A Method for Uncertainty Analysis of Full-Spectrum Hyperspectral Earth Remote Sensing Imaging Measurements

Abstract

This invention discloses a method for analyzing the uncertainty of full-spectrum hyperspectral Earth remote sensing imaging measurements, comprising the following steps: (1) simulating and calculating the entrance pupil radiance and restored radiance spectral imaging signals of the atmosphere using surface reflectance, surface emissivity, surface temperature, topographic parameters, atmospheric parameters, and imaging system parameters; (2) evaluating the uncertainty of surface reflectance, surface emissivity, and surface temperature; (3) evaluating the uncertainty of topographic parameters per pixel and the correlation coefficient between topographic parameters; (4) evaluating the spectral uncertainty of atmospheric parameters per pixel and the correlation coefficient between atmospheric parameters; (5) constructing an uncertainty propagation model for the radiative transfer link and synthesizing the entrance pupil radiance uncertainty; (6) constructing an uncertainty propagation model for the imaging measurement link and synthesizing the restored radiance uncertainty; (7) analyzing the uncertainty components in the restored radiance and ranking the uncertainty contributions of each link. This invention constructs an uncertainty propagation model for the forward modeling process of hyperspectral remote sensing based on analytical formulas for uncertainty modeling and Monte Carlo distribution propagation. This model can quantify the uncertainty contributions of radiative transfer and imaging measurement, providing technical support for the quantitative application performance analysis and optimization of full-spectrum hyperspectral remote sensing.

Description

Technical Field

[0001] This invention relates to a method for analyzing the uncertainty of full-spectrum hyperspectral Earth remote sensing imaging measurements, belonging to the field of hyperspectral remote sensing technology, and is applicable to the prediction and evaluation of the performance of full-spectrum hyperspectral imaging measurements. Background Technology

[0002] Remote sensing is essentially a non-contact measurement process of the observed target by collecting and measuring its radiation signals. Uncertainty in remote sensing information arises, is transmitted, and accumulates alongside the acquisition, processing, and transmission of this information. A complete measurement result should include both the best estimate of the measured value and parameters characterizing its dispersion. The uncertainty of remote sensing measurements is influenced by a combination of factors, including the level of natural surface signals, the randomness of atmospheric transmission, payload characteristics, and radiometric correction uncertainties. Along the forward modeling process of remote sensing measurements, this uncertainty is transmitted from the surface through ground-atmosphere coupling, atmospheric transmission, payload imaging, and radiometric correction to the full-spectrum hyperspectral reconstructed radiance data product, such as… Figure 2 As shown.

[0003] During the design and development phases of imaging spectrometers, payload development units often provide design values ​​or laboratory calibration results for parameters such as signal-to-noise ratio, noise-equivalent entrance pupil temperature difference, and radiometric calibration accuracy to qualitatively reflect the system's uncertainty. However, users of hyperspectral quantitative remote sensing are concerned with the quantitative results of uncertainties in general data products such as restored radiance spectra, surface temperature, surface reflectance spectra, and surface emissivity spectra. Therefore, constructing an uncertainty model of the remote sensing process, describing the remote sensing process from the perspective of traceability, and analyzing the uncertainty in obtaining the true remote sensing values ​​are of great significance for the design optimization of application-oriented remote sensing systems, the quantitative application of remote sensing data, and the verification of data accuracy. Summary of the Invention

[0004] To address the problem that the design specifications of full-spectrum hyperspectral imaging systems cannot quantitatively describe the measurement accuracy of surface signals and entrance pupil radiance signals, and the uncertainty contribution introduced in remote sensing measurements, this invention provides a method for uncertainty analysis of full-spectrum hyperspectral Earth remote sensing imaging measurements. The technical solution of this invention includes the following steps:

[0005] Step 1: Simulate and calculate the spectral imaging signals of the top atmospheric entrance pupil radiance and restored radiance using surface reflectance, surface emissivity, surface temperature, topographic parameters, atmospheric parameters, and imaging system parameters:

[0006] The actual atmospheric conditions, observation geometry, and surface elevation of the remote sensing imaging area are input into the atmospheric radiative transfer model MODTRAN5.3 to obtain full-spectrum atmospheric parameters corresponding to different surface elevations, including direct spectral irradiance, atmospheric diffuse solar spectral irradiance, atmospheric thermal emission and thermal scattering radiation, atmospheric hemispherical albedo, atmospheric scattering transmittance, atmospheric direct transmittance, atmospheric stratified extinction coefficient and scattering coefficient, and atmospheric path radiation. Based on the surface elevation model, the topographic parameters of each pixel in the imaging area are calculated, including slope, projection shadow coefficient, cosine of solar illumination incident angle, and sky visibility factor.

[0007] Based on the forward transmission process of remote sensing signals, the full-spectrum solar and atmospheric spectral radiation illumination received by the natural Earth's surface is first calculated. :

[0008]

[0009] in, Indicates the spatial location of pixels in the imaging region. Represents spatial coordinates along the orbital direction. Spatial coordinates representing the direction perpendicular to the orbit; Represents a pixel The corresponding surface elevation; Indicates wavelength; Indicates altitude The solar direct spectral irradiance received at a horizontal surface; This represents the projection shadow coefficient of a pixel, with a value between 0 and 1. 0 indicates that sunlight is completely blocked, and 1 indicates that there is no obstruction. Represents the cosine of the angle of incidence of solar illumination; Indicates altitude Solar spectral irradiance received at a horizontal surface; Indicates altitude The atmospheric thermal emission and thermal scattering spectral irradiance received at a horizontal surface; Represents pi; This represents the sky visibility factor corresponding to the undulating terrain pixel; This represents the anisotropy correction term for solar diffused illumination.

[0010]

[0011] in, Indicates atmospheric downward transmittance. The slope of the earth's surface is represented by the three terms added in the formula, which respectively represent the proportions of anisotropic scattered radiation, isotropic scattered light, and horizontal scattered light in the circumpolar direction.

[0012] Calculate the total solar and atmospheric spectral radiation reflected from the Earth's surface, along with its thermal emission from the Earth's surface, to determine the combined surface radiance. :

[0013]

[0014] in, Indicates surface reflectance, Indicates surface emissivity, Indicates surface temperature. This represents the blackbody thermal radiation calculated using Planck's formula. Represents a pixel The pixel coordinates of the region and its surrounding area This indicates a lighting correction for undulating terrain.

[0015]

[0016] in, For slope pixels Normal and arrive The angle between the lines, For slope pixels Normal and arrive The angle between the lines, express arrive Spatial distance, for arrive Atmospheric extinction coefficient, For pixels The area.

[0017] Then, the ground-based radiance, encompassing the full spectrum of atmospheric and undulating surface trapping effects, is calculated. :

[0018]

[0019] in, Indicates atmospheric albedo; This represents the average ground-based radiance within the imaging area. Represents a pixel The equivalent background reflectance in the adjacent area is obtained by weighting the average values ​​using topographic parameters:

[0020]

[0021]

[0022] Thus, the full-spectrum atmospheric top entrance pupil radiance signal under undulating surface conditions was simulated. :

[0023]

[0024] in, This represents the direct transmittance along the path from the ground surface to the sensor. This represents the scattering transmittance along the instantaneous field of view path from nearby ground objects to the sensor. Indicates atmospheric path radiation. This represents the normalized atmospheric proximity effect contribution factor obtained from the atmospheric stratification scattering model.

[0025] Using the platform motion point spread function Point spread function of optical system Optical system transmittance Spectroscopic optical system diffraction efficiency Spectral response function Optical system F-number Detector pixel area Quantum efficiency of detectors Point spread function of detectors and electronic systems Integral Time Quantization bit depth Standard deviation of equivalent number of readout noise Standard deviation of equivalent electron count for circuit noise Standard deviation of equivalent electron count for quantization noise Background electron count Detector dark current The reference voltage V of the readout circuit REF and detector charge conversion rate C VF Simulations were performed using the response parameters of the hyperspectral imager. The number of signal electrons received by the area array detector was calculated. The formula is:

[0026]

[0027] in, Denotes Planck's constant. Represents the speed of light. This represents the convolution operation.

[0028] Furthermore, the DN value signal of the full-spectrum hyperspectral imaging is calculated. The formula for the DN value is:

[0029]

[0030] in, This represents the random relative error caused by the nonlinearity and inhomogeneity of the response of a full-spectrum hyperspectral imager; Indicates the number of electrons in random additive noise. The calculation formula is: ,in, Indicated by Using the standard deviation as the standard deviation and 0 as the mean, Gaussian random noise is generated.

[0031] Radiometric calibration and correction were performed in the linear response region of the hyperspectral imager to simulate and restore the radiance imaging signal. The linear radiation correction formula is: ,in, and This represents the radiation response correction coefficient of a full-spectrum hyperspectral imager.

