CN114296061A - Cross calibration method based on multivariate variable detection and different radiation transmission models - Google Patents
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Abstract
The invention discloses a cross calibration method based on multivariate variable detection and different radiation transmission models, relates to the technical field of remote sensing application, and solves the problems that the prior art uses default modes and experience parameters aiming at atmospheric modes, surface BRDF characteristics and the like, does not consider the influence caused by surface feature changes at different observation times and the uncertainty caused by different radiation transmission models, has larger irrationality, uncertainty and the like, obtains real atmospheric profile, surface BRDF and invariable surface features, considers the influence caused by various radiation transmission models, improves the traditional method of using atmospheric experience modes, not considering BRDF characteristics, using a single radiation transmission model and not considering the surface feature changes to realize cross calibration, obtains the real atmospheric profile, BRDF and other parameters, extracts invariable surface features in an experimental area according to a multivariate variable detection method, meanwhile, the spectral matching factor is calculated by combining the MODTRAN and 6S radiation transmission models, and then the calculation of cross calibration is more scientifically realized.
Description
Technical Field
The invention relates to the technical field of remote sensing application, in particular to a cross calibration method based on multivariate variable detection and different radiation transmission models.
Background
With the increasing quantization of remote sensing application, the comprehensive application of multi-temporal and multi-sensor data and the development of quantitative remote sensing technology, the radiometric calibration of the remote sensing sensor with high precision is urgently needed, and is the basis of high-precision quantitative remote sensing. The remote sensing image can convert an original DN (image numerical value) value into an equivalent performance value at the entrance pupil of the sensor only through radiometric calibration, and remote sensing inversion products such as vegetation, water, atmosphere and the like are obtained through atmospheric correction and some inversion algorithms, so that large-area multi-time-domain remote sensing image information is provided for the fields of national defense, agriculture, forestry, disaster protection and the like. The implementation of radiometric calibration depends on the conditions such as calibration site spectrum and atmospheric parameters when the satellite passes through the border, and in addition, the BRDF (ground Bidirectional reflection Distribution Function) characteristics of the calibration site need to be strictly evaluated and analyzed. The radiometric calibration method of the visible near-infrared band can be divided into pre-emission laboratory calibration, in-orbit satellite radiometric calibration, in-orbit alternative radiometric calibration, cross calibration and the like according to the running state of the sensor.
The sensor needs to be calibrated in a laboratory before launching and lifting off, and the performance of the detector is affected by vibration and the surrounding environment after the sensor is lifted off, so that the performance of the detector is attenuated to different degrees, the radiation performance of the detector is changed, the error of the result calculated by the calibration parameters in the laboratory is large, and the radiation performance of the detector needs to be monitored in each quarter to correct the calibration parameters so as to ensure the accuracy of the remote sensing image quantification. The existing common radiometric calibration method is field radiometric calibration, but the calibration method consumes higher manpower and material resources, is influenced by weather during satellite transit, and cannot monitor the radiometric performance for a long time. The cross radiometric calibration is to calibrate the sensor to be calibrated by using a calibrated reference sensor through the conversion of radiance, and the cross radiometric calibration is a research hotspot gradually because of lower cost. On the basis of atmospheric profile, multi-angle reflection characteristics of the earth surface, invariant ground object points and the like, the invention integrates the optimal and defective experiment cross calibration of two common radiation transmission models at present, and better accords with the real situation.
The current calculations for cross-scaling are mainly using spectral matching factors to correct for differences between different sensors. The calculation of the spectrum matching factor is to input the observation geometry, atmospheric conditions, surface parameters and the like of the reference sensor and the sensor to be calibrated into the radiation transmission model to obtain the ratio of the top radiance of the atmospheric layer. The method has the advantages that default modes and empirical parameters are used in the radiation transmission model for atmospheric modes, ground BRDF characteristics and the like, influences caused by surface feature changes at different observation times and uncertainties caused by different radiation transmission models are not considered, the method is unreasonable and uncertain, and therefore a cross calibration method based on multivariate variable detection and different radiation transmission models is needed.
The method is improved aiming at the traditional method for realizing cross calibration by using an empirical atmosphere mode, not considering BRDF characteristics, using a single radiation transmission model and not considering ground object changes, so that real atmosphere profile, BRDF and other parameters are obtained, invariant ground objects in an experimental area are extracted according to a multivariate variable detection method, and meanwhile, a spectral matching factor is calculated by combining a MODTRAN and a 6S radiation transmission model, so that the cross calibration is more scientifically calculated.
