CN117538875A - Lunar surface elevation inversion method based on single-navigation full-polarization SAR data - Google Patents
Lunar surface elevation inversion method based on single-navigation full-polarization SAR data Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
- G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C5/00—Measuring height; Measuring distances transverse to line of sight; Levelling between separated points; Surveyors' levels
Abstract
The invention provides a lunar surface elevation inversion method based on single-navigation full-polarization SAR data, which belongs to the technical field of radars and comprises the following steps: estimating a polarization azimuth angle related to terrain through full polarization SAR data according to radar side-looking imaging geometry and an electromagnetic wave polarization theory; based on a Lambertian backscattering model, establishing a relation between SAR image intensity and azimuth and ground pitch gradient, and estimating the azimuth and ground pitch gradient through a Sinclair polarized backscattering matrix and a polarized coherent matrix; establishing a relation between the relative elevation of the surface and the two-dimensional gradient through a poisson equation, and solving the poisson equation based on a weighted complete multiple grid algorithm to obtain the relative elevation of the lunar surface; the relative elevation extracted based on the fully polarized SAR data is converted to an absolute elevation by the attachment points of the lunar surface where the precise elevation is known. The invention improves the precision of the full polarization SAR inversion terrain.
Description
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a lunar surface elevation inversion method based on single-navigation full-polarization SAR data.
Background
The earth is located in the universe like a half of the sea. Exploration of the vast universe is a necessary choice, deep space exploration is a stage for competing in various aerospace countries, and is an extremely important development direction in the aerospace field. The spaceborne synthetic aperture radar (Synthetic Aperture Radar, SAR) can image the target of interest in a high resolution all the time and all the weather. The active microwave sensor can play a significant role in deep space exploration, and serve the research of the problems of significant scientific value such as universe origin and evolution, life origin and evolution and the like. The spaceborne SAR takes electromagnetic waves as an information carrier, and the image information of the spaceborne SAR has multidimensional characteristics. Among them, electromagnetic wave polarization characteristics are susceptible to physical characteristics such as surface characteristics, dielectric constant, geometry, and the like of an irradiated object. Therefore, more abundant ground feature information can be acquired by utilizing the polarization characteristic of the electromagnetic wave.
The full polarization SAR data provides another method of terrain inversion, especially when only polarization SAR data is available. Many shadow areas exist on the moon, which are difficult to detect by optical devices. In particular for the later in situ detection of lunar water ice, it is necessary to determine a relatively flat area in the permanently hatched area in order for the deep space detector to land. Therefore, it is of great significance to study inversion of lunar surface elevation based on fully polarized SAR data. In addition, the moon surface is exposed and dry, free of shielding and free of vegetation interference. Therefore, the SAR back-scatter echoes of the lunar surface can well reflect the topographic features.
However, the current technology suffers from two-dimensional slope estimation ambiguity and is subject to data jitter at relatively flat areas. Aiming at the problems, the invention provides a novel two-dimensional gradient estimation method, which further improves the terrain inversion precision based on the full-polarization SAR.
Disclosure of Invention
In order to solve the technical problems, the invention provides a lunar surface elevation inversion method based on single navigation through full polarization SAR data, which further improves the accuracy of full polarization SAR inversion terrain by deriving a new two-dimensional gradient estimation equation and combining ground connection points.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a lunar surface elevation inversion method based on single-navigation full-polarization SAR data comprises the following steps:
step 1, estimating a polarization azimuth angle by adopting a circular polarization algorithm through full-polarization SAR data according to radar side-looking imaging geometry and an electromagnetic wave polarization theory;
step 2, estimating azimuth gradient and ground pitch gradient based on a Lambertian backscattering model, and eliminating singular points in gradient estimated values of the azimuth gradient and the ground pitch gradient;
step 3, solving a poisson equation based on a weighted complete multiple grid algorithm to obtain a lunar surface relative elevation extracted based on full-polarization SAR data;
and 4, converting the relative elevation of the lunar surface extracted based on the full-polarization SAR data into an absolute elevation through the connection point of the known precise elevation of the lunar surface.
Further, the step 1 includes:
the estimated polarization azimuth angle using the circular polarization algorithm is as follows:
，
wherein,represents an arctangent function, +.>Representing the real part->Represents the polarization azimuth angle estimated by circular polarization algorithm, < +.>Intermediate values representing the polarization azimuth estimates, obtained from the full polarization data, superscript +.>Represents a conjugation operation and is carried out,representing taking space or time levelsAll(s)>Representing an amplitude value; />For complex scattering coefficients, X is H or V, Y is H or V, H represents horizontal polarization, and V represents vertical polarization;
for ground features meeting Bragg scattering model, the polarization azimuth angle estimated by adopting circular polarization algorithmThe following corrections were made:
，
wherein,represents the final polarization azimuth estimate, +.>For the Huynen parameters estimated based on the full polarization data,and->To de-orient homopolar elements in the scattering matrix.
