harmonic coefficient. The method suppresses real geophysical signals while removing noise, and the spatial resolution of the gravity field model is reduced. The other is a decorrelation method, which achieves the purpose of removing noise by subtracting the correlation between bit coefficients. The method has good noise removing effect in high latitude areas, but the filtering effect in the area near the equator is not ideal. Therefore, the noise removal capability and the signal-to-noise ratio of the filtered signal of the current stripe noise removal method are to be improved.
Disclosure of Invention
Based on this, there is a need to provide an EMD filtering method and system for time-varying gravitational field to enhance the noise removal capability and improve the signal-to-noise ratio after filtering.
In order to achieve the purpose, the invention provides the following scheme:
a method of EMD filtering for a time-varying gravitational field, comprising:
acquiring equivalent water height data; the equivalent water height data is obtained by calculating time-varying gravity field model data;
respectively carrying out empirical mode decomposition on the equivalent water height data according to latitude zones to obtain a limited number of inherent modal function components and a residual component;
calculating a cross-correlation coefficient between the equivalent water height data and each inherent modal function component;
determining an inherent modal function component corresponding to a first local minimum value point in all cross-correlation coefficients as an aliasing modal component;
and reconstructing based on the inherent modal function component after the aliasing modal component and the residual component to obtain the equivalent water height data after denoising.
Optionally, the acquiring equivalent water height data specifically includes:
acquiring time-varying gravity field model data; the time-varying gravitational field model data is global time-varying gravitational field information acquired by a gravity measurement satellite;
and calculating to obtain equivalent water height data based on the time-varying gravity field model data.
Optionally, the empirical mode decomposition is performed on the equivalent water height data according to a latitude band, so as to obtain a limited number of inherent modal function components and a residual component, specifically:
Figure BDA0002858657830000021
wherein θ represents latitude, xθ(λ) represents the equivalent water height data at the λ -th sampling point on the θ latitude band, imfθ,i(λ) represents the i-th natural mode function component of the equivalent water height data decomposition at the λ -th sampling point on the theta latitude band, rθAnd (lambda) represents a residual component decomposed from equivalent water height data at a lambda-th sampling point on the theta latitude band, wherein lambda is the number of the sampling points, and n is the total number of inherent mode function components decomposed from the equivalent water height data in the theta latitude band.
Optionally, the calculating a cross-correlation coefficient between the equivalent water height data and each of the eigenmode function components specifically includes:
Figure BDA0002858657830000022
wherein θ represents latitude, xθData representing equivalent water height in the theta latitude band, imfθ,iThe component of the ith natural mode function, R (x), of the theta latitude band equivalent water height data decomposition is expressedθ,imfθ,i) Representing the cross-correlation coefficient, x, between the theta latitude band equivalent water height data and the ith eigenmode function componentθ(λ) represents the equivalent water height data at the λ -th sampling point on the θ latitude band, imfθ,i(lambda) represents the ith inherent modal function component decomposed by equivalent water height data at the lambda-th sampling point on the theta latitude band, lambda is the number of the sampling points, t represents the number of the sampling points on the theta latitude band,
Figure BDA0002858657830000023
represents the average value of the data of the equivalent water height of the latitude theta,
Figure BDA0002858657830000024
and (3) an average value of the ith natural mode function component of the equivalent water height data on the theta latitude band.
Optionally, before determining the natural mode function component corresponding to the first local minimum point in all the cross-correlation coefficients as an aliasing mode component, the method further includes:
judging whether local minimum values exist in all the cross-correlation coefficients;
if not, determining the first inherent modal function component as an aliasing modal component.
Optionally, reconstructing the intrinsic mode function component after the aliasing mode component and the residual component to obtain the denoised equivalent water height data, specifically:
Figure BDA0002858657830000031
wherein θ represents latitude, yθ(λ) represents the equivalent water height data at the λ -th sampling point on the denoised θ latitude band, imfθ,i(λ) represents the i-th natural mode function component of the equivalent water height data decomposition at the λ -th sampling point on the theta latitude band, rθ(λ) represents the latitude of θAnd the residual component is decomposed from the equivalent water height data at the lambda-th sampling point on the band, lambda is the number of the sampling points, n is the total number of the natural modal function components decomposed from the equivalent water height data at the theta latitude band, k represents the number of aliasing modal components, and k +1 represents the number of modal demarcation points.