Disclosure of Invention
The invention provides a cross calibration method based on multivariate variable detection and different radiation transmission models, aiming at solving the problems that in the prior art, a default mode and empirical parameters are used for atmospheric mode, earth surface BRDF characteristics and the like, influence caused by ground object change at different observation time and uncertainty caused by different radiation transmission models are not considered, and the problems of greater irrationality, uncertainty and the like exist.
The cross calibration method based on multivariate variable detection and different radiation transmission models is realized by the following steps:
acquiring atmospheric profile data, atmospheric aerosol data and BRDF model parameters;
inputting the observation geometry, water vapor and spectral response functions of different sensors and the atmospheric profile data, the atmospheric aerosol data and the BRDF parameters acquired in the step one into the MODRAN and the 6S radiation transmission model respectively and calculating the radiance of different sensors; the specific process is as follows:
inputting the observation geometry, water vapor and spectral response functions of the reference sensor and the sensor to be calibrated, the atmospheric profile data, the atmospheric aerosol data and the BRDF parameters obtained in the step one into a 6S radiation transmission model to obtain the radiance of the reference sensor and the sensor to be calibrated;
inputting the observation geometry, water vapor and spectral response functions of the reference sensor and the sensor to be calibrated, the atmospheric profile data, the atmospheric aerosol data and the BRDF parameters obtained in the step one into an MODTRAN radiation transmission model to obtain the radiance of the reference sensor and the sensor to be calibrated;
thirdly, calculating a spectrum matching factor;
selecting an original image to obtain a reference sensor radiance image and a corresponding earth surface reflectivity image;
step two, respectively inputting the earth surface reflectivity serving as a real reflectivity into an MODTRAN radiation transmission model and a 6S radiation transmission model, and simulating radiance corresponding to the real reflectivity; performing regression calculation on the reference sensor radiance as real radiance and radiance corresponding to the real reflectivity, wherein the following formula is adopted:
Radtrue＝Rad6S*a+Radmodtran*b+c
in the formula, RadtrueFor the final calculated radiance, Rad6SAnd RadmodtranRespectively simulating radiance by a 6S radiation transmission model and a MODTRAN radiation transmission model, wherein a, b and c are coefficients of regression calculation respectively;
inputting the radiance of the reference sensor and the sensor to be calibrated simulated by the 6S radiation transmission model in the first step and the radiance of the reference sensor and the sensor to be calibrated simulated by the MODTRAN radiation transmission model in the second step into the regression calculation formula to respectively obtain the final radiance of the reference sensor and the final radiance of the sensor to be calibrated;
step three, carrying out a ratio of the final radiance of the sensor to be calibrated obtained in the step three to the final radiance of the reference sensor to obtain a spectrum matching factor;
extracting the unchanged ground objects of the experimental area by using a multivariate variable detection method;
masking the reference sensor radiance image to obtain the radiance of the unchanged ground object of the reference image;
step six, resampling the image to be calibrated by a bilinear interpolation method, and performing linear fitting on the resampled image and the radiance of the unchanged ground object obtained in the step five to obtain a correction coefficient; the specific process is as follows:
step six, multiplying the radiance of the image of the reference sensor by the spectral matching factor obtained in the step three to obtain the radiance of the image of the sensor to be calibrated;
step two, resampling the original image of the sensor to be calibrated to the resolution of the original image of the reference sensor by adopting a bilinear interpolation method, and extracting an invariant ground object pixel;
and sixthly, performing linear fitting on the original image of the sensor to be calibrated and the ground object radiance and the gray value DN without change, and calculating to obtain the gain and the offset of the calibration coefficient of the sensor to be calibrated.
The invention has the beneficial effects that: the cross calibration calculation method is an improvement on the cross calibration calculation method. The invention obtains a real atmosphere profile, a ground BRDF and an invariant ground object, considers the influence brought by a plurality of radiation transmission models, improves the traditional method for realizing cross calibration by using an empirical atmosphere mode, not considering BRDF characteristics, using a single radiation transmission model and not considering ground object change, obtains parameters such as the real atmosphere profile, the BRDF and the like, extracts the invariant ground object in an experimental area according to a multivariate variable detection method, and simultaneously calculates a spectrum matching factor by combining the MODTRAN and the 6S radiation transmission model, thereby more scientifically realizing the calculation of the cross calibration.
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FIG. 1 is a schematic block diagram of a cross-calibration method based on multivariate detection and different radiation transmission models according to the present invention;
FIG. 2 is a view showing the effect of the radiation corrected field image;
FIG. 3 is a diagram of the effects of the NCEP atmospheric broadline data;
FIG. 4 is a diagram of the effect of spectral response functions of a reference sensor and a sensor to be calibrated;
FIG. 5 is a flow chart of a regression experiment for different radiative transfer models;
FIG. 6 is a graph showing the effect of Dunhuang correction field Landsat8 reflectivity and corresponding radiance;
FIG. 7 is a diagram illustrating a comparison effect between a simulated radiance result of a MODTRAN and 6S model and a real radiance result;
FIG. 8 is a graph showing the effect of an invariant feature obtained by multivariate test method;
FIG. 9 is a diagram of the final fitting effect of cross calibration obtained by the method of the present invention.
Detailed Description
The present embodiment is described with reference to fig. 1 to 9, and the cross-calibration method based on multivariate variable detection and different radiation transmission models is as follows: the method comprises the following steps:
A. acquiring the atmosphere profile data of the NCEP (National Centers for environmental Prediction), the atmospheric aerosol data of the MODIS (Medium resolution Imaging spectrometer) and the BRDF model parameters;
in the step, firstly, the temperature and the pressure of 17 atmospheric layers are obtained through the NCEP atmospheric profile data, and the elevation is calculated;
in the formula, H0 is the elevation of a survey station, Hs is the elevation of a standard isobaric surface, P0 is ground pressure, Ps is the average height of a gas column, R and g are constants, an NCEP re-analysis data set comprises 144 lattice points, 73 lattice points and a data range covers a global isobaric surface layer (totally 17 layers), so that the pressure and temperature values of each layer in four time periods are read according to the specified time longitude and latitude information when a file is read, and finally linear interpolation is carried out according to the observation time to obtain a final result;
then, aerosol optical thickness (AOD) and water vapor were obtained by MODIS aerosol data. The MCD19A 2V 6 data product can provide daily atmospheric parameters with the resolution of 1 km, and if no data exists in an experimental area, a buffer area of 1 km can be established to obtain average atmospheric parameters;
finally, obtaining BRDF parameters of an experimental area through MODIS bidirectional reflection distribution function model parameters, wherein a Ross-Li nuclear driving model is selected as the data;
wherein:
tanθv’＝P5tanθv(5)
tanθs’＝P5tanθs(6) middle thetav’θs’ 
Respectively an observation zenith angle, a solar zenith angle and a relative azimuth angle; thetav’,θs’And t are all intermediate variables, P4＝h/b＝2，P5＝b/r＝1,P1,P2,P3The isotropy, geometric parameters and volume parameters can be obtained from the MODIS image.
B. The method comprises the following steps of respectively inputting observation geometry, atmospheric profile data, AOD (aerosol optical thickness), water vapor, BRDF parameters and spectral response functions (the observation geometry is the state of a sensor when the sensor shoots an image, such as the azimuth and the angle posture of the sensor at the moment, the atmospheric parameters are the weather condition of the sensor when the sensor shoots, the cloud is thick, the weather is humid and the like, the spectral response functions are parameters inside the sensor during manufacturing, the BRDF is a characteristic of the sensor shooting a ground object target, and the characteristic means the reflectivity of a ground object in different directions, whether the surface is uniform and the like) of different sensors into a 6S radiation transmission model and a MODTRAN radiation transmission model, and calculating the radiance of the different sensors; the specific process is as follows:
b1: inputting the observation geometry, atmospheric parameters, spectral response function, BRDF parameters and the like of the reference sensor and the sensor to be calibrated into the 6S radiation transmission model to obtain the radiance of the reference sensor and the sensor to be calibrated
B2: inputting the observation geometry, atmospheric parameters, spectral response function, BRDF parameters and the like of the reference sensor and the sensor to be calibrated into the MODTRAN radiation transmission model to obtain the radiance of the reference sensor and the sensor to be calibrated
Step C, calculating a spectrum matching factor;
in past cross-calibration experiments, a single radiation transmission model is often used, and results of different radiation transmission models are greatly different and the emphasis of simulation calculation is different. The simulation result of the 6S radiation transmission model in the visible near-infrared band is good, but the defects are that the number of input parameters is small and the spectrum range is short; the MODTRAN radiation transmission model can simulate the result of calculating all wavelengths, but the input parameters are more, and the operation is more complicated. Under the condition of the same parameters, the simulation results of the two models have little deviation, in order to reduce the difference between different radiation transmission models, in the embodiment, the land surface reflectivity image corresponding to the landscaping correction site reference sensor Landsat8 radiance image is selected, and Landsat8 terrestrial surface reflectivity is to input the original image into the LEDAPS software for atmospheric correction to realize the conversion from the top radiance of the atmospheric layer to the terrestrial surface reflectivity. The LEDAPS software needs to input various atmospheric parameters to construct an atmospheric model, the parameters mainly comprise the output of a DEM and a 6S radiation transmission model, ozone, ground pressure, temperature, water vapor and other parameters simulated by the national environmental prediction center (NCEP), and the data can be downloaded in a Google Earth Engine.
As shown in fig. 6, in the present embodiment, the surface reflectivity and radiance points of different areas of the dunhuang correction site are extracted as experimental data, the surface reflectivity is used as the known real reflectivity and is respectively input into the MODTRAN and 6S radiation transmission models to obtain the corresponding radiance, and regression calculation is performed on the Landsat8 radiance as the real radiance and the radiance calculated by the two models, so as to obtain the following formula:
Radtrue＝Rad6S*a+Radmodtran*b+c (7)
in the formula, RadtrueFor the final calculated radiance, Rad6SAnd RadmodtranThe radiance was modeled for 6S and MODTRAN, and a, b, c are coefficients for regression calculation.
And finally, inputting the results calculated by different radiation transmission models of the reference sensor and the sensor to be calibrated in the step B into the formula to obtain a final radiance result, and carrying out a ratio on the final radiance of the sensor to be calibrated and the final radiance of the reference sensor to obtain a spectrum matching factor. The method combines the simulation results of two radiation transmission models, optimizes the experimental process of calculating the spectrum matching factor in the cross calibration experiment, and further reduces the uncertainty brought by the radiation transmission model;
D. extracting the unchanged and stable ground objects of the experimental area by using a multivariate variable detection method;
d1: acquiring two images of a sensor to be calibrated at different time phases in an experimental area;
d2: extracting invariant ground objects of each wave band of the reference sensor image in the experimental area according to a multivariate variable detection Method (MAD):
wherein F ═ F1+F2+…+Fn]And G ═ G1+G2+…+Gn]Respectively representing two groups of images in different time periods, n is the number of image wave bands, aTAnd bTAre all constants, minimizing the positive correlation between U and V by a linear combination between F and G then:
Var(U-V)＝Var(U)+Var(v)-2Cov(U,V)→maximum (9)
in the formula, Var is variance, Cov is covariance, and maximum represents maximum values U and V respectively satisfying the following limiting conditions:
from the above formula, it can be further derived:
in the formula, rho is a typical correlation coefficient between U and V, and then two groups of linear combinations are subtracted to obtain the linear combination
From the above formula we can obtain (U)i-Vi) And (U)i-Vi) Variance of (2)
After combination, the following formula is obtained:
Z(j,k)u representing jth row and kth column of imagei-ViAnd Ui-ViSum of squares of variance ratiosGenerally, Z of all the pixel numbers of a single band can be considered to satisfy the chi-square distribution with the degree of freedom n, and the chi-square distribution with the degree of freedom n is distributed in Z(j,k)The distribution function value at a point can be defined as
The invariant probability for each pixel is then expressed as:
finally P is addedrThe image element with (no change) > t is regarded as an unchanged ground object point, wherein t is a set threshold value.
In this embodiment, to ensure that the invariant features extracted by multivariate variable detection can be used for cross calibration, the threshold t is set to be 0.85, 0.86, … …, 0.94, and 0.95, respectively, the number of the selected invariant feature points is required to be more than 10% of the total number of pixels, and the correlation coefficient of the pixel values between the invariant feature points of the two-scene reference sensor image at different time phases is maximum, and finally the threshold t is set to be 0.93.
E. Masking the reference sensor radiance image to obtain the radiance of the unchanged ground object point;
F. and resampling the image to be calibrated by a bilinear interpolation method, and performing linear fitting on the resampled image and the radiance of the invariant ground object point of the reference sensor to obtain a correction coefficient.
F1: multiplying the radiance of the reference image by a spectrum matching factor to obtain the radiance of the image of the sensor to be calibrated;
f2: resampling the image of the sensor to be calibrated to the resolution of the image of the reference sensor by utilizing a bilinear interpolation method, and extracting an invariant ground pixel;
f3: and performing linear fitting calculation on the image invariant ground object radiance and the DN value of the sensor to be calibrated to obtain the gain and the offset of the calibration coefficient of the sensor to be calibrated.
The second embodiment is described with reference to fig. 1 to 6, and this embodiment is an example of the cross-calibration method based on multivariate variable detection and different radiation transmission models according to the first embodiment:
in the present embodiment, the GF1-B image of 17 th month in 2018 is used as the image to be calibrated, the Landsat-8 image of 15 th month in 2018 is used as the reference image, and the dunhuang calibration field is used as the experimental area for cross calibration. According to the method flowchart shown in fig. 1, the method comprises the steps of:
firstly, acquiring a remote sensing image of a Dunhuang correction field as shown in figure 2; acquiring atmospheric pressure and temperature of Dunhuang correction site through NCEP atmospheric profile data, and calculating according to formula (1) to obtain corresponding elevation, as shown in FIG. 3; AOD data above Dunhuang correction site are obtained according to MODIS AOD image, and AOD results of 7 month 17 days and 7 month 15 are 0.255 and 0.282 respectively.
And secondly, obtaining BRDF parameters of Dunhuang correction field by using the formula (2) -6 and MODIS BRDF coefficient images.
Inputting the observation geometry, atmospheric parameters, spectral response function, BRDF parameters and the like of the reference sensor and the sensor to be calibrated into a 6S radiation transmission model and a MODTRAN radiation transmission model, and obtaining the radiance of the reference sensor and the sensor to be calibrated according to the formula (7)
Acquiring a radiance image of the reference sensor and a corresponding earth surface reflectivity image, inputting the earth surface reflectivity as a real reflectivity into the radiation transmission model A and the radiation transmission model B respectively, and simulating radiance corresponding to the real reflectivity; performing regression calculation on the reference sensor radiance as real radiance and radiance corresponding to the real reflectivity, wherein the following formula is adopted:
Radtrue＝Rad6S*a+Radmodtran*b+c
in the formula, RadtrueFor the final calculated radiance, Rad6SAnd RadmodtranRespectively simulating radiance by a 6S radiation transmission model and a MODTRAN radiation transmission model, wherein a, b and c are coefficients of regression calculation respectively;
and finally, inputting the results calculated by different radiation transmission models of the reference sensor and the sensor to be calibrated into the formula to obtain a final radiance result, and carrying out a ratio on the final radiance of the sensor to be calibrated and the final radiance of the reference sensor to obtain a spectrum matching factor. The spectral scale factors of the blue, green, red and near infrared bands are respectively: 0.999, 1.014, 1.036 and 1.658.
Sixthly, obtaining an image of the unchanged land features of the Dunhuang correction field according to a formula (8) - (14) and two GF1-BCD images in different time periods, masking most of the land features such as artificial land features, vegetation water bodies and the like by a multivariate variable detection method shown in figure 8, and obtaining all the obtained unchanged land features which are stable land features such as sand land and the like.
Seventhly, masking the radiance image of the reference sensor to obtain the radiance of the unchanged ground object point; .
And eighthly, multiplying the radiance of the reference image by the spectrum matching factor to obtain the radiance of the image of the sensor to be calibrated, resampling the image of the sensor to be calibrated to the resolution of the image of the reference sensor by using a bilinear interpolation method, and extracting an invariant ground object pixel.
And ninthly, performing linear fitting on the constant ground object radiance of the image of the sensor to be calibrated and the DN value to calculate and obtain the gain and the offset of the calibration coefficient of the sensor to be calibrated, and referring to the result in FIG. 9.
Ten, the R of each wave band can be seen from the calculation result2All of the components are more than 0.95,
the experimental procedure is shown in FIGS. 6 and 7, and the regression coefficients and the correlation R of each band are shown2As shown in the following table:
the blue wave band is greatly influenced by atmospheric scattering, so that the fitting effect is relatively poor, and the fitting result difference of other wave bands is small, so that the cross calibration method improves certain cross precision compared with the conventional cross calibration method.
Claims (2)
1. The cross calibration method based on multivariate variable detection and different radiation transmission models is characterized by comprising the following steps: the method is realized by the following steps:
acquiring atmospheric profile data, atmospheric aerosol data and BRDF model parameters;
inputting the observation geometry, water vapor and spectral response functions of different sensors and the atmospheric profile data, the atmospheric aerosol data and the BRDF parameters obtained in the step one into a MODTRAN and 6S radiation transmission model respectively and calculating the radiance of different sensors; the specific process is as follows:
inputting the observation geometry, water vapor and spectral response functions of the reference sensor and the sensor to be calibrated, the atmospheric profile data, the atmospheric aerosol data and the BRDF parameters obtained in the step one into a 6S radiation transmission model to obtain the radiance of the reference sensor and the sensor to be calibrated;
inputting the observation geometry, water vapor and spectral response functions of the reference sensor and the sensor to be calibrated, the atmospheric profile data, the atmospheric aerosol data and the BRDF parameters obtained in the step one into an MODTRAN radiation transmission model to obtain the radiance of the reference sensor and the sensor to be calibrated;
thirdly, calculating a spectrum matching factor;
step three, obtaining a reference sensor radiance image and a corresponding earth surface reflectivity image;
step two, respectively inputting the earth surface reflectivity serving as a real reflectivity into an MODTRAN radiation transmission model and a 6S radiation transmission model, and simulating radiance corresponding to the real reflectivity; performing regression calculation on the reference sensor radiance as real radiance and radiance corresponding to the real reflectivity, wherein the following formula is adopted:
Radtrue＝Rad6S*a+Radmodtran*b+c
in the formula, RadtrueFor the final calculated radiance, Rad6SAnd RadmodtranRespectively simulating radiance by a 6S radiation transmission model and a MODTRAN radiation transmission model, wherein a, b and c are coefficients of regression calculation respectively;
inputting the radiance of the reference sensor and the sensor to be calibrated simulated by the 6S radiation transmission model in the first step and the radiance of the reference sensor and the sensor to be calibrated simulated by the MODTRAN radiation transmission model in the second step into the regression calculation formula to respectively obtain the final radiance of the reference sensor and the final radiance of the sensor to be calibrated;
step three, carrying out a ratio of the final radiance of the sensor to be calibrated obtained in the step three to the final radiance of the reference sensor to obtain a spectrum matching factor;
extracting the unchanged ground objects of the experimental area by using a multivariate variable detection method;
step five, masking the radiance of the reference sensor image out of the radiance of the unchanged ground object of the reference image;
step six, resampling the image to be calibrated by a bilinear interpolation method, and performing linear fitting on the resampled image and the radiance of the unchanged ground object obtained in the step five to obtain a correction coefficient; the specific process is as follows:
step six, multiplying the radiance of the image of the reference sensor by the spectral matching factor obtained in the step three to obtain the radiance of the image of the sensor to be calibrated;
step two, resampling the original image of the sensor to be calibrated to the resolution of the original image of the reference sensor by adopting a bilinear interpolation method, and extracting an invariant ground object pixel;
and sixthly, performing linear fitting on the original image of the sensor to be calibrated and the constant ground object radiance and DN value, and calculating to obtain the gain and the offset of the calibration coefficient of the sensor to be calibrated.
2. The method of claim 1, wherein the cross-scaling is based on multivariate detection and different radiation transmission models, and wherein: the concrete process of the step four is as follows:
step four, acquiring two groups of sensor images to be calibrated in different time periods in an experimental area;
step two, extracting the invariant ground objects of each wave band of the reference sensor image in the experimental area according to a multivariate variable detection method:
wherein F ═ F1+F2+…+Fn]And G ═ G1+G2+…+Gn]Respectively representing two groups of images in different time periods, n is the number of image wave bands, aTAnd bTAre all constant, minimizing the positive correlation between U and V by a linear combination between F and G, then:
Var(U-V)＝Var(U)+Var(v)-2Cov(U，V)→maximum
in the formula, Var is variance, Cov is covariance, and maxim represents maximum; u and V respectively satisfy the following limiting conditions:
from the above formula, it can be further derived:
in the formula, rho is a typical correlation coefficient between U and V, and then two groups of linear combinations are subtracted to obtain
Obtaining (U)i-Vi) And (U)i-Vi) Variance of (2)
After combination, the following formula is obtained:
Z(j，k)u representing jth row and kth column of reference sensor imagei-ViAnd Ui-ViThe sum of squares of the variance ratios can be generally regarded as that Z of all the pixel numbers of a single band satisfies the chi-square distribution with the degree of freedom n, and the chi-square distribution with the degree of freedom n is distributed in Z(j，k)The distribution function value at a point can be defined as
The invariant probability for each pixel is then expressed as:
finally P is addedrThe image element with (no change) > t is regarded as an unchanged ground object point, wherein t is a set threshold value.
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