A PolInSAR forest height inversion method with dual constraints of parameter correlation and scattering difference

Abstract

The present invention discloses a PolInSAR forest height inversion method with dual constraints of parameter association and scattering difference, which belongs to the field of remote sensing information processing technology. The method comprises the following steps: using forest height prior information to determine the Fourier-Legendre polynomial coefficient constraint interval; constructing inequality constraints based on the polarization scattering difference between the forest canopy and the bottom layer; combining the constraints, using a nonlinear least squares iterative algorithm to invert the forest height and vertical structure parameters. The polynomial coefficient constraint interval is determined by statistically analyzing the coefficient values ​​corresponding to different forest heights, and the scattering difference constraint is constructed based on the relationship between the top and bottom scattering powers of the polarization modes dominated by volume scattering and surface scattering. The objective function is the sum of squares of the measured value of the complex coherence coefficient and the estimated residual, and the iterative termination conditions include the number of times, function tolerance and parameter tolerance. Experiments show that compared with the conventional unconstrained nonlinear iterative method, the RMSE of forest height estimation is reduced by 12%, effectively improving the inversion accuracy and stability.

Description

Technical Field

[0001] The present invention relates to the technical field of remote sensing information processing, and in particular to a PolInSAR forest height inversion method with dual constraints of parameter correlation and scattering difference. Background Art

[0002] Currently, forest height is a key parameter in forestry resource surveys and an important input for estimating aboveground biomass, carbon storage, and understory topography. Therefore, obtaining large-scale, high-precision, and timely forest height information is crucial for forest resource surveys, disaster prevention and control, understory topography inversion, and phenological research. Polarimetric Interferometric Synthetic Aperture Radar (PolInSAR), sensitive to the shape, direction, and spatial distribution of vegetation scatterers and capable of distinguishing different scattering heights within the same resolution unit, has become one of the most promising technologies for large-scale, timely forest height inversion.

[0003] By leveraging the scattering mechanism of PolInSAR signals in forested areas and constructing a PolInSAR coherent scattering model, it is possible to establish correlation functions between forest height parameters and observed information, thereby enabling the inversion of forest height physical parameters. The Random Volume Over Ground (RVoG) model proposed by Treuhaft et al. is a commonly used model for PolInSAR forest height inversion. However, this model represents the propagation of radar signals through vegetation as an empirical exponential function, which makes it difficult to accurately characterize the influence of complex forest vertical structure. This, to a certain extent, limits the accuracy of forest height inversion and makes it difficult to extract detailed information about forest vertical structure. To address this issue, Cloude et al. proposed the polarization coherence tomography (PCT) technique for inverting forest vertical structure in 2006. This technique uses Fourier-Legendre (FL) polynomials to represent forest vertical structure. Compared to empirical exponential functions, PCT has better variability and adaptability, and can more accurately characterize the influence of complex forest vertical structure. In 2007, Cloude further proposed the dual-baseline PCT technique, which uses the truncated singular value method to address ill-posed issues in the inversion of forest vertical structure parameters, improving the accuracy of forest vertical structure inversion. PCT uses forest height as an input parameter to invert forest vertical structure, making it difficult to invert high-level forest parameters. In response to this, Zhang et al. proposed a nonlinear least-squares iterative inversion algorithm for forest height and vertical structure based on the Fourier-Legendre model. This algorithm utilizes different scattering information corresponding to different polarization modes, thereby obtaining richer information about forest vertical structure. Zhao et al. constructed the vertical structure of each resolution unit based on the Fourier-Legendre model and used a small amount of LiDAR data to optimize and calibrate forest height. However, due to the complex vertical structure of the forest, the coefficients of the Fourier-Legendre polynomials are complex and diverse, making it impossible to accurately obtain both forest height and vertical structure simultaneously. When using nonlinear least-squares methods for iterative solution, it is difficult to reasonably determine the value boundaries of the polynomial coefficients, resulting in poor stability and convergence of the iterative algorithm, which seriously affects the reliability of parameter estimation. Summary of the Invention