[0032] Step 2: Evaluate the uncertainties of surface reflectance, surface emissivity, and surface temperature, including two approaches: one for remote sensing applications and the other for comparing measurement uncertainties across different spectrometers.

[0033] (1) For remote sensing application tasks, the root mean square error of surface reflectance, surface emissivity and surface temperature required for quantitative remote sensing application tasks are used as the standard uncertainty of surface reflectance. Standard uncertainty of surface emissivity and the standard uncertainty of surface temperature The evaluation results.

[0034] (2) For the task of comparing the measurement uncertainties of different spectrometers, multiple measurements of the ground features of interest are performed using the spectrometer, and the standard deviation of the measurements is used as the uncertainty of surface reflectance and emissivity. According to Kirchhoff's law, if the sum of surface emissivity and reflectance is 1, then the uncertainties of the two are equal, i.e. The temperature of ground object samples is measured using methods such as radiation thermometers or thermocouple thermometers, and the uncertainty of this measurement is used as the uncertainty of the ground surface temperature. .

[0035] Step 3: Evaluate the uncertainty of terrain parameters per pixel and the correlation coefficients between terrain parameters. The steps for calculating the uncertainty of terrain parameters and the correlation coefficients using the Monte Carlo-based distribution propagation method include:

[0036] (1) Based on the imaging area and imaging geometry parameters of the imager, spatial cropping, registration and spatial resampling are performed on the surface elevation digital model product, i.e., DEM data.

[0037] (2) Based on the product manual and verification data of the digital model of surface elevation, the horizontal standard uncertainty and vertical standard uncertainty of the DEM data are obtained using the Type B uncertainty assessment method.

[0038] (3) Using the Monte Carlo-based distribution propagation method, the horizontal and vertical standard uncertainties of the DEM data are calculated. As a source of uncertainty in topographic parameters, according to the central limit theorem, the standard deviations of the DEM data are respectively... and The random Gaussian horizontal error and random Gaussian vertical error were calculated. Monte Carlo simulation was performed pixel by pixel to calculate four terrain parameters: slope, projection shadow coefficient, cosine of solar illumination incident angle, and sky visibility factor. The standard deviation of these terrain parameters was calculated respectively. The number of simulation experiments was increased until the difference between two consecutive standard deviations was less than 5%.

[0039] (4) The standard deviation of the terrain parameter sequence obtained by the pixel-by-pixel statistical Monte Carlo simulation is used as the standard uncertainty of the terrain parameters, including the standard uncertainty of the slope. Standard uncertainty of the projected shadow coefficient Standard uncertainty of the cosine of the incident angle of solar illumination Standard uncertainty of sky visibility factor There are a total of 4 uncertainty components.

[0040] (5) Statistical analysis of the linear correlation coefficient between any two sets of terrain parameter sequences obtained from Monte Carlo simulation on a pixel-by-pixel basis. ,in and This corresponds to two different parameters among slope, shadow projection coefficient, cosine of solar illumination incident angle, and sky visibility factor.

[0041] Step 4: Evaluate the spectral uncertainty of atmospheric parameters per pixel and the correlation coefficients between atmospheric parameters. The steps for calculating the uncertainty of terrain parameters and the correlation coefficients using the Monte Carlo-based distribution propagation method include:

[0042] (1) Determine the local meteorological parameters, including atmospheric visibility, atmospheric temperature and atmospheric profile, based on the imaging area and imaging time of the imager. The atmospheric profile can be selected from the standard atmospheric model profile of MODTRAN5.3, or the sounding profile of the meteorological station in the imaging area or the spatiotemporal interpolation profile of atmospheric reanalysis data.

[0043] (2) Using the Type B uncertainty assessment method and referring to the empirical conclusions given in the user manual of the atmospheric radiative transfer model MODTRAN, the absolute accuracy of transmittance is generally better than ±0.005, and the absolute accuracy of radiation is about ±2%. Under the assumption of normal distribution and considering a 95% confidence probability, the standard uncertainty of transmittance caused by the MODTRAN model is taken as 0.003, and the standard relative uncertainty of radiation is taken as 1%. These are used to calculate the model standard uncertainty corresponding to the MODTRAN simulation of atmospheric transmittance and radiation, respectively. .

[0044] (3) Based on the user's accuracy requirements or measurement experience, the uncertainty and probability density function of the main variable parameters of the atmosphere across the entire spectrum, such as total water vapor column, atmospheric temperature, visibility, and carbon dioxide concentration, are determined by using the Type B uncertainty assessment method.

[0045] (4) Using the Monte Carlo-based distribution propagation method, the uncertainty of the main variable parameters of the atmosphere across the entire spectrum is used as the solar direct spectral irradiance. Solar scattering spectral irradiance Atmospheric thermal emission and thermal scattering spectral irradiance Atmospheric albedo Direct sunlight transmittance Scattering transmittance and atmospheric radiation There are seven sources of uncertainty for atmospheric parameters. Based on the uncertainties and probability density functions of the main variable atmospheric parameters across the entire spectrum, random errors are superimposed on the main variable atmospheric parameters across the entire spectrum, such as total water vapor column, atmospheric temperature, visibility, and carbon dioxide concentration. Monte Carlo simulations are then performed pixel-by-pixel and band-by-band. , , , , , and There are a total of 7 atmospheric parameters. The standard deviation of each atmospheric parameter is calculated. The number of simulation experiments is increased until the difference between two consecutive standard deviations is less than 5%.

[0046] (5) The standard deviations of the atmospheric parameter sequences obtained by pixel-by-pixel and band-by-band statistical Monte Carlo simulations are used as the standard uncertainties of the atmospheric parameters, and as the components of the solar direct spectral irradiance uncertainty caused by the uncertainty of the main variable parameters of the atmosphere across the entire spectrum. Components of uncertainty in solar scattering spectral irradiance Uncertainty components of atmospheric thermal emission and thermal scattering spectral irradiance Atmospheric albedo uncertainty component Direct transmittance uncertainty component scattering transmittance uncertainty component Atmospheric path radiation uncertainty components Considering the model uncertainty in atmospheric parameter calculations caused by the MODTRAN model, the standard uncertainty of each atmospheric parameter can be synthesized as follows:

[0047]

[0048] in, express , , , , , and Any one of the atmospheric parameters, express Standard uncertainty;

[0049] (6) Statistical analysis of the linear correlation coefficient between any two sets of atmospheric parameter sequences obtained by Monte Carlo simulation per pixel and per band. ,in and correspond , , , , , and Two different parameters;

[0050] Step 5: Construct a model for the uncertainty propagation of the radiative transfer process and synthesize the uncertainty of the entrance pupil radiance. Using the process described in Step 1 of calculating the entrance pupil radiance from surface reflectivity, surface emissivity, and surface temperature signals as the radiative transfer process, and using atmospheric parameters, topographic parameters, and surface signals as sources of uncertainty, calculate the entrance pupil radiance uncertainty step by step.

[0051] First, without considering the correlation between atmospheric and topographic parameters, the uncertainty sources of ground-based radiance include uncertainties in surface reflectivity, surface emissivity, surface temperature, slope, cast shadow coefficient, cosine of solar incidence angle, and sky visibility factor. The combined standard uncertainty of ground-based radiance is... The formula is:

[0052]

[0053] in, This indicates that the first-order partial derivative is used to calculate the effect of the parameter on the radiance above the ground. The sensitivity coefficient, Indicates the standard uncertainty of the slope. This represents the standard uncertainty of the projected shadow coefficient. This represents the standard uncertainty of the cosine of the incident angle of solar illumination. This represents the standard uncertainty of the sky visibility factor. The standard uncertainty of atmospheric albedo is represented by... The standard uncertainty of solar direct spectral irradiance The standard uncertainty of solar scattering spectral irradiance. The standard uncertainty of atmospheric thermal emission radiation and thermal scattering radiation spectral irradiance.

[0054] Then, considering the sources of uncertainty in the entrance pupil radiance, including the uncertainties in direct transmittance, scattered transmittance, ground-level radiance, and atmospheric path radiation, the standard uncertainty of the entrance pupil radiance is synthesized. The formula is:

[0055]

[0056] in, This indicates that the entrance pupil radiance is calculated using the first-order partial derivative with respect to the parameters. The sensitivity coefficient, The standard uncertainty of direct light transmittance. The standard uncertainty of scattering transmittance is represented by The standard uncertainty of atmospheric path radiation is expressed as follows: This represents the uncertainty component caused by the correlation between atmospheric parameters. This represents the uncertainty component caused by the correlation between terrain parameters.

[0057] The formula for calculating the uncertainty component caused by the correlation between atmospheric parameters is:

[0058]

[0059] in, The value is 7, indicating the number of atmospheric parameters; and These represent two different atmospheric parameters among direct solar spectral irradiance, diffuse solar spectral irradiance, atmospheric thermal emission and thermal scattering spectral irradiance, atmospheric albedo, direct transmittance, diffuse transmittance, and atmospheric path radiation. and These represent the entrance pupil radiance to the [missing information]. and The first-order partial derivative is also the sensitivity coefficient; This represents the linear correlation coefficient between two atmospheric parameters; and express and The standard uncertainty.