The invention also provides an EMD filtering system for a time-varying gravitational field, comprising:
the equivalent water height data acquisition module is used for acquiring equivalent water height data; the equivalent water height data is obtained by calculating time-varying gravity field model data;
the modal decomposition module is used for respectively carrying out empirical modal decomposition on the equivalent water height data according to latitude zones to obtain a limited number of inherent modal function components and a residual component;
the cross correlation coefficient calculation module is used for calculating the cross correlation coefficient between the equivalent water height data and each inherent modal function component;
an aliasing modal component determining module, configured to determine an inherent modal function component corresponding to a first local minimum point in all cross-correlation coefficients as an aliasing modal component;
and the modal reconstruction module is used for reconstructing based on the inherent modal function component after the aliasing modal component and the residual component to obtain the equivalent water height data after denoising.
Optionally, the equivalent water height data obtaining module specifically includes:
the data acquisition unit is used for acquiring time-varying gravity field model data; the time-varying gravitational field model data is global time-varying gravitational field information acquired by a gravity measurement satellite;
and the equivalent water height calculating unit is used for calculating to obtain equivalent water height data based on the time-varying gravitational field model data.
Optionally, the mode decomposition module specifically includes:
Figure BDA0002858657830000041
wherein θ represents latitude, xθ(λ) represents the equivalent water height data at the λ -th sampling point on the θ latitude band, imfθ,i(λ) represents the i-th natural mode function component of the equivalent water height data decomposition at the λ -th sampling point on the theta latitude band, rθAnd (lambda) represents a residual component decomposed from equivalent water height data at a lambda-th sampling point on the theta latitude band, wherein lambda is the number of the sampling points, and n is the total number of inherent mode function components decomposed from the equivalent water height data in the theta latitude band.
Optionally, the cross-correlation coefficient calculating module specifically includes:
Figure BDA0002858657830000042
wherein θ represents latitude, xθData representing equivalent water height in the theta latitude band, imfθ,iThe component of the ith natural mode function, R (x), of the theta latitude band equivalent water height data decomposition is expressedθ,imfθ,i) Representing the cross-correlation coefficient, x, between the theta latitude band equivalent water height data and the ith eigenmode function componentθ(λ) represents the equivalent water height data at the λ -th sampling point on the θ latitude band, imfθ,i(lambda) represents the ith inherent modal function component decomposed by equivalent water height data at the lambda-th sampling point on the theta latitude band, lambda is the number of the sampling points, t represents the number of the sampling points on the theta latitude band,
Figure BDA0002858657830000043
represents the average value of the data of the equivalent water height of the latitude theta,
Figure BDA0002858657830000044
and (3) an average value of the ith natural mode function component of the equivalent water height data on the theta latitude band.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides an EMD filtering method and system for a time-varying gravity field, which are characterized in that empirical mode decomposition is respectively carried out on equivalent water height data according to a latitude band to obtain a limited number of inherent modal function components and a residual component, then cross-correlation coefficients between the equivalent water height data and the inherent modal function components are calculated, the inherent modal function component corresponding to a first local minimum value point in all the cross-correlation coefficients is determined as an aliasing modal component, and finally reconstruction is carried out on the basis of the inherent modal function component after the aliasing modal component and the residual component to obtain the de-noised equivalent water height data. Compared with the traditional decorrelation method, the method has stronger noise removing capability and higher signal-to-noise ratio of the filtered signal; compared with the traditional Gaussian smooth filtering, the method can better keep the real signal and obtain more accurate results; the method does not need prior information or an error model, can be directly applied to data of different months and different mechanisms, and has the advantage of universality.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
Fig. 1 is a flowchart of an EMD filtering method for a time-varying gravitational field according to an embodiment of the present invention;
fig. 2 is a diagram illustrating an implementation process of the EMD filtering method for a time-varying gravitational field according to an embodiment of the present invention;
FIG. 3 is a global mass variation graph for unfiltered time varying gravity field model data inversion;
FIG. 4 is a diagram showing imf component and r component decomposed by EMD with the equivalent water level of the latitude zone as the original signal (taking the equatorial section as an example);
FIG. 5 is a schematic diagram of a correlation coefficient of the original signal and imf components;
FIG. 6 is a schematic diagram of a filtered signal;
FIG. 7 is a graph comparing an original signal with a filtered signal;
fig. 8 is a global mass change diagram of time-varying gravity field model data inversion after EMD filtering.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Fig. 1 is a flowchart of an EMD filtering method for a time-varying gravitational field according to an embodiment of the present invention.
