Bistatic SAR image space-variant ambiguity calculation method based on positioning equation

Abstract

The invention relates to the technical field of synthetic aperture radars, and discloses a bistatic SAR image space-variant ambiguity calculation method based on a positioning equation, and the method comprises the steps: setting the parameters of an SAR image, carrying out the traversal calculation in a range ambiguity period range and a Doppler ambiguity period range, and obtaining an image ambiguity distance and an image Doppler ambiguity frequency; constructing an earth-centered earth-fixed coordinate system, calculating to obtain an instantaneous slope distance and an instantaneous Doppler frequency of an image target point, and constructing an ellipsoid function about an image fuzzy point; calculating through a bistatic positioning equation set to obtain image blurring point coordinates; calculating azimuth angles and pitch angles from the radar transmitting point and the radar receiving point to the image blurring point based on the coordinates of the image blurring point; obtaining a radar transmitting point gain coordinate and a radar receiving point gain coordinate; and obtaining the ambiguity of the image target point through an ambiguity calculation formula. According to the invention, the technical problems of low ambiguity point positioning precision, unreasonable ambiguity period traversal and rough antenna gain acquisition in the prior art are solved.

Description

Technical Field

[0001] This invention relates to the field of synthetic aperture radar technology and discloses a method for calculating spatially varied ambiguity of bi-base SAR images based on positioning equations. Background Technology

[0002] Synthetic Aperture Radar (SAR) has been widely used in remote sensing due to its all-weather, all-day, and high-resolution imaging capabilities. Among them, bistatic SAR, with its separate deployment of transmitter and receiver, has stronger anti-jamming capabilities, a wider observation angle, and richer target scattering information, making it an important direction for the development of SAR technology.

[0003] During bistatic SAR imaging, images are prone to spatially variable ambiguity (i.e., the ambiguity changes with the position of the target point in the image) due to the influence of pulse repetition frequency (PRF), pulse repetition interval (PRI), and the motion characteristics of the radar system. This manifests as the target signal and the ambiguity signal superimposed in the range and azimuth directions, severely affecting image resolution and target detection accuracy. Therefore, accurately calculating the spatially variable ambiguity of bistatic SAR images is a crucial prerequisite for suppressing ambiguity and improving image quality.

[0004] Existing methods for calculating spatially varying ambiguity in bistatic SAR images have the following shortcomings: I. Low accuracy of fuzzy point positioning: Most methods use the "Earth sphere model" to approximate the shape of the Earth, without considering the geometric characteristics of the Earth as a rotating ellipsoid, which leads to systematic deviations in the calculation of fuzzy point coordinates; 2. Unreasonable traversal of fuzzy periods: The traversal range of distance fuzzy periods and Doppler fuzzy periods is not defined. Either the range is too narrow and does not cover the main fuzzy cases, or the range is too wide and results in low computational efficiency. 3. Coarse antenna gain acquisition: Simplified antenna pattern models (such as rectangular patterns) are often used, without combining the actual azimuth and elevation angles of the ambiguous points for accurate interpolation, resulting in large errors in radar gain calculation and ultimately affecting the accuracy of ambiguity. Summary of the Invention

[0005] This invention aims to solve the technical problems of low positioning accuracy of fuzzy points, unreasonable fuzzy period traversal, and coarse antenna gain acquisition in existing systems, and provides a method for calculating spatially varied fuzziness of bistatic SAR images based on positioning equations.