Further, the step 2 includes:
ground clearance gradientIs expressed as:
，
wherein,is an arcsine function>As an intermediate parameter, expressed as: /> ，
Wherein,is a sine function +.>As cosine function +.>For SAR image intensity, ++>Represents flat area power; />Represents the azimuth gradient->Representative grade of ground distance>Representing radar perspective;
azimuth gradientIs expressed as:
，
wherein,is an arcsine function>As a sign function +.>As an intermediate parameter, expressed as:
，
wherein,representing a tangent function.
The beneficial effects are that:
the method is based on inversion of lunar surface elevation of single-navigation full-polarization SAR data, is simpler in implementation compared with an orthogonal double-navigation mode, and has a wider application range. Meanwhile, the invention provides a new two-dimensional gradient estimation method, further improves the terrain inversion precision, and provides a new technical approach and solution for moon surface elevation inversion.
Drawings
FIG. 1 is a conceptual diagram of a lunar surface elevation inversion method based on single-navigation over-all-polarization SAR data;
FIG. 2a is a schematic diagram of onboard SAR data acquisition geometry;
FIG. 2b is a surface normalAt->Schematic of (2);
FIG. 2c is a surface normalAt->Schematic of (2);
FIG. 3 is a terrain inversion flow chart;
FIG. 4a is a lunar surface L-band full polarization SAR image;
FIG. 4b is an inverted lunar surface relative elevation;
FIG. 4c is a 3D display of the inverted moon surface relative elevation.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
The lunar surface elevation inversion method based on single-navigation full-polarization SAR data, as shown in figure 1, comprises the following steps:
first, according to radar side-looking imaging geometry and electromagnetic wave polarization theory, a polarization azimuth POA (Polarimetric Orientation Angle) related to the terrain is estimated by a polarization coherence matrix generated based on the full polarization SAR data.
Consider the case of single-station backscatter,a dimension-compounded backscattering matrix>The method comprises the following steps:
，
wherein,for complex scattering coefficients, the diagonal elements represent the "co-polarized" term, the non-diagonal elements represent the "cross-polarized" term, X is H or V, Y is H or V, H represents horizontal polarization, and V represents vertical polarization.
According to fig. 2a, 2b, 2c, for a reflection symmetric medium, the polarization azimuth POA can be expressed as:
，
wherein,represents a tangent function>Representing a sine function>Representing the cosine function>Representing the final polarization azimuth estimate, +.>Represents the azimuth gradient->Representative grade of ground distance>Representing radar perspective.
In the view of figure 2a,is azimuth, is->Is the direction of ground distance, is->Is surface normal->And->And->Form a right-hand Cartesian coordinate system, +.>、/>And->Respectively->At->、/>And->The upper component, H represents horizontal polarization, V represents vertical polarization,>representing the radar line of sight direction.
In the view of figure 2b,represents->At->Projection on plane, ">And->Respectively represent gradient at->And->Projection onto a projection plane.
In the view of figure 2c,represents->At->Projection on plane, ">Representing the gradient of +.>Projection onto a projection plane.
Based on the full polarization data, the polarization azimuth POA can be estimated by a circular polarization algorithm (Circular Polarization Algorithm, CPA), as follows:
，
wherein,represents an arctangent function, +.>Representing the real part->Represents the polarization azimuth angle estimated by circular polarization algorithm, < +.>Intermediate values representing the polarization azimuth estimates, obtained from the full polarization data, superscript +.>Represents a conjugation operation and is carried out,representing taking a spatial or temporal average,/->Representing taking the amplitude value.
Pair complex backscattering matrixPerforming orientation removal:
，
wherein,representing the complex backscatter matrix after the de-orientation. For ground objects meeting Bragg scattering model, the polarization azimuth angle estimated by adopting circular polarization algorithm is +.>The following corrections were made:
，
wherein,represents the final polarization azimuth POA estimate,/->Huynen parameters estimated for based on fully polarized data, < >>And->For removing homopolar elements in the oriented scattering matrix, wherein +.>Represents horizontal polarization, +.>Representing vertical polarization, the Bragg scattering model is a theoretical modeling of a slightly rough surface.
And secondly, estimating the azimuth gradient and the ground range gradient based on a Lambertian backscattering model, namely performing two-dimensional gradient estimation, and eliminating singular points in gradient estimation values.
The Lambertian backscattering model requires that the following three assumptions be satisfied:
1) The ground is locally flat; 2) The terrain is smooth enough; 3) The surface of the ground object is uniformly scattered.
SAR image intensity for terrain meeting Lambertian backscatter modelThe following relationship exists with the two-dimensional gradient:
，
wherein,for SAR image intensity, ++>For scaling constant, +.>Representing the backscattering coefficient, ">And->The ground range resolution and the azimuth resolution of the SAR image are sequentially shown.
