A method for InSAR model construction and height reconstruction of high-rise buildings

Abstract

The present invention discloses an InSAR model construction and height reconstruction method for a high-rise building, and the method is as follows: 1. Analyze the roof scattering of the high-rise building and determine its interference phase and phase gradient expression; 2. Analyze the side facade scattering of the high-rise building and determine its interference phase and phase gradient expression; 3. Analyze the ground scattering and determine its interference phase and phase gradient expression; 4. Establish a scattering model of a high-rise building with a complex scattering mechanism, determine the interference coefficient and the expression of the interference phase gradient, and analyze the interference phase change and equivalent height change in the overlapping area; 5. Reconstruct the "pure" side facade phase of the high-rise building with a complex scattering mechanism, and then reconstruct the building height. The present invention solves the problem that the complex interference phase of a high-rise building with a complex scattering mechanism is difficult to use for the building height reconstruction, and realizes the reconstruction of the building side facade interference phase and the accurate reconstruction of the building height.

Description

Technical Field

[0001] The invention belongs to the technical field of remote sensing image processing and relates to an InSAR model construction and height reconstruction method of a high-rise building. Background Art

[0002] Compared with two-dimensional images, the three-dimensional model of urban buildings has more spatial information and better visual effects, so it is widely used in urban planning and construction. SAR remote sensing technology is an important means to obtain three-dimensional information of buildings. It has the advantages of high spatial position of sensors and is not affected by bad weather and darkness. Through signal and image processing, a wide range of ground images and three-dimensional information of buildings can be quickly obtained. Among the many SAR three-dimensional reconstruction technologies, interferometric synthetic aperture radar (InSAR) technology has the advantages of high sensitivity to targets and low data consumption, so it has great potential in three-dimensional reconstruction of buildings and urban DSM acquisition.

[0003] In the past, InSAR technology was usually used to obtain large-scale DEM and deformation data. Due to the low image resolution and complex scattering process of buildings, InSAR technology is rarely used to obtain the height of artificial buildings. Compared with the SAR image amplitude, the interference phase is less affected by the data acquisition platform, building materials and environment, and has a higher dependence on the building geometry. Therefore, with the improvement of SAR image resolution, the importance of interference phase in building detection and height reconstruction has been further enhanced, and preliminary research has been conducted. However, in the current research on building 3D reconstruction based on InSAR technology, there is a lack of detailed theoretical analysis of the overlapping interference phase of buildings, which is insufficient to support the subsequent reconstruction of building height. At the same time, most of these studies are limited to rectangular buildings with very simple structures, and are not applicable to buildings with slightly more complex structures. Therefore, constructing a reasonable InSAR model for the building and analyzing the phase changes in detail, and then accurately reconstructing its height are urgent problems that need to be solved in the current research on building height reconstruction based on InSAR. Summary of the invention

[0004] In order to break through the limitation of the simple model assumption of buildings in the research of building height reconstruction based on InSAR technology, construct a reasonable InSAR and interferometric phase model for high-rise buildings with complex scattering mechanisms, and solve the problem of difficult height reconstruction caused by complex interferometric phase changes, the present invention provides an InSAR model construction and height reconstruction method for high-rise buildings. The method comprehensively analyzes the actual physical scattering process of the building, constructs the corresponding building scattering model, InSAR model and interferometric phase gradient model, reconstructs the side elevation interferometric phase of the high-rise building and realizes the height reconstruction of the building.

[0005] The objective of the present invention is achieved through the following technical solutions:

[0006] A method for constructing an InSAR model and reconstructing the height of a high-rise building comprises the following steps:

[0007] Step 1: Analyze the roof scattering of high-rise buildings and determine its interference phase and phase gradient expression. The specific steps are as follows:

[0008] Step 1: Equivalently treat the scattering from the building roof as surface scattering, and its scattering intensity depends on the roughness of the building roof; model the roof of a high-rise building as a rough surface with a certain roughness, and its InSAR model is as follows:

[0009]

[0010] Among them, γ roof is the interference coefficient of the roof rough surface model, s 1 represents the main image, s 2 Indicates the secondary image, symbol * represents conjugate multiplication, A 1r represents the surface scattering intensity of the roof in the main image, A 2r represents the surface scattering intensity of the roof in the secondary image, λ represents the wavelength, and ρ 1r represents the slant distance between the roof scattering point and the SAR sensor in the main image, ρ 2r represents the slant distance between the roof scattering point and the SAR sensor in the secondary image, B represents the baseline length, α represents the angle between the baseline and the horizontal plane, and θ r represents the radar viewing angle at the roof scattering point, θ 0r h is the radar downward viewing angle at the scattering point on the reference plane and at the same slant distance scattering unit as the roof scattering point, r Indicates the height of the roof scattering point relative to the reference plane;

[0011] Step 12: According to the InSAR model in step 11, assume that the scattering points in adjacent scattering units on the roof are P′ br and P′ fr The scattering points at the same slant distance scattering unit and located on the reference plane are P br and P fr , scattering point P′ br and P′ fr The height relative to the reference plane is h r , the interferometric phase gradient model Δφ of the scattering point on the roof roof as follows:

[0012]

[0013] in, is the scattering point P′ in the next slant range scattering unit on the roof fr The interference phase at is the scattering point P′ within the previous slant range scattering unit on the roof br The interference phase at θ fr represents the reference plane scattering point P fr The radar viewing angle at br represents the scattering point P on the reference plane br The radar viewing angle at br Represents the scattering point P in the main image br The slant range from the SAR sensor, Δρ represents the slant range resolution, Δh r Represents the height variation between adjacent scattering points on the roof, and its value is zero.

[0014] Step 2: Analyze the side facade scattering of high-rise buildings and determine its interference phase and phase gradient expression. The specific steps are as follows:

[0015] Step 21: Equivalently treat the scattering from the side facade of the building as surface scattering, and its scattering intensity depends on the roughness of the side facade; model the side facade of the building as a rough surface with a certain roughness, and its InSAR model is as follows:

[0016]

[0017] Among them, γ facade is the interference coefficient of the rough surface model of the side elevation, A 1f represents the equivalent surface scattering intensity of the side elevation in the main image, A 2f represents the equivalent surface scattering intensity of the side elevation in the secondary image, ρ 1f represents the slant distance between the side elevation scattering point and the SAR sensor in the main image, ρ 2f represents the slant distance between the side elevation scattering point and the SAR sensor in the secondary image, θ f represents the radar viewing angle at the side elevation scattering point, θ 0f h is the radar downward viewing angle at the scattering point on the reference plane and at the same slant range scattering unit as the side elevation scattering point, f Indicates the height of the side elevation scattering point relative to the reference plane;

[0018] Step 22: According to the InSAR model in step 21, assume that the scattering points in adjacent scattering units on the side elevation are P′ bf and P′ bf The scattering points at the same slant distance scattering unit and located on the reference plane are P bf and P bf , scattering point P′ bf and P′ff The height relative to the reference plane is h bf and h ff , the interference phase gradient Δφ of the scattering point on the side surface facade The model is as follows:

[0019]

[0020] Among them, Δφ flat represents the flat-earth phase, Δφ terrain represents the terrain phase, θ bf represents the scattering point P on the reference plane bf The radar viewing angle at bf Represents the scattering point P on the main image bf Slant distance to the SAR sensor, Δh f Yes ff With h bf difference.

