CN114047510A - Low-sidelobe forest TomosAR nonparametric spectrum estimation method and system - Google Patents

Low-sidelobe forest TomosAR nonparametric spectrum estimation method and system Download PDF

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CN114047510A
CN114047510A CN202111242996.3A CN202111242996A CN114047510A CN 114047510 A CN114047510 A CN 114047510A CN 202111242996 A CN202111242996 A CN 202111242996A CN 114047510 A CN114047510 A CN 114047510A
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汪友军
彭星
龙诗琳
江俊池
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China University of Geosciences
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Abstract

The invention relates to the field of remote sensing image processing, and provides a low-sidelobe forest TomosAR nonparametric spectrum estimation method and system, which comprises the following steps: s1: acquiring N-scene SLC image data, and preprocessing the SLC image data to obtain related initial variables; s2: obtaining an optimal estimation covariance matrix through iterative calculation of the related initial variables; s3: and performing nonparametric spectrum estimation through the optimal estimation covariance matrix to obtain a low side lobe chromatographic spectrum. The invention linearly combines the eigenvalue of the covariance matrix and the logarithm value of the corresponding eigenvector, and fully excavates the effective information contained in the covariance matrix to reflect the main characteristics of the target; the problem that the uniformity of the sample covariance matrix and the real covariance matrix cannot be guaranteed due to the fact that the sample covariance matrix is directly utilized in the prior art is solved, the influence of imaging noise on spectrum estimation is considered, the interpretation difficulty of chromatographic spectra is reduced, and the precision of parameter inversion is improved.

Description

Low-sidelobe forest TomosAR nonparametric spectrum estimation method and system
Technical Field
The invention relates to the field of remote sensing image processing, in particular to a low-sidelobe forest TomosAR nonparametric spectrum estimation method and system.
Background
TomosAR three-dimensional imaging actually acquires the distribution of backscattering signals of a target ground object in the height direction, so that the TomosAR three-dimensional imaging can be regarded as a problem of spectral estimation. The nonparametric spectrum estimation method does not need any prior information, and is high in calculation efficiency. And the parameter spectrum estimation needs some prior information of the known scattering scene, such as the number of scatterers in each resolution unit. However, in forest regions, it is almost impossible to accurately estimate the number of scatterers. In addition, the sparse spectrum estimation algorithm is suitable for sparse or compressible signals, and forest canopy backscatter signals are continuous, so sparse bases such as wavelet sparse bases are required to be used for sparse expression of forest backscatter signals, and the method is huge in calculation amount.
In forest regions, nonparametric spectral estimation methods are often applied for forest three-dimensional imaging. In the algorithm, the algorithms such as FFT, Beamforming, Capon and the like have low resolution, and the identification of different scatterers in each resolution unit can be influenced. In order to solve this problem, some researchers have proposed an iterative adaptive (IAA) SAR tomographic three-dimensional imaging algorithm. The method calculates the maximum likelihood estimation value of the covariance matrix through a loop iteration process so as to carry out SAR tomography, and the SAR tomography result is more accurate. However, the IAA method is still susceptible to noise, and inevitably generates side lobes, which affect accurate interpretation of the chromatogram, thereby reducing accuracy of the inversion of the subsurface topography.
The above is only for the purpose of assisting understanding of the technical aspects of the present invention, and does not represent an admission that the above is prior art.
Disclosure of Invention
The invention mainly aims to solve the technical problems that in the prior art, covariance matrix estimation is inaccurate, more side lobes are easy to appear in a chromatographic spectrum, and chromatographic spectrum interpretation and parameter inversion are influenced and inaccurate.
In order to achieve the aim, the invention provides a low sidelobe forest TomosAR nonparametric spectrum estimation method, which comprises the following steps:
s1: acquiring N-scene SLC image data, and preprocessing the SLC image data to obtain related initial variables;
s2: obtaining an optimal estimation covariance matrix through iterative calculation of the related initial variables;
s3: and performing nonparametric spectrum estimation through the optimal estimation covariance matrix to obtain a low side lobe chromatographic spectrum.