Referring to fig. 1, the EMD filtering method for a time-varying gravitational field according to the present embodiment includes:
step 101: acquiring equivalent water height data; the equivalent water height data is obtained by calculating time-varying gravity field model data. Specifically, the method comprises the following steps:
acquiring time-varying gravity field model data; the time-varying gravitational field model data is global time-varying gravitational field information acquired by a gravity measurement satellite; calculating to obtain equivalent water height data X ═ X (X) based on the time-varying gravity field model data1,x2,x3,…,xm)TWherein x isθAnd (3) representing equivalent water height data (equivalent water height value) along the theta-th latitude band, wherein m is the total number of the latitudes needing to be processed.
Step 102: and respectively carrying out empirical mode decomposition on the equivalent water height data according to a latitude zone to obtain a limited number of inherent modal function components and a residual component. Specifically, the method comprises the following steps:
for original signal xθPerforming Empirical Mode Decomposition (EMD), generating n intrinsic mode function (imf) components and a residual component r,
Figure BDA0002858657830000061
wherein θ represents latitude, xθ(λ) represents the equivalent water height data at the λ -th sampling point on the θ latitude band, imfθ,i(λ) represents the i-th natural mode function component of the equivalent water height data decomposition at the λ -th sampling point on the theta latitude band, rθAnd (lambda) represents a residual component decomposed from equivalent water height data at a lambda-th sampling point on the theta latitude band, wherein lambda is the number of the sampling points, and n is the total number of inherent mode function components decomposed from the equivalent water height data in the theta latitude band.
Step 103: and calculating a cross-correlation coefficient between the equivalent water height data and each inherent modal function component. Specifically, the method comprises the following steps:
calculating the original signal xθAnd each imfθ,iThe cross-correlation coefficient between the components is,
Figure BDA0002858657830000062
wherein θ represents latitude, xθData representing equivalent water height in the theta latitude band, imfθ,iThe component of the ith natural mode function, R (x), of the theta latitude band equivalent water height data decomposition is expressedθ,imfθ,i) Representing the cross-correlation coefficient, x, between the theta latitude band equivalent water height data and the ith eigenmode function componentθ(λ) represents the equivalent water height data at the λ -th sampling point on the θ latitude band, imfθ,i(lambda) represents the ith inherent modal function component decomposed by equivalent water height data at the lambda-th sampling point on the theta latitude band, lambda is the number of the sampling points, t represents the number of the sampling points on the theta latitude band,
Figure BDA0002858657830000071
represents the average value of the data of the equivalent water height of the latitude theta,
Figure BDA0002858657830000072
representing equivalence on theta latitude bandAverage value of the i-th natural mode function component of the water height data.
Step 104: and determining the inherent modal function component corresponding to the first local minimum value point in all the cross-correlation coefficients as an aliasing modal component. Specifically, the method comprises the following steps:
and judging whether local minimum values exist in all the cross-correlation coefficients. If yes, determining the inherent modal function component corresponding to the first local minimum value point (the first local minimum value point in all the cross correlation coefficients) in all the cross correlation coefficients as an aliasing modal component, and recording the aliasing modal component as imfkThen imfk+1Is the boundary between the noise mode and the signal mode. If not, k is set to 1, i.e., the first natural mode function component is determined to be an aliasing mode component, imf2Is the boundary between the noise mode and the signal mode.