[0021] Step 3: Analyze the ground scattering and determine its interference phase and phase gradient expression. The specific steps are as follows:

[0022] Step 3: Surface scattering occurs on the ground; the ground in the building area is modeled as a rough surface, and its InSAR model is as follows:

[0023]

[0024] Among them, γ ground is the interference coefficient of the ground rough surface model, A 1g Represents the surface scattering intensity of the ground in the main image, A 2g represents the surface scattering intensity of the ground in the secondary image, ρ 1g represents the slant distance between the ground scattering point and the SAR sensor in the main image, ρ 2g represents the slant distance between the ground scattering point and the SAR sensor in the secondary image, θ g represents the radar downward viewing angle at the ground scattering point, θ 0g h represents the radar downward viewing angle at the scattering point that is in the same scattering distance unit as the ground scattering point and is located on the reference plane, g Represents the height of the ground scattering point relative to the reference plane.

[0025] Step 3.2: According to the InSAR model in step 3.1, assume that the scattering points in adjacent scattering units on the ground are P′ bg and P′ fg The scattering point P is located on the reference plane and is at the same slant distance from the scattering unit. bg and P fg , the interferometric phase gradient model Δφ of the scattering point on the groundground as follows:

[0026]

[0027] in, is the scattering point P′ in the next slant range scattering unit on the ground fg The interference phase at is the scattering point P′ within the previous slant range scattering unit on the ground bg The interference phase at θ fg represents the reference plane scattering point P fg The radar viewing angle at bg represents the reference plane scattering point P bg The radar viewing angle at fg Represents the scattering point P in the main image fg Slant range from the SAR sensor, ρ bg Represents the scattering point P in the main image bg Slant distance to the SAR sensor, Δh g It represents the height change between adjacent scattering points on the ground, its value is zero, and Δρ represents the slant range resolution.

[0028] Step 4: Combine the scattering mechanism, geometric relationship, interference phase and interference phase gradient of the roof, side facade and ground of the high-rise building, establish a scattering model of the high-rise building with complex scattering mechanism, determine the expression of interference coefficient and interference phase gradient, and analyze the interference phase change and equivalent height change in the overlap area. The specific steps are as follows:

[0029] Step 41: Integrate steps 1 to 3, combine the geometric relationship of each scattering point in the InSAR system, and establish the InSAR model of the overlapping area of ​​high-rise buildings:

[0030]

[0031] The subscripts r, f, and g represent the scattering points from the roof, side facade, and ground, respectively; A 1 and A 2 Represent the scattering intensity of the main image and the secondary image respectively; ρ 1 and ρ 2 Represent the slant distances between the scattering point and the main antenna and the secondary antenna respectively; θ i represents the radar viewing angle at each scattering point, θ 0 represents the radar downward viewing angle at the scattering point that is in the same scattering unit as the roof scattering point, the side facade scattering point and the ground scattering point and is located on the reference plane; α represents the angle between the baseline and the horizontal plane; h i Represents the height of each scattering point relative to the reference plane; represents the equivalent scattering intensity; hequ represents the equivalent scattering height;

[0032] Step 42: According to the InSAR model in step 41, the superposition of three scattering vectors from planes at different heights is equivalent to the surface scattering generated by a scattering point at a certain height. Assume that the equivalent scattering points in adjacent scattering units are P′ be and P′ fe The scattering points in the same scattering unit and located on the reference plane are P be and P fe , equivalent scattering point P′ be and P′ fe The height relative to the reference plane is h be and h fe , the interference phase gradient model Δφ of the equivalent scattering point in the overlapping area of ​​high-rise buildings is as follows:

[0033]

[0034] Among them, Δφ flat is the phase gradient caused by the change of the equivalent scattering point on the plane, Δφ terrain is the terrain phase gradient caused by the change in height of the equivalent scattering point, h fe represents the height of the next equivalent scattering point relative to the reference plane, h be represents the height of the previous equivalent scattering point relative to the reference plane, Δh e =h fe -h be , is the equivalent scattering point P′ in the next slant range scattering unit fe The interference phase at is the equivalent scattering point P′ in the previous slant range scattering unit be The interference phase at θ fe represents the scattering point P on the reference plane fe The radar viewing angle at be represents the scattering point P on the reference plane be The radar viewing angle at fe Represents the scattering point P in the main image fe Slant range from the SAR sensor, ρ be Represents the scattering point P in the main image be The slant range from the SAR sensor, Δρ represents the slant range resolution;

[0035] Step 43: Combining the InSAR model established in step 41 and the interferometric phase gradient model established in step 42, the interferometric phase changes in the imaging area of ​​the high-rise building and the adjacent area have the following characteristics:

[0036] 1) In the building imaging area and adjacent areas, unknown phase jumps will occur when the scattering components change;

[0037] 2) For the overlapping area of ​​buildings, the surface scattering from the ground is weak and can be ignored. However, due to the change of scattering components inside the overlapping area, the interference phase changes are inconsistent, which is manifested as follows: the interference phase change in the long-distance overlapping area is characterized by the interference phase change of the side facade, the phase gradient is approximately the same, and the scattering point changes along the side facade; the scattering components in the close-distance overlapping area are superimposed, the interference phase changes are complex, and the equivalent scattering point height changes are complex, and this height cannot represent the height change of the scattering point on the side facade, so it cannot be directly used for building height reconstruction.

[0038] Step 5: Reconstruct the "pure" side elevation phase of a high-rise building with a complex scattering mechanism, and then reconstruct the building height. The specific steps are as follows:

[0039] Step 51: Reference interferometric phase gradient estimation

[0040] A sliding window is established on the interference pattern, and the standard deviation of the interference phase gradient in the window is calculated. The window slides from the dihedral angle scattering point to the beginning of the overlap area. When the standard deviation of the interference phase gradient in the window exceeds the threshold, the sliding is terminated, and the area from the dihedral angle scattering point to the end point of the window sliding is considered to be a long-distance overlap area, and the interference phase gradient in this area is used as a reference interference phase gradient;

[0041] Step 52: Side-view interferometry phase reconstruction

[0042] According to the reference interference phase gradient and the partial side elevation interference phase obtained in step 51, the side elevation interference phase of the entire overlapping area is calculated;

[0043] Step 53: Building Height Reconstruction

[0044] Unwrap the side elevation interference phase and calculate the side elevation interference phase difference Δφ of the entire overlapping area facade ; Further combined with the 2π blur height h of the interference image pair am , calculate the building height h:

[0045]

[0046] Compared with the prior art, the present invention has the following advantages:

[0047] 1. The present invention can be applied to the field of remote sensing image processing. It comprehensively analyzes the scattering process of high-rise buildings with complex scattering mechanisms, constructs a corresponding scattering model for high-rise buildings, and constructs an InSAR model of the overlapping area of ​​high-rise buildings. It derives the interference phase gradient model of the overlapping area of ​​high-rise buildings, and analyzes the interference phase changes in the high-rise building area in detail, providing a theoretical basis for the height reconstruction of artificial buildings based on the interference phase.