Preferably, step S1 is specifically:
s11: performing single-view complex image sequence registration, flat ground removing effect and phase compensation operation on the SLC image data to obtain denoised SLC image data, wherein the phase compensation operation comprises the following steps: declivity, atmospheric disturbance and orbit error removal;
s12: performing multi-view processing on the denoised SLC image data to obtain a sample covariance matrix R, wherein the calculation formula is as follows:
Figure BDA0003319876690000021
wherein L represents a multi-view, U represents an observation vector, (-)HRepresents a conjugate transpose;
s13: and calculating a characteristic vector set e and a characteristic value set lambda of the sample covariance matrix, wherein the calculation formula is as follows:
[e,λ]＝eig(R)
wherein, the characteristic vector set e ═ { e ] of the sample covariance matrixn,n＝1,…,N}，enRepresenting the eigenvector of the sample covariance matrix corresponding to the nth SLC image data; eigenvalue set λ ═ λ of sample covariance matrixn,n＝1,…,N}，λnRepresenting the eigenvalue of the sample covariance matrix corresponding to the nth SLC image data; n represents the total number of the SLC image data, and is a positive integer greater than 1;
s14: and calculating to obtain a characteristic value constraint factor set mu through the characteristic vector set e and the characteristic value set lambda, wherein the calculation formula is as follows:
Figure BDA0003319876690000022
wherein the characteristic value constrains the factor setμ＝{μn,n＝1,…,N}，μnAnd representing the characteristic value constraint factor corresponding to the nth SLC image data.
Preferably, the relevant initial variables include: the method comprises the steps of setting an eigenvalue set e of a sample covariance matrix, setting an eigenvalue set lambda of the sample covariance matrix and a eigenvalue constraint factor set mu.
Preferably, step S2 is specifically:
s21: iterative computation of characteristic coefficients I by means of said correlated initial variable loopnThe calculation formula is as follows:
Figure BDA0003319876690000023
wherein λ isnRepresenting the eigenvalue, mu, of the sample covariance matrix corresponding to the nth SLC image datanRepresenting a characteristic value constraint factor, lambda, corresponding to the nth view SLC image datakRepresenting the eigenvalue, mu, of the sample covariance matrix corresponding to the kth view SLC image datakRepresenting a characteristic value constraint factor corresponding to the k view SLC image data; n represents the total number of the SLC image data, and is a positive integer greater than 1;
s22: by said characteristic coefficient InCalculating the optimal estimation covariance matrix by loop iteration
Figure BDA0003319876690000031
The calculation formula is as follows:
Figure BDA0003319876690000032
wherein e isnAnd representing the eigenvector of the sample covariance matrix corresponding to the nth SLC image data.
Preferably, the calculation formula of the low side lobe chromatogram in step S3 is:
Figure BDA0003319876690000033
wherein the content of the first and second substances,
Figure BDA0003319876690000034
represents the optimal estimated covariance matrix, a ═ a (z)1),a(z2),…,a(zD)]TTo map the matrix, zdRepresents the d-th altitude, and T is a transpose; a (z)d)＝[exp(jkz(1)zd),exp(jkz(2)zd),…,exp(jkz(N)zd)]TIs the d mapping vector of the mapping matrix A, j is the complex imaginary symbol;
Figure BDA0003319876690000035
represents the vertical wave number, b⊥nIs the vertical baseline, W, between the nth SLC image data and the main imageLDenotes wavelength, r denotes slope distance, and θ denotes incident angle.
A low sidelobe forest TomosAR nonparametric spectrum estimation system comprises:
a related initial variable acquisition module, configured to acquire N-scene SLC image data, and pre-process the SLC image data to obtain a related initial variable; n represents the total number of the SLC image data, and is a positive integer greater than 1;
the optimal estimation covariance matrix calculation module is used for obtaining an optimal estimation covariance matrix through the iterative calculation of the related initial variables;
and the low side lobe chromatographic spectrum acquisition module is used for carrying out nonparametric spectral estimation through the optimal estimation covariance matrix to acquire a low side lobe chromatographic spectrum.
The invention has the following beneficial effects:
1. carrying out linear combination on the eigenvalue of the covariance matrix and the logarithm value of the corresponding eigenvector of the covariance matrix, and fully mining effective information contained in the covariance matrix to reflect the main characteristics of a target;
2. the problem that the uniformity of the sample covariance matrix and the real covariance matrix cannot be guaranteed due to the fact that the sample covariance matrix is directly utilized in the prior art is solved, the influence of imaging noise on spectrum estimation is considered, the interpretation difficulty of chromatographic spectra is reduced, and the precision of parameter inversion is improved.