[0004] The purpose of the present invention is to provide a PolInSAR forest height inversion method with dual constraints of parameter correlation and scattering difference. The method utilizes the correlation between forest vertical structure and forest height, uses prior information of forest height parameters to estimate polynomial coefficients, and constructs a constraint interval for the polynomial coefficient values. On this basis, the vertical upward scattering differences of different polarization modes are considered to construct polynomial coefficient constraint conditions. Then, a forest height inversion constraint least squares method considering the correlation of model parameters and the vertical polarization scattering differences of forests is given, thereby improving the inversion stability of FL model parameters and the inversion accuracy of forest height parameters.

[0005] To achieve the above object, the present invention provides a PolInSAR forest height inversion method with dual constraints of parameter correlation and scattering difference, comprising the following steps:

[0006] S1. Using the forest height prior information, the Fourier-Legendre polynomial coefficients are calculated with different forest heights as initial values, and the constraint interval is determined by the statistical coefficient estimation interval;

[0007] S2. Based on the polarization scattering difference between the forest canopy and the bottom layer, a scattering difference inequality constraint is constructed;

[0008] S3. Using a nonlinear least squares iterative algorithm, combined with the coefficient constraint interval of step S1 and the inequality constraint of step S2, the forest height and vertical structure parameters are inverted.

[0009] Preferably, in step S1, the constraint interval is determined by:

[0010] The forest height value interval is constructed based on the forest height prior information;

[0011] Solve the polynomial coefficients using the forest high initial values ​​in the interval;

[0012] The maximum and minimum values ​​of the statistical polynomial coefficients form the coefficient value constraint interval.

[0013] Preferably, in step S2, the scattering difference inequality constraint condition is specifically: the volume scattering-dominated polarization mode satisfies the condition that the scattered power at the bottom of the forest is not greater than that at the top, and the surface scattering-dominated polarization mode satisfies the condition that the scattered power at the bottom of the forest is not less than that at the top;

[0014] The constraints are implemented by the following mathematical expressions:

[0015] ;

[0016] ;

[0017] in, 、 、 are the coefficients of the Fourier–Legendre polynomials.

[0018] Preferably, in step S3, the complex coherence model used is based on a third-order Fourier-Legendre polynomial expansion, the mathematical expression of which is:

[0019] ;

[0020] in, Indicates the polarization mode, 、 、 are the Fourier-Legendre polynomial coefficients, is the surface phase, is the Fourier-Legendre expansion term; Representative Baseline.

[0021] Preferably, in step S3, the objective function of the nonlinear least squares iteration is the residual sum of squares between the measured complex coherence coefficient and the model calculated value;

[0022] The mathematical expression of the objective function is:

[0023] ;

[0024] in, is the actual complex coherent observation value; represents the complex coherence estimate computed from the parameter estimates.

[0025] Preferably, the termination condition of the nonlinear least squares iteration includes:

[0026] The number of iterations reaches the preset maximum value;

[0027] The change in the objective function is less than the preset tolerance;

[0028] The parameter change is less than the preset tolerance.

[0029] Preferably, the specific parameters of the termination condition are:

[0030] The maximum number of iterations is 300;

[0031] The objective function tolerance is 0.001;

[0032] The parameter variation tolerance is 0.001.

[0033] Therefore, the present invention adopts a PolInSAR forest high-resolution inversion method with dual constraints of parameter correlation and scattering difference of the above structure, which has the following beneficial effects:

[0034] (1) In the present invention, the inversion of forest high parameters and forest vertical structure parameters restricts and influences each other. The forest vertical structure parameter value range is constructed by using the prior information of forest high parameters, which is conducive to improving the accuracy and reliability of forest high parameter inversion.