[0048] 2. The present invention can be applied to the field of remote sensing image processing. It solves the problem that the complex interference phase of high-rise buildings with complex scattering mechanisms is difficult to use for building height reconstruction, realizes the reconstruction of the interference phase of the side facade of the building, and realizes the accurate reconstruction of the building height. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a flat surface model of the building roof and a scattering diagram;

[0050] Figure 2 It is a non-flat surface model of the building roof and a scattering diagram;

[0051] Figure 3 is the geometric equivalent of dihedral scattering;

[0052] Figure 4 It is the equivalent rough surface model and equivalent surface scattering of the building roof;

[0053] Figure 5 It is the geometric relationship of the scattering points on the roof surface in the InSAR imaging system;

[0054] Figure 6 It is a schematic diagram of the geometric relationship between the scattering points of adjacent scattering units on the roof;

[0055] Figure 7 It is a flat surface model of the building's side elevation and a scattering diagram;

[0056] Figure 8 It is a non-flat surface model and scattering diagram of the building's side elevation;

[0057] Fig. 9 It is the equivalent rough surface model and equivalent surface scattering of the building side facade;

[0058] Fig.10 It is the geometric relationship of the scattering points on the side elevation in the InSAR imaging system;

[0059] Fig.11 It is a schematic diagram of the geometric relationship between the scattering points of adjacent scattering units on the side elevation;

[0060] Fig.12It is the equivalent rough surface model of the ground and the equivalent surface scattering;

[0061] Fig.13 It is the geometric relationship of the scattering points on the ground in the InSAR imaging system;

[0062] Fig.14 It is a schematic diagram of the geometric relationship between the scattering points of adjacent scattering units on the ground;

[0063] Fig.15 It is a model of the scattering mechanism of high-rise buildings;

[0064] Fig.16 It is the geometric relationship of each scattering point on different planes in the imaging area of ​​the high-rise building in the InSAR system;

[0065] Fig.17 It is a schematic diagram of the geometric relationship between the equivalent scattering points of adjacent scattering units in the overlapping area of ​​high-rise buildings;

[0066] Fig.18 It is the division of the slant range imaging area of ​​high-rise buildings;

[0067] Fig.19 It is the interference phase change diagram of the building imaging area;

[0068] Fig. 20 It is the relationship between the side elevation interference phase distribution range and the overlap area;

[0069] Fig.21 It is the side elevation interferometry phase reconstruction effect;

[0070] Fig. 22 is the SAR amplitude map of the experimental area;

[0071] Fig.23 It is an optical image of a building in the experimental scene;

[0072] Fig.24 It is the SAR amplitude map of a building in the experimental scene;

[0073] Fig.25 is the interference phase pattern of a building in the experimental scene;

[0074] Fig.26 It is the unwrapped phase image without side elevation interferometry phase reconstruction;

[0075] Fig. 27 is the reconstructed side elevation interferometer phase;

[0076] Fig.28 It is a three-dimensional image of the building height using interferometric phase recovery without side elevation reconstruction;

[0077] Fig.29It is a 3D image of the building height using reconstructed side elevation interferometry phase recovery. DETAILED DESCRIPTION

[0078] The technical solution of the present invention is further described below in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0079] The present invention provides a method for constructing an InSAR model of a high-rise building and reconstructing its height, the method comprising the following steps:

[0080] Step 1: Analyze the roof scattering of high-rise buildings and determine its interference phase and phase gradient expression.

[0081] For the roofs of high-rise buildings, they can be divided into two types according to actual conditions:

[0082] 1) Flat surface. For the flat surface of the roof, it is not completely smooth, but a flat surface with a certain degree of roughness. When electromagnetic waves are irradiated on a surface with a certain degree of roughness, first-order Bragg scattering usually occurs, also known as surface scattering (see Figure 1 , the part encircled by the dashed parallelogram on the right is the flat surface model of the building roof; the left is the local structure method image of the flat surface of the roof and the corresponding scattering type, where the lines with arrows represent the actual directional incident electromagnetic waves and scattered electromagnetic waves, the dashed lines represent scattered electromagnetic waves that are not propagated along the radar line of sight, and the solid lines represent electromagnetic waves that propagate along the radar line of sight). Due to the non-directional nature of surface scattering, its scattering intensity is relatively small.

[0083] 2) Non-flat surfaces with structures. For the roof of an artificial high-rise building with a certain structure, the entire roof not only contains a plane with a certain degree of roughness, but also contains a considerable part of dihedral structures. The plane with a certain degree of roughness has surface scattering with low scattering intensity; while for the dihedral structure, dihedral scattering occurs. Since the electromagnetic wave will return along the original direction after irradiating the dihedral structure, the dihedral scattering has directionality, and the scattering intensity is relatively large (refer to Figure 2 , the part circled by the dotted parallelogram on the right is the non-flat surface model of the building roof; the three figures in the left column are enlarged views of the local structure of the non-flat surface and the corresponding scattering types. From top to bottom, they are schematic diagrams of surface scattering caused by the local flat surface, dihedral scattering caused by the concave structure, and dihedral scattering caused by the convex structure. For dihedral scattering, the dotted line represents the actual scattering path of the electromagnetic wave, and the solid line represents the equivalent scattering path).

[0084] According to the electromagnetic wave propagation path, dihedral scattering is equivalent to surface scattering occurring at the junction of two orthogonal planes of the dihedral structure (refer to Figure 3 , the dotted line represents the actual path of dihedral scattering, and the solid line represents the equivalent scattering path of dihedral scattering), and its scattering intensity is greater than that of normal surface scattering.

[0085] In summary, the roof of a high-rise building is modeled as a surface with a certain roughness (see Figure 4 , the lines with arrows represent the actual directional incident electromagnetic waves and scattered electromagnetic waves, the dotted lines represent scattered electromagnetic waves that are not propagated along the radar line of sight, and the solid lines represent electromagnetic waves that propagate along the radar line of sight). The roughness depends on the number and size of the dihedral structures on the actual roof surface. The scattering on the roof is equivalent to surface scattering, and its scattering intensity is related to the roughness. It can also be said that its scattering intensity is related to the number and size of the dihedral structures. If the surface of the building roof is smooth and there is no dihedral structure, the equivalent roughness is small and the equivalent surface scattering intensity is small; if the surface of the building roof is not smooth, the more dihedral structures it has, and the larger the dihedral structures are, the greater the equivalent roughness is and the greater the equivalent surface scattering intensity is.