[0060] The formula for calculating the uncertainty component caused by the correlation between topographic parameters is:

[0061]

[0062] in, The value is 4, indicating the number of terrain parameters; and This represents two different parameters among slope, shadow projection coefficient, cosine of solar illumination incident angle, and sky visibility factor; and These represent the calculation of the above-ground radiance using first-order partial derivatives. and Sensitivity coefficient; This represents the linear correlation coefficient between two terrain parameters; and express and The standard uncertainty.

[0063] Step 6: Construct an uncertainty propagation model for the imaging measurement process and synthesize the restored radiance uncertainty. Using the process described in Step 1 of calculating the restored radiance from the entrance pupil radiance signal as the imaging measurement process, and taking the entrance pupil radiance, the random error of the full-spectrum hyperspectral imager, and the error of the radiometric correction coefficient obtained from the radiometric calibration process as sources of uncertainty, calculate the restored radiance uncertainty step by step.

[0064] First, the formula for calculating the standard uncertainty of the number of electrons in the signal is:

[0065]

[0066] in, Indicates spatial location ,wavelength The standard uncertainty of the entrance pupil radiance at that location, This represents the sensitivity coefficient of the detector pixel signal electron count to the entrance pupil radiance signal within the pixel imaging region, calculated using the first derivative:

[0067]

[0068] Then, consider the standard uncertainty of the random relative error caused by the nonlinearity and inhomogeneity of the full-spectrum hyperspectral imager's response. The standard deviation of the number of random additive noise electrons in the full-spectrum hyperspectral imager is used as the noise uncertainty. Calculate the standard uncertainty of the DN value. The formula is:

[0069]

[0070] Then, absolute radiometric correction is performed based on a linear regression model. The radiometric correction coefficients and their uncertainties are estimated according to the least squares linear regression model. The uncertainty of the DN value and the uncertainty of the radiometric correction coefficients are calculated according to the random error propagation formula, and the uncertainty of the restored radiance is synthesized. :

[0071]

[0072] in, Represents the radiation correction gain coefficient Standard uncertainty Represents the radiation correction bias coefficient Standard uncertainty express and The uncertainty component caused by the correlation.

[0073] Based on the linear radiation correction formula described in step 1, with DN value as the independent variable and energy level radiance as the variable... As the dependent variable, for Least squares linear regression analysis was performed on the radiance and DN values ​​corresponding to each energy level. The analysis revealed that the sources of uncertainty in the radiation correction coefficient included... The uncertainty of the DN value of each energy level and radiance of each energy level The uncertainties; among them, for the laboratory radiometric calibration process, the primary uncertainties corresponding to the DN value and energy level radiance include: random relative errors caused by the nonlinearity and response inhomogeneity of the full-spectrum hyperspectral imager. Random additive noise electron number The following are uncertainties: random center wavelength drift and random half-width error caused by spectral calibration uncertainty; standard uncertainty of standard lamp irradiance in the visible-shortwave infrared band; uncertainty of diffuse reflectance of the visible-shortwave infrared band; uncertainty of measurement of diffuse reflectance by radiometer in the visible-shortwave infrared band; uncertainty of integrating sphere light source in the visible-shortwave infrared band; uncertainty of measurement of integrating sphere by radiometer in the visible-shortwave infrared band; uncertainty of blackbody temperature in the mid-wave-longwave infrared band; uncertainty of blackbody emissivity in the mid-wave-longwave infrared band; and uncertainty caused by stray light in the system.

[0074] Using the aforementioned primary uncertainty as the standard deviation, random errors are generated and superimposed onto the simulated spectra of DN value and energy level radiance, respectively. The simulation is performed according to the formula for DN value described in step 1 of claim 1. The corresponding energy level radiance A sequence of DN values; and estimates the radiometric correction coefficients for each spectral channel of the full-spectrum hyperspectral imager based on least-squares linear regression. and Calculate the variance of the radiation correction factor. and And the covariance between the two radiation correction coefficients. The formula is:

[0075]

[0076]

[0077]

[0078] The standard deviation of the radiation correction factor and and the covariance between the two radiation correction coefficients Uncertainty components, respectively, used as correction coefficients: , , .

[0079] Step 7: Analyze the uncertainty components in the restored radiance and rank the uncertainty contributions of each step:

[0080] Based on the different sources of primary uncertainty, the relative uncertainty of the restored radiance is divided into four components, and the relative uncertainty of the restored radiance is expressed as:

[0081]

[0082] in, This represents the relative uncertainty in the relative restored radiance. , , and The four components represent the relative uncertainty of the restored radiance introduced by the surface signal, atmospheric parameters, topographic parameters, imaging, and calibration processes, respectively.

[0083] The primary uncertainty sources were categorized into four components corresponding to different stages. By controlling variables, the standard uncertainty of the restored radiance under the influence of uncertainty factors in a single stage was calculated, and this was used as... , , and The estimated values ​​are used to rank the impact of each factor on the uncertainty of the restored radiance. The primary sources of uncertainty for the surface signal factor include the uncertainty of surface emissivity, surface reflectivity, and surface temperature. The primary sources of uncertainty for the atmospheric parameters factor include the uncertainty of major variable atmospheric parameters across the entire spectrum, such as total water vapor column, atmospheric temperature, visibility, and carbon dioxide concentration. The primary sources of uncertainty for the topographic parameters factor include the horizontal and vertical uncertainties of the surface elevation data products. The primary sources of uncertainty for the imaging and calibration factors include random additive noise in the imaging measurement DN value data, the nonlinearity and response inhomogeneity of the hyperspectral imager, and the uncertainty of the radiometric correction coefficient.

[0084] This invention constructs an uncertainty propagation model for the full-spectrum hyperspectral remote sensing forward modeling process. It synthesizes uncertainties related to surface signal fluctuations, atmospheric parameters, topographic parameters, random noise and response nonlinearity errors in the imaging process, and radiometric correction, enabling the source tracing of uncertainties in the full-spectrum hyperspectral entrance pupil radiance signal and the restored radiance spectrum. This allows for quantitative comparison and ranking of the surface uncertainty components, atmospheric parameter uncertainty components, topographic parameter uncertainty components, and uncertainties in the imaging and calibration processes that affect the restored radiance uncertainty. This provides technical support for error allocation and performance optimization in the design of full-spectrum hyperspectral imaging measurement systems. Attached Figure Description

[0085] Figure 1 This is a flowchart illustrating the technical process of this method.

[0086] Figure 2 For the forward modeling process of remote sensing measurements, the signal and uncertainty transmission link is used.

[0087] Figure 3 Example of relative uncertainty in entrance pupil radiance per pixel;

[0088] Figure 4 Example of a spectral curve for the relative uncertainty of entrance pupil radiance;

[0089] Figure 5 Here is an example of restoring the radiance spectrum and the uncertainty range;

[0090] Figure 6 Comparative examples of contributions to the reconstructed radiance spectrum. Detailed Implementation

[0091] To better illustrate the uncertainty analysis method for full-spectrum hyperspectral Earth remote sensing imaging measurement involved in this invention, the design parameters of the long-wave infrared channel of a full-spectrum imager prototype are used to predict and analyze the uncertainty of Earth remote sensing imaging measurement.

[0092] A specific embodiment of the uncertainty analysis method for full-spectrum hyperspectral Earth remote sensing imaging disclosed in this invention is as follows:

[0093] Data and spectrometer parameter preparation:

[0094] For the experimental area, the Mingsha Mountain region south of Dunhuang City, Gansu Province, my country, was selected, including some urban scenes. In this embodiment, typical long-wave infrared emissivity spectra of ground features measured in the field and typical ground feature spectra obtained from the ASTER spectral library were used, combined with the Sentinel-2 10m ground feature classification results for the region and surface abundance data obtained based on the Gaofen-5 visible-short-wave infrared hyperspectral imager. A linear mixture model was used to simulate the emissivity spectra of ground features at each pixel level. Based on the principle of undulating surface thermal balance, the surface temperature at each pixel was simulated as the surface temperature signal. Regarding atmospheric parameters, radiance simulation and uncertainty analysis were conducted at two time points: July 14, 2019, and December 21, 2019, corresponding to typical summer and winter scenarios, respectively. Dunhuang City, Gansu Province, my country, has a warm temperate arid climate, with higher humidity and temperature in summer than in winter. In this embodiment, MODTRAN 5.3 was used to calculate atmospheric parameters. The summer atmospheric model was the mid-latitude summer model from the six built-in MODTRAN models, and the winter atmospheric model was the mid-latitude winter model. Atmospheric visibility was set to 30 km and carbon dioxide concentration was set to 390 ppmv. For terrain parameters, DEM data from the selected imaging area in the ASTER GDEM V3 dataset was used to calculate terrain parameters and evaluate the pixel-by-pixel terrain parameter uncertainty and correlation coefficient. The Japan Aerospace Exploration Agency's validation report on the ASTER GDEM V3 dataset gives a standard deviation of 12.1 m for the vertical error, a horizontal spatial sampling interval of approximately 30 m, and a horizontal spatial resolution of 72 m. Using the standard deviation of 12.1 m for the vertical error as the vertical uncertainty of the DEM data, and referring to GUM, its horizontal uncertainty was evaluated using the horizontal resolution of the DEM data. Half of the horizontal spatial resolution was used as the error limit for the horizontal spatial coordinates. Assuming that the horizontal error of the DEM follows a uniform distribution, the horizontal uncertainty of the DEM data was set as follows: .

