Method for determining surface radar scattering coefficient based on correlation function uniform model

Abstract

The application provides a method for determining a ground radar scattering coefficient based on a unified model of a correlation function, ground rough surface parameters and radar parameters are respectively set; radar scattering model parameters are set or calculated; a Whittle-Matérn covariance function is used as a unified correlation function, and different methods are selected according to smooth parameters of the Whittle-Matérn covariance function to calculate n-order Fourier transforms of the Whittle-Matérn covariance function to obtain n-order power spectrum densities; the n-order power spectrum densities, the ground rough surface parameters and the radar parameters and the radar scattering model parameters are input into a radar scattering model to obtain the ground radar scattering coefficient. The technical scheme solves the technical problem that a classical correlation function in the prior art cannot accurately describe the real state of a rough surface, and that forced conversion of surface statistical data into a fixed form of a correlation function may cause systematic deviation in modeling backscattering.

Description

Technical Field

[0001] This application belongs to the field of synthetic aperture radar technology and relates to a method for determining the surface radar scattering coefficient based on a unified model of correlation functions. Background Technology

[0002] Despite progress in microwave scattering theory, soil moisture retrieval based on synthetic aperture radar (SAR) observations still faces challenges, stemming from the "ill-conditioned" nature of the remote sensing retrieval problem. Radar surface scattering signals are a coupled response of dielectric properties (determined by water content) and surface geometry (primarily influenced by roughness). Separating these influencing factors requires accurate modeling of surface statistical parameters, especially correlation functions. Correlation functions describe the attenuation of surface elevation changes with distance and are fundamental input parameters for physical scattering models (such as physical optics, PO) and unified models (typically represented by the Integral Equation Model, IEM, and its advanced versions such as AIEM, IEM2Mc, EAIEM, and mEAIEM). Physical scattering models and unified models link surface parameters with radar backscattering coefficients (i.e., radar scattering coefficients).

[0003] Currently, there are two widely used correlation functions:

[0004] 1) An exponential function model used to describe rugged and rapidly correlated rough surfaces.

[0005] 2) Gaussian function model suitable for smooth, slowly changing terrain.

[0006] However, the widespread adoption of these two correlation functions stems from their ease of analysis, rather than their ability to accurately characterize the surface conditions of real farmland. The surface conditions of real farmland are influenced by a combination of factors, including tillage conditions (such as plowing, harrowing, and compaction), topographic fractal characteristics, and sensor resolution scale. Forcing surface statistics into a fixed form of correlation function can lead to systematic biases in backscattering modeling, which then propagate nonlinearly to soil moisture estimation. Observational results indicate that using exponential or Gaussian correlation functions introduces systematic biases into backscattering models, resulting in soil moisture retrieval errors exceeding 30-82%. Summary of the Invention

[0007] This application provides a method for determining the radar scattering coefficient of the Earth's surface based on a unified model of correlation functions. This method addresses the technical problem that the classical correlation functions in the prior art are insufficient in characterizing the true state of rough surfaces, and that forcibly converting surface statistical data into a fixed form of correlation function may lead to systematic biases in the modeling of backscattering.

[0008] In a first aspect, this application provides a method for determining the radar scattering coefficient of a land surface based on a unified correlation function model, comprising the following steps: setting the surface roughness parameters and radar parameters respectively; setting or calculating the radar scattering model parameters; using the Whittle-Matérn covariance function as the unified correlation function, and based on the smoothing parameter of the Whittle-Matérn covariance function... Different methods are selected to calculate the nth-order Fourier transform of the Whittle-Matérn covariance function to obtain the nth-order power spectral density; the nth-order power spectral density, the surface roughness parameters, the radar parameters, and the radar scattering model parameters are input into the radar scattering model to obtain the surface radar scattering coefficient.

