Ground-based bistatic radar lunar imaging geometry correction method, device and equipment

Abstract

The application provides a ground-based bistatic radar lunar imaging geometry correction method, device and equipment, and relates to the technical field of synthetic aperture radar. The geometry correction method comprises the following steps: constructing a two-way slant range model according to the geometric relationship between the ground-based bistatic radar and the lunar imaging area, determining the mapping relationship between the lunar geographic coordinate system and the delay-Doppler coordinate system based on the two-way slant range model; constructing an initial rational polynomial coefficient model based on the mapping relationship, projecting the delay-Doppler domain image result obtained by the ground-based bistatic radar to the lunar geographic coordinate system by using the initial rational polynomial coefficient model, and obtaining a preliminary geometry correction result; analyzing the system error of the ground-based bistatic radar, adding an affine transformation in the initial rational polynomial coefficient model according to the analysis result, obtaining an improved rational polynomial coefficient model, and projecting the delay-Doppler domain image result to the lunar geographic coordinate system again based on the improved rational polynomial coefficient model, and obtaining a final geometry correction result.

Description

Technical Field

[0001] This invention relates to the field of Synthetic Aperture Radar (SAR) technology, specifically to a ground-based bistatic radar method, apparatus, device, and storage medium for geometric correction of lunar imaging. Background Technology

[0002] Ground-based radar imaging of the moon is a crucial component of deep space exploration. It utilizes large radar equipment on Earth to transmit electromagnetic waves towards the moon and receives the reflected echo signals. By employing SAR imaging technology, it acquires images of the lunar surface, providing a vital tool for lunar scientific research. Ground-based radar lunar SAR imaging primarily employs delayed-Doppler technology. This technology performs envelope and phase compensation on the complete scene based on the distance history of the scene center within the imaging time. According to the time delay information and Doppler frequency information of each point in the scene relative to the scene center, the imaging scene is divided into different delayed-Doppler units, thus obtaining a two-dimensional SAR image of the lunar surface. Since the imaging results obtained by delayed-Doppler technology are delayed-Doppler domain images, they need to undergo coordinate projection and geometric correction processing to obtain an image in the lunar geographic coordinate system. Summary of the Invention

[0003] In view of this, the present invention provides a method, apparatus, device and storage medium for geometric correction of lunar imaging by a ground-based bistatic radar.

[0004] According to a first aspect of the present invention, a method for geometric correction of lunar imaging by a ground-based bistatic radar is provided, comprising: constructing a two-way slant range model based on the geometric relationship between the ground-based bistatic radar and the lunar imaging region; determining the mapping relationship between the lunar geographic coordinate system and the delayed-Doppler coordinate system based on the two-way slant range model; constructing an initial rational polynomial coefficient model based on the mapping relationship; projecting the delayed-Doppler domain image results acquired by the ground-based bistatic radar onto the lunar geographic coordinate system using the initial rational polynomial coefficient model to obtain a preliminary geometric correction result; analyzing the systematic error of the ground-based bistatic radar; adding an affine transformation to the initial rational polynomial coefficient model based on the analysis results to obtain an improved rational polynomial coefficient model; and projecting the delayed-Doppler domain image results back onto the lunar geographic coordinate system based on the improved rational polynomial coefficient model to obtain the final geometric correction result.

[0005] According to an embodiment of the present invention, constructing a two-way slant range model based on the geometric relationship between a ground-based bistatic radar and a lunar imaging region includes: determining the transmission slant range corresponding to a specified time and the receiving slant range corresponding to a specified time delay based on the radar ephemeris, the lunar digital elevation model, and single-way optical time correction; adding the transmission slant range and the receiving slant range to obtain the two-way slant range at the specified time; and fitting the two-way slant range at different times using a polynomial to obtain the two-way slant range model.

[0006] According to an embodiment of the present invention, determining the mapping relationship between the lunar geographic coordinate system and the delay-Doppler coordinate system based on the two-way slant range model includes: determining the polynomial coefficients of the center point and any non-center point of the lunar imaging region using the two-way slant range model; determining the residual two-way slant range of any non-center point relative to the center point based on the respective polynomial coefficients; extracting the difference between the constant term and the first-order term coefficients from the coefficients of the residual two-way slant range, and determining the delay time and Doppler frequency of any non-center point in the delay-Doppler coordinate system based on the difference between the constant term and the first-order term coefficients; and converting the delay time and Doppler frequency into specific pixel coordinates of the radar image based on the radar range sampling rate and pulse repetition frequency to obtain the mapping relationship.