[0095] Regarding spectrometer parameters, the design parameters of a full-spectrum hyperspectral imager prototype were selected for experiments on its long-wave infrared channel. The design parameters of the spectrometer's long-wave infrared channel are as follows: band range of 8.0 μm to 12.5 μm, spectral sampling interval of 0.1 μm, spectral half-width at half-maximum of 0.079 μm, total static modulation transfer function of 0.17, ground sampling interval of 100 m, average total transmittance of the optical system of 0.33, average diffraction efficiency of the spectrometer of 0.89, average quantum efficiency of the detector of 0.45, F-number of the optical system of 4.8, and detector pixel size of 7.68 × 10⁻⁶. −10 m 2 The integration time is 0.3 ms, the quantization bit depth is 14 bits, the detector output voltage is 3V, and the detector full-well electron count is 1.125 × 10⁻⁶. 7 e− The equivalent blackbody temperature of the background thermal radiation of the optomechanical system is set to 100K, the equivalent voltage of the circuit noise is 0.3mV, and the dark current is set to 3×10⁻⁶. −9 A / pixel, readout noise electron count standard deviation 4000 e − The system response nonlinearity is 0.5%, the spectral calibration uncertainty is 0.003λ, the calibration relative uncertainty of the radiation calibration blackbody emissivity is set to 1%, and the blackbody temperature calibration uncertainty is set to 0.1K.

[0096] According to the uncertainty analysis steps of the full-spectrum hyperspectral Earth remote sensing imaging measurement of the present invention, the imaging signal and uncertainty are predicted, and the uncertainty contribution of each step is analyzed:

[0097] Step 1: Simulate and calculate the spectral imaging signals of the top atmospheric entrance pupil radiance and restored radiance using surface reflectance, surface emissivity, surface temperature, topographic parameters, atmospheric parameters, and imaging system parameters:

[0098] The actual atmospheric conditions, observation geometry, and surface elevation of the remote sensing imaging area are input into the atmospheric radiative transfer model MODTRAN5.3 to obtain full-spectrum atmospheric parameters corresponding to different surface elevations, including direct spectral irradiance, atmospheric diffuse solar spectral irradiance, atmospheric thermal emission and thermal scattering radiation, atmospheric hemispherical albedo, atmospheric scattering transmittance, atmospheric direct transmittance, atmospheric stratified extinction coefficient and scattering coefficient, and atmospheric path radiation. Based on the surface elevation model, the topographic parameters of each pixel in the imaging area are calculated, including slope, projection shadow coefficient, cosine of solar illumination incident angle, and sky visibility factor.

[0099] Based on the forward transmission process of remote sensing signals, the full-spectrum solar and atmospheric spectral radiation illumination received by the natural Earth's surface is first calculated. :

[0100]

[0101] in, Indicates the spatial location of pixels in the imaging region. Represents spatial coordinates along the orbital direction. Spatial coordinates representing the direction perpendicular to the orbit; Represents a pixel The corresponding surface elevation; Indicates wavelength; Indicates altitude The solar direct spectral irradiance received at a horizontal surface; This represents the projection shadow coefficient of a pixel, with a value between 0 and 1. 0 indicates that sunlight is completely blocked, and 1 indicates that there is no obstruction. Represents the cosine of the angle of incidence of solar illumination; Indicates altitude Solar spectral irradiance received at a horizontal surface; Indicates altitude The atmospheric thermal emission and thermal scattering spectral irradiance received at a horizontal surface; Represents pi; This represents the sky visibility factor corresponding to the undulating terrain pixel; This represents the anisotropy correction term for solar diffused illumination.

[0102]

[0103] in, Indicates atmospheric downward transmittance. The slope of the earth's surface is represented by the three terms added in the formula, which respectively represent the proportions of anisotropic scattered radiation, isotropic scattered light, and horizontal scattered light in the circumpolar direction.

[0104] Calculate the total solar and atmospheric spectral radiation reflected from the Earth's surface, along with its thermal emission from the Earth's surface, to determine the combined surface radiance. :

[0105]

[0106] in, Indicates surface reflectance, Indicates surface emissivity, Indicates surface temperature. This represents the blackbody thermal radiation calculated using Planck's formula. Represents a pixel The pixel coordinates of the region and its surrounding area This indicates a lighting correction for undulating terrain.

[0107]

[0108] in, For slope pixels Normal and arrive The angle between the lines, For slope pixels Normal and arrive The angle between the lines, express arrive Spatial distance, for arrive Atmospheric extinction coefficient, For pixels The area.

[0109] Then, the ground-based radiance, encompassing the full spectrum of atmospheric and undulating surface trapping effects, is calculated. :

[0110]

[0111] in, Indicates atmospheric albedo; This represents the average ground-based radiance within the imaging area. Represents a pixel The equivalent background reflectance in the adjacent area is obtained by weighting the average values ​​using topographic parameters:

[0112]

[0113]

[0114] Thus, the full-spectrum atmospheric top entrance pupil radiance signal under undulating surface conditions was simulated. :

[0115]

[0116] in, This represents the direct transmittance along the path from the ground surface to the sensor. This represents the scattering transmittance along the instantaneous field of view path from nearby ground objects to the sensor. Indicates atmospheric path radiation. This represents the normalized atmospheric proximity effect contribution factor obtained from the atmospheric stratification scattering model.

[0117] Using the platform motion point spread function Point spread function of optical system Optical system transmittance Spectroscopic optical system diffraction efficiency Spectral response function Optical system F-number Detector pixel area Quantum efficiency of detectors Point spread function of detectors and electronic systems Integral Time Quantization bit depth Standard deviation of equivalent number of readout noise Standard deviation of equivalent electron count for circuit noise Standard deviation of equivalent electron count for quantization noise Background electron count Detector dark current The reference voltage V of the readout circuit REF and detector charge conversion rate C VFSimulations were performed using the response parameters of the hyperspectral imager. The number of signal electrons received by the area array detector was calculated. The formula is:

[0118]

[0119] in, Denotes Planck's constant. Represents the speed of light. This represents the convolution operation.

[0120] Furthermore, the DN value signal of the full-spectrum hyperspectral imaging is calculated. The formula for the DN value is:

[0121]

[0122] in, This represents the random relative error caused by the nonlinearity and inhomogeneity of the response of a full-spectrum hyperspectral imager; Indicates the number of electrons in random additive noise. The calculation formula is: ,in, Indicated by Using the standard deviation as the standard deviation and 0 as the mean, Gaussian random noise is generated.

[0123] Radiometric calibration and correction were performed in the linear response region of the hyperspectral imager to simulate and restore the radiance imaging signal. The linear radiation correction formula is: ,in, and This represents the radiation response correction coefficient of a full-spectrum hyperspectral imager.

[0124] Step 2: Evaluate the uncertainties of surface reflectance, surface emissivity, and surface temperature.

[0125] For remote sensing applications, the root mean square error indices of surface reflectance, surface emissivity, and surface temperature required for quantitative remote sensing applications are used as the standard uncertainty of surface reflectance. Standard uncertainty of surface emissivity and the standard uncertainty of surface temperature The evaluation results are as follows. Based on the requirements of quantitative remote sensing applications using thermal infrared, the standard uncertainty of surface temperature is set to 1 K, and the standard uncertainty of surface emissivity is set to 0.01. According to Kirchhoff's laws, the sum of surface reflectivity and emissivity is considered to be 1; therefore, the standard uncertainty of surface reflectivity is also set to 0.01.

[0126] Step 3: Evaluate the uncertainty of terrain parameters per pixel and the correlation coefficients between terrain parameters. The steps for calculating the uncertainty of terrain parameters and the correlation coefficients using the Monte Carlo-based distribution propagation method include:

[0127] (1) Based on the imaging area and imaging geometry parameters of the imager, spatial cropping, registration and spatial resampling are performed on the surface elevation digital model product, i.e., DEM data.

[0128] (2) Based on the product manual and verification data of the digital model of surface elevation, the horizontal standard uncertainty and vertical standard uncertainty of the DEM data are obtained using the Type B uncertainty assessment method.