Ground clearance gradientCan be expressed as:
，
wherein,is an arcsine function>As an intermediate parameter, expressed as: />，/>Representing flat area power.
Azimuth gradientCan be expressed as:
，
wherein,is an inverse cosine function>Is an intermediate parameter, expressed as->，As a sign function.
SAR images have geometric deformations such as speckle noise, shading, perspective shrinkage, top-bottom inversion, and the like. These are the causes of "singular points", i.e. where the image information cannot represent the actual topography change features. The correction can be based on the following principle: if the ground-to-azimuth pixel spacing is the same, then the integral of the slope along the closed loop should be zero.
Thirdly, solving a poisson equation based on a weighted complete multi-Grid algorithm WFMG (Weighted Full Multi-Grid) to obtain the relative elevation of the lunar surface.
The poisson equation establishes a link between elevation and two-dimensional slope, which can be expressed as follows:
，
wherein,representing Laplace operator->，/>Representative is located at->The elevation value at which the position is located,representative is located at->Surface curvature at the location. The discrete form thereof can be expressed as:
，
wherein,can be decomposed into a ground distance direction at +.>Surface curvature of the region->And azimuth is at->Surface curvature of the region->：
，
And->Expressed as:
，
wherein,and->Respectively representing the elevation difference of the ground distance direction and the elevation difference of the azimuth direction, +.>Represents->Azimuth gradient of the part>Represents->Ground clearance gradient at the location.
WFMG transfers the low frequency error to the high frequency component and removes it by Gauss-Seidel relaxation. Because poisson's equation is solved for the relative elevation, the relative elevation is converted into absolute elevation by the connecting point of the known accurate elevation of part of the ground. A specific terrain inversion flow is shown in fig. 3.
Fourth, the relative elevation extracted based on the full polarization SAR data is converted through the ground connection point with the known accurate elevation on the lunar surface, and the absolute elevation is estimated.
The connection points may be extracted from DEM or laser altimeter altimetric data, with the vertical accuracy and spatial resolution of the connection points affecting the vertical accuracy and spatial resolution of the final absolute elevation. The inversion result of the moon surface relative elevation obtained by the method is shown in fig. 4a, 4b and 4 c. Wherein fig. 4a is a lunar surface L-band full-polarization SAR image, with azimuth direction and distance direction in vertical direction; FIG. 4b is an inverted lunar surface relative elevation; fig. 4c is the result of the 3D display of the inverted lunar surface relative elevation.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (3)
1. The lunar surface elevation inversion method based on the single-navigation full-polarization SAR data is characterized by comprising the following steps of:
step 1, estimating a polarization azimuth angle by adopting a circular polarization algorithm through full-polarization SAR data according to radar side-looking imaging geometry and an electromagnetic wave polarization theory;
step 2, estimating azimuth gradient and ground pitch gradient based on a Lambertian backscattering model, and eliminating singular points in gradient estimated values of the azimuth gradient and the ground pitch gradient;
step 3, solving a poisson equation based on a weighted complete multiple grid algorithm to obtain a lunar surface relative elevation extracted based on full-polarization SAR data;
and 4, converting the relative elevation of the lunar surface extracted based on the full-polarization SAR data into an absolute elevation through the connection point of the known precise elevation of the lunar surface.
2. The lunar surface elevation inversion method based on single-navigation-over-all-polarization SAR data according to claim 1, wherein said step 1 comprises:
the estimated polarization azimuth angle using the circular polarization algorithm is as follows:
，
wherein,represents an arctangent function, +.>Representing the real part->Represents the polarization azimuth angle estimated by circular polarization algorithm, < +.>Intermediate values representing the polarization azimuth estimates, obtained from the full polarization data, superscript +.>Represents conjugation operations,/->Representing taking a spatial or temporal average,/->Representing an amplitude value; />For complex scattering coefficients, X is H or V, Y is H or V, H represents horizontal polarization, and V represents vertical polarization;
for ground features meeting Bragg scattering model, the polarization azimuth angle estimated by adopting circular polarization algorithmThe following corrections were made:
，
wherein,representative ofFinal polarization azimuth estimate,/>Huynen parameters estimated for based on fully polarized data, < >>And (3) withTo de-orient homopolar elements in the scattering matrix.
3. The lunar surface elevation inversion method based on single-navigation-over-all-polarization SAR data according to claim 2, wherein said step 2 comprises:
ground clearance gradientIs expressed as:
，
wherein,is an arcsine function>As an intermediate parameter, expressed as: /> ，
Wherein,is a sine function +.>As cosine function +.>For SAR image intensity, ++>Represents flat area power; />Represents the azimuth gradient->Representative grade of ground distance>Representing radar perspective;
azimuth gradientIs expressed as:
，
wherein,is an arcsine function>As a sign function +.>As an intermediate parameter, expressed as:
，
wherein,representing a tangent function.
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