[0009] In this application, the Whittle-Matérn covariance function is used as the unified correlation function, and the smoothing parameter in the Whittle-Matérn covariance function is adjusted. Correlation functions (exponential or Gaussian correlation functions) for surfaces with different spatial statistical properties are generated, thus overcoming the limitations of existing single correlation functions in scale representation and achieving a more accurate characterization of multi-scale roughness of natural surfaces and a more efficient scattering simulation. Furthermore, based on the smoothing parameter of the Whittle-Matérn covariance function... Different methods were selected to calculate the nth-order Fourier transform of the Whittle-Matérn covariance function to obtain the nth-order power spectral density, thus realizing for the first time the smoothing parameter φ as the radar scattering coefficient φ. 0 The technical effect of quantitative analysis of independent control parameters.

[0010] In one implementation of the first aspect, setting or calculating the radar scattering model parameters includes:

[0011] Set the incident angle respectively and scattering angle Azimuth and and wavenumber ;

[0012] The effective space wavenumber is calculated using the following formula. :

[0013] ;

[0014] in This refers to the relevant length in the roughness parameters;

[0015] Based on the adaptive convergence criterion Calculating truncated class :

[0016]

[0017] when When it is less than the threshold, the corresponding minimum This is the truncation order.

[0018] In one implementation of the first aspect, the expression for the Whittle-Matérn covariance function is as follows:

[0019]

[0020] in, This represents the Euclidean distance between two surfaces. The root mean square height of the rough surface. For length scale factor, For gamma function, This refers to the smoothing parameter in the roughness parameters. This is a modified Bessel function of the second kind;

[0021] When the smoothing parameter When the coefficient of variation is 0.5, the Whittle-Matérn covariance function simplifies to an exponential correlation function; when the smoothing parameter... At that time, the Whittle-Matérn covariance function converges to the Gaussian correlation function.

[0022] In one implementation of the first aspect, the roughness parameters include relevant lengths. The relevant length It is a function of the length scale factor. It is the smoothing parameter The function; the relevant length The Whittle-Matérn covariance function is reduced to its peak value. Distance at time.

[0023] In one implementation of the first aspect, the smoothing parameter based on the Whittle-Matérn covariance function... Different methods are selected to calculate the nth-order Fourier transform of the Whittle-Matérn covariance function to obtain the nth-order power spectral density; including: if the smoothing parameter ν is greater than a preset threshold, then the asymptotic method is used to solve for the nth-order power spectral density of the Whittle-Matérn covariance function; if the smoothing parameter ν is less than or equal to the preset threshold, then the Monte Carlo method is used to solve for the nth-order power spectral density of the Whittle-Matérn covariance function.

[0024] In one implementation of the first aspect, the asymptotic method is:

[0025]

[0026] in, For the nth order power spectral density, Let Variance be the variance.

[0027] In one implementation of the first aspect, the Monte Carlo method includes:

[0028] Construct a gamma distribution; where its shape parameter... for Scale parameters for The corresponding probability density function is:

[0029]

[0030] Random variables with a preset Monte Carlo parameter sample size are drawn from the gamma distribution, and each group contains... Let be independent and identically distributed samples, denoted as . ( (), where the sample size of the Monte Carlo parameters is 5000;

[0031] For the Second sampling ( ), calculate the integrand Its expression is as follows:

[0032]

[0033] Calculate the arithmetic mean of the integrand values ​​for all samples to obtain the aforementioned multiple integral. The estimated value and .

[0034] In one implementation of the first aspect, the radar scattering model adopts the AIEM model, and the expression for the radar scattering coefficient is:

[0035]

[0036] in, ;

[0037] in, , , and , , These are the components of the incident wave vector and the scattered wave vector, respectively; For Kirchhoff field amplitude, The amplitude is the complementary field amplitude.

[0038] Secondly, this application provides a method for inversely estimating the soil dielectric constant by fitting the radar scattering coefficient obtained by the above method with synthetic aperture radar observations.

[0039] Thirdly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by an electronic device, implements the above-described method for determining the surface radar scattering coefficient based on a unified correlation function.

[0040] As described above, the method for determining the surface radar scattering coefficient based on the unified model of correlation functions described in this application has the following beneficial effects:

[0041] 1) The Whittle-Matérn covariance function is used as the unified correlation function for rough surfaces, and this unified correlation function is integrated into the radar scattering model to simulate the radar scattering coefficient. This avoids the need for fixed-form transformations of surface statistical data, achieving a more accurate characterization of multi-scale roughness of natural surfaces and more efficient scattering simulation. This technical solution is applicable to multi-resolution synthetic aperture radar systems.

[0042] 2) Based on the smoothing parameter of the Whittle-Matérn covariance function. Different methods were selected to calculate the nth-order Fourier transform of the Whittle-Matérn covariance function to obtain the nth-order power spectral density, thus realizing for the first time the smoothing parameter φ as the radar scattering coefficient φ. 0 The technical effect of quantitative analysis of independent control parameters.

[0043] 3) Express the Whittle-Matérn covariance function in a scale mixture form, and... This is interpreted as calculating the mathematical expectation of multiple independent random variables and solving it using the Monte Carlo method, thus achieving... It achieves efficient and stable calculation of high-order spectral densities with a complexity of [unclear].

[0044] 4) Smoothing parameters The following was derived in the case of a larger value (greater than 50): The asymptotic solution. Attached Figure Description

[0045] Figure 1 The diagram shown is a flowchart illustrating a method for determining the surface radar scattering coefficient based on a unified correlation function, as described in an embodiment of this application.

[0046] Figure 2The diagram shown illustrates the normalized correlation length corresponding to the Whittle-Matérn covariance function in a method for determining the surface radar scattering coefficient based on a unified correlation function, as described in an embodiment of this application.

[0047] Figure 3 This diagram illustrates the relationship between the normalized correlation length and the smoothing parameter in the Whittle-Matérn covariance function of a method for determining the surface radar scattering coefficient based on a unified correlation function, as described in an embodiment of this application.

[0048] Figure 4 The diagram shows the power spectral density of the Whittle-Matérn covariance function in a method for determining the surface radar scattering coefficient based on a unified correlation function, as described in an embodiment of this application.

[0049] Figure 5 This image shows a result verification of the power spectral density obtained by using an asymptotic method to solve the Whittle-Matérn covariance function in a method for determining the surface radar scattering coefficient based on a unified correlation function, as described in an embodiment of this application.

[0050] Figure 6 This is another verification result of the power spectral density obtained by solving the Whittle-Matérn covariance function using an asymptotic method in the method for determining the surface radar scattering coefficient based on a unified correlation function as described in the embodiments of this application.

[0051] Figure 7 This diagram illustrates a comparison of the power spectral density obtained using the Monte Carlo method provided in this application to solve the Whittle-Matérn covariance function with the theoretical computational efficiency of the general Monte Carlo method.

[0052] Figure 8 The diagram shows the relationship between the incident angle and the radar scattering coefficient under VV polarization in a method for determining the surface radar scattering coefficient based on a unified correlation function provided in this application embodiment.

[0053] Figure 9 The diagram shown illustrates the relationship between the incident angle and the radar scattering coefficient under HH polarization in a method for determining the surface radar scattering coefficient based on a unified correlation function provided in this application embodiment.

[0054] Figure 10 The method for determining the surface radar scattering coefficient based on a unified correlation function, shown in the embodiments of this application, employs radar scattering coefficients under VV polarization to adjust the smoothing parameter. A schematic diagram of dependency characteristics.

[0055] Figure 11 The method for determining the surface radar scattering coefficient based on a unified correlation function, shown in the embodiments of this application, uses the radar scattering coefficient under HH polarization to adjust the smoothing parameter. A schematic diagram of dependency characteristics. Detailed Implementation

[0056] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. This application can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, unless otherwise specified, the following embodiments and features in the embodiments can be combined with each other.

[0057] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. Therefore, the drawings only show the components related to this application and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0058] The technical solutions in the embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0059] like Figure 1 The diagram shown is a flowchart illustrating a method for determining the surface radar scattering coefficient based on a unified correlation function, provided in this embodiment. (Reference) Figure 1 The method for determining the surface radar scattering coefficient includes the following steps:

[0060] Step S101: Set the surface roughness parameters and radar parameters respectively.

[0061] Step S102: Set or calculate radar scattering model parameters.

[0062] Step S103: Use the Whittle-Matérn covariance function as the unified correlation function, and select different methods to calculate the nth order Fourier transform of the Whittle-Matérn covariance function according to the smoothing parameter ν of the Whittle-Matérn covariance function to obtain the nth order power spectral density.

[0063] Step S104: Input the nth-order power spectral density, the surface roughness parameters, the radar parameters, and the radar scattering model parameters into the radar scattering model to obtain the surface radar scattering coefficient.

[0064] This technical solution provides a simulation method to simulate the scattering field generated by the surface current (which is affected by the surface roughness) when radar waves irradiate the ground surface, so as to calculate the radar scattering coefficient of the ground surface.

[0065] In step S101 above, it is necessary to set the roughness parameters and radar parameters.

[0066] Specifically, the roughness parameters include: relevant length. The range is 0-0.5m, the root mean square height s is 0-0.05m, and the smoothing parameter is... The values ​​are 0.5, 0.8, 1, 2, 5, 10, and 100, and the relative permittivity of the rough surface is a complex number (the real part of this complex number is 12, and the imaginary part is 1.8). The relevant length... Smoothing parameters are used to describe the scale of surface roughness variation; the relative permittivity of a rough surface is determined by soil moisture and texture. (Also known as the roughness parameter) is used to adjust the surface to exhibit different spatial statistical properties (from smooth to rough, from single-scale to multi-scale). The root mean square height s is used to control the total energy of the scattered data. When other parameters remain constant, the larger the root mean square height s, the larger the radar scattering coefficient is usually.

[0067] The radar parameters include: a set radar frequency of 5.4 GHz, and polarization mode where both transmission and reception use the same polarization, including HH (horizontal polarization for both transmission and reception) and VV (vertical polarization for both transmission and reception). The radar wave incident angle... It is 35°.

[0068] In step S102 above, the radar scattering model adopts the AIEM (Advanced Integral Equation Model), which is a semi-empirical and semi-theoretical electromagnetic scattering model suitable for simulating radar scattering from random, rough surfaces. Its core is to calculate the radar scattering coefficient by solving the integral form of Maxwell's equations, combined with the surface correlation function and dielectric constant. The AIEM model decomposes the total scattered field into coherent scattering (spectral reflection) and incoherent scattering (diffuse scattering), focusing on calculating the incoherent scattering component.

[0069] Specifically, this step includes:

[0070] Step S1021: Set the incident angle respectively and scattering angle Azimuth and and wavenumber .

[0071] Among them, the angle of incidence and scattering angle Both are 35°, azimuth angle For 0° and The wave number (k) is 180°. It represents the wave number of the electromagnetic wave emitted by the radar itself, indicating the number of radians of phase change per unit distance in the direction of propagation. It is a fundamental parameter describing the spatial oscillation frequency of electromagnetic waves. The larger the wave number (k) value, the shorter the wavelength (λ). The value of the wave number determines the detection scale of the radar system and its sensitivity to the roughness of the earth's surface.

[0072] Step S1022: Calculate the effective spatial wavenumber according to the following formula. :

[0073]

[0074] The effective spatial wavenumber It is a specific direction determined by the incident and scattering directions, and can be understood as the magnitude of the difference between the surface component of the scattered wave vector and the surface component of the incident wave vector. Among these, This refers to the relevant length in the roughness parameters.

[0075] Step S1023: Based on the adaptive convergence criterion Calculating truncated class ,in, The expression is as follows:

[0076]

[0077] when When it is less than the criterion threshold, the corresponding minimum This is the truncation order.

[0078] Here, the truncation order n refers to the upper limit of the number of terms (n) actually calculated and accumulated in the infinite series summation formula for calculating the scattering coefficient in a radar scattering model (such as the IEM model), that is, it represents the highest complexity order of the interaction between the electromagnetic wave and the rough surface under consideration. If n=1, it is dominated by single scattering, and the larger the n is, the more complex the multiple interactions it contains.