[0129] (3) Using the Monte Carlo-based distribution propagation method, the horizontal and vertical standard uncertainties of the DEM data are calculated. As a source of uncertainty in topographic parameters, according to the central limit theorem, the standard deviations of the DEM data are respectively... and The random Gaussian horizontal error and random Gaussian vertical error were calculated. Monte Carlo simulation was performed pixel by pixel to calculate four terrain parameters: slope, projection shadow coefficient, cosine of solar illumination incident angle, and sky visibility factor. The standard deviation of these terrain parameters was calculated respectively. The number of simulation experiments was increased until the difference between two consecutive standard deviations was less than 5%.

[0130] (4) The standard deviation of the terrain parameter sequence obtained by the pixel-by-pixel statistical Monte Carlo simulation is used as the standard uncertainty of the terrain parameters, including the standard uncertainty of the slope. Standard uncertainty of the projected shadow coefficient Standard uncertainty of the cosine of the incident angle of solar illumination Standard uncertainty of sky visibility factor There are a total of 4 uncertainty components.

[0131] (5) Statistical analysis of the linear correlation coefficient between any two sets of terrain parameter sequences obtained from Monte Carlo simulation on a pixel-by-pixel basis. ,in and This corresponds to two different parameters among slope, shadow projection coefficient, cosine of solar illumination incident angle, and sky visibility factor.

[0132] Step 4: Evaluate the spectral uncertainty of atmospheric parameters per pixel and the correlation coefficients between atmospheric parameters. The steps for calculating the uncertainty of terrain parameters and the correlation coefficients using the Monte Carlo-based distribution propagation method include:

[0133] (1) Determine the local meteorological parameters, including atmospheric visibility, atmospheric temperature and atmospheric profile, based on the imaging area and imaging time of the imager. The atmospheric profile can be selected from the standard atmospheric model profile of MODTRAN5.3, or the sounding profile of the meteorological station in the imaging area or the spatiotemporal interpolation profile of atmospheric reanalysis data.

[0134] (2) Using the Type B uncertainty assessment method and referring to the empirical conclusions given in the user manual of the atmospheric radiative transfer model MODTRAN, the absolute accuracy of transmittance is generally better than ±0.005, and the absolute accuracy of radiation is about ±2%. Under the assumption of normal distribution and considering a 95% confidence probability, the standard uncertainty of transmittance caused by the MODTRAN model is taken as 0.003, and the standard relative uncertainty of radiation is taken as 1%. These are used to calculate the model standard uncertainty corresponding to the MODTRAN simulation of atmospheric transmittance and radiation, respectively. .

[0135] (3) Based on the user's accuracy requirements or measurement experience, the uncertainty and probability density function of the main variable parameters of the atmosphere across the entire spectrum, such as total water vapor column, atmospheric temperature, visibility, and carbon dioxide concentration, are determined by using the Type B uncertainty assessment method.

[0136] (4) Using the Monte Carlo-based distribution propagation method, the uncertainty of the main variable parameters of the atmosphere across the entire spectrum is used as the solar direct spectral irradiance. Solar scattering spectral irradiance Atmospheric thermal emission and thermal scattering spectral irradiance Atmospheric albedo Direct sunlight transmittance Scattering transmittance and atmospheric radiation There are seven sources of uncertainty for atmospheric parameters. Based on the uncertainties and probability density functions of the main variable atmospheric parameters across the entire spectrum, random errors are superimposed on the main variable atmospheric parameters across the entire spectrum, such as total water vapor column, atmospheric temperature, visibility, and carbon dioxide concentration. Monte Carlo simulations are then performed pixel-by-pixel and band-by-band. , , , , , and There are a total of 7 atmospheric parameters. The standard deviation of each atmospheric parameter is calculated. The number of simulation experiments is increased until the difference between two consecutive standard deviations is less than 5%.

[0137] (5) The standard deviations of the atmospheric parameter sequences obtained by pixel-by-pixel and band-by-band statistical Monte Carlo simulations are used as the standard uncertainties of the atmospheric parameters, and as the components of the solar direct spectral irradiance uncertainty caused by the uncertainty of the main variable parameters of the atmosphere across the entire spectrum. Components of uncertainty in solar scattering spectral irradiance Uncertainty components of atmospheric thermal emission and thermal scattering spectral irradiance Atmospheric albedo uncertainty component Direct transmittance uncertainty component scattering transmittance uncertainty component Atmospheric path radiation uncertainty components Considering the model uncertainty in atmospheric parameter calculations caused by the MODTRAN model, the standard uncertainty of each atmospheric parameter can be synthesized as follows:

[0138]

[0139] in, express , , , , , and Any one of the atmospheric parameters, express Standard uncertainty;

[0140] (6) Statistical analysis of the linear correlation coefficient between any two sets of atmospheric parameter sequences obtained by Monte Carlo simulation per pixel and per band. ,in and correspond , , , , , and Two different parameters;

[0141] Step 5: Construct a model for the uncertainty propagation of the radiative transfer process and synthesize the uncertainty of the entrance pupil radiance. Using the process described in Step 1 of calculating the entrance pupil radiance from surface reflectivity, surface emissivity, and surface temperature signals as the radiative transfer process, and using atmospheric parameters, topographic parameters, and surface signals as sources of uncertainty, calculate the entrance pupil radiance uncertainty step by step.

[0142] First, without considering the correlation between atmospheric and topographic parameters, the uncertainty sources of ground-based radiance include uncertainties in surface reflectivity, surface emissivity, surface temperature, slope, cast shadow coefficient, cosine of solar incidence angle, and sky visibility factor. The combined standard uncertainty of ground-based radiance is... The formula is:

[0143]

[0144] in, This indicates that the first-order partial derivative is used to calculate the effect of the parameter on the radiance above the ground. The sensitivity coefficient, Indicates the standard uncertainty of the slope. This represents the standard uncertainty of the projected shadow coefficient. This represents the standard uncertainty of the cosine of the incident angle of solar illumination. This represents the standard uncertainty of the sky visibility factor. The standard uncertainty of atmospheric albedo is represented by... The standard uncertainty of solar direct spectral irradiance The standard uncertainty of solar scattering spectral irradiance. The standard uncertainty of atmospheric thermal emission radiation and thermal scattering radiation spectral irradiance.

[0145] Then, considering the sources of uncertainty in the entrance pupil radiance, including the uncertainties in direct transmittance, scattered transmittance, ground-level radiance, and atmospheric path radiation, the standard uncertainty of the entrance pupil radiance is synthesized. The formula is:

[0146]

[0147] in, This indicates that the entrance pupil radiance is calculated using the first-order partial derivative with respect to the parameters. The sensitivity coefficient, The standard uncertainty of direct light transmittance. The standard uncertainty of scattering transmittance is represented by The standard uncertainty of atmospheric path radiation is expressed as follows: This represents the uncertainty component caused by the correlation between atmospheric parameters. This represents the uncertainty component caused by the correlation between terrain parameters.

[0148] The formula for calculating the uncertainty component caused by the correlation between atmospheric parameters is:

[0149]

[0150] in, The value is 7, indicating the number of atmospheric parameters; and These represent two different atmospheric parameters among direct solar spectral irradiance, diffuse solar spectral irradiance, atmospheric thermal emission and thermal scattering spectral irradiance, atmospheric albedo, direct transmittance, diffuse transmittance, and atmospheric path radiation. and These represent the entrance pupil radiance to the [missing information]. and The first-order partial derivative is also the sensitivity coefficient; This represents the linear correlation coefficient between two atmospheric parameters; and express and The standard uncertainty.

[0151] The formula for calculating the uncertainty component caused by the correlation between topographic parameters is:

[0152]

[0153] in, The value is 4, indicating the number of terrain parameters; and This represents two different parameters among slope, shadow projection coefficient, cosine of solar illumination incident angle, and sky visibility factor; and These represent the calculation of the above-ground radiance using first-order partial derivatives. and Sensitivity coefficient; This represents the linear correlation coefficient between two terrain parameters; and express and The standard uncertainty.

[0154] In this embodiment, the relative uncertainty of the pixel-by-pixel entrance pupil radiance at the 11μm center wavelength within the imaging region is obtained. like Figure 3 As shown, the relative uncertainty of the entrance pupil radiance varies for each pixel, but the average value is approximately 0.02 in both summer and winter. The relative uncertainty spectra of the entrance pupil radiance for typical pixels on typical desert shady and sunny slopes under summer and winter conditions are shown below. Figure 4 As shown, the relative uncertainty of the long-wave infrared entrance pupil radiance of most bands in summer is less than that in winter for the same pixel, while the total water vapor content is greater in summer than in winter, and the relative uncertainty of the entrance pupil radiance in the water vapor absorption band is also greater in summer than in winter.

[0155] Step 6: Construct an uncertainty propagation model for the imaging measurement process and synthesize the restored radiance uncertainty. Using the process described in Step 1 of calculating the restored radiance from the entrance pupil radiance signal as the imaging measurement process, and taking the entrance pupil radiance, the random error of the full-spectrum hyperspectral imager, and the error of the radiometric correction coefficient obtained from the radiometric calibration process as sources of uncertainty, calculate the restored radiance uncertainty step by step.

[0156] First, the formula for calculating the standard uncertainty of the number of electrons in the signal is:

[0157]

[0158] in, Indicates spatial location ,wavelength The standard uncertainty of the entrance pupil radiance at that location, This represents the sensitivity coefficient of the detector pixel signal electron count to the entrance pupil radiance signal within the pixel imaging region, calculated using the first derivative:

[0159]

[0160] Then, consider the standard uncertainty of the random relative error caused by the nonlinearity and inhomogeneity of the full-spectrum hyperspectral imager's response. The standard deviation of the number of random additive noise electrons in the full-spectrum hyperspectral imager is used as the noise uncertainty. Calculate the standard uncertainty of the DN value. The formula is:

[0161]

[0162] Then, absolute radiometric correction is performed based on a linear regression model. The radiometric correction coefficients and their uncertainties are estimated according to the least squares linear regression model. The uncertainty of the DN value and the uncertainty of the radiometric correction coefficients are calculated according to the random error propagation formula, and the uncertainty of the restored radiance is synthesized. :

[0163]

[0164] in, Represents the radiation correction gain coefficient Standard uncertainty Represents the radiation correction bias coefficient Standard uncertainty express and The uncertainty component caused by the correlation.

[0165] Based on the linear radiation correction formula described in step 1, with DN value as the independent variable and energy level radiance as the variable... As the dependent variable, for Least squares linear regression analysis was performed on the radiance and DN values ​​corresponding to each energy level. The analysis revealed that the sources of uncertainty in the radiation correction coefficient included... The uncertainty of the DN value of each energy level and radiance of each energy level The uncertainties; among them, for the laboratory radiometric calibration process, the primary uncertainties corresponding to the DN value and energy level radiance include: random relative errors caused by the nonlinearity and response inhomogeneity of the full-spectrum hyperspectral imager. Random additive noise electron number The following are uncertainties: random center wavelength drift and random half-width error caused by spectral calibration uncertainty; standard uncertainty of standard lamp irradiance in the visible-shortwave infrared band; uncertainty of diffuse reflectance of the visible-shortwave infrared band; uncertainty of measurement of diffuse reflectance by radiometer in the visible-shortwave infrared band; uncertainty of integrating sphere light source in the visible-shortwave infrared band; uncertainty of measurement of integrating sphere by radiometer in the visible-shortwave infrared band; uncertainty of blackbody temperature in the mid-wave-longwave infrared band; uncertainty of blackbody emissivity in the mid-wave-longwave infrared band; and uncertainty caused by stray light in the system.

[0166] Using the aforementioned primary uncertainty as the standard deviation, random errors are generated and superimposed onto the simulated spectra of DN value and energy level radiance, respectively. The simulation is performed according to the formula for DN value described in step 1 of claim 1. The corresponding energy level radiance A sequence of DN values; and estimates the radiometric correction coefficients for each spectral channel of the full-spectrum hyperspectral imager based on least-squares linear regression. and Calculate the variance of the radiation correction factor. and And the covariance between the two radiation correction coefficients. The formula is:

[0167]

[0168]

[0169]

[0170] The standard deviation of the radiation correction factor and and the covariance between the two radiation correction coefficients Uncertainty components, respectively, used as correction coefficients: , , .

[0171] In this embodiment, the estimated values ​​of the restored radiance signals of typical desert sunny and shady slope pixels in summer and winter, and their three-times standard uncertainty intervals, are obtained. )like Figure 5 As shown, the true value of the entrance pupil radiance under the corresponding experimental conditions is... ~ The confidence probability is 99.7%.

[0172] Step 7: Analyze the uncertainty components in the restored radiance and rank the uncertainty contributions of each step:

[0173] Based on the different sources of primary uncertainty, the relative uncertainty of the restored radiance is divided into four components, and the relative uncertainty of the restored radiance is expressed as:

[0174]

[0175] in, This represents the relative uncertainty in the relative restored radiance. , , and The four components represent the relative uncertainty of the restored radiance introduced by the surface signal, atmospheric parameters, topographic parameters, imaging, and calibration processes, respectively.

[0176] The primary uncertainty sources were categorized into four components corresponding to different stages. By controlling variables, the standard uncertainty of the restored radiance under the influence of uncertainty factors in a single stage was calculated, and this was used as... , , and The estimated values ​​are used to rank the impact of each factor on the uncertainty of the restored radiance. The primary sources of uncertainty for the surface signal factor include the uncertainty of surface emissivity, surface reflectivity, and surface temperature. The primary sources of uncertainty for the atmospheric parameters factor include the uncertainty of major variable atmospheric parameters across the entire spectrum, such as total water vapor column, atmospheric temperature, visibility, and carbon dioxide concentration. The primary sources of uncertainty for the topographic parameters factor include the horizontal and vertical uncertainties of the surface elevation data products. The primary sources of uncertainty for the imaging and calibration factors include random additive noise in the imaging measurement DN value data, the nonlinearity and response inhomogeneity of the hyperspectral imager, and the uncertainty of the radiometric correction coefficient.

[0177] In this embodiment, the relative uncertainty contributions of pixels on typical desert sunny and shady slopes are obtained as follows: Figure 6As shown. It can be seen that, It fluctuates between 0.01 and 0.02. It is generated by surface signal fluctuations. As a reference standard, the uncertainty components generated by the four stages are compared. For pixels with varying temperatures (both winter and summer conditions), most bands are compared. Greater than . The uncertainty introduced by the atmosphere and topography is the most significant. Under winter conditions, the temperature on the shady slopes of the desert is very low, and the area receives little solar and atmospheric downdraft illumination; therefore, the signal level corresponding to this pixel is low. This leads to an increase in measurement uncertainty. Based on the above analysis, the factors influencing the uncertainty of the restored radiance at each stage can be ranked from largest to smallest: uncertainty in imaging and calibration, surface signal fluctuations, topographic parameter uncertainty, and atmospheric parameter uncertainty. Further analysis of the uncertainty in imaging and calibration reveals that the DN value data uncertainty, constituted by noise and nonlinear errors in the imaging measurement process, has the greatest impact on the restored radiance, followed by the uncertainty contribution of the correlation between the two radiometric correction coefficients obtained from least squares linear regression.

[0178] This invention addresses the problem of modeling and analyzing the quantitative relationship between the accuracy of full-spectrum hyperspectral Earth remote sensing measurements and the design specifications of imaging systems. It constructs an uncertainty propagation model for the forward modeling process of full-spectrum hyperspectral remote sensing and proposes a method for analyzing the uncertainty of full-spectrum hyperspectral Earth remote sensing imaging measurements. This invention synthesizes uncertainties related to surface signal fluctuations, atmospheric parameters, topographic parameters, random noise and response nonlinearity errors in the imaging process, and radiometric correction uncertainty. This enables the tracing of uncertainties in the full-spectrum hyperspectral entrance pupil radiance signal and the restored radiance spectrum, as well as the quantitative comparison and ranking of uncertainties introduced at each stage.

[0179] It should be understood that those skilled in the art can make improvements and modifications based on the above description and the characteristics of the actual imaging system to achieve the task of analyzing the uncertainty of Earth remote sensing imaging measurements, and all such improvements and modifications should fall within the scope of protection of the claims of this invention.