[0006] To achieve the above-mentioned technical effects, the technical solution adopted by this invention is: a method for calculating spatially varied ambiguity of bi-base SAR images based on positioning equations, comprising: The SAR image parameters are set, including the range blur period range and the Doppler blur period range. The image blur distance and the image Doppler blur frequency are obtained by traversing and calculating the range blur period range and the Doppler blur period range. A geocentric coordinate system is constructed, in which a radar transmitting point and a radar receiving point, as well as an image target point and an image blurred point are set. The radar transmitting point transmits a signal to the image target point, and the radar receiving point receives the echo signal of the image target point to obtain the instantaneous slant range and instantaneous Doppler frequency of the image target point. Using the instantaneous slant range and instantaneous Doppler frequency of the target point in the image, we construct the instantaneous slant range function and instantaneous Doppler frequency function for the blurred points in the image. By using the WGS-84 ellipsoid model, we construct the ellipsoid function for the blurred points in the image. Using the instantaneous slant range function, instantaneous Doppler frequency function, and ellipsoid function of the blurred image point, a set of bibasic localization equations is constructed for the blurred image point, and the coordinates of the blurred image point are obtained by calculating the bibasic localization equations. The radar transmits a signal to the blurred point in the image, and the radar receives the echo signal from the blurred point. Based on the coordinates of the blurred point, the azimuth and elevation angles from the radar transmit point and the radar receive point to the blurred point are calculated. Based on the azimuth and elevation angles from the radar transmitting point and the radar receiving point to the blurred point in the image, a two-dimensional antenna pattern is constructed from the radar transmitting point and the radar receiving point to the blurred point in the image. By interpolating in the two-dimensional antenna pattern, the gain coordinates of the radar transmitting point and the gain coordinates of the radar receiving point are obtained. The ambiguity of the target point in the image is obtained by using the ambiguity calculation formula based on the gain coordinates of the radar transmitting point and the gain coordinates of the radar receiving point.

[0007] As a preferred embodiment, the formula for calculating the instantaneous slant distance of the image target point is:

[0008] Among them, R s S is the instantaneous slant range of the target point in the image, T is the coordinates of the radar transmitting point, R is the coordinates of the radar receiving point, and S is the coordinates of the target point in the image. The formula for calculating the Doppler blur frequency of the image target point is:

[0009] Among them, F d V is the image Doppler blur frequency of the target point in the image, λ is the radar wavelength, and V T For radar transmission speed, U T V is the distance from the radar transmitting point to the target point. RFor radar receiving speed, U R This represents the distance from the radar receiver to the target point.

[0010] As a preferred embodiment, the instantaneous slant distance function of the blurred image point is:

[0011] in, R is the instantaneous slant distance of the blurred point in the image. s is the instantaneous slant range of the target point in the image, m is the image blur distance, c is the speed of light, and PRI is the pulse repetition interval; The instantaneous Doppler frequency function of the blurred point in the image is:

[0012] in, F is the instantaneous Doppler frequency of the blurred point in the image. d denoted as the image Doppler blur frequency of the target point, n is the image Doppler blur frequency, and PRF is the pulse repetition frequency; The ellipsoid function of the blurred points in the image is:

[0013] Wherein, the coordinates of the fuzzy point are , a=6378137, b=6356752.3142.

[0014] As a preferred embodiment, the formula for calculating the azimuth angle from the radar emission point to the ambiguity point is:

[0015] The formula for calculating the elevation angle from the radar transmission point to the ambiguous point is:

[0016] The formula for calculating the azimuth angle from the radar receiving point to the ambiguous point is:

[0017] The formula for calculating the elevation angle from the radar receiving point to the ambiguous point is:

[0018] in, The azimuth angle of the radar transmission point. The elevation angle of the radar transmission point. The azimuth angle of the radar receiving point. Let y be the elevation angle of the radar receiving point. T The x-axis coordinate of the radar transmission point. THere, T represents the X-axis coordinate of the radar transmission point, and y represents the X-axis coordinate of the radar transmission point. R The X value represents the Y-axis coordinate of the radar receiving point. R Here, R represents the X-axis coordinate of the radar receiver point. The Y-axis coordinates of the blurred point. The X-axis coordinates of the blurred point. These are the coordinates of the target point in the image.

[0019] As a preferred embodiment, the ambiguity calculation formula is:

[0020] Where A is the ambiguity of the target point. The radar transmission point gain coordinates, The azimuth angle of the radar transmission point. The elevation angle of the radar launch point. For radar receiver gain coordinates, The azimuth angle of the radar receiving point. The elevation angle of the radar receiving point. The instantaneous slant range from the radar transmission point to the blurred point in the image. NS is the instantaneous slant range from the radar receiving point to the blurred point in the image, and NS is the blur energy of the target point in the image.

[0021] As a preferred embodiment, both the distance ambiguity period range and the Doppler ambiguity period range are -20 to 20.

[0022] Compared with the prior art, the beneficial effects of this invention are: I. High accuracy in fuzzy point positioning: The WGS-84 ellipsoid model is used instead of the traditional spherical model, which conforms to the actual geometry of the earth, reducing the calculation error of fuzzy point coordinates and making it suitable for medium and high resolution SAR systems. II. Balancing computational efficiency and accuracy: The range of distance and Doppler blur period is clearly defined as -20 to 20, which avoids unnecessary calculations while covering the main blurry scenes; 3. High antenna gain accuracy: The two-dimensional antenna pattern interpolation method based on the actual azimuth and elevation angles of the ambiguity points reduces the gain error compared with the simplified pattern model, and significantly improves the accuracy of ambiguity calculation. IV. Wide applicability: It can be applied to dual-base SAR systems with different orbits (such as low orbit and medium orbit) and different frequency bands (such as X-band and C-band), especially meeting the requirements of high ambiguity suppression in scenarios such as high-resolution remote sensing and precise target detection. Attached Figure Description

[0023] Figure 1 This is a logic diagram of the bi-base SAR image spatial variation ambiguity calculation method of the present invention. Detailed Implementation

[0024] The present invention will now be described in further detail with reference to the embodiments and accompanying drawings. However, this should not be construed as limiting the scope of the above-described subject matter of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0025] refer to Figure 1 Example 1: A method for calculating spatially varied ambiguity in bi-base SAR images based on positioning equations, comprising: Step 1: Set SAR image parameters and iterate through and calculate blur parameters First, the core image parameters of the dual-base SAR system are set, including: range ambiguity period range: -20 to 20; Doppler ambiguity period range: -20 to 20. Other parameters: radar wavelength λ, speed of light c, pulse repetition interval PRI, pulse repetition frequency PRF (PRF=1 / PRI), radar transmission speed V T Radar receiving speed V R .

[0026] Within the aforementioned range of distance blur period and Doppler blur period, the number of blurs (distance blur number m, Doppler blur number n) is traversed and calculated to obtain the image blur distance and the image Doppler blur frequency.

[0027] Step 2: Construct a geocentric coordinate system and calculate key parameters of the target point. Coordinate system construction: The Earth-centered and Earth-fixed (ECEF) coordinate system is adopted. This coordinate system has the Earth's center of mass as the origin, the X-axis points to the intersection of the Prime Meridian and the equator, the Y-axis points to the intersection of 90° East longitude and the equator, and the Z-axis points to the Earth's North Pole. It can accurately describe the spatial positional relationship between the radar and the target.

[0028] Key point definition: Define 4 core points in the ECEF coordinate system: Radar transmission point T (coordinates are (x) T ,y T ,z T ); Radar receiver point R (coordinates are (x) R ,y R ,z R ); Image target point S (coordinates (x, y, z) is the target location where the blur of image target point S is to be calculated; The blurred point S' (coordinates (x', y', z') in the image is a virtual point formed by the blurred signal of the target point S, which needs to be solved by the positioning equation.

[0029] 2.1 Calculate the instantaneous slant distance of the target point in the image and the Doppler blur frequency of the target point in the image; The formula for calculating the instantaneous slant distance of the target point in the image is:

[0030] Among them, R s S is the instantaneous slant range of the target point in the image, T is the coordinates of the radar transmitting point, R is the coordinates of the radar receiving point, and S is the coordinates of the target point in the image. The formula for calculating the Doppler blur frequency of the image target point is:

[0031] Among them, F d V is the image Doppler blur frequency of the target point in the image, λ is the radar wavelength, and V T For radar transmission speed, U T V is the distance from the radar transmitting point to the target point. R For radar receiving speed, U R This represents the distance from the radar receiver to the target point.

[0032] Step 3: Construct the constraint function for fuzzy points Using the instantaneous slant range function, instantaneous Doppler frequency function, and ellipsoid function of the blurred image point, a set of bibasic localization equations is constructed for the blurred image point, and the coordinates of the blurred image point are obtained by calculating the bibasic localization equations. The instantaneous slant distance function of the blurred points in the image is:

[0033] in, R is the instantaneous slant distance of the blurred point in the image. s is the instantaneous slant range of the target point in the image, m is the image blur distance, c is the speed of light, and PRI is the pulse repetition interval; The instantaneous Doppler frequency function of the blurred point in the image is:

[0034] in, F is the instantaneous Doppler frequency of the blurred point in the image. d denoted as the image Doppler blur frequency of the target point, n is the image Doppler blur frequency, and PRF is the pulse repetition frequency; The ellipsoid function of the blurred points in the image is:

[0035] Wherein, the coordinates of the fuzzy point are , a=6378137, b=6356752.3142.

[0036] The bibasic localization equations of the blurred point in the image are solved by numerical iterative methods (such as the Newton-Raphson method), and the coordinates of the blurred point S' in the ECEF coordinate system are calculated.

[0037] Step 5: Calculate the azimuth and elevation angles of the radar and the ambiguous point. Azimuth and elevation angles are key parameters describing the spatial pointing relationship between the radar and the ambiguous point. The azimuth and elevation angles from the radar transmitting point T to the ambiguous point S' and from the radar receiving point R to the ambiguous point S' need to be calculated separately. The formula for calculating the azimuth angle from the radar emission point to the ambiguous point is:

[0038] The formula for calculating the elevation angle from the radar transmission point to the ambiguous point is:

[0039] The formula for calculating the azimuth angle from the radar receiving point to the ambiguous point is:

[0040] The formula for calculating the elevation angle from the radar receiving point to the ambiguous point is:

[0041] in, The azimuth angle of the radar transmission point. The elevation angle of the radar transmission point. The azimuth angle of the radar receiving point. Let y be the elevation angle of the radar receiving point. T The x-axis coordinate of the radar transmission point. T Here, T represents the X-axis coordinate of the radar transmission point, and y represents the X-axis coordinate of the radar transmission point. R The X value represents the Y-axis coordinate of the radar receiving point. R Here, R represents the X-axis coordinate of the radar receiver point. The Y-axis coordinates of the blurred point. The X-axis coordinates of the blurred point. These are the coordinates of the target point in the image.

[0042] Step 6: Interpolate to obtain radar antenna gain coordinates Constructing two-dimensional antenna radiation patterns: Based on the bistatic SAR system, construct two-dimensional radiation patterns for the transmitting antenna and the receiving antenna respectively. The radiation pattern data can be obtained through actual antenna measurements or electromagnetic simulation.

[0043] Antenna gain interpolation calculation: The result obtained in step 5 , Substituting the transmit antenna pattern, the transmit point gain coordinates are obtained through bilinear interpolation (or cubic spline interpolation). Similarly, , Substituting the receiving antenna pattern, the gain coordinates of the receiving point can be obtained by interpolation. .

[0044] Step 7: Calculate the blur of the target point in the image. Based on the antenna gain coordinates obtained in step 6, and combined with the slant range of the ambiguity point and the ambiguity energy of the target point, the ambiguity A of the target point S is solved using the ambiguity calculation formula. The formula for calculating ambiguity is:

[0045] Where A is the ambiguity of the target point. The radar transmission point gain coordinates, The azimuth angle of the radar transmission point. The elevation angle of the radar launch point. For radar receiver gain coordinates, The azimuth angle of the radar receiving point. The elevation angle of the radar receiving point. The instantaneous slant range from the radar transmission point to the blurred point in the image. NS is the instantaneous slant range from the radar receiving point to the blurred point in the image, and NS is the blur energy of the target point in the image.

[0046] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating spatially varied ambiguity in bi-base SAR images based on positioning equations, characterized in that, include: Set SAR image parameters, which include range blur period range and Doppler blur period range. Perform traversal calculations on the range blur period range and Doppler blur period range respectively to obtain the image blur distance and image Doppler blur frequency. A geocentric coordinate system is constructed, in which a radar transmitting point, a radar receiving point, an image target point, and an image blurred point are set. The radar transmitting point transmits a signal to the image target point, and the radar receiving point receives the echo signal of the image target point to obtain the instantaneous slant range and instantaneous Doppler frequency of the image target point. Using the instantaneous slant range and the instantaneous Doppler frequency, an instantaneous slant range function and an instantaneous Doppler frequency function for the blurred points of the image are constructed. By using the WGS-84 ellipsoid model, an ellipsoid function for the blurred points of the image is constructed. Using the instantaneous slant range function, the instantaneous Doppler frequency function, and the ellipsoid function, a set of bibasic localization equations is constructed for the blurred points in the image, and the coordinates of the blurred points in the image are calculated using the set of bibasic localization equations. By transmitting a signal from the radar transmitting point to the blurred point in the image, and calculating the azimuth and elevation angles from the radar transmitting point and the radar receiving point to the blurred point in the image based on the coordinates of the blurred point; Based on the azimuth and elevation angles from the radar transmitting point and the radar receiving point to the blurred point in the image, a two-dimensional antenna pattern is constructed from the radar transmitting point and the radar receiving point to the blurred point in the image. Interpolation is performed on the two-dimensional antenna pattern to obtain the gain coordinates of the radar transmitting point and the gain coordinates of the radar receiving point. The ambiguity of the target point in the image is obtained by using the ambiguity calculation formula based on the gain coordinates of the radar transmitting point and the gain coordinates of the radar receiving point.