[0079] The adaptive convergence criterion refers to the mathematical conditions and computational logic used to dynamically and automatically determine when a series summation can terminate. Its goal is to find the minimum truncation order n while meeting preset accuracy requirements, thereby completing the calculation in the most efficient way. In this embodiment, the criterion threshold is 1×10⁻⁶. -6 In step S103 above, the Whittle-Matérn variance function is used as the unified correlation function, and the smoothing parameter of the Whittle-Matérn covariance function is used. Different methods were selected to calculate the nth-order Fourier transform of the Whittle-Matérn covariance function to obtain the nth-order power spectral density.

[0080] Specifically, the expression for the Whittle-Matérn covariance function is as follows:

[0081]

[0082] in, This represents the Euclidean distance between two surface points. The root mean square height of the rough surface. The length scaling factor controls the correlation between two points as a function of distance. Modulate the horizontal scale by increasing and decreasing the rate of decay; For gamma function, The smoothing parameter is one of the roughness parameters. This is a modified Bessel function of the second type.

[0083] like Figure 2 The diagram shown is a schematic of the normalized correlation length corresponding to the Whittle-Matérn covariance function in the method for determining the surface radar scattering coefficient based on the unified correlation function described in the embodiments of this application.

[0084] Those skilled in the art will understand that the Whittle-Matérn covariance function describes how the covariance of the undulations between two points in space (e.g., on the Earth's surface) varies with their distance. Variation. In the Whittle-Matérn covariance function, the normalized distance refers to the actual spatial distance between two points on the Earth's surface. With length scale factor The ratio, i.e. This is a dimensionless quantity used to measure the distance between two points as a multiple of the surface roughness characteristic scale. Through normalization, the Whittle-Matérn covariance function no longer depends on specific physical units or absolute scales. Whether the surface is microscopically rough (e.g., micrometer-scale) or macroscopically topographical (e.g., kilometer-scale), as long as… If they are the same, then their covariance structures are similar.

[0085] refer to Figure 2 Root mean square height of rough surface =1.0, length scale factor =2.2. Different smoothing parameters The covariance function curves of different colors correspond to the graph, with the horizontal axis representing the normalized distance (the actual spatial distance between two points). With length scale factor The ratio of the two points on the Earth's surface (the vertical axis represents the covariance between the two points) is given by the smoothing parameter. When the coefficient of variation is 0.5, the Whittle-Matérn covariance function simplifies to an exponential correlation function, while when the smoothing parameter... At that time, the Whittle-Matérn covariance function converges to the Gaussian correlation function.

[0086] like Figure 3 The diagram shows the relationship between the normalized correlation length and the smoothing parameter in the Whittle-Matérn covariance function of a method for determining the surface radar scattering coefficient based on a unified correlation function.

[0087] refer to Figure 3 The relevant length The length scale factor The function, It is the smoothing parameter The function. The relevant length The Whittle-Matérn covariance function is reduced to its peak value. Distance over time. Based on given smoothing parameters. The Whittle-Matérn covariance function value was calculated using the bisection method and decreased to its peak value. of Combined with the given Determine the length scale factor When the smoothing parameter When the Whittle-Matérn covariance function converges to the Gaussian correlation function, the Gaussian limit is: .

[0088] Furthermore, the core of calculating the Whittle-Matérn covariance function lies in efficiently and stably solving for the modified Bessel function of the second kind. The second type of modified Bessel function In order When the value is very large or very small, and its independent variable is within a specific range, there are serious numerical computational difficulties. For example, when When it is very large (e.g.) >100), the function value may exceed the representation range of a double-precision floating-point number (overflow), or its series representation may converge very slowly, making direct computation costly and unstable. For example, when very small And when the independent variable is also very small, the modified Bessel function of the second kind It exhibits logarithmic singularity and requires special handling to avoid precision loss. When When the parameter is any real number, a general algorithm is needed to cover the entire parameter space.

[0089] In this embodiment, when calculating the nth-order Fourier transform of the Whittle-Matérn covariance function to obtain the nth-order power spectral density, a smoothing parameter is set. The preset threshold is 50, and it is based on the smoothing parameter. Whether the value exceeds the preset threshold, different methods can be selected to solve for the nth-order power spectral density of the Whittle-Matérn covariance function.