Claims

1. A method for analyzing the measurement uncertainty of full-spectrum hyperspectral Earth remote sensing imaging, characterized in that, It includes the following steps: Step 1: Simulate and calculate the spectral imaging signals of the top atmospheric entrance pupil radiance and restored radiance using surface reflectance, surface emissivity, surface temperature, topographic parameters, atmospheric parameters, and imaging system parameters: The actual atmospheric conditions, observation geometry, and surface elevation of the remote sensing imaging area are input into the atmospheric radiative transfer model MODTRAN5.3 to obtain full-spectrum atmospheric parameters corresponding to different surface elevations, including direct spectral irradiance, atmospheric diffuse solar spectral irradiance, atmospheric thermal emission and thermal scattering radiation, atmospheric hemispherical albedo, atmospheric diffuse transmittance, atmospheric direct transmittance, atmospheric stratified extinction coefficient and scattering coefficient, and atmospheric path radiation. Based on the surface elevation model, the topographic parameters of each pixel in the imaging area are calculated, including slope, projection shadow coefficient, cosine of solar illumination incident angle, and sky visibility factor. According to the forward transmission process of remote sensing measurement signals, the full-spectrum solar and atmospheric spectral irradiance received by the natural surface is first calculated. : in, Indicates the spatial location of pixels in the imaging region. Represents spatial coordinates along the orbital direction. Spatial coordinates representing the direction perpendicular to the orbit; Represents a cell The corresponding surface elevation; Indicates wavelength; Indicates altitude The solar direct spectral irradiance received at a horizontal surface; This represents the projection shadow coefficient of a pixel, with a value between 0 and 1. 0 indicates that sunlight is completely blocked, and 1 indicates that there is no obstruction. Represents the cosine of the incident angle of solar illumination; Indicates altitude Solar irradiance received at a horizontal surface; Indicates altitude The atmospheric thermal emission and thermal scattering spectral irradiance received at a horizontal surface; Represents pi; This represents the sky visibility factor corresponding to the undulating terrain pixel; This represents the anisotropy correction term for solar diffused illumination. in, Indicates atmospheric downward transmittance. The slope of the earth's surface is represented by the three terms added in the formula, which respectively represent the proportions of anisotropic scattered radiation, isotropic scattered light, and horizontal scattered light in the circumpolar direction. Calculate the total solar and atmospheric spectral radiation reflected from the Earth's surface, along with its thermal emission from the Earth's surface, to determine the combined surface radiance. : in, Indicates surface reflectance, Indicates surface emissivity, Indicates surface temperature. This represents the blackbody thermal radiation calculated using Planck's formula. Represents a cell The pixel coordinates of the region and its surrounding area This indicates the lighting correction for undulating terrain. in, For slope pixels Normal and arrive The angle between the lines, For slope pixels Normal and arrive The angle between the lines, express arrive Spatial distance, for arrive Atmospheric extinction coefficient, For pixels The area; Then, the ground-based radiance, encompassing the full spectrum of atmospheric and undulating surface trapping effects, is calculated. : in, Indicates atmospheric albedo; This represents the average ground-based radiance within the imaging area. Represents a cell The equivalent background reflectance in the adjacent area is obtained by weighting the average values ​​using topographic parameters: Thus, the full-spectrum atmospheric top entrance pupil radiance signal under undulating surface conditions was simulated. : in, This represents the direct transmittance along the path from the ground surface to the sensor. This represents the scattering transmittance along the instantaneous field of view path from nearby ground objects to the sensor. Indicates atmospheric path radiation. This represents the normalized atmospheric proximity effect contribution factor obtained from the atmospheric stratification scattering model. Using the platform motion point spread function Point spread function of optical system Optical system transmittance Spectroscopic optical system diffraction efficiency Spectral response function Optical system F-number Detector pixel area Quantum efficiency of detectors Point spread function of detectors and electronic systems Integral Time Quantization bit depth Standard deviation of equivalent number of readout noise Standard deviation of equivalent electron count for circuit noise Standard deviation of equivalent electron count for quantization noise Background electron count Detector dark current The reference voltage V of the readout circuit REF and detector charge conversion rate C VF Simulations were performed to calculate the number of signal electrons received by the array detector. The formula is: in, Denotes Planck's constant. Represents the speed of light. This represents the convolution operation; Furthermore, the DN value signal of the full-spectrum hyperspectral imaging is calculated. The formula for the DN value is: in, This represents the random relative error caused by the nonlinearity and inhomogeneity of the response of a full-spectrum hyperspectral imager; This represents the number of electrons in random additive noise. The calculation formula is ,in, Indicated by Using the standard deviation and a mean of 0, Gaussian random noise is generated. Radiometric calibration and correction were performed in the linear response region of the hyperspectral imager to simulate and restore the radiance imaging signal. The linear radiation correction formula is: ,in, and This represents the radiation response correction coefficient of a full-spectrum hyperspectral imager; Step 2: Evaluate the uncertainties of surface reflectance, surface emissivity, and surface temperature, including two approaches: one for remote sensing applications and the other for comparing measurement uncertainties across different spectrometers. (1) For remote sensing application tasks, the root mean square error of surface reflectance, surface emissivity and surface temperature required for quantitative remote sensing application tasks are used as the standard uncertainty of surface reflectance. Standard uncertainty of surface emissivity and the standard uncertainty of surface temperature The evaluation results; (2) For the task of comparing the measurement uncertainties of different spectrometers, multiple measurements of the ground features of interest are performed using the spectrometer, and the standard deviation of the measurements is used as the uncertainty of surface reflectance and emissivity. According to Kirchhoff's law, if the sum of surface emissivity and reflectance is 1, then the uncertainties of the two are equal, i.e. The temperature of ground object samples is measured using a radiation thermometer or thermocouple thermometer, and the uncertainty of this measurement is used as the uncertainty of the ground surface temperature. ; Step 3: Evaluate the uncertainty of terrain parameters per pixel and the correlation coefficients between terrain parameters; Step 4: Evaluate the spectral uncertainty of atmospheric parameters per pixel and the correlation coefficients between atmospheric parameters; Step 5: Construct a model for the uncertainty propagation of the radiative transfer process, and synthesize the uncertainty of the entrance pupil radiance. Taking the process of calculating the entrance pupil radiance from surface reflectivity, surface emissivity, and surface temperature signals in Step 1 as the radiative transfer process, and using atmospheric parameters, topographic parameters, and surface signals as sources of uncertainty, calculate the entrance pupil radiance uncertainty step by step: First, without considering the correlation between atmospheric and topographic parameters, the uncertainty sources of ground-based radiance include uncertainties in surface reflectivity, surface emissivity, surface temperature, slope, cast shadow coefficient, cosine of solar incidence angle, and sky visibility factor. The combined standard uncertainty of ground-based radiance is... The formula is: in, This indicates that the first-order partial derivative is used to calculate the effect of the parameter on the radiance above the ground. The sensitivity coefficient, Indicates the standard uncertainty of the slope. This represents the standard uncertainty of the projected shadow coefficient. This represents the standard uncertainty of the cosine of the incident angle of solar illumination. This represents the standard uncertainty of the sky visibility factor. The standard uncertainty of atmospheric albedo is represented by... The standard uncertainty of solar direct spectral irradiance The standard uncertainty of solar scattering spectral irradiance. The standard uncertainty of atmospheric thermal emission and thermal scattering spectral irradiance; Then, considering the sources of uncertainty in the entrance pupil radiance, including the uncertainties in direct transmittance, scattered transmittance, ground-level radiance, and atmospheric path radiation, the standard uncertainty of the entrance pupil radiance is synthesized. The formula is: in, This indicates that the entrance pupil radiance is calculated using the first-order partial derivative with respect to the parameters. The sensitivity coefficient, The standard uncertainty of direct light transmittance. The standard uncertainty of scattering transmittance is represented by The standard uncertainty of atmospheric path radiation is expressed as follows: This represents the uncertainty component caused by the correlation between atmospheric parameters. This represents the uncertainty component caused by the correlation between terrain parameters; The formula for calculating the uncertainty component caused by the correlation between atmospheric parameters is: in, The value is 7, indicating the number of atmospheric parameters; and These represent two different atmospheric parameters among direct solar spectral irradiance, diffuse solar spectral irradiance, atmospheric thermal emission and thermal scattering spectral irradiance, atmospheric albedo, direct transmittance, diffuse transmittance, and atmospheric path radiation. and These represent the entrance pupil radiance to the [missing information]. and The first-order partial derivative is also the sensitivity coefficient; This represents the linear correlation coefficient between two atmospheric parameters; and express and Standard uncertainty; The formula for calculating the uncertainty component caused by the correlation between topographic parameters is: in, The value is 4, indicating the number of terrain parameters; and This represents two different parameters among slope, shadow projection coefficient, cosine of solar illumination incident angle, and sky visibility factor; and These represent the calculation of the above-ground radiance using first-order partial derivatives. and Sensitivity coefficient; This represents the linear correlation coefficient between two terrain parameters; and express and Standard uncertainty; Step 6: Construct an uncertainty propagation model for the imaging measurement process, synthesize the restored radiance uncertainty, taking the process of calculating the restored radiance from the entrance pupil radiance signal in Step 1 as the imaging measurement process, and taking the entrance pupil radiance, the random error of the full-spectrum hyperspectral imager, and the error of the radiometric correction coefficient obtained from the radiometric calibration process as the sources of uncertainty, and calculate the restored radiance uncertainty step by step: First, calculate the standard uncertainty of the number of signal electrons. The formula is: in, Indicates spatial location ,wavelength The standard uncertainty of the entrance pupil radiance at that location, This represents the sensitivity coefficient of the detector pixel signal electron count to the entrance pupil radiance signal within the pixel imaging region, calculated using the first derivative: Then, consider the standard uncertainty of the random relative error caused by the nonlinearity and inhomogeneity of the full-spectrum hyperspectral imager's response. The standard deviation of the number of random additive noise electrons in the full-spectrum hyperspectral imager is used as the noise uncertainty. Calculate the standard uncertainty of the DN value. The formula is: Then, absolute radiometric correction is performed based on a linear regression model. The radiometric correction coefficients and their uncertainties are estimated according to the least squares linear regression model. The uncertainty of the DN value and the uncertainty of the radiometric correction coefficients are calculated according to the random error propagation formula, and the uncertainty of the restored radiance is synthesized. : in, Represents the radiation correction gain coefficient Standard uncertainty, Indicates the radiation correction bias coefficient Standard uncertainty, express and The uncertainty component caused by correlation; Step 7: Analyze the uncertainty components in the restored radiance and rank the uncertainty contributions of each step: Based on the different sources of primary uncertainty, the relative uncertainty of the restored radiance is divided into four components, and the relative uncertainty of the restored radiance is expressed as: in, This represents the relative uncertainty in the relative restored radiance. , , and The four components represent the relative uncertainty of the restored radiance introduced by the surface signal, atmospheric parameters, topographic parameters, imaging, and calibration processes, respectively. The primary uncertainty sources were categorized into four components corresponding to different stages. By controlling variables, the standard uncertainty of the restored radiance under the influence of uncertainty factors in a single stage was calculated, and this was used as... , , and The estimated values ​​are used to rank the impact of the uncertainties on the restored radiance. The primary sources of uncertainty for the surface signal stage include uncertainties in surface emissivity, surface reflectivity, and surface temperature. The primary sources of uncertainty for the atmospheric parameters stage are the uncertainties of the main variable atmospheric parameters across the entire spectrum, including the uncertainties of total water vapor column, atmospheric temperature, visibility, and carbon dioxide concentration. The primary sources of uncertainty for the topographic parameters stage include the horizontal and vertical uncertainties of the surface elevation data products. The primary sources of uncertainty for the imaging and calibration stages include random additive noise in the imaging measurement DN value data, the nonlinearity and response inhomogeneity of the hyperspectral imager, and the uncertainty of the radiometric correction coefficient.