[0086] For the equivalent rough surface model of the roof, its geometric relationship in the InSAR system refers to Figure 5 , and its InSAR model is as follows:

[0087]

[0088] Among them, γ roof is the interference coefficient of the roof rough surface model, s 1 represents the main image, s 2 Indicates the secondary image, symbol * represents conjugate multiplication, A 1r represents the surface scattering intensity of the roof in the main image, A 2r represents the surface scattering intensity of the roof in the secondary image, λ represents the wavelength, and ρ 1r represents the slant distance between the roof scattering point and the SAR sensor in the main image, ρ 2r represents the slant distance between the roof scattering point and the SAR sensor in the secondary image, B represents the baseline length, α represents the angle between the baseline and the horizontal plane, and θ r represents the radar viewing angle at the roof scattering point, θ 0r h is the radar downward viewing angle at the scattering point on the reference plane and at the same slant distance scattering unit as the roof scattering point, r Indicates the height of the roof scattering point relative to the reference plane.

[0089] According to the above InSAR model, it is assumed that the scattering points in adjacent scattering units on the roof are P′br and P′ fr The scattering points at the same slant distance scattering unit and located on the reference plane are P br and P fr , scattering point P′ br and P′ fr The height relative to the reference plane is h r (See Figure 6 ), the interference phase gradient model Δφ at the roof can be derived and obtained roof as follows:

[0090]

[0091] in, is the scattering point P′ in the next slant range scattering unit on the roof fr The interference phase at is the scattering point P′ within the previous slant range scattering unit on the roof br The interference phase at ,λ represents the wavelength, B represents the baseline length, α represents the angle between the baseline and the horizontal plane, θ fr represents the reference plane scattering point P fr The radar viewing angle at br represents the reference plane scattering point P br The radar viewing angle at h r represents the height of the roof scattering point relative to the reference plane, ρ fr Represents the scattering point P in the main image fr Slant range from the SAR sensor, ρ br Represents the scattering point P in the main image br Slant distance to the SAR sensor, Δh r Represents the adjacent scattering point P′ on the roof br and P′ fr The height variation between .

[0092] When the scattering points change on the roof, the height change between adjacent scattering points is 0, that is, Δh r = 0. Therefore, the interference phase gradient model Δφ at the roof roof can be simplified to:

[0093]

[0094] Where Δρ represents the slant range resolution.

[0095] Step 2: Analyze the side facade scattering of high-rise buildings and determine its interference phase and phase gradient expression.

[0096] For the side facades of high-rise buildings, they can be divided into two types according to actual conditions:

[0097] 1) Flat surface. Such a flat side surface usually refers to the side without structures such as balconies and windows. It can also be equivalent to a surface with a certain roughness. When electromagnetic waves irradiate the flat side surface, surface scattering with a small scattering intensity occurs (refer to Figure 7 , the part circled by the dotted parallelogram on the right is the flat surface model of the side facade of the building; the left is the local structure method image of the flat surface of the side facade and the corresponding scattering type, where the lines with arrows represent the actual directional incident electromagnetic waves and scattered electromagnetic waves, the dotted lines represent scattered electromagnetic waves that do not propagate along the direction of the radar line of sight, and the solid lines represent electromagnetic waves that propagate along the direction of the radar line of sight).

[0098] 2) Non-flat surface with certain structure. This kind of side facade usually refers to the side facade of a building with regularly and densely arranged balconies and windows. The side facade contains both flat surface structure and densely arranged balconies and windows, which often contain many small dihedral structures. When electromagnetic waves are irradiated on the side facade of the building, surface scattering occurs at the local flat surface and dihedral scattering occurs at the numerous dihedral structures (see Figure 8 , the part encircled by the dashed parallelogram on the left is the non-flat surface model of the building's side elevation; the three figures in the right column are enlarged views of the local structure of the non-flat surface and the corresponding scattering types. From top to bottom, they are schematic diagrams of surface scattering generated by the local flat surface, dihedral scattering generated by the concave structure, and dihedral scattering generated by the convex structure. For dihedral scattering, the dashed line represents the actual scattering path of the electromagnetic wave, and the solid line represents the equivalent scattering path). Due to the directional determinism of dihedral scattering, the echo energy from the dihedral structure is stronger, and the sun-facing side of the building usually appears brighter on the SAR image.

[0099] Similarly, the dihedral scattering occurring at the dihedral structure on the side facade of the building is equivalent to surface scattering (see Figure 3 ), the equivalent surface scattering has a stronger scattering intensity.

[0100] In summary, the side facade of the building is also modeled as a surface with a certain roughness (see Fig. 9 , the lines with arrows represent the actual directional incident electromagnetic waves and scattered electromagnetic waves, the dotted lines represent scattered electromagnetic waves that are not propagated along the radar line of sight, and the solid lines represent electromagnetic waves that propagate along the radar line of sight). The roughness depends on the number and size of the dihedral structures on the side facade, and the scattering intensity is related to the equivalent roughness. If the side facade of the building is smooth and has no dihedral structures, the equivalent roughness is small and the equivalent surface scattering intensity is small; if the side facade of the building is not smooth, the more dihedral structures it has, and the larger the dihedral structures, the greater the equivalent roughness and the greater the equivalent surface scattering intensity.

[0101] For the rough surface model of the side elevation, the geometric relationship of the side elevation scattering points in the InSAR system is shown in Figure 10, and the InSAR model is as follows:

[0102]

[0103] Among them, γ facade is the interference coefficient of the rough surface model of the side elevation, s 1 represents the main image, s 2 Indicates the secondary image, symbol * represents conjugate multiplication, A 1f represents the equivalent surface scattering intensity of the side elevation in the main image, A 2f represents the equivalent surface scattering intensity of the side surface in the secondary image, λ represents the wavelength, and ρ 1f represents the slant distance between the side elevation scattering point and the SAR sensor in the main image, ρ 2f represents the slant distance between the side scattering point and the SAR sensor in the secondary image, B represents the baseline length, α represents the angle between the baseline and the horizontal plane, and θ f represents the radar viewing angle at the side elevation scattering point, θ 0 h is the radar downward viewing angle at the scattering point on the reference plane and at the same slant range scattering unit as the side elevation scattering point, f Indicates the height of the side elevation scattering point relative to the reference plane.

[0104] According to the above InSAR model, it is assumed that the scattering points in adjacent scattering units on the side elevation are P′ bf and P′ ff The scattering points at the same slant distance scattering unit and located on the reference plane are P bf and P ff , scattering point P′ bf and P′ ff The height relative to the reference plane is h bf and h ff (See Fig.11 ), the interference phase gradient model Δφ of the scattering point located on the side surface can be derived and obtained facade as follows:

[0105]

[0106]

[0107]

[0108] in, is the scattering point P′ in the next slant range scattering unit on the side elevation ff The interference phase at is the scattering point P′ in the previous slant range scattering unit on the side elevation bf The interference phase at ,λ represents the wavelength, B represents the baseline length, α represents the angle between the baseline and the horizontal plane, θ ff represents the reference plane scattering point P ff The radar viewing angle at bf represents the reference plane scattering point P bf The radar viewing angle at h bf represents the height of the scattering point in front of the side elevation relative to the reference plane, h ff represents the height of the scattering point behind the side elevation relative to the reference plane, ρ ff Represents the scattering point P in the main image ff Slant range from the SAR sensor, ρ bf Represents the scattering point P in the main image bf The slant range from the SAR sensor, Δρ represents the slant range resolution.

[0109] According to the above formula, when the scattering point changes on the side elevation, the generated phase gradient can be divided into two parts, where Δφ flat It is called the flat-earth phase, which is caused by the change of the scattering point on the plane, Δφ terrain This is called terrain phase and is caused by the variation in altitude of the scattering points.

[0110] Terrain phase Δφ terrain Further derivation and simplification can be obtained as follows:

[0111]

[0112] Where Δθ represents the downward viewing angle θ ff With θ bf difference.

[0113] There are also:

[0114]

[0115]

[0116]

[0117] but:

[0118]

[0119] Where Δh f Yes ff With h bf difference.

[0120] So the topographic phase gradient Δφ in the phase gradient of the scattering point on the side elevation terrain It can be written as:

[0121]

[0122] In summary, the interference phase gradient Δφ of the scattering point on the side surface facade The model is as follows:

[0123]

[0124] Step 3: Analyze the ground scattering and determine its interference phase and phase gradient expression.

[0125] The ground in built-up areas is usually flat and smooth, so it is modeled as a flat surface with low roughness (see Fig.12 , the lines with arrows represent the actual directional incident electromagnetic waves and scattered electromagnetic waves, the dotted lines represent the scattered electromagnetic waves that are not propagated along the direction of the radar line of sight, and the solid lines represent the electromagnetic waves that propagate along the direction of the radar line of sight). When the electromagnetic waves hit the ground, surface scattering occurs. Because the surface roughness is relatively small, the scattering intensity is also relatively small.

[0126] For the surface model with less roughness, the geometric relationship of the scattering points on the ground in the InSAR system is referenced Fig.13 , and its InSAR model is as follows,

[0127]

[0128] Among them, γ ground is the interference coefficient of the ground rough surface model, s 1 represents the main image, s 2 Indicates the secondary image, symbol * represents conjugate multiplication, A 1g Represents the surface scattering intensity of the ground in the main image, A 2g represents the surface scattering intensity of the ground in the secondary image, λ represents the wavelength, and ρ 1g represents the slant distance between the ground scattering point and the SAR sensor in the main image, ρ 2g represents the slant distance between the ground scattering point and the SAR sensor in the secondary image, B represents the baseline length, α represents the angle between the baseline and the horizontal plane, and θ g represents the radar downward viewing angle at the ground scattering point, θ 0g h is the radar downward viewing angle at a scattering point that is in the same scattering unit as the ground scattering point and is located on the reference plane, g Represents the height of the ground scattering point relative to the reference plane.

[0129] According to the above InSAR model, it is assumed that the scattering points in adjacent scattering units on the ground are P′ bg and P′ fgThe scattering point P is located on the reference plane and is at the same slant distance from the scattering unit. bg and P fg (See Fig.14 ), the interferometric phase gradient model Δφ of the scattering point on the ground can be derived and obtained ground as follows:

[0130]

[0131] in, is the scattering point P′ in the next slant range scattering unit on the ground fg The interference phase at is the scattering point P′ within the previous slant range scattering unit on the ground bg The interference phase at ,λ represents the wavelength, B represents the baseline length, α represents the angle between the baseline and the horizontal plane, θ fg represents the reference plane scattering point P fg The radar viewing angle at bg represents the reference plane scattering point P bg The radar viewing angle at fg Represents the scattering point P in the main image fg Slant range from the SAR sensor, ρ bg Represents the scattering point P in the main image bg The slant range from the SAR sensor, Δρ represents the slant range resolution.

[0132] The interference phase gradient model on the ground is similar to the interference phase gradient model on the roof, because the scattering points all change on the plane, and the generated phase gradients can be considered as flat ground phase gradients, which do not change in height. Therefore, the terrain phase gradient generated by the height change is 0.

[0133] Step 4: Combined with the scattering mechanism, geometric relationship, interference phase and interference phase gradient of the roof, side facade and ground of the high-rise building, a scattering model of the high-rise building with a complex scattering mechanism is established, the expression of the interference coefficient and the interference phase gradient is determined, and the interference phase change and equivalent height change in the overlapping area are analyzed.

[0134] A dihedral structure is formed between the side facade of the building and the ground. When electromagnetic waves are irradiated on the dihedral structure, dihedral scattering occurs. The dihedral structure is large in scale, so the dihedral scattering intensity is relatively large. Combining the equivalent analysis of the scattering of the roof and the side facade of the building in step one and step two, the scattering mechanism model of the entire building can be established as: equivalent surface scattering from the roof, equivalent surface from the side facade, and strong dihedral scattering from the dihedral structure formed by the side facade and the ground (see Fig.15, the lines with arrows represent the actual directional incident electromagnetic waves and scattered electromagnetic waves, the dotted lines represent the scattered electromagnetic waves that are not propagated along the radar line of sight, and the solid lines represent the electromagnetic waves that propagate along the radar line of sight).

[0135] Due to the slant range imaging of SAR images and the vertical height variation of buildings, buildings appear overlapped in SAR images, and there is scattering from the ground, side facades and roof in the overlapped area. Combining steps 1 to 3, combined with the geometric relationship of each scattering point in the InSAR system (see Fig.16 ), the InSAR model for the overlapping area of ​​high-rise buildings is established as follows:

[0136]

[0137] The subscripts r, f, and g represent the scattering points from the roof, side facade, and ground, respectively; A 1 and A 2 Represent the scattering intensity of the main image and the secondary image respectively; ρ 1 and ρ 2 represents the slant distance between the scattering point and the main antenna and the auxiliary antenna respectively; λ represents the wavelength; B represents the baseline length; θ i represents the radar viewing angle at each scattering point, θ 0 represents the radar viewing angle at the scattering point at the same distance as each scattering point but located on the reference plane; α represents the angle between the baseline and the horizontal plane; h i Represents the height of each scattering point relative to the reference plane; represents the equivalent scattering intensity; h equ Represents the equivalent scattering height.

[0138] At this time, the equivalent height h equ It is the height of the equivalent scattering point after the superposition of three scattering vectors from the roof, side facade and ground, which is different from any height of the roof, side facade and ground scattering points.

[0139] According to the above InSAR model, the superposition of three scattering vectors from planes at different heights can be equivalent to the surface scattering generated by a scattering point at a certain height. Assuming that the equivalent scattering points in adjacent scattering units are P′ be and P′ fe The scattering points in the same scattering unit and located on the reference plane are P be and P fe , equivalent scattering point P′ be and P′ fe The height relative to the reference plane is h be and h fe (See Fig.17), the interference phase gradient model Δφ of the equivalent scattering point in the overlapping area of ​​high-rise buildings can be derived as follows:

[0140]

[0141] Among them, Δφ flat is the phase gradient caused by the change of the equivalent scattering point on the plane, Δφ terrain is the terrain phase gradient caused by the change in height of the equivalent scattering point, h fe represents the height of the next equivalent scattering point relative to the reference plane, h be represents the height of the previous equivalent scattering point relative to the reference plane, Δh e is the equivalent scattering point P′ fe and P′ be The height difference between e =h fe -h be , is the equivalent scattering point P′ in the next slant range scattering unit fe The interference phase at is the equivalent scattering point P′ in the previous slant range scattering unit be The interference phase at ,λ represents the wavelength, B represents the baseline length, α represents the angle between the baseline and the horizontal plane, θ fe represents the scattering point P on the reference plane fe The radar viewing angle at be represents the scattering point P on the reference plane be The radar viewing angle at fe Represents the scattering point P in the main image fe Slant range from the SAR sensor, ρ be Represents the scattering point P in the main image be The slant range from the SAR sensor, Δρ represents the slant range resolution.