[0090] First, power spectral density This is the two-dimensional Fourier transform of the Whittle-Matérn covariance function, and the transformation formula is as follows:

[0091]

[0092] For an isotropic two-dimensional random surface Become It depends only on the radial wavenumber. It can be processed by the zeroth-order Hankel transform, and the transformation formula is as follows:

[0093]

[0094] in, It is a zero-order Bessel function of the first kind, for It allows The closed form is expressed as:

[0095]

[0096] It is easy to know that when hour, It is the spectral expression of the exponential correlation function; in hour, It is the spectral expression of the Gaussian correlation function.

[0097] like Figure 4 The image shows a schematic diagram of the power spectral density of the Whittle-Matérn covariance function. (Reference) Figure 4 Different smoothing parameters For an isotropic two-dimensional random surface, corresponding to curves of different colors, under a defined smoothing parameter... Under these conditions, the power spectral density of the Whittle-Matérn covariance function is only related to the radial wavenumber. Related.

[0098] Furthermore, the Whittle-Matérn covariance function It can be represented as a scale mixing form:

[0099]

[0100] Wherein, the mixing density function Follows a gamma distribution

[0101]

[0102] The Fourier transform of the correlation function raised to the nth power (whose radial component is the wave function covariance) can be expressed as:

[0103]

[0104] Wherein, the mixing density function It follows a gamma distribution. It can be interpreted as That is to 1 independent and identically distributed random variable Seeking expectations.

[0105] In the above formula, there exists the following Multiple integrals ( )

[0106]

[0107] in, It is the probability density function of the gamma distribution. When hour, The second-order asymptotic expansion is:

[0108]

[0109] Based on the above theory, this embodiment uses smoothing parameters. Choose different calculation methods.

[0110] Specifically, when the smoothing parameter If the value is greater than 50, the asymptotic method is used to solve for the nth-order power spectral density of the Whittle-Matérn covariance function; when the smoothing parameter If the value is less than or equal to 50, the Monte Carlo method is used to solve for the nth-order power spectral density of the Whittle-Matérn covariance function.

[0111] asymptotic methods

[0112] The formula for the nth-order power spectral density of the asymptotic method is as follows:

[0113]

[0114] in, For the nth order power spectral density, Let Variance be the variance.

[0115] To verify the correctness of the results of the asymptotic method proposed in this invention, the case of n=3 is examined, in which a baseline value can be obtained (represented by the hybrid method, which uses the trapezoidal rule for triple integration). When n=3, the expansion is as follows:

[0116]

[0117] like Figure 5 and Figure 6 The figure shown is a verification result of solving the power spectral density of the Whittle-Matérn covariance function using an asymptotic method in a method for determining the surface radar scattering coefficient based on a unified correlation function provided in an embodiment of this application.

[0118] refer to Figure 5 For amplitude spectrum analysis, when the smoothing parameter When taking a large value (e.g., 500), the result of using the asymptotic method ( Figure 5 (Red dot broken line) and the reference value ( Figure 5 The blue dots and solid lines (representing the mixed method) almost perfectly match. Meanwhile, the results using the Monte Carlo method ( Figure 5 The solid green dot (in the middle) is also highly consistent with the benchmark value.

[0119] refer to Figure 6 The results of the asymptotic method are compared with different smoothing parameters. The performance was tested at values ​​of , when the smoothing parameter was . When the value is greater than 100, the relative error is less than 1%, even with smoothing parameters. Even at a low value of 50, the relative error can still be kept below 2%.

[0120] Monte Carlo Method

[0121] Specifically, the steps include the following:

[0122] 1) Construct a gamma distribution; where its shape parameter is... for Scale parameters for The corresponding probability density function is:

[0123]

[0124] 2) Random variables with a preset Monte Carlo parameter sample size are drawn from the gamma distribution, with each group containing... Let be independent and identically distributed samples, denoted as . ( (); where the Monte Carlo parameter sample size is 5000.