[0035] (2) The radar wave scattering power expression based on Fourier-Legendre polynomials in the present invention is only related to the polynomial coefficients at the top and bottom of the forest. This characteristic is used to construct vertical structure parameter constraints, which effectively improves the stability of model parameter inversion.

[0036] (3) The forest high-parameter inversion experiment provided by the present invention shows that compared with the conventional unconstrained nonlinear iterative method, the nonlinear least squares iterative method with additional double constraints reduces the RMSE of forest high-parameter estimation by 12%, effectively improving the accuracy of forest high-parameter inversion.

[0037] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 A schematic diagram of the vertical structure of a forest using a PolInSAR forest height inversion method with dual constraints of parameter correlation and scattering difference according to the present invention;

[0039] Figure 2 This is a diagram showing the visualization of the first four Legendre polynomials of a PolInSAR forest high-resolution inversion method with dual constraints of parameter correlation and scattering difference according to the present invention;

[0040] Figure 3 Schematic diagram of the experimental data range in the Lopé region for a PolInSAR forest high inversion method with dual constraints of parameter correlation and scattering difference according to the present invention;

[0041] Figure 4 Schematic diagram of the inversion of forest vertical structure profile based on PCT technology using a PolInSAR forest height inversion method with dual constraints of parameter correlation and scattering difference in the present invention; (a) is the initial value of forest height; (b) is the vertical structure profile inverted using the PDHigh polarization mode; (c) is the vertical structure profile inverted using the PDLow polarization mode;

[0042] Figure 5 Schematic diagram of the PDHigh forest vertical structure profile inverted by the algorithm of the PolInSAR forest high inversion method with dual constraints of parameter correlation and scattering difference in the present invention; (a) is the vertical structure at position f1; (b) is the vertical structure at position f2; (c) is the vertical structure at position f3; (d) is the vertical structure at position f4;

[0043] Figure 6Schematic diagram of forest height inversion results using a PolInSAR forest height inversion method with dual constraints of parameter association and scattering difference according to the present invention; (a) is a three-stage algorithm; (b) is a conventional method; (c) is a parameter association constraint method; (d) is a vertical scattering difference constraint method; (e) is a dual constraint method; and (f) is LiDAR forest height.

[0044] Figure 7 Schematic diagram of the cross-validation of forest height inversion results of each method and LiDAR forest height; (a) is the three-stage algorithm; (b) is the conventional method; (c) is the parameter association constraint method; (d) is the vertical scattering difference constraint method; (e) is the double constraint method;

[0045] Figure 8 The figure is a flow chart of a PolInSAR forest height inversion method with dual constraints of parameter correlation and scattering difference according to the present invention. DETAILED DESCRIPTION

[0046] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0047] Unless otherwise defined, the technical or scientific terms used in the present invention shall have the usual meanings understood by persons of ordinary skill in the field to which the present invention belongs. The words "first", "second" and similar terms used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Words such as "include" or "comprise" mean that the elements or objects preceding the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Words such as "connect" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0048] Example 1

[0049] Affected by the complex vertical structure of forests, the nonlinear least squares algorithm for forest height inversion based on the Fourier-Legendre model struggles to effectively determine the effective range of vertical structure parameters, severely impacting the stability and reliability of forest height inversion. In light of this, this paper proposes a PolInSAR forest height inversion method with dual constraints of parameter correlation and scattering difference. This method leverages the correlation between forest height and vertical structure parameters, as well as the vertical polarization scattering difference of the forest, to construct Fourier-Legendre polynomial coefficient constraints. The introduction of a nonlinear least squares iterative algorithm significantly improves the reliability and stability of forest height inversion results.

[0050] like Figure 8 As shown, the present invention provides a PolInSAR forest height inversion method with dual constraints of parameter correlation and scattering difference, comprising the following steps:

[0051] S1. Using the forest height prior information, the Fourier-Legendre polynomial coefficients are calculated with different forest heights as initial values, and the constraint interval is determined by the statistical coefficient estimation interval;

[0052] S2. Based on the polarization scattering difference between the forest canopy and the bottom layer, a scattering difference inequality constraint is constructed;

[0053] S3. Using a nonlinear least squares iterative algorithm, combined with the coefficient constraint interval of step S1 and the inequality constraint of step S2, the forest height and vertical structure parameters are inverted.

[0054] In step S1, when constructing the Fourier-Legendre model, due to the influence of the complex vertical structure of the forest, when the microwave signal penetrates the forest vegetation layer, its scattering process will change with the change of forest height. Therefore, the change of microwave scattering power can be expressed as the penetration depth Function ,like Figure 1 shown.

[0055] Figure 1 middle, represents the lower elevation of the forest canopy; is the upper boundary elevation; is the forest canopy thickness, that is, the forest height. In this case, the interference complex coherence can be obtained The expression is:

[0056] (1);

[0057] Substituting the upper and lower bounds of the integral in formula (1), we can obtain formula (2):

[0058] (2);

[0059] in, is the effective vertical wave number, which is a function of the vertical baseline length, the incident angle, the distance from the microwave launch platform to the scatterer, and the microwave wavelength. It determines the sensitivity of the interferometric measurement system to the forest height. The vertical structure inversion of the forest mainly uses a set of orthogonal Fourier-Legendre polynomials to approximate the vertical structure function. The vertical structure function can be obtained from the Fourier-Legendre polynomials. The expression is:

[0060] (3);

[0061] in represents the unknown coefficient that determines the shape of the vertical structure function; is a Legendre polynomial defined in the interval [-1,1]. After substituting formula (3) into formula (2) and performing the transformation, the polarization complex coherence of the forest height inversion model based on Fourier-Legendre polynomials can be expressed as:

[0062] (4);

[0063] in, 、 、 are the coefficients of the Fourier-Legendre polynomials; With forest height and vertical effective wave number Related; is the surface phase, which is related to the surface elevation and vertical effective wave number Related; is the Fourier-Legendre expansion term; Representative Baseline.

[0064] In step S2, when analyzing the correlation between forest vertical structure parameters, it is known that different forest heights often correspond to different forest vertical structures, based on the growth characteristics of forest vegetation. Changes in the scattered power of radar waves penetrating different forest heights are closely related to changes in forest vertical structure. Therefore, in the PolInSAR observation scenario, changes in forest vertical structure are correlated with changes in forest height. The values ​​of the Fourier-Legendre polynomial coefficients used in the model to express changes in radar wave scattered power and the values ​​of the forest height parameters should mutually constrain and influence each other.

[0065] When using iterative algorithms to estimate forest height parameters, it is crucial to determine the appropriate search intervals for the Fourier-Legendre polynomial coefficients and the forest height parameters to improve their stability and reliability. However, due to the complexity of the forest's vertical structure and the uncertainty of radar scattering, it is difficult to obtain prior information about the Fourier-Legendre polynomial coefficients, making it difficult to determine the search intervals for the iterative inversion of the polynomial coefficients. Considering that the forest height parameters can be more easily determined using prior knowledge and that the forest's vertical structure and the forest height parameters are closely related, the forest height parameter value intervals can be used to calculate the Fourier-Legendre polynomial coefficients corresponding to different forest height parameters. These values ​​serve as the polynomial coefficient value intervals, constraining the polynomial coefficient estimates to fall within the corresponding forest height parameter value range. This theoretically improves the stability of the estimation of the forest height and vertical structure parameters.

[0066] Expanding the Fourier-Legendre polynomials to higher order terms can more accurately represent the changes in the coherence coefficient caused by the scattering process and obtain higher-resolution vertical structures of the forest. However, when the order of the polynomial is large, although higher-resolution vertical structures of the forest can be obtained, it will be more sensitive to noise and more susceptible to errors, resulting in poor stability of the inversion results. Considering The coefficients of the and higher order expansion terms are close to zero, which has little effect on the function, and the higher order terms are more susceptible to errors. In the expression of , the expansion of the Fourier-Legendre polynomial to the third order can meet the needs of forest height and vertical structure inversion. From formula (4), the complex coherence coefficient expression under the third-order polynomial can be obtained as:

[0067] (5);

[0068] in, represents the polarization mode. As can be seen from formula (5), after using the three-stage method to determine the initial values ​​of the forest height and surface phase, the a priori value range of the forest height parameter, combined with the observed values ​​of the complex coherence coefficient, can effectively estimate the values ​​of the Fourier-Legendre polynomial coefficients corresponding to different forest heights, and then statistically determine the value range of the polynomial coefficients. This value range can constrain the changes in the vertical structure of the forest to within the effective forest height range, thereby narrowing the parameter iterative search range and improving the stability and reliability of the parameter estimation.

[0069] In step S2, the forest vertical structure function is defined in formula (1) as , which represents the continuous change of forest layer scattered energy with forest height. Expressed as

[0070] (6);

[0071] In summary, the core principle of PCT forest vertical structure inversion is to use a set of standard Legendre polynomials to fit and approximate the relative reflectivity function that is difficult to mathematically model. Limited by the stability of the observation model, the vertical structure function is mainly represented by a third-order polynomial, which is in the form of:

[0072] (7);

[0073] in , , The value range is . And the forest vertical structure function is a non-negative function, then The value range is .

[0074] Figure 2 shows a visualization of the first four Legendre polynomials, where When is -1, 0, 1, the corresponding Legendre polynomial has the particularity of its value, as shown in formula (8):

[0075] (8);

[0076] From formula (8), we can see that at the bottom and top of vegetation, the vertical structure function of the forest is the radar scattering power function. Only with polynomial coefficients 、 、 The value of Only with polynomial coefficients The value of is related. Therefore, it is possible to consider using these characteristics to establish reasonable polynomial coefficient constraints. From the scattering characteristics of different PolInSAR polarization modes in forested areas, it can be seen that the scattering power of the polarization mode dominated by volume scattering (such as PDHigh) at the bottom of the forest should not be greater than that at the top of the forest, while the scattering power of the polarization mode dominated by surface scattering (such as PDLow) at the bottom of the forest should not be less than that at the top of the forest. Based on this, when satisfying Under the condition of , the constraint condition can be constructed by combining formula (8):

[0077] (9);

[0078] In summary, the process of the nonlinear iterative algorithm for forest high-resolution inversion with additional constraint information based on the FL model is as follows:

[0079] S31. Calculate the Fourier-Legendre coefficient based on the prior value interval of forest high parameters based on PCT technology 、 、 The maximum and minimum values ​​of the parameters are determined 、 、 Iterative search interval.

[0080] S32, using the FL vertical structure function to express the characteristics of the forest canopy and bottom layers, based on the volume scattering dominant polarization mode PDHigh and the surface scattering dominant polarization mode PDLow, respectively, to construct 、 、 Equal polynomial coefficient constraints are introduced to introduce iterative calculation.

[0081] S33. Based on the least squares estimation criterion, using multi-baseline complex coherent observations, iteratively invert the model parameters, with a maximum number of iterations of 300, a function tolerance of 0.001, and a parameter tolerance of 0.001 as the iteration termination conditions, to obtain the final forest high parameter estimate. Among them, the objective function of the nonlinear least squares iteration is expressed as:

[0082] (10);

[0083] in, is the actual complex coherent observation value; represents the complex coherence estimate computed from the parameter estimates.

[0084] The above method was applied to the Lopé National Forest Park in Gabon, Africa. Its vegetation is mainly composed of tropical rainforest and tropical savanna. The two vegetation types grow together, forming a unique ecological environment. The terrain environment and forest height distribution are complex, making it an ideal testing ground for verifying the multi-baseline inversion scheme.

[0085] The P-band polarimetric SAR data of Lopé National Park obtained in the AfriSAR2016 project were selected for forest height inversion verification. The test area is located as follows: Figure 3 As shown, the forest height ranges from 3 m to 60 m, with an average forest height of approximately 35 m. Three interferometer pairs from three baselines were selected for verification. For each interferometer pair, the coherence separation optimization (PD) algorithm was used to obtain the complex coherence of the PDHigh and PDLow polarization modes.

[0086] The LVIS LiDAR forest height product obtained from the Afri-SAR2016 project was selected for accuracy verification. The resolution of the selected LVIS forest height product is 25m×25m.

[0087] Using the P-band PolInSAR data of the experimental area, the PCT technique and the new algorithm were used to invert the vertical structure function of the forest. The inversion results are shown in the figure below. Figure 4 、 Figure 5 shown. Figure 4 (a) is the initial value of forest height without geographical correction, Figure 4(b) and (c) are cross-sectional views of the forest vertical structure retrieved using PCT technology for the red-lined area in Figure (a). Figure (b) shows the cross-sectional view retrieved using the PDHigh polarization method. As can be seen from the cross-sectional view, the vertical scattered power in the forest, where volume scattering is dominant, is significantly greater at the top than at the bottom, consistent with theoretical analysis. Regions of higher scattered power also exist in the middle and lower parts of the forest. This is primarily due to the complex ecological environment of the lower vegetation in tropical rainforests, where the presence of short, sturdy vegetation increases scattered power. Figure (c) shows the cross-sectional view retrieved using the PDLow polarization method. As can be seen, the vertical scattered power in the forest, where surface scattering is dominant, is significantly greater at the bottom than at the top, also consistent with theoretical analysis. This demonstrates the feasibility of constructing Fourier-Legendre coefficient constraints using the differences in vertical scattered power across the forest, based on different polarization methods.

[0088] Figure 5 The above figure shows the vertical structure profile of the PDHigh forest in the red area inverted by the new algorithm. Figure 4 As for (b), there is not much difference between the two in the vertical structure curve, and the waveforms tend to be consistent. The contrast between different layers of the vertical structure profile inverted by the method provided by the present invention is more obvious, and the middle and low layers are more prominent. Figure 5 (a) to (d) are the vertical structure functions corresponding to 500 pixels, 1000 pixels, 2200 pixels, and 2700 pixels in the profile. The vertical structure functions show that different forest heights exist in different regions, and the vertical structure functions are also different. This indicates that the forest vegetation layer is inhomogeneous and has a complex and diverse vertical structure, making it difficult to use a single empirical function to describe the complex variations in radar wave scattering power. Although there are differences in the vertical scattering power variation of PDHigh polarization in different regions, the scattering power at the top of the forest is consistently greater than that at the bottom of the forest, further verifying the effectiveness of the constraints of the method provided by this invention.

[0089] In order to verify the effectiveness of the forest height inversion method provided by the present invention, five methods, including a three-stage algorithm, a conventional nonlinear least squares iterative method, a nonlinear least squares iterative method with additional parameter association constraints, a nonlinear least squares iterative method with additional vertical scattering difference constraints, and a nonlinear least squares iterative method with additional parameter association and vertical scattering difference dual constraints, are used to invert forest height parameters. The inversion results are shown in Figure 2. Figure 6 .

[0090] contrast Figure 6 (a) with Figure 6 (b) It can be seen that the forest height inversion results of the conventional nonlinear least squares iteration method are improved compared with the three-stage method, but there is a significant overestimation compared with the LiDAR results. Figure 6 (c) with Figure 6 (d) After introducing parameter correlation constraints and vertical scattering difference constraints respectively, the inversion results are improved to a certain extent. In particular, after introducing parameter correlation constraints, the overestimation phenomenon is significantly improved. Figure 6 (e) After introducing the dual constraints of parameter correlation and vertical scattering difference, the forest height inversion result is further optimized and closer to the LiDAR forest height result. This shows that introducing parameter correlation and vertical scattering difference constraints can effectively improve the accuracy of forest height inversion.