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FIG. 1 is a flow chart of a method according to an embodiment of the present invention;
FIG. 2 is a plot of the location of the region of interest and the spectral estimation profile line according to an embodiment of the present invention;
FIG. 3 is a plot of large height difference backscattered energy for an embodiment of the present invention;
FIG. 4 is a plot of the backscattered energy with a small height difference for an embodiment of the invention;
FIG. 5 is a chromatogram estimation of different polarization channels according to an embodiment of the present invention;
FIG. 6 is a system block diagram according to an embodiment of the present invention;
the implementation, functional features and advantages of the objects of the present invention will be further explained with reference to the accompanying drawings.
Detailed Description
It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Referring to fig. 1, the invention provides a low sidelobe forest TomoSAR nonparametric spectrum estimation method for carrying out SAR tomography three-dimensional imaging; the method linearly combines the eigenvalue of the covariance matrix and the logarithm value of the corresponding eigenvector, fully excavates effective information contained in the covariance matrix to reflect the main characteristics of a target, and obtains an optimal estimation result; the method makes up the problem that the uniformity of the sample covariance matrix and a real covariance matrix cannot be ensured by directly utilizing the sample covariance matrix in the prior art, considers the influence of imaging noise on spectrum estimation, and extracts the real characteristic information of the target scatterer;
the method specifically comprises the following steps:
s1: acquiring N-scene SLC image data, and preprocessing the SLC image data to obtain related initial variables;
s2: obtaining an optimal estimation covariance matrix through iterative calculation of the related initial variables;
s3: and performing nonparametric spectrum estimation through the optimal estimation covariance matrix to obtain a low side lobe chromatographic spectrum.
In this embodiment, step S1 specifically includes:
s11: performing single-view complex image sequence registration, flat ground removing effect and phase compensation operation on the SLC image data to obtain denoised SLC image data, wherein the phase compensation operation comprises the following steps: declivity, atmospheric disturbance and orbit error removal;
in the specific implementation, the single-view complex image sequence registration comprises coarse registration and fine registration, the registration method can select an image based on a region or a characteristic, and the main image is generally selected to be an image with a central time base line and a central space base line, so that the time decorrelation effect and the space decorrelation effect are reduced as much as possible, and the quality of an interferogram is ensured; the land leveling effect is mainly to remove the land leveling phase which is caused by the flat ground and has periodic change in the distance direction and the azimuth direction, and a frequency estimation method based on observation data or a frequency estimation method based on imaging geometric system parameters can be selected; the phase compensation can be phase compensation based on permanent Scatterer InSAR (PSInSAR) or phase compensation method based on Small Baseline set interference (SBAS);
s12: performing multi-view processing on the denoised SLC image data to obtain a sample covariance matrix R, wherein the calculation formula is as follows:
Figure BDA0003319876690000051
wherein L represents a multi-view, U represents an observation vector, (-)HRepresents a conjugate transpose;
s13: and calculating a characteristic vector set e and a characteristic value set lambda of the sample covariance matrix, wherein the calculation formula is as follows:
[e,λ]＝eig(R)
wherein, the characteristic vector set e ═ { e ] of the sample covariance matrixn,n＝1,…,N}，enRepresenting the eigenvector of the sample covariance matrix corresponding to the nth SLC image data; eigenvalue set λ ═ λ of sample covariance matrixn,n＝1,…,N}，λnIndicating correspondence of SLC image data of nth viewEigenvalues of the sample covariance matrix; n represents the total number of the SLC image data, and is a positive integer greater than 1;
s14: and calculating to obtain a characteristic value constraint factor set mu through the characteristic vector set e and the characteristic value set lambda, wherein the calculation formula is as follows:
Figure BDA0003319876690000052
wherein, the eigenvalue constraint factor set μ ═ { μ ═ μn,n＝1,…,N}，μnAnd representing the characteristic value constraint factor corresponding to the nth SLC image data.
In this embodiment, the relevant initial variables include: the method comprises the steps of setting an eigenvalue set e of a sample covariance matrix, setting an eigenvalue set lambda of the sample covariance matrix and a eigenvalue constraint factor set mu.