[0142] This model is similar to the side elevation interferometric phase gradient model, except that the equivalent scattering point P′ is be and P′ fe It does not necessarily change on the side elevation, but changes in the height of adjacent equivalent scattering points at a certain unknown height, that is, h be to h fe The changes are more complex.

[0143] According to the different scattering components of the overlapping area, the overlapping area is divided into two parts from near to far on the slant distance: the near-distance overlapping area and the far-distance overlapping area. The near-distance overlapping area includes scattering from the roof, side facades and ground, and the far-distance overlapping area includes scattering from the side facades and ground. Considering the area adjacent to the building, the entire area is divided from near to far on the slant distance: 1) ground, 2) near-distance overlapping area, 3) far-distance overlapping area, 4) dihedral angle scattering bright line, 5) shadow and 6) ground (see Fig.18 ).

[0144] Combining the established InSAR model and interferometric phase gradient model, the interferometric phase changes in the imaging area and adjacent areas of high-rise buildings have the following characteristics (see Fig.19 , the symbol ↓ indicates a decrease in scattering intensity, and the symbol ↑ indicates an increase in scattering intensity). In the following characteristics, the roughness of each surface of the building changes as follows: at the beginning, the roughness of the side facade is the largest, the roughness of the roof is the smallest and is approximately a smooth plane, then the roughness of the side facade decreases, the roughness of the roof increases, and finally the roughness of the roof is much greater than the roughness of the side facade.

[0145] Assumption B ⊥ = Bcos(θ 0 -α)<0, that is, Δφ flat > 0. Use the scattered intensity A from the side facade, roof and ground f , A r and A g To reflect the roughness of each surface respectively.

[0146] 1) The roughness of the side facade is the largest, the ground and roof are approximately smooth and the scattering is negligible, that is, A f >>A r ,A g hour.

[0147] At this time, according to the distance from near to far, the interference phase and changes in the ground area are as described in step 3. The interference phase gradient is locally similar and changes evenly, and it appears in a strip shape due to phase winding; the interference phase change inside the overlapping area is simplified to the interference phase of the side facade of the building. At this time, since the height of the scattering point on the side facade decreases with the increase of the slant distance, the interference phase gradient is smaller than the interference phase gradient on the ground, and changes evenly, also appearing in a strip shape. At the boundary between the ground and the overlapping area, there is a phase jump due to the change of the scattering component; the shadow area has low scattering energy and is easily affected by noise, so the interference phase is also similar to noise (see Fig.19 a)).

[0148] 2) The roughness of the side facade decreases, the roughness of the roof increases, the ground is approximately smooth and the scattering is negligible, that is, A f >Ar >>A g hour.

[0149] At this time, the interference phase changes of the ground, the long-distance overlapping area and the shadow are as shown in 1), but for the close-distance overlapping area, as the scattering component of the roof increases, the interference phase gradient changes uniformly on the whole, but small pulse fluctuations appear locally. At the same time, there is a phase jump at the junction of area 1) to area 6), and the following situations all have such phase characteristics, which will not be repeated (see Fig.19 b)).

[0150] 3) The roughness of the side facade continues to decrease, while the roughness of the roof continues to increase, and the two are equal. The ground is approximately smooth and the scattering can be ignored, that is, A f =A r >>A g hour.

[0151] At this time, the interference phase changes of the ground, the long-distance overlapping area and the shadow are still the same as 1), but for the close-distance overlapping area, the interference phase changes are more complex, and the overall change is uniform. The interference phase gradient is larger than 2), and the local small pulse fluctuations become phase jumps (see Fig.19 c)).

[0152] 4) The roughness of the side facade continues to decrease, the roughness of the roof continues to increase, the ground is approximately smooth and the scattering is negligible, making A r >A f >>A g hour.

[0153] At this time, the interference phase changes of the ground, distant overlapping areas and shadows are still the same as 1). For the close overlapping areas, the overall interference phase shows a uniform change, and the interference phase gradient is larger than 3) and close to the interference phase gradient of the ground area. This is because the scattering component from the roof plane is dominant. At the same time, since the scattering from the side facades cannot be ignored, the interference phase of the close overlapping area has small pulse fluctuations locally (see Figure 19d)).

[0154] 5) The roughness of the roof continues to increase, the side facade and the ground are approximately smooth and the scattering is negligible, that is, A r >>A f ,A g hour.

[0155] At this time, the interference phase changes of the ground, the long-distance overlapping area and the shadow are still the same as 1). For the close-distance overlapping area, the interference phase change is uniform and the interference phase gradient is approximately equal to the interference phase gradient of the ground area (see Fig.19 e)).

[0156] Based on the above analysis, we can draw the following conclusions:

[0157] 1) In the building imaging area and adjacent areas, unknown phase jumps will occur when the scattering components change;

[0158] 2) For the overlapping area of ​​buildings, the surface scattering from the ground is weak and can be ignored. However, due to the change of scattering components inside the overlapping area, the interference phase changes are inconsistent, which is manifested as follows: the interference phase change in the long-distance overlapping area is characterized by the interference phase change of the side facade, the phase gradient is approximately the same, and the scattering point changes along the side facade; the scattering components in the close-distance overlapping area are superimposed, the interference phase changes are complex, and the equivalent scattering point height changes are complex, and this height cannot represent the height change of the scattering point on the side facade, so it cannot be directly used for building height reconstruction.

[0159] Step 5: Reconstruct the “pure” side elevation phase of a high-rise building with a complex scattering mechanism, and then reconstruct the building height.

[0160] The ideal situation for estimating the building height based on the interference phase of the overlapping area is that there is only scattering from the side facade in the entire overlapping area, so that the real scattering point changes in the vertical direction. The interference phase of the overlapping area at this time is called the side facade interference phase. However, when there are multiple types of scattering in the overlapping area, the interference phase is now obtained based on the geometry of the equivalent scattering point. The equivalent scattering point is synthesized by scattering points on different planes, and its height does not represent the actual building height. At the same time, based on the scattering analysis and interference phase analysis of the actual high-rise building in steps one and two, it can be obtained that the interference phase of the overlapping area of ​​the actual building is complex, and the side facade phase that can be used for building height estimation cannot be directly obtained. Therefore, it is necessary to extract the side facade phase from the interference phase of the complex overlapping area to realize the reconstruction of the side facade phase, and further use the side facade phase to realize the building height estimation.

[0161] According to the overlap region interference phase analysis in step 1, for high-rise buildings, in the long-distance overlap region, the scattering only comes from the side facades, which is exactly the required side facade interference phase. However, it is not the complete side facade interference phase. The length of the overlap region is determined by the height of the high-rise building, that is, the existence range of the side facade interference phase is the entire overlap region (see Fig. 20 ).

[0162] The side elevation of the overlapping area can be reconstructed through the partial side elevation phase of the long-distance overlapping area. The process is as follows:

[0163] 1) Reference interference phase gradient estimation. A sliding window is established on the interference pattern, and the standard deviation of the interference phase gradient in the window is calculated. The window slides from the dihedral angle scattering point to the beginning of the overlap area. When the standard deviation of the interference phase gradient in the window exceeds the threshold, the sliding is terminated, and the area from the dihedral angle scattering point to the end point of the window sliding is considered to be a long-distance overlap area. The interference phase gradient in this area is used as the reference interference phase gradient. Since the side elevation interference phase in the long-distance overlap area is approximately unchanged locally, and the interference phase in the close-distance overlap area changes complexly, the standard deviation of the interference phase gradient is used to detect the close-distance overlap area and further estimate the interference phase gradient.

[0164] 2) Lateral interferometric phase reconstruction. Based on the reference interferometric phase gradient and partial lateral interferometric phase obtained in step 1), the lateral interferometric phase of the entire overlapping area is calculated (reference Fig.21 ).

[0165] 3) Building height reconstruction. Unwrap the side elevation interference phase and calculate the side elevation interference phase difference Δφ of the entire overlapping area. facade ; Further combined with the 2π blur height h of the interference image pair am , the building height h can be calculated,

[0166]

[0167] Among them, λ is the wavelength, ρ is the slant distance, B is the baseline length, θ is the radar downward viewing angle, and α is the angle between the baseline and the horizontal plane.

[0168] Embodiment 1:

[0169] This embodiment uses two TerraSAR-X interferometric data to verify the proposed interferometric phase change analysis and height reconstruction method. The SAR amplitude diagram is shown in Figure 2. Fig. 22 The parameter settings of TerraSAR-X images are shown in Table 1.

[0170] Table 1 TerraSAR-X image parameters

[0171]

[0172]

[0173] Fig.23 is an optical image of a building in the selected image scene. It can be seen from the image that there are some dihedral structures on the roof of the building, while the side facades are relatively smooth and flat. These dihedral structures from the roof produce strong dihedral scattering in the close-up overlapping area of ​​the building, making the close-up overlapping area appear brighter on the SAR image, such as Fig.23As shown in the middle ellipse area; and because the side facade is relatively smooth and flat, the scattering intensity of the building's close-range overlapping area and long-range overlapping area in the SAR image is quite different, as shown in Fig.24 As shown in (the black solid ellipse is the close-range overlapping area. For this building, the scattering intensity in the close-range overlapping area is relatively large). At the same time, the interference phase of the overlapping area of ​​the building and the adjacent area is as follows: Fig.25 As shown, it can be seen that the interference phase inside the overlap region (see Fig.25 The black thick line part in the middle) changes inconsistently, and the interference phase changes in the long-distance overlap area (see Fig.25 The black dotted ellipse in the middle) is similar to the interference phase change of the side elevation, but the interference phase change in the close overlap area (see Fig.25 The black solid line ellipse in the middle is different from the change of the interference phase of the side elevation, and is more complicated. The interference phase change of the overlapping area of ​​the building is consistent with the analysis in step 1, which proves the rationality and correctness of the building interference phase analysis of the present invention.

[0174] The unwrapped phase of the overlapped area without side elevation interferometry phase reconstruction is as follows Fig.26 As shown, the reconstructed side elevation interference phase is as follows Fig. 27 Comparing the two phase images, it can be seen that for the phase image without side elevation interferometric phase reconstruction, the overall interference changes in the overlap area are inconsistent, especially at the beginning of the overlap area, that is, the close overlap area, the interference phase is more complicated (see Fig.26 As for the reconstructed interference phase of the overlapped region, the interference phase changes evenly in the entire overlapped region, which is consistent with the analysis of the side elevation interference phase change in step 1.

[0175] The three-dimensional image of the building height is restored by interferometric phase reconstruction without side elevation phase reconstruction. Fig.28 As shown in the figure, the three-dimensional image of the building height is restored by reconstructing the side elevation interferometry phase. Fig.29 The actual height of the building in the experimental area is about 85m. It can be seen that the building height without using the reconstructed side elevation interferometry phase recovery is obviously wrong (refer to Fig.28The overall height is underestimated, and the reconstructed height is about 80m. However, the building height using the reconstructed side elevation interferometric phase recovery has a relatively uniform height change on the side elevation, and the top height of the building is close to the real height of 85m, with a good reconstruction effect. The building height reconstruction results and accuracy evaluation are shown in Table 2. As can be seen from Table 2, the reconstructed height of the buildings in the scene is very close to the real height of 85m from the perspective of average height, and the absolute error of the average height of all buildings is 1.76m; from the perspective of root mean square error, the highest root mean square error RMSE is 2.23m, the lowest RMSE is 1.04m, and the overall RMSE can reach 1.55m, with a good reconstruction effect.

[0176] Table 2 Building height reconstruction results and accuracy evaluation

[0177]