[0091] In order to further quantitatively compare the forest overestimation accuracy of each method, 3192 forest plots were evenly selected in the figure to calculate the root mean square error of the forest overestimation of each method. Figure 7 The accuracy verification scatter plots between different inversion algorithms and LiDAR forest height products are given. Figure 7 (a) It can be seen that the correlation coefficient corresponding to the three-stage algorithm result is relatively low, which is 0.84, and the corresponding RMSE is relatively high, which is 6.73m. Figure 7 (b), (c), (d), and (e) are the forest height inversion results of the nonlinear iterative algorithm under different conditions based on the Fourier-Legendre model. The correlation coefficients are 0.88, 0.90, 0.89, and 0.91, respectively, and the RMSE are 5.85m, 5.36m, 5.50m, and 5.14m, respectively. Figure 7 (b) The high-value RMSE of the conventional nonlinear least squares iterative forest method decreased by 13% compared with the three-stage method; Figure 7 (c) The RMSE of the nonlinear least squares iteration method considering parameter association constraints is reduced by 20% compared with the three-stage method and by 8% compared with the conventional nonlinear least squares iteration method; Figure 7 (d) The RMSE of the nonlinear least squares iterative method with the vertical scattering difference constraint is reduced by 18% compared with the three-stage method and by 6% compared with the conventional nonlinear least squares iterative method. Figure 7 (e) The RMSE of the nonlinear least squares iteration method with dual constraints decreased by 24% compared to the three-stage method and by 12% compared to the conventional nonlinear least squares iteration method. These quantitative comparisons further validate the effectiveness of introducing parameter correlation constraints and vertical scattering difference constraints in improving the accuracy of high-resolution forest inversion using the nonlinear iteration method.

[0092] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A PolInSAR forest height inversion method with dual constraints of parameter correlation and scattering difference, characterized by: The following steps are involved: S1. Using the forest height prior information, the Fourier-Legendre polynomial coefficients are calculated with different forest heights as initial values, and the constraint interval is determined by the statistical coefficient estimation interval; In step S1, the constraint interval is determined by: The forest height value interval is constructed based on the forest height prior information; Solve the polynomial coefficients using the forest high initial values ​​in the interval; The maximum and minimum values ​​of the statistical polynomial coefficients form the coefficient value constraint interval; S2. Based on the polarization scattering difference between the forest canopy and the bottom layer, a scattering difference inequality constraint is constructed; In step S2, the scattering difference inequality constraint conditions are specifically: the volume scattering-dominated polarization mode satisfies the condition that the scattered power at the bottom of the forest is not greater than that at the top, and the surface scattering-dominated polarization mode satisfies the condition that the scattered power at the bottom of the forest is not less than that at the top; The constraints are implemented by the following mathematical expressions: ； in, 、 、 are the Fourier-Legendre polynomial coefficients, PDHigh The polarization mode dominated by volume scattering is PDLow The surface scattering is the dominant polarization mode; S3, using a nonlinear least squares iterative algorithm, combined with the coefficient constraint interval of step S1 and the inequality constraint of step S2, to invert the forest height and vertical structure parameters; In step S3, the objective function of the nonlinear least squares iteration is the residual sum of squares between the measured complex coherence coefficient and the estimated complex coherence coefficient calculated by the model; The mathematical expression of the objective function is: ； in, is the actual complex coherent observation value; represents the complex coherence estimate computed from the parameter estimates.

2. The PolInSAR forest height inversion method with dual constraints of parameter correlation and scattering difference according to claim 1 is characterized by: The termination conditions for the nonlinear least squares iteration include: The number of iterations reaches the preset maximum value; The change in the objective function is less than the preset tolerance; The parameter change is less than the preset tolerance.

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