Step 105: and reconstructing based on the inherent modal function component after the aliasing modal component and the residual component to obtain the equivalent water height data after denoising. The method specifically comprises the following steps:
Figure BDA0002858657830000073
wherein θ represents latitude, yθ(λ) represents the equivalent water height data at the λ -th sampling point on the denoised θ latitude band, imfθ,i(λ) represents the i-th natural mode function component of the equivalent water height data decomposition at the λ -th sampling point on the theta latitude band, rθ(lambda) represents the residual component decomposed from the equivalent water height data at the lambda-th sampling point on the theta latitude band, lambda is the number of the sampling points, n is the total number of the natural modal function components decomposed from the equivalent water height data in the theta latitude band, k represents the number of aliasing modal components, k +1 represents the number of modal demarcation points, imfkRepresenting aliasing modal components, imfk+1Representing the demarcation component of the noise mode and the signal mode. Finally, the denoised equivalent water height data can be recorded as Y ═ Y1,y2,y3,…,ym)T. The specific implementation of the EMD filtering method for time-varying gravitational fields is shown in fig. 2.
The EMD filtering method for time-varying gravitational fields described above is verified below.
The processed data are month 10 2005 and month 05 2008 data provided by CSRRL 06. The picture of 10 months in 2005 is the process and result of 1000 EMD iterations. The 2008 05 month is the process and result of 1000 and 2000 EMD iterations. (different month data were chosen in order to verify that the method gave good results for different month data, where 2008's 05 month data processed the equatorial profile using two iterations gave the same number of components, but there was still a slight difference, so the results shown in FIGS. 3-8 all differed).
Fig. 3 is a global mass change plot for unfiltered time-varying gravity field model data inversion, where part (a) of fig. 3 is a global mass change plot for unfiltered time-varying gravity field model data inversion at 10 months 2005; wherein part (b) of fig. 3 is a global quality map of an inversion of unfiltered time-varying gravity field variation model data of month 05 2008.
Fig. 4 is a diagram illustrating imf components and r components decomposed by EMD with the equivalent water height of the latitude band as the original signal (taking an equatorial section as an example), wherein part (a) of fig. 4 is imf components and r components decomposed 1000 times by EMD iteration of data month 10 2005, wherein part (b) of fig. 4 is imf components and r components decomposed 1000 times by EMD iteration of data month 05 2008, and wherein part (c) of fig. 4 is imf components and r components decomposed 2000 times by EMD iteration of data month 05 2008.
Fig. 5 is a schematic diagram of correlation coefficients of the original signal and the imf component obtained by calculation, where in part (a) of fig. 5, correlation coefficients of the original signal and the imf component obtained by performing EMD iteration 1000 times for data of month 10 2005 are schematically illustrated, where in part (b) of fig. 5, correlation coefficients of the original signal and the imf component obtained by performing EMD iteration 1000 times for data of month 05 2008 are schematically illustrated, and where in part (c) of fig. 5, correlation coefficients of the original signal and the imf component obtained by performing EMD iteration 2000 times for data of month 05 2008 are schematically illustrated.
Fig. 6 is a schematic diagram of filtered signals, where part (a) of fig. 6 is a schematic diagram of filtered signals for 1000 EMD iterations for data in month 10 2005, where part (b) of fig. 6 is a schematic diagram of filtered signals for 1000 EMD iterations for data in month 05 2008, and where part (c) of fig. 6 is a schematic diagram of filtered signals for 2000 EMD iterations for data in month 05 2008.
Fig. 7 is a graph comparing an original signal and a filtered signal, in which part (a) of fig. 7 is a graph comparing an original signal and a filtered signal at 1000 iterations of data EMD at 10 months 2005, in which part (b) of fig. 7 is a graph comparing an original signal and a filtered signal at 1000 iterations of data EMD at 05 months 2008, and in which part (c) of fig. 7 is a graph comparing an original signal and a filtered signal at 2000 iterations of data EMD at 05 months 2008.
Fig. 8 is a global mass change image of time-varying gravity field model data inversion after EMD filtering, where part (a) of fig. 8 is a global mass change image of time-varying gravity field model data inversion after EMD iteration of 1000 times EMD filtering for data in month 10 2005, where part (b) of fig. 8 is a global mass change image of time-varying gravity field model data inversion after EMD iteration of 1000 times EMD filtering for data in month 05 2008, and where part (c) of fig. 8 is a global mass change image of time-varying gravity field model data inversion after EMD iteration of 2000 times EMD filtering for data in month 05 2008.