Claims

1. A method for constructing an InSAR model of a high-rise building and reconstructing its height, characterized in that The method comprises the following steps: Step 1: Analyze the roof scattering of high-rise buildings and determine its interference phase and interference phase gradient expression. The specific steps are as follows: Step 1: Equivalently treat the scattering from the building roof as surface scattering, and its scattering intensity depends on the roughness of the building roof; model the roof of a high-rise building as a rough surface with a certain roughness, and its InSAR model is as follows: Among them, γ roof is the interference coefficient of the roof rough surface model, s1 represents the main image, s2 represents the secondary image, and the symbol * represents conjugation, A 1r represents the surface scattering intensity of the roof in the main image, A 2r represents the surface scattering intensity of the roof in the secondary image, λ represents the wavelength, and ρ 1r represents the slant distance between the roof scattering point and the SAR sensor in the main image, ρ 2r represents the slant distance between the roof scattering point and the SAR sensor in the secondary image, B represents the baseline length, α represents the angle between the baseline and the horizontal plane, and θ r represents the radar viewing angle at the roof scattering point, θ 0r h is the radar downward viewing angle at the scattering point on the reference plane and at the same slant distance scattering unit as the roof scattering point, r Indicates the height of the roof scattering point relative to the reference plane; Step 12: According to the InSAR model in step 11, assume that the scattering points in adjacent scattering units on the roof are P b ' r and P f ' r The scattering points at the same slant distance scattering unit and located on the reference plane are P br and P fr , scattering point P b ' r and P f ' r The height relative to the reference plane is h r , the interferometric phase gradient model Δφ of the scattering point on the roof roof as follows: in, is the scattering point P in the next slant range scattering unit on the roof f ' r The interference phase at is the scattering point P within the previous slant range scattering unit on the roof b ' r The interference phase at θ fr represents the reference plane scattering point P fr The radar viewing angle at br represents the scattering point P on the reference plane br The radar viewing angle at br Represents the scattering point P in the main image br The slant range from the SAR sensor, Δρ represents the slant range resolution, Δh r represents the height variation between adjacent scattering points on the roof, and its value is zero; Step 2: Analyze the side facade scattering of high-rise buildings and determine its interference phase and interference phase gradient expression. The specific steps are as follows: Step 21: Equivalently treat the scattering from the side facade of the building as surface scattering, and its scattering intensity depends on the roughness of the side facade; model the side facade of the building as a rough surface with a certain roughness, and its InSAR model is as follows: Among them, γ facade is the interference coefficient of the rough surface model of the side elevation, A 1f represents the equivalent surface scattering intensity of the side elevation in the main image, A 2f represents the equivalent surface scattering intensity of the side elevation in the secondary image, ρ 1f represents the slant distance between the side elevation scattering point and the SAR sensor in the main image, ρ 2f represents the slant distance between the side elevation scattering point and the SAR sensor in the secondary image, θ f represents the radar downward viewing angle at the side elevation scattering point, θ 0f h is the radar downward viewing angle at the scattering point on the reference plane and at the same slant range scattering unit as the side elevation scattering point, f Indicates the height of the side elevation scattering point relative to the reference plane; Step 22: According to the InSAR model in step 21, assume that the scattering points in adjacent scattering units on the side elevation are P b ' f and P f ' f The scattering points at the same slant distance scattering unit and located on the reference plane are P bf and P ff , scattering point P b ' f and P f ' f The height relative to the reference plane is h bf and h ff , the interference phase gradient Δφ of the scattering point on the side surface facade The model is as follows: Among them, Δφ flat represents the flat-earth phase, Δφ terrain represents the terrain phase, θ bf represents the scattering point P on the reference plane bf The radar viewing angle at bf Represents the scattering point P on the main image bf Slant distance to the SAR sensor, Δh f Yes ff With h bf difference; Step 3: Analyze the ground scattering and determine its interference phase and interference phase gradient expression. The specific steps are as follows: Step 3: Surface scattering occurs on the ground; the ground in the building area is modeled as a rough surface, and its InSAR model is as follows: Among them, γ ground is the interference coefficient of the ground rough surface model, A 1g Represents the surface scattering intensity of the ground in the main image, A 2g represents the surface scattering intensity of the ground in the secondary image, ρ 1g represents the slant distance between the ground scattering point and the SAR sensor in the main image, ρ 2g represents the slant distance between the ground scattering point and the SAR sensor in the secondary image, θ g represents the radar downward viewing angle at the ground scattering point, θ 0g h represents the radar downward viewing angle at the scattering point that is in the same scattering distance unit as the ground scattering point and is located on the reference plane, g Represents the height of the ground scattering point relative to the reference plane; Step 3.2: According to the InSAR model in step 3.1, assume that the scattering points in adjacent scattering units on the ground are P b ' g and P f ' g The scattering point P is located on the reference plane and is at the same slant distance from the scattering unit. bg and P fg , the interferometric phase gradient model Δφ of the scattering point on the ground ground as follows: in, is the scattering point P in the next slant range scattering unit on the ground f ' g The interference phase at is the scattering point P within the previous slant range scattering unit on the ground b ' g The interference phase at θ fg represents the reference plane scattering point P fg The radar viewing angle at bg represents the reference plane scattering point P bg The radar viewing angle at fg Represents the scattering point P in the main image fg Slant range from the SAR sensor, ρ bg Represents the scattering point P in the main image bg Slant distance to the SAR sensor, Δh g It represents the height change between adjacent scattering points on the ground, and its value is zero. Δρ represents the slant range resolution; Step 4: Combine the scattering mechanism, geometric relationship, interference phase and interference phase gradient of the roof, side facade and ground of the high-rise building, establish a scattering model of the high-rise building with complex scattering mechanism, determine the expression of interference coefficient and interference phase gradient, and analyze the interference phase change and equivalent height change in the overlap area. The specific steps are as follows: Step 41: Integrate steps 1 to 3, combine the geometric relationship of each scattering point in the InSAR system, and establish the InSAR model of the overlapping area of ​​high-rise buildings: Wherein, the subscripts r, f, and g represent the scattering points from the roof, side facade, and ground, respectively; A1 and A2 represent the scattering intensities of the primary image and the secondary image, respectively; ρ1 and ρ2 represent the slant distances between the scattering point and the primary antenna and the secondary antenna, respectively; θ i represents the radar downward viewing angle at each scattering point, θ0 represents the radar downward viewing angle at the scattering point that is in the same scattering unit as the roof scattering point, the side facade scattering point and the ground scattering point and is located on the reference plane; α represents the angle between the baseline and the horizontal plane; h i Represents the height of each scattering point relative to the reference plane; represents the equivalent scattering intensity; h equ represents the equivalent scattering height; Step 42: According to the InSAR model in step 41, the superposition of three scattering vectors from planes at different heights is equivalent to the surface scattering generated by a scattering point at a certain height. Assume that the equivalent scattering points in adjacent scattering units are P b ' e and P f ' e The scattering points in the same scattering unit and located on the reference plane are P be and P fe , equivalent scattering point P b ' e and P f ' e The height relative to the reference plane is h be and h fe , the interference phase gradient model Δφ of the equivalent scattering point in the overlapping area of ​​high-rise buildings is as follows: Among them, Δφ flat is the phase gradient caused by the change of the equivalent scattering point on the plane, Δφ terrain is the terrain phase gradient caused by the change in height of the equivalent scattering point, h fe represents the height of the next equivalent scattering point relative to the reference plane, h be represents the height of the previous equivalent scattering point relative to the reference plane, Δh e =h fe -h be , is the equivalent scattering point P in the next slant range scattering unit f ' e The interference phase at is the equivalent scattering point P in the previous slant range scattering unit b ' e The interference phase at θ fe represents the scattering point P on the reference plane fe The radar viewing angle at be represents the scattering point P on the reference plane be The radar viewing angle at fe Represents the scattering point P in the main image fe Slant range from the SAR sensor, ρ be Represents the scattering point P in the main image be The slant range from the SAR sensor, Δρ represents the slant range resolution; Step 5: Reconstruct the "pure" side elevation phase of a high-rise building with a complex scattering mechanism, and then reconstruct the building height. The specific steps are as follows: Step 51: Reference interferometric phase gradient estimation A sliding window is established on the interference pattern, and the standard deviation of the interference phase gradient in the window is calculated. The window slides from the dihedral angle scattering point to the beginning of the overlap area. When the standard deviation of the interference phase gradient in the window exceeds the threshold, the sliding is terminated, and the area from the dihedral angle scattering point to the end point of the window sliding is considered to be a long-distance overlap area, and the interference phase gradient in this area is used as a reference interference phase gradient; Step 52: Side-view interferometry phase reconstruction According to the reference interference phase gradient and the partial side elevation interference phase obtained in step 51, the side elevation interference phase of the entire overlapping area is calculated; Step 53: Building Height Reconstruction Unwrap the side elevation interference phase and calculate the side elevation interference phase difference Δφ of the entire overlapping area facade ; Further combined with the 2π blur height h of the interference image pair am , calculate the building height h:

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