2. The method for calculating spatially varied ambiguity of bi-base SAR images based on positioning equations according to claim 1, characterized in that, The formula for calculating the instantaneous slant distance of the target point in the image is: ； Among them, R s S is the instantaneous slant range of the target point in the image, T is the coordinates of the radar transmitting point, R is the coordinates of the radar receiving point, and S is the coordinates of the target point in the image. The formula for calculating the Doppler blur frequency of the image target point is: ； Among them, F d V is the image Doppler blur frequency of the target point in the image, λ is the radar wavelength, and V T For radar transmission speed, U T V is the distance from the radar transmitting point to the target point. R For radar receiving speed, U R This represents the distance from the radar receiver to the target point.

3. The method for calculating spatially varied ambiguity of bi-base SAR images based on positioning equations according to claim 1, characterized in that, The expression for the instantaneous slant distance function of the blurred points in the image is: ； in, R is the instantaneous slant distance of the blurred point in the image. s is the instantaneous slant range of the target point in the image, m is the image blur distance, c is the speed of light, and PRI is the pulse repetition interval; The expression for the instantaneous Doppler frequency function of the blurred points in the image is: ； in, F is the instantaneous Doppler frequency of the blurred point in the image. d denoted as the image Doppler blur frequency of the target point, n is the image Doppler blur frequency, and PRF is the pulse repetition frequency; The ellipsoid function of the blurred points in the image is: ； Wherein, the coordinates of the blurred points in the image are , a=6378137, b=6356752.3142.

4. The method for calculating spatially varied ambiguity of bi-base SAR images based on positioning equations according to claim 1, characterized in that, The formula for calculating the azimuth angle from the radar emission point to the blurred point in the image is: ； The formula for calculating the elevation angle from the radar emission point to the blurred point in the image is: ； The formula for calculating the azimuth angle from the radar receiving point to the blurred point in the image is: ； The formula for calculating the elevation angle from the radar receiving point to the blurred point in the image is: ； in, The azimuth angle of the radar transmission point. The elevation angle of the radar transmission point. The azimuth angle of the radar receiving point. Let y be the elevation angle of the radar receiving point. T The x-axis coordinate of the radar transmission point. T Here, T represents the X-axis coordinate of the radar transmission point, and y represents the X-axis coordinate of the radar transmission point. R The X value represents the Y-axis coordinate of the radar receiving point. R Here, R represents the X-axis coordinate of the radar receiver point. The Y-axis coordinates of the blurred points in the image. The X-axis coordinates of the blurred points in the image. These are the coordinates of the target point in the image.

5. The method for calculating spatially varied ambiguity of bi-base SAR images based on positioning equations according to claim 1, characterized in that, The formula for calculating ambiguity is: ； Where A is the ambiguity of the target point. The radar transmitter gain coordinates, The azimuth angle of the radar transmission point. The elevation angle of the radar launch point. For radar receiver gain coordinates, The azimuth angle of the radar receiving point. The elevation angle of the radar receiving point. The instantaneous slant range from the radar transmission point to the blurred point in the image. NS is the instantaneous slant range from the radar receiving point to the blurred point in the image, and NS is the blur energy of the target point in the image.

6. The method for calculating spatially varied ambiguity of bi-base SAR images based on positioning equations according to claim 1, characterized in that, The distance ambiguity period range and the Doppler ambiguity period range are both -20 to 20.

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