2. The method for analyzing measurement uncertainty of full-spectrum hyperspectral Earth remote sensing imaging according to claim 1, characterized in that: Step 3, which involves evaluating the uncertainty of terrain parameters per pixel and the correlation coefficients between terrain parameters, and calculating the uncertainty and correlation coefficients using a Monte Carlo-based distribution propagation method, includes the following steps: (1) Based on the imaging area and imaging geometry parameters of the imager, perform spatial cropping, registration and spatial resampling on the digital model product of land elevation, i.e., DEM data; (2) Based on the product manual and verification data of the digital model of surface elevation, the horizontal standard uncertainty and vertical standard uncertainty of the DEM data are obtained using the Type B uncertainty assessment method. (3) Using the Monte Carlo-based distribution propagation method, the horizontal and vertical standard uncertainties of the DEM data are calculated. As a source of uncertainty in topographic parameters, according to the central limit theorem, the standard deviations of the DEM data are respectively... and The random Gaussian horizontal error and random Gaussian vertical error were calculated. Monte Carlo simulation was performed pixel by pixel to calculate four terrain parameters: slope, shadow coefficient, cosine of solar illumination incident angle, and sky visibility factor. The standard deviation of these terrain parameters was calculated. The number of simulation experiments was increased until the difference between two consecutive standard deviations was less than 5%. (4) The standard deviation of the terrain parameter sequence obtained by the pixel-by-pixel statistical Monte Carlo simulation is used as the standard uncertainty of the terrain parameters, including the standard uncertainty of the slope. Standard uncertainty of the projected shadow coefficient Standard uncertainty of the cosine of the incident angle of solar illumination Standard uncertainty of sky visibility factor There are a total of 4 uncertainty components; (5) Statistical analysis of the linear correlation coefficient between any two sets of terrain parameter sequences obtained from Monte Carlo simulation on a pixel-by-pixel basis. ,in and This corresponds to two different parameters among slope, shadow projection coefficient, cosine of solar illumination incident angle, and sky visibility factor.

3. The method for analyzing the measurement uncertainty of full-spectrum hyperspectral Earth remote sensing imaging according to claim 1, characterized in that: Step 4, which describes evaluating the spectral uncertainty of atmospheric parameters per pixel and the correlation coefficient between atmospheric parameters, involves calculating the uncertainty of terrain parameters and the correlation coefficient using a Monte Carlo-based distribution propagation method. (1) Determine local meteorological parameters, including atmospheric visibility, atmospheric temperature and atmospheric profile, based on the imaging area and imaging time of the imager. The atmospheric profile can be selected from the standard atmospheric model profile of MODTRAN5.3, or the sounding profile of the meteorological station in the imaging area or the spatiotemporal interpolation profile of the atmospheric reanalysis data. (2) Using the Type B uncertainty assessment method, under the assumption of normal distribution and considering a 95% confidence probability, the standard uncertainty of transmittance caused by the MODTRAN model is taken as 0.003, and the standard relative uncertainty of radiation is taken as 1%, which are used to calculate the model standard uncertainty corresponding to the MODTRAN simulation of atmospheric transmittance and radiation, respectively. ; (3) Based on the user's accuracy requirements or measurement experience, use the Type B uncertainty assessment method to determine the uncertainty and probability density function of the main variable parameters of the atmosphere across the entire spectrum; (4) Using the Monte Carlo-based distribution propagation method, the uncertainty of the main variable parameters of the atmosphere across the entire spectrum is used as the solar direct spectral irradiance. Solar scattering spectral irradiance Atmospheric thermal emission and thermal scattering spectral irradiance Atmospheric albedo Direct sunlight transmittance Scattering transmittance and atmospheric radiation There are seven sources of uncertainty for atmospheric parameters. Based on the uncertainties and probability density functions of the main variable atmospheric parameters across the entire spectrum, random errors are superimposed on the main variable atmospheric parameters across the entire spectrum, and Monte Carlo simulations are performed pixel-by-pixel and band-by-band. , , , , , and There are a total of 7 atmospheric parameters. The standard deviation of each atmospheric parameter is calculated. The number of simulation experiments is increased until the difference between two consecutive standard deviations is less than 5%. (5) The standard deviations of the atmospheric parameter sequences obtained by pixel-by-pixel and band-by-band statistical Monte Carlo simulations are used as the standard uncertainties of the atmospheric parameters, and as the components of the solar direct spectral irradiance uncertainty caused by the uncertainty of the main variable parameters of the atmosphere across the entire spectrum. Components of uncertainty in solar scattering spectral irradiance Uncertainty components of atmospheric thermal emission and thermal scattering spectral irradiance Atmospheric albedo uncertainty component Direct transmittance uncertainty component scattering transmittance uncertainty component Atmospheric path radiation uncertainty components Considering the model uncertainty in atmospheric parameter calculations caused by the MODTRAN model, the standard uncertainty of each atmospheric parameter is synthesized as follows: in, express , , , , , and Any one of the atmospheric parameters, express Standard uncertainty; (6) Statistical analysis of the linear correlation coefficient between any two sets of atmospheric parameter sequences obtained by Monte Carlo simulation per pixel and per band. ,in and correspond , , , , , and Two different parameters.

4. The method for analyzing the measurement uncertainty of full-spectrum hyperspectral Earth remote sensing imaging according to claim 1, characterized in that: The uncertainty in estimating the radiation correction coefficients using the least squares linear regression model described in step 6 is based on the linear radiation correction formula, with DN value as the independent variable and energy level radiance as the variable. As the dependent variable, for Least squares linear regression analysis was performed on the radiance and DN values ​​corresponding to each energy level. The analysis revealed that the sources of uncertainty in the radiation correction coefficient included... The uncertainty of the DN value of each energy level and radiance of each energy level The uncertainties; among them, for the laboratory radiometric calibration process, the primary uncertainties corresponding to the DN value and energy level radiance include: random relative errors caused by the nonlinearity and response inhomogeneity of the full-spectrum hyperspectral imager. Random additive noise electron number The following are uncertainties: random center wavelength drift and random half-width error caused by spectral calibration uncertainty; standard uncertainty of standard lamp irradiance in the visible-shortwave infrared band; uncertainty of diffuse reflectance of the visible-shortwave infrared band; uncertainty of measurement of diffuse reflectance by radiometer in the visible-shortwave infrared band; uncertainty of integrating sphere light source in the visible-shortwave infrared band; uncertainty of measurement of integrating sphere by radiometer in the visible-shortwave infrared band; uncertainty of blackbody temperature in the mid-wave-longwave infrared band; uncertainty of blackbody emissivity in the mid-wave-longwave infrared band; and uncertainty caused by stray light in the system. Random errors are generated using the aforementioned primary sources of uncertainty as standard deviations, and these errors are superimposed onto the simulated spectra of DN values ​​and energy level radiance. Based on the formula for the DN value, the simulation... The corresponding energy level radiance A sequence of DN values; and estimates the radiometric correction coefficients for each spectral channel of the full-spectrum hyperspectral imager based on least-squares linear regression. and Calculate the variance of the radiation correction factor. and and the covariance between the two radiation correction coefficients The formula is: The standard deviation of the radiation correction factor and and the covariance between the two radiation correction coefficients Uncertainty components, respectively, used as correction coefficients: , , .

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