Compared with the traditional decorrelation method, the EMD filtering method for the time-varying gravity field provided by the embodiment has the advantages that the noise removing capability is stronger, and the signal-to-noise ratio of the filtered signal is higher; compared with the traditional Gaussian smooth filtering, the method can better keep the real signal and obtain more accurate results; the method does not need prior information or an error model, can be directly applied to data of different months and different mechanisms, and has the advantage of universality; the method is simple to use, and the separation of noise and signals is realized by a demarcation point selection algorithm according to original data without manually setting parameters.
The invention also provides an EMD filtering system for a time-varying gravitational field, comprising:
the equivalent water height data acquisition module is used for acquiring equivalent water height data; the equivalent water height data is obtained by calculating time-varying gravity field model data.
And the modal decomposition module is used for performing empirical modal decomposition on the equivalent water height data according to latitude zones to obtain a limited number of inherent modal function components and a residual component.
And the cross-correlation coefficient calculation module is used for calculating the cross-correlation coefficient between the equivalent water height data and each inherent modal function component.
And the aliasing modal component determining module is used for determining the inherent modal function component corresponding to the first local minimum value point in all the cross-correlation coefficients as the aliasing modal component.
And the modal reconstruction module is used for reconstructing based on the inherent modal function component after the aliasing modal component and the residual component to obtain the equivalent water height data after denoising.
As an optional implementation manner, the equivalent water level data obtaining module specifically includes:
the data acquisition unit is used for acquiring time-varying gravity field model data; the time-varying gravitational field model data is global time-varying gravitational field information acquired by a gravity measurement satellite.
And the equivalent water height calculating unit is used for calculating to obtain equivalent water height data based on the time-varying gravitational field model data.
As an optional implementation manner, the modal decomposition module specifically includes:
Figure BDA0002858657830000101
wherein θ represents latitude, xθ(λ) represents the equivalent water height data at the λ -th sampling point on the θ latitude band, imfθ,i(λ) represents the i-th natural mode function component of the equivalent water height data decomposition at the λ -th sampling point on the theta latitude band, rθAnd (lambda) represents a residual component decomposed from equivalent water height data at a lambda-th sampling point on the theta latitude band, wherein lambda is the number of the sampling points, and n is the total number of inherent mode function components decomposed from the equivalent water height data in the theta latitude band.
As an optional implementation manner, the cross-correlation coefficient calculation module specifically includes:
Figure BDA0002858657830000102
wherein θ represents latitude, xθData representing equivalent water height in the theta latitude band, imfθ,iThe component of the ith natural mode function, R (x), of the theta latitude band equivalent water height data decomposition is expressedθ,imfθ,i) Representing the cross-correlation coefficient, x, between the theta latitude band equivalent water height data and the ith eigenmode function componentθ(λ) represents the equivalent water height data at the λ -th sampling point on the θ latitude band, imfθ,i(lambda) represents the ith inherent modal function component decomposed by equivalent water height data at the lambda-th sampling point on the theta latitude band, lambda is the number of the sampling points, t represents the number of the sampling points on the theta latitude band,