In this embodiment, step S2 specifically includes:
s21: iterative computation of characteristic coefficients I by means of said correlated initial variable loopnThe calculation formula is as follows:
Figure BDA0003319876690000053
wherein λ isnRepresenting the eigenvalue, mu, of the sample covariance matrix corresponding to the nth SLC image datanRepresenting a characteristic value constraint factor, lambda, corresponding to the nth view SLC image datakRepresenting the eigenvalue, mu, of the sample covariance matrix corresponding to the kth view SLC image datakRepresenting a characteristic value constraint factor corresponding to the k view SLC image data; n represents the total number of the SLC image data, and is a positive integer greater than 1;
s22: by said characteristic coefficient InCalculating the optimal estimation covariance matrix by loop iteration
Figure BDA0003319876690000054
The calculation formula is as follows:
Figure BDA0003319876690000061
wherein e isnAnd representing the eigenvector of the sample covariance matrix corresponding to the nth SLC image data.
In this embodiment, the formula for calculating the low side lobe chromatogram in step S3 is as follows:
Figure BDA0003319876690000062
wherein the content of the first and second substances,
Figure BDA0003319876690000063
represents the optimal estimated covariance matrix, a ═ a (z)1),a(z2),…,a(zD)]TTo map the matrix, ZdRepresents the d-th altitude, and T is a transpose; a (z)d)＝[exp(jkz(1)zd),exp(jkz(2)zd),…,exp(jkz(N)zd)]TIs the d mapping vector of the mapping matrix A, j is the complex imaginary symbol;
Figure BDA0003319876690000064
represents the vertical wave number, b⊥nIs the vertical baseline, W, between the nth SLC image data and the main imageLDenotes wavelength, r denotes slope distance, and θ denotes incident angle.
Referring to fig. 2-5, the nonparametric spectrum estimation method of the low sidelobe forest TomoSAR of the present invention is verified through experiments, wherein fig. 2 is a comparison of results of different methods when Δ H is 30 m: (a) SNR is 20 dB; (b) SNR is 5 dB; fig. 3 shows the results of different methods when Δ H is 10 m: (a) SNR is 20 dB; (b) SNR is 5 dB. FIG. 4(a) is a study area location, and FIG. 4(b) is a selected cross-section (red solid line) located on a LiDAR DTM; FIG. 5 shows the selected cross-sectional estimated chromatograms with the left column being the HH channel result, the middle column being the HV channel result, and the right column being the VV channel result; (a) (f) represents the Beamforming estimation result, (b) represents the Capon estimation result, (c) represents the MUSIC estimation result, (d) represents the IAA estimation result, (e) represents the G-Pisarenko estimation result, and (k) represents the G-Pisarenko estimation result;
the experiment utilizes the imaging parameters of an airborne SAR system in a real experiment to obtain simulation data, and the specific parameters are shown in table 1; the analog signal consists of two parts of ground and canopy scattered signals, which have phase centers and angular spreads at different heights, wherein the canopy scattered signal has a larger angular spread than the ground scattered signal; based on the above assumptions, in this experiment, from the time when the height difference between the ground scattering center and the canopy scattering center is large (30m) and the time when the height difference between the ground scattering center and the canopy scattering center is small (10m), the reconstruction performance of the five spectrum estimation algorithms on the forest signal backscatter power distribution under different signal-to-noise ratios (SNRs) is respectively obtained.