[0125] 3) Regarding the first Second sampling ( ), calculate the integrand Its expression is as follows:

[0126]

[0127] Calculate the arithmetic mean of the integrand values ​​for all samples to obtain the aforementioned multiple integral. The estimated value and .

[0128] like Figure 7 The diagram shown is a comparison of the theoretical computational efficiency of the Monte Carlo method provided in this application for solving the power spectral density of the Whittle-Matérn covariance function with that of the general Monte Carlo method.

[0129] refer to Figure 7 When n=6, a comparison of the theoretical computational efficiency of the Monte Carlo method used in this embodiment with that of the general Monte Carlo method shows that, since multiple integrals are regarded as the expectation and importance sampling is embedded in the gamma distribution, the relative error of the Monte Carlo method used in this embodiment is one order of magnitude smaller than that of the general Monte Carlo method when the number of samples is the same. This illustrates the advantage of the technical solution of the present invention in terms of computational speed while ensuring accuracy.

[0130] In step S104 above, the nth-order power spectral density, the surface roughness parameters, the radar parameters, and the radar scattering model parameters are input into the radar scattering model to obtain the surface radar scattering coefficient.

[0131] Specifically, the radar scattering model used in this embodiment is the AIEM (Advanced Integral Equation Model), and the expression for the radar scattering coefficient is as follows:

[0132]

[0133] in, .

[0134] in, , , and , , These are the components of the incident wave vector and the scattered wave vector, respectively; For Kirchhoff field amplitude, The amplitude is the complementary field amplitude.

[0135] like Figure 8 and Figure 9 The diagram illustrates the relationship between the incident angle and the radar scattering coefficient under VV and HH polarization schemes in a method for determining the surface radar scattering coefficient based on a unified correlation function, as provided in an embodiment of this application. Figure 8 For VV polarization, Figure 9 It is an HH polarization mode. Figure 8 and Figure 9 The angular response characteristics of the radar scattering coefficient are shown, i.e., the radar scattering coefficient decreases at different rates as the incident angle increases. The smaller the value, the slower the decay.

[0136] like Figure 10 and Figure 11 The illustration shows the radar scattering coefficients with respect to smoothing parameters under VV polarization and HH polarization modes in a method for determining the surface radar scattering coefficients based on a unified correlation function provided in this application. A diagram illustrating the dependency characteristics. Among them, Figure 10 For VV polarization, Figure 11 It is an HH polarization mode. Figure 10 and Figure 11 It shows that the radar scattering coefficient varies with The pattern of change shows that its dependency relationship is not monotonous and is closely related to the angle of incidence.

[0137] On the other hand, this application also provides a soil moisture inversion method based on synthetic aperture radar, which inversely calculates the soil dielectric constant by fitting the radar scattering coefficient obtained by the method described above with the synthetic aperture radar observation value.

[0138] The scope of protection of the method for determining the surface radar scattering coefficient based on the unified correlation function described in this application is not limited to the order of steps listed in this embodiment. Any scheme implemented by adding, subtracting, or replacing steps in the prior art based on the principles of this application is included within the scope of protection of this application.

[0139] In the embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, or methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative. For instance, the division of modules / units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or units may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection of apparatuses or modules or units may be electrical, mechanical, or other forms.

[0140] The modules / units described as separate components may or may not be physically separate. The components shown as modules / units may or may not be physical modules; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules / units can be selected to achieve the objectives of the embodiments of this application, depending on actual needs. For example, the functional modules / units in the various embodiments of this application may be integrated into one processing module, or each module / unit may exist physically separately, or two or more modules / units may be integrated into one module / unit.

[0141] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0142] This application also provides a computer-readable storage medium. Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing a processor. The program can be stored in a computer-readable storage medium, which is a non-transitory medium, such as random access memory, read-only memory, flash memory, hard disk, solid-state drive, magnetic tape, floppy disk, optical disk, and any combination thereof. The storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., digital video disc (DVD)), or a semiconductor medium (e.g., solid-state drive (SSD)).

[0143] The descriptions of the processes or structures corresponding to the above figures each have their own emphasis. For parts of a process or structure that are not described in detail, please refer to the relevant descriptions of other processes or structures.

[0144] The above embodiments are merely illustrative of the principles and effects of this application and are not intended to limit this application. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of this application. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in this application should still be covered by the claims of this application.

Claims

1. A method for determining the surface radar scattering coefficient based on a unified correlation function, characterized in that, Includes the following steps: Set the surface roughness parameters and radar parameters respectively; Set or calculate radar scattering model parameters; The Whittle-Matérn covariance function is used as the unified correlation function, and the smoothing parameter of the Whittle-Matérn covariance function is used accordingly. Different methods were selected to calculate the nth-order Fourier transform of the Whittle-Matérn covariance function to obtain the nth-order power spectral density; The nth-order power spectral density, the surface roughness parameters, the radar parameters, and the radar scattering model parameters are input into the radar scattering model to obtain the surface radar scattering coefficient.

2. The method according to claim 1, characterized in that, The parameters for setting or calculating the radar scattering model include: Set the incident angle respectively and scattering angle Azimuth and and wavenumber ; The effective space wavenumber is calculated using the following formula. : ;in This refers to the relevant length in the roughness parameters; Based on the adaptive convergence criterion Calculating truncated class : in, The root mean square height of the rough surface; when When it is less than the criterion threshold, the corresponding minimum This is the truncation order.

3. The method according to claim 1, characterized in that, The expression for the Whittle-Matérn covariance function is as follows: in, This represents the Euclidean distance between two points on the surface. The root mean square height of the rough surface. For length scale factor, For gamma function, The smoothing parameter is one of the roughness parameters. This is a modified Bessel function of the second kind; When the smoothing parameter When the coefficient of variation is 0.5, the Whittle-Matérn covariance function simplifies to an exponential correlation function; when the smoothing parameter... At that time, the Whittle-Matérn covariance function converges to the Gaussian correlation function.

4. The method according to claim 3, characterized in that, The roughness parameters include relevant lengths. ; The relevant length It is a function of the length scale factor. It is the smoothing parameter The function; the relevant length The Whittle-Matérn covariance function is reduced to its peak value. Distance at time.

5. The method according to claim 3, characterized in that, The smoothing parameter based on the Whittle-Matérn covariance function Different methods were selected to calculate the nth-order Fourier transform of the Whittle-Matérn covariance function to obtain the nth-order power spectral density; including: If the smoothing parameter If the value is greater than a preset threshold, the nth power spectral density of the Whittle-Matérn covariance function is solved using an asymptotic method. If the smoothing parameter If the value is less than or equal to a preset threshold, the Monte Carlo method is used to solve for the nth-order power spectral density of the Whittle-Matérn covariance function.

6. The method according to claim 5, characterized in that, The asymptotic method is as follows: in, For the nth order power spectral density, Let Variance be the variance.

7. The method according to claim 5, characterized in that, The Monte Carlo method includes: Construct a gamma distribution; where its shape parameter is... for Scale parameters for The corresponding probability density function is: Random variables with a preset Monte Carlo parameter sample size are drawn from the gamma distribution, and each group contains... Let be independent and identically distributed samples, denoted as . ,in The sample size of the Monte Carlo parameters is 5000. For the first Second sampling, of which Calculate the integrand Its expression is as follows: Calculate the arithmetic mean of the integrand values ​​for all samples to obtain the multiple integral. The estimated value and .

8. The method according to claim 5, characterized in that, The radar scattering model adopts the AIEM model, and the expression for the radar scattering coefficient is as follows: in, ; in, , , and , , These are the components of the incident wave vector and the scattered wave vector, respectively; For Kirchhoff field amplitude, The amplitude is the complementary field amplitude.

9. A soil moisture inversion method based on synthetic aperture radar, characterized in that, The soil dielectric constant is inversely derived by fitting the radar scattering coefficient obtained by any one of claims 1 to 8 with synthetic aperture radar observations.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by an electronic device, it implements the method of any one of claims 1 to 8.

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