Figure BDA0002858657830000103
represents the average value of the data of the equivalent water height of the latitude theta,
Figure BDA0002858657830000104
and (3) an average value of the ith natural mode function component of the equivalent water height data on the theta latitude band.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (10)

1.一种用于时变重力场的EMD滤波方法，其特征在于，包括：1. an EMD filtering method for time-varying gravity field, is characterized in that, comprises: 获取等效水高数据；所述等效水高数据是由时变重力场模型数据计算得到的；Obtaining equivalent water height data; the equivalent water height data is calculated from time-varying gravity field model data; 对所述等效水高数据按纬度带分别进行经验模态分解，得到有限个固有模态函数分量和一个残余分量；Perform empirical mode decomposition on the equivalent water height data according to the latitude band, and obtain a finite number of intrinsic mode function components and a residual component; 计算所述等效水高数据与各所述固有模态函数分量之间的互相关系数；calculating the cross-correlation coefficient between the equivalent water height data and each of the natural mode function components; 将所有互相关系数中第一个局部极小值点对应的固有模态函数分量确定为混叠模态分量；Determine the intrinsic modal function component corresponding to the first local minimum point in all the cross-correlation coefficients as the aliased modal component; 基于所述混叠模态分量之后的固有模态函数分量与所述残余分量进行重构，得到去噪后的等效水高数据。Reconstruction is performed based on the intrinsic modal function component after the aliased modal component and the residual component to obtain denoised equivalent water height data. 2.根据权利要求1所述的一种用于时变重力场的EMD滤波方法，其特征在于，所述获取等效水高数据，具体包括：2. a kind of EMD filtering method for time-varying gravity field according to claim 1, is characterized in that, described obtaining equivalent water height data, specifically comprises: 获取时变重力场模型数据；所述时变重力场模型数据是由重力测量卫星获取的全球时变重力场信息；Obtaining time-varying gravity field model data; the time-varying gravity field model data is the global time-varying gravity field information acquired by a gravimetric satellite; 基于所述时变重力场模型数据计算得到等效水高数据。Equivalent water height data is calculated based on the time-varying gravity field model data. 3.根据权利要求1所述的一种用于时变重力场的EMD滤波方法，其特征在于，所述对所述等效水高数据按纬度带分别进行经验模态分解，得到有限个固有模态函数分量和一个残余分量，具体为：3. a kind of EMD filtering method for time-varying gravitational field according to claim 1, is characterized in that, described to described equivalent water height data respectively carry out empirical mode decomposition by latitude band, obtain finite inherent Modal function components and a residual component, specifically:
Figure FDA0002858657820000011
Figure FDA0002858657820000011
 其中，θ表示纬度，xθ(λ)表示θ纬度带上第λ个采样点处的等效水高数据，imfθ,i(λ)表示θ纬度带上第λ个采样点处的等效水高数据分解出的第i个固有模态函数分量，rθ(λ)表示θ纬度带上第λ个采样点处的等效水高数据分解出的残余分量，λ为采样点编号，n为θ纬度带等效水高数据分解出的固有模态函数分量的总个数。Among them, θ represents the latitude, x θ (λ) represents the equivalent water height data at the λth sampling point on the θ latitude band, and imf θ,i (λ) represents the equivalent water height at the λth sampling point on the θ latitude band. The i-th natural mode function component decomposed from the water height data, r θ (λ) represents the residual component decomposed from the equivalent water height data at the λth sampling point on the θ latitude band, λ is the sampling point number, n It is the total number of natural mode function components decomposed from the equivalent water height data in the latitude zone of theta. 4.根据权利要求1所述的一种用于时变重力场的EMD滤波方法，其特征在于，所述计算所述等效水高数据与各所述固有模态函数分量之间的互相关系数，具体为：4. A kind of EMD filtering method for time-varying gravity field according to claim 1, is characterized in that, described calculating the mutual relation between described equivalent water height data and each described natural mode function component number, specifically:
Figure FDA0002858657820000021
Figure FDA0002858657820000021
 其中，θ表示纬度，xθ表示θ纬度带等效水高数据，imfθ,i表示θ纬度带等效水高数据分解出的第i个固有模态函数分量，R(xθ,imfθ,i)表示θ纬度带等效水高数据与第i个固有模态函数分量之间的互相关系数，xθ(λ)表示θ纬度带上第λ个采样点处的等效水高数据，imfθ,i(λ)表示θ纬度带上第λ个采样点处的等效水高数据分解出的第i个固有模态函数分量，λ为采样点编号，t表示θ纬度带上采样点个数，
Figure FDA0002858657820000022
表示θ纬度带等效水高数据的平均值,
Figure FDA0002858657820000023
表示θ纬度带上等效水高数据的第i个固有模态函数分量的平均值。Among them, θ represents the latitude, x θ represents the equivalent water height data with the latitude θ, imf θ, i represents the i-th natural mode function component decomposed from the equivalent water height data with the latitude θ, R(x θ , imf θ ,i ) represents the cross-correlation coefficient between the equivalent water height data in the θ latitude belt and the i-th natural mode function component, x θ (λ) represents the equivalent water height data at the λth sampling point in the θ latitude belt , imf θ,i (λ) represents the i-th intrinsic modal function component decomposed from the equivalent water height data at the λ-th sampling point on the θ-latitude band, λ is the sampling point number, and t represents the up-sampling in the θ-latitude band number of points,
Figure FDA0002858657820000022
represents the mean value of the equivalent water height data in the latitude zone of theta,
Figure FDA0002858657820000023
Represents the mean value of the i-th natural mode function component of the equivalent water height data in the theta latitude band. 5.根据权利要求1所述的一种用于时变重力场的EMD滤波方法，其特征在于，在所述将所有互相关系数中第一个局部极小值点对应的固有模态函数分量确定为混叠模态分量之前，还包括：5. a kind of EMD filtering method for time-varying gravitational field according to claim 1, is characterized in that, in the described natural mode function component corresponding to the first local minimum point in all the cross-correlation coefficients Before being determined as aliased modal components, also include: 判断所有互相关系数中是否存在局部极小值；Determine whether there is a local minimum in all the cross-correlation coefficients; 若否，则将第一个固有模态函数分量确定为混叠模态分量。If not, the first natural mode function component is determined to be the aliased mode component. 6.根据权利要求1所述的一种用于时变重力场的EMD滤波方法，其特征在于，所述基于所述混叠模态分量之后的固有模态函数分量与所述残余分量进行重构，得到去噪后的等效水高数据，具体为：6 . The EMD filtering method for a time-varying gravity field according to claim 1 , wherein the intrinsic modal function component based on the aliased modal component and the residual component are repeated. 7 . to obtain the equivalent water height data after denoising, specifically:
Figure FDA0002858657820000024
Figure FDA0002858657820000024
 其中，θ表示纬度，yθ(λ)表示去噪后θ纬度带上第λ个采样点处的等效水高数据，imfθ,i(λ)表示θ纬度带上第λ个采样点处的等效水高数据分解出的第i个固有模态函数分量，rθ(λ)表示θ纬度带上第λ个采样点处的等效水高数据分解出的残余分量，λ为采样点编号，n为θ纬度带等效水高数据分解出的固有模态函数分量的总个数，k表示混叠模态分量的编号，k+1表示模态分界点的编号。Among them, θ represents the latitude, y θ (λ) represents the equivalent water height data at the λ-th sampling point on the θ-latitude band after denoising, and imf θ,i (λ) represents the λ-th sampling point on the θ-latitude band. The i- th natural modal function component decomposed from the equivalent water height data of the number, n is the total number of natural modal function components decomposed from the equivalent water height data in the θ latitude zone, k represents the number of aliased modal components, and k+1 represents the number of modal demarcation points. 7.一种用于时变重力场的EMD滤波系统，其特征在于，包括：7. A kind of EMD filtering system for time-varying gravity field, is characterized in that, comprises: 等效水高数据获取模块，用于获取等效水高数据；所述等效水高数据是由时变重力场模型数据计算得到的；The equivalent water height data acquisition module is used to obtain the equivalent water height data; the equivalent water height data is calculated from the time-varying gravity field model data; 模态分解模块，用于对所述等效水高数据按纬度带分别进行经验模态分解，得到有限个固有模态函数分量和一个残余分量；The modal decomposition module is used to perform empirical modal decomposition on the equivalent water height data according to the latitude band, to obtain a limited number of intrinsic modal function components and a residual component; 互相关系数计算模块，用于计算所述等效水高数据与各所述固有模态函数分量之间的互相关系数；a cross-correlation coefficient calculation module, used for calculating the cross-correlation coefficient between the equivalent water height data and each of the intrinsic modal function components; 混叠模态分量确定模块，用于将所有互相关系数中第一个局部极小值点对应的固有模态函数分量确定为混叠模态分量；The aliasing modal component determination module is used to determine the intrinsic modal function component corresponding to the first local minimum point in all the cross-correlation coefficients as the aliasing modal component; 模态重构模块，用于基于所述混叠模态分量之后的固有模态函数分量与所述残余分量进行重构，得到去噪后的等效水高数据。The modal reconstruction module is configured to reconstruct based on the intrinsic modal function component after the aliased modal component and the residual component to obtain denoised equivalent water height data. 8.根据权利要求7所述的一种用于时变重力场的EMD滤波系统，其特征在于，所述等效水高数据获取模块，具体包括：8. a kind of EMD filtering system for time-varying gravity field according to claim 7, is characterized in that, described equivalent water height data acquisition module, specifically comprises: 数据获取单元，用于获取时变重力场模型数据；所述时变重力场模型数据是由重力测量卫星获取的全球时变重力场信息；a data acquisition unit for acquiring time-varying gravity field model data; the time-varying gravity field model data is the global time-varying gravity field information acquired by a gravity measurement satellite; 等效水高计算单元，用于基于所述时变重力场模型数据计算得到等效水高数据。An equivalent water height calculation unit, configured to calculate and obtain equivalent water height data based on the time-varying gravity field model data. 9.根据权利要求7所述的一种用于时变重力场的EMD滤波系统，其特征在于，所述模态分解模块，具体为：9. a kind of EMD filtering system for time-varying gravity field according to claim 7, is characterized in that, described modal decomposition module, is specially:
Figure FDA0002858657820000031
Figure FDA0002858657820000031
 其中，θ表示纬度，xθ(λ)表示θ纬度带上第λ个采样点处的等效水高数据，imfθ,i(λ)表示θ纬度带上第λ个采样点处的等效水高数据分解出的第i个固有模态函数分量，rθ(λ)表示θ纬度带上第λ个采样点处的等效水高数据分解出的残余分量，λ为采样点编号，n为θ纬度带等效水高数据分解出的固有模态函数分量的总个数。Among them, θ represents the latitude, x θ (λ) represents the equivalent water height data at the λth sampling point on the θ latitude band, and imf θ,i (λ) represents the equivalent water height at the λth sampling point on the θ latitude band. The i-th natural mode function component decomposed from the water height data, r θ (λ) represents the residual component decomposed from the equivalent water height data at the λth sampling point on the θ latitude band, λ is the sampling point number, n It is the total number of natural mode function components decomposed from the equivalent water height data in the latitude zone of theta. 10.根据权利要求7所述的一种用于时变重力场的EMD滤波系统，其特征在于，所述互相关系数计算模块，具体为：10. a kind of EMD filtering system for time-varying gravity field according to claim 7, is characterized in that, described cross-correlation coefficient calculation module is specifically:
Figure FDA0002858657820000041
Figure FDA0002858657820000041
 其中，θ表示纬度，xθ表示θ纬度带等效水高数据，imfθ,i表示θ纬度带等效水高数据分解出的第i个固有模态函数分量，R(xθ,imfθ,i)表示θ纬度带等效水高数据与第i个固有模态函数分量之间的互相关系数，xθ(λ)表示θ纬度带上第λ个采样点处的等效水高数据，imfθ,i(λ)表示θ纬度带上第λ个采样点处的等效水高数据分解出的第i个固有模态函数分量，λ为采样点编号，t表示θ纬度带上采样点个数，
Figure FDA0002858657820000042
表示θ纬度带等效水高数据的平均值,
Figure FDA0002858657820000043
表示θ纬度带上等效水高数据的第i个固有模态函数分量的平均值。Among them, θ represents the latitude, x θ represents the equivalent water height data with the latitude θ, imf θ, i represents the i-th natural mode function component decomposed from the equivalent water height data with the latitude θ, R(x θ , imf θ ,i ) represents the cross-correlation coefficient between the equivalent water height data in the θ latitude belt and the i-th natural mode function component, x θ (λ) represents the equivalent water height data at the λth sampling point in the θ latitude belt , imf θ,i (λ) represents the i-th intrinsic modal function component decomposed from the equivalent water height data at the λ-th sampling point on the θ-latitude band, λ is the sampling point number, and t represents the up-sampling in the θ-latitude band number of points,
Figure FDA0002858657820000042
represents the mean value of the equivalent water height data in the latitude zone of theta,
Figure FDA0002858657820000043
Represents the mean value of the i-th natural mode function component of the equivalent water height data in the theta latitude band.
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