TABLE 1P band F-SAR airborne SAR system parameters
Figure BDA0003319876690000065
Figure BDA0003319876690000071
Fig. 2 shows the inversion capability of five different methods under high and low signal-to-noise ratio conditions in a forest tree flourishing area (Δ H ═ 30 m); as can be seen from fig. 2(a), under the condition of high signal-to-noise ratio (SNR ═ 20dB), the scattering phase centers of the ground and the canopy can be found by the five methods, but the more serious sidelobe effect appears by the three methods of Beamforming, Capon and MUSIC, which hardly appears in the results obtained by the IAA and G-Pisarenko methods; fig. 2(b) shows the estimation result of low signal-to-noise ratio (SNR ═ 5dB), as the signal-to-noise ratio decreases, all five methods are affected by noise and the sidelobe effect is more severe in case of higher signal-to-noise ratio, but the G-Pisarenko method is affected the least; therefore, the robustness of the method of the invention to signal-to-noise ratio variations is best;
when the forest vegetation is short (Δ H ═ 10m), the estimation results of the five methods are shown in fig. 3; limited by the resolution in the height direction, when the ground scattering phase center is closer to the canopy scattering phase center, the five methods can find the ground scattering phase center, but the found canopy scattering phase center has a difference value with the real value; as in the case of Δ H ═ 30m, the G-Pisarenko method suppresses noise signals in the chromatogram, reducing side lobe effects; moreover, the inversion effect is better under the condition of low signal-to-noise ratio;
from the analysis of the above two cases, compared with the other four methods, the method of the present invention has better noise robustness under the condition of ensuring to find the ground and canopy scattering phase centers, and is favorable for image interpretation and information extraction; thus, the method herein was validated in simulation experiments and will be subsequently used for further validation in real experiments;
in order to further verify the advantages of the method, 10-scene P waveband airborne full-polarization AfriSAR data flying by the German space navigation bureau DLR is utilized to carry out SAR chromatography three-dimensional imaging, and relevant parameters of an airborne platform are shown in a table 1; the data set is acquired from a Lope region of African galaxy, the terrain of the region is mainly hilly, and the fluctuation range of the terrain is 163m to 583 m; in addition, in order to verify the correctness of the tomography SAR imaging, the Digital Terrain Model (DTM) and the Canopy Height Model (CHM) are obtained by utilizing LiDAR point clouds;
FIG. 4(a) shows Pauli-based images of the Lope region, (b) where the solid red line (2000 pixels) is the distance-wise cross-sectional location we have chosen, which will be analyzed in subsequent experiments;
in order to comprehensively verify the effectiveness of the method, the data chromatographic results of HH, HV and VV channels of the selected section are obtained by using five methods respectively; as shown in FIG. 5, the five methods can obtain complete chromatogram, but the first four methods (Beamforming, Capon, MUSIC, IAA) all have obvious side lobe effect; even though IAA has certain improvement compared with Beamforming, Capon and MUSIC, the effect is far less than that of G-Pisarenko; therefore, the method has obvious advantages in three polarization channels; furthermore, as can be seen from fig. 5, the scattered energy of the HH channel comes mainly from the ground, the signal of the canopy is mostly contained in the HV channel, and the energy of the VV channel is intermediate between the HH channel and the HV channel.
Referring to fig. 6, the present invention provides a low sidelobe forest TomoSAR nonparametric spectrum estimation system, including:
a related initial variable obtaining module 10, configured to obtain N-scene SLC image data, and pre-process the SLC image data to obtain a related initial variable; n represents the total number of the SLC image data, and is a positive integer greater than 1;
an optimal estimation covariance matrix calculation module 20, configured to obtain an optimal estimation covariance matrix through the iterative calculation of the relevant initial variables;
and the low side lobe chromatographic spectrum acquisition module 30 is used for performing nonparametric spectral estimation through the optimal estimation covariance matrix to acquire a low side lobe chromatographic spectrum.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or system. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or system that comprises the element.
The above-mentioned serial numbers of the embodiments of the present invention are merely for description and do not represent the merits of the embodiments. In the unit claims enumerating several means, several of these means may be embodied by one and the same item of hardware. The use of the words first, second, third and the like do not denote any order, but rather the words first, second and the like may be interpreted as indicating any order.
The above description is only a preferred embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes, which are made by using the contents of the present specification and the accompanying drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.

Claims (6)

1. A low sidelobe forest TomosAR nonparametric spectrum estimation method is characterized by comprising the following steps:
s1: acquiring N-scene SLC image data, and preprocessing the SLC image data to obtain related initial variables;
s2: obtaining an optimal estimation covariance matrix through iterative calculation of the related initial variables;
s3: and performing nonparametric spectrum estimation through the optimal estimation covariance matrix to obtain a low side lobe chromatographic spectrum.
2. The method for estimating the nonparametric spectrum of the low-sidelobe forest tomoSAR according to claim 1, wherein the step S1 specifically comprises:
s11: performing single-view complex image sequence registration, flat ground removing effect and phase compensation operation on the SLC image data to obtain denoised SLC image data, wherein the phase compensation operation comprises the following steps: declivity, atmospheric disturbance and orbit error removal;
s12: performing multi-view processing on the denoised SLC image data to obtain a sample covariance matrix R, wherein the calculation formula is as follows:
Figure FDA0003319876680000011
wherein L represents a multi-view, U represents an observation vector, (-)HRepresents a conjugate transpose;
s13: and calculating a characteristic vector set e and a characteristic value set lambda of the sample covariance matrix, wherein the calculation formula is as follows:
[e，λ]＝eig(R)
wherein, the characteristic vector set e ═ { e ] of the sample covariance matrixn，n＝1，…，N}，enRepresenting the eigenvector of the sample covariance matrix corresponding to the nth SLC image data; eigenvalue set λ ═ λ of sample covariance matrixnN is 1, … N, λ N represents the eigenvalue of the sample covariance matrix corresponding to the nth scene SLC image data; n represents the total number of SLC image dataN is a positive integer greater than 1;
s14: and calculating to obtain a characteristic value constraint factor set mu through the characteristic vector set e and the characteristic value set lambda, wherein the calculation formula is as follows:
Figure FDA0003319876680000012
wherein, the eigenvalue constraint factor set μ ═ { μ ═ μn，n＝1，…，N}，μnAnd representing the characteristic value constraint factor corresponding to the nth SLC image data.
3. The method of claim 2, wherein the associated initial variables comprise: the method comprises the steps of setting an eigenvalue set e of a sample covariance matrix, setting an eigenvalue set lambda of the sample covariance matrix and a eigenvalue constraint factor set mu.
4. The method for estimating the nonparametric spectrum of the low-sidelobe forest tomoSAR according to claim 1, wherein the step S2 specifically comprises:
s21: iterative computation of characteristic coefficients I by means of said correlated initial variable loopnThe calculation formula is as follows:
Figure FDA0003319876680000021
wherein λ isnRepresenting the eigenvalue, mu, of the sample covariance matrix corresponding to the nth SLC image datanRepresenting a characteristic value constraint factor, lambda, corresponding to the nth view SLC image datakRepresenting the eigenvalue, mu, of the sample covariance matrix corresponding to the kth view SLC image datakRepresenting a characteristic value constraint factor corresponding to the k view SLC image data; n represents the total number of the SLC image data, and is a positive integer greater than 1;
s22: by said characteristic coefficient InCalculating the optimal estimation covariance matrix by loop iteration
Figure FDA0003319876680000022
The calculation formula is as follows:
Figure FDA0003319876680000023
wherein e isnAnd representing the eigenvector of the sample covariance matrix corresponding to the nth SLC image data.
5. The method for estimating the nonparametric spectrum of the low-sidelobe forest tomoSAR according to claim 1, wherein the formula for calculating the low-sidelobe tomography spectrum in the step S3 is as follows:
Figure FDA0003319876680000024
wherein the content of the first and second substances,
Figure FDA0003319876680000025
represents the optimal estimated covariance matrix, a ═ a (z)1)，a(z2)，…，a(zD)]TTo map the matrix, zdRepresents the d-th altitude, and T is a transpose; a (z)d)＝[exp(jkz(1)zd)，exp(jkz(2)zd)，…，exp(jkz(N)zd)]TIs the d mapping vector of the mapping matrix A, j is the complex imaginary symbol;
Figure FDA0003319876680000026
represents the vertical wave number, b⊥nIs the vertical baseline, W, between the nth SLC image data and the main imageLDenotes wavelength, r denotes slope distance, and θ denotes incident angle.
6. A low sidelobe forest TomosAR nonparametric spectrum estimation system is characterized by comprising:
a related initial variable acquisition module, configured to acquire N-scene SLC image data, and pre-process the SLC image data to obtain a related initial variable; n represents the total number of the SLC image data, and is a positive integer greater than 1;
the optimal estimation covariance matrix calculation module is used for obtaining an optimal estimation covariance matrix through the iterative calculation of the related initial variables;
and the low side lobe chromatographic spectrum acquisition module is used for carrying out nonparametric spectral estimation through the optimal estimation covariance matrix to acquire a low side lobe chromatographic spectrum.
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CN115166741A (en) * 2022-09-08 2022-10-11 中国科学院空天信息创新研究院 Simplified model-based dual-phase central polarization chromatography decomposition method

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CN115166741A (en) * 2022-09-08 2022-10-11 中国科学院空天信息创新研究院 Simplified model-based dual-phase central polarization chromatography decomposition method
CN115166741B (en) * 2022-09-08 2022-11-29 中国科学院空天信息创新研究院 Simplified model-based dual-phase central polarization chromatography decomposition method

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