[0007] According to an embodiment of the present invention, constructing an initial rational polynomial coefficient model based on a mapping relationship includes: establishing multiple uniformly distributed elevation layers according to the elevation range of the lunar imaging region, with uniformly distributed lunar geographic coordinate points set on each elevation layer; determining the delayed-Doppler image coordinate points corresponding to each lunar geographic coordinate point in each elevation layer according to the mapping relationship; and fitting rational polynomial coefficients based on the coordinate pairs formed by each lunar geographic coordinate point and the corresponding delayed-Doppler image coordinate points to obtain the initial rational polynomial coefficient model.

[0008] According to an embodiment of the present invention, the analysis of the system error of a ground-based bistatic radar includes: determining the time synchronization error and center frequency error of the ground-based bistatic radar, wherein the time synchronization error and center frequency error constitute the system error; determining the echo signal model under the influence of the system error; obtaining the delay-Doppler domain echo signal model by performing range compression, joint correction of envelope and phase, and azimuth-to-Fourier transform on the echo signal model; and characterizing the analysis results of the delay-Doppler domain echo signal model.

[0009] According to an embodiment of the present invention, adding an affine transformation to the initial rational polynomial coefficient model based on the analysis results to obtain an improved rational polynomial coefficient model includes: obtaining the matching error of each coordinate point between the preliminary geometric correction result and the optical digital orthophoto; using the least squares method to solve for the correction parameters corresponding to the matching errors in the range and azimuth directions to obtain the affine transformation coefficients; determining the system error correction value in each direction based on the affine transformation coefficients, and adding the system error correction value to the initial rational polynomial coefficient model to obtain the improved rational polynomial coefficient model.

[0010] According to an embodiment of the present invention, obtaining the matching error of each coordinate point between the preliminary geometric correction result and the optical digital orthophoto image includes: using a light-radar image matching algorithm based on an improved phase-consistent model to obtain the matching error of each coordinate point between the preliminary geometric correction result and the optical digital orthophoto image.

[0011] A second aspect of the present invention provides a geometric correction device for lunar imaging using a ground-based bistatic radar, comprising: a determination module, configured to construct a two-way slant range model based on the geometric relationship between the ground-based bistatic radar and the lunar imaging region, and determine the mapping relationship between the lunar geographic coordinate system and the delayed-Doppler coordinate system based on the two-way slant range model; a first correction module, configured to construct an initial rational polynomial coefficient model based on the mapping relationship, and project the delayed-Doppler domain image results acquired by the ground-based bistatic radar onto the lunar geographic coordinate system using the initial rational polynomial coefficient model to obtain a preliminary geometric correction result; and a second correction module, configured to analyze the system error of the ground-based bistatic radar, add an affine transformation to the initial rational polynomial coefficient model based on the analysis results to obtain an improved rational polynomial coefficient model, and project the delayed-Doppler domain image results back onto the lunar geographic coordinate system based on the improved rational polynomial coefficient model to obtain the final geometric correction result.

[0012] A third aspect of the present invention provides an electronic device comprising: one or more processors; and a storage device for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors perform the method in any of the above embodiments.

[0013] A fourth aspect of the present invention provides a computer-readable storage medium having a computer program or instructions stored thereon, wherein the computer program or instructions, when executed by a processor, implement the steps of the method in any of the above embodiments. Attached Figure Description

[0014] The above-described features, other objects, and advantages of the present invention will become clearer from the following description of embodiments of the invention with reference to the accompanying drawings, in which:

[0015] Figure 1 This diagram illustrates the principle of delayed Doppler imaging.

[0016] Figure 2 A flowchart illustrating a ground-based bistatic radar lunar imaging geometric correction method according to an embodiment of the present invention is shown.

[0017] Figure 3 A flowchart illustrating a ground-based bistatic radar lunar imaging geometric correction method according to yet another embodiment of the present invention is shown.

[0018] Figure 4 A schematic diagram illustrating a two-way slant range image of a ground-based bistatic radar for lunar imaging according to an embodiment of the present invention is shown.

[0019] Figure 5 A schematic diagram of a ground-based bistatic radar lunar imaging geometric correction device according to an embodiment of the present invention is shown.

[0020] Figure 6 A block diagram of an electronic device suitable for implementing a ground-based bistatic radar lunar imaging geometric correction method according to an embodiment of the present invention is shown schematically. Detailed Implementation

[0021] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the invention. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the invention for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0022] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention. The terms “comprising,” “including,” etc., as used herein indicate the presence of features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0023] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0024] When using expressions such as "at least one of A, B and C", they should generally be interpreted in accordance with the meaning that is commonly understood by those skilled in the art (e.g., "a system having at least one of A, B and C" should include, but is not limited to, a system having A alone, a system having B alone, a system having C alone, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B and C, etc.).

[0025] The applicant discovered in their research that existing geometric correction methods for lunar imaging using ground-based bistatic radar primarily rely on coordinate transformation and physical quantity calculations to establish a precise mapping relationship between lunar surface points (defined by the lunar geographic coordinate system) and corresponding delay-Doppler cells in the original radar data. First, any point on the lunar reference grid is converted into three-dimensional coordinates in a lunar-fixed coordinate system with the lunar center as the origin, using its geographic longitude and latitude, combined with the average radius of the moon. Second, based on physical quantities such as the latitude and longitude of the ground-based radar sub-Radar Point (SRP), the apparent lunar rotation angular velocity, and the direction of the rotation axis, the conversion from the lunar-fixed coordinate system to the radar observation coordinate system is achieved. Figure 1The diagram illustrates the principle of dividing the lunar imaging region and determining the resolvable cells using time delay and Doppler information. Finally, in the radar observation coordinate system, the time delay and Doppler cells corresponding to each point on the lunar surface in the raw radar data are calculated.

[0026] Existing technologies provide a basic framework for geolocation of lunar imaging results from ground-based radar, but the following problems exist in practical applications.

[0027] (1) The geometric description of Earth-Moon observations is not accurate enough. First, existing methods typically assume the Moon is a sphere with a single average radius when converting lunar geographic coordinates to Cartesian coordinates. This simplified model cannot accurately reflect the complex and undulating terrain features of the lunar surface, leading to a discrepancy between the geometric correction results and the actual terrain. This, in turn, introduces positioning errors and geometric distortions in high-resolution image processing. For lunar polar regions or areas with drastic terrain changes, the errors introduced by the simplified model are more significant. Second, actual ground-based lunar radar observation systems often employ a dual-station configuration with separate transmitting and receiving antennas due to requirements for transmit power and receive sensitivity. Existing methods approximate the dual-station observation geometry as a single-station observation geometry when processing dual-station lunar observation scenarios, resulting in discrepancies between the calculated delay and Doppler cells and the true values, causing geometric distortions in the geometrically corrected images.

[0028] (2) Highly sensitive to the accuracy of physical parameters. The core of existing methods lies in accurately establishing the mapping relationship between the lunar geographic coordinate system and the radar observation coordinate system. This is highly dependent on a series of precise input parameters, including SRP latitude and longitude, lunar apparent rotation angular velocity, and the relative distance between the radar and the moon. Small errors in these parameters will directly accumulate and propagate to the geometric correction results, leading to a decrease in the final positioning accuracy.

[0029] (3) The delay and Doppler cell offset introduced by radar system errors are not considered. Existing methods mainly focus on the positioning effects caused by the relative motion of the Earth and Moon and geometric transformations, but ignore the deviations caused by the inherent errors of the radar system itself. In a bistatic observation system, clock drift and frequency instability of the radar transmitting and receiving systems will lead to delays in the actual echo signal and deviations between the Doppler frequency and the theoretical value. This system error will directly cause the positional offset of the imaging cell in the delay-Doppler domain, resulting in inaccurate positioning and geometric distortion in the geometrically corrected image.

[0030] To address the limitations of existing methods, this invention proposes a novel method for coordinate projection and geometric correction of lunar imaging results from ground-based bistatic SAR. Figure 2A flowchart illustrating a ground-based bistatic radar lunar imaging geometric correction method according to an embodiment of the present invention is shown. In this document, ground-based bistatic radar, ground-based radar, and ground-based bistatic SAR are used interchangeably. The ground-based bistatic radar includes a transmitting radar and a receiving radar located on Earth. The transmitting radar transmits electromagnetic waves toward the moon, and the receiving radar receives the echo signals reflected from the moon.

[0031] like Figure 2 As shown, the geometric correction method for lunar imaging by a ground-based bistatic radar may include steps S210 to S230.

[0032] In step S210, a two-way slant range model is constructed based on the geometric relationship between the ground-based bistatic radar and the lunar imaging area, and the mapping relationship between the lunar geographic coordinate system and the delayed-Doppler coordinate system is determined based on the two-way slant range model.

[0033] In step S220, an initial rational polynomial coefficients (RPC) model is constructed based on the mapping relationship, and the delayed Doppler domain image results acquired by the ground-based bistatic radar are projected onto the lunar geographic coordinate system using the initial rational polynomial coefficients model to obtain preliminary geometric correction results.

[0034] In step S230, the system error of the ground-based bistatic radar is analyzed. Based on the analysis results, an affine transformation is added to the initial rational polynomial coefficient model to obtain an improved rational polynomial coefficient model. Based on the improved rational polynomial coefficient model, the delayed Doppler domain image results are projected again onto the lunar geographic coordinate system to obtain the final geometric correction result.

[0035] The geometric correction method for lunar imaging provided by this invention achieves accurate theoretical calculations of delay and Doppler frequency by calculating the two-way slant range between the high-precision ground-based transceiver radar and the center of the target area on the lunar surface, thus solving the problem of inaccurate geometric description of Earth-Moon observations. Based on the latitude and longitude coordinates and delay-Doppler domain coordinate pairs obtained from theoretical calculations, an RPC model is fitted to achieve a one-step transformation of the imaging scene from the delay-Doppler domain to the lunar geographic coordinate system projection, avoiding the high dependence of the transformation results on the accuracy of physical parameters. Based on the analysis of the delay-Doppler cell offset form introduced by system errors, an affine transformation is introduced into the traditional RPC model to solve the problem of the impact of bistatic SAR system errors on the accuracy of geometric correction.

[0036] Figure 3 A flowchart illustrating a ground-based bistatic radar lunar imaging geometric correction method according to yet another embodiment of the present invention is shown.

[0037] like Figure 3As shown, the ground-based bistatic radar lunar imaging geometric correction method in this embodiment can realize the mapping from the lunar geographic coordinate system (latitude, longitude, and altitude) to the delayed-Doppler coordinate system based on the accurate delayed-Doppler information calculation model, providing support for RPC coefficient fitting. Then, based on the coordinate pairs formed by the geographic coordinates and image coordinates obtained by theoretical calculation, RPC coefficient fitting is realized, constructing the coordinate transformation relationship of the entire imaging area, realizing the projection of the imaging result from the delayed-Doppler domain to the lunar geographic coordinate system. The RPC model provides the foundation for subsequent geometric correction. Then, based on the system error analysis results, affine transformation is added to the original RPC model to correct the positioning deviation introduced by the system error. According to the matching error between the optical digital orthophoto map (DOM) and the projected SAR image, affine transformation coefficient fitting is realized, and finally, the geometric correction of the entire scene is achieved.

[0038] The key to achieving accurate calculation of delayed Doppler information lies in calculating a precise two-way slant range model based on the geometric relationship between the transmitting radar, the receiving radar, and the lunar target area. The two-way slant range is the sum of the transmitting slant range and the receiving slant range. The transmitting slant range refers to the distance the radar pulse signal wavefront travels from the transmitting radar to the target, while the receiving slant range refers to the distance the lunar backscattered signal wavefront travels from the target to the receiving radar. The change of the two-way slant range over time within the synthetic aperture time (SAP) constitutes the two-way slant range model. With an average Earth-Moon distance of 380,000 kilometers and a signal transmission / reception interval of approximately 2.5 seconds, the receiving radar's position changes by more than 1 kilometer during this period, resulting in a significant transmission / reception separation phenomenon. Figure 4 The diagram schematically illustrates a two-way slant range plot of lunar imaging by a ground-based bistatic radar according to an embodiment of the present invention.

[0039] like Figure 4 As shown, for time The position of the transmitting radar at the moment of signal transmission in the geocentric J2000 coordinate system is denoted as: The location of the receiving radar is recorded as The location of the lunar target area is denoted as The times when the signal arrived on the lunar surface and the positions of the three locations are recorded as follows: The positions of the three points at the time of signal return to the receiving radar are respectively denoted as follows: The launch slant range is denoted as... The corresponding signal propagation time is denoted as The receiving slant range is denoted as The corresponding signal propagation time is denoted as .

[0040] In some embodiments, the transmit slant range at a specified time and the receive slant range after a delay at a specified time can be determined based on radar ephemeris, lunar digital elevation model, and single-way optical time correction. The transmit slant range and the receive slant range are then added together to obtain the two-way slant range at the specified time. A polynomial is then used to fit the two-way slant range at different times to obtain a two-way slant range model.

[0041] For example, the transmission slant range at time η can be calculated based on radar ephemeris, lunar DEM data, and one-way optical time correction. and time Let c be the speed of light, and calculate the time η+τ. T Receiving slant range R R (η+τ T ) and τ R =R R (η+τ T If ) / c, then the two-way slant distance R at time η is... bi (η) can be expressed as:

[0042]

[0043] In some embodiments, considering the complex relative motion between the Earth and the Moon, a two-way slant distance model can be established using a 5th-order polynomial:

[0044]

[0045] Where r0, r1, r2, r3, r4, and r5 represent polynomial coefficients.

[0046] Next, the mapping relationship between the lunar geographic coordinate system and the delay-Doppler coordinate system is determined based on the two-way slant range model. In some embodiments, the polynomial coefficients of the center point and any non-center point of the lunar imaging region can be determined using the two-way slant range model. Then, based on their respective polynomial coefficients, the residual two-way slant range of any non-center point relative to the center point is determined. Next, the difference between the constant term and the first-order coefficient is extracted from the coefficients of the residual two-way slant range, and the delay time and Doppler frequency of any non-center point in the delay-Doppler coordinate system are determined based on the difference between the constant term and the first-order coefficient. Finally, based on the radar range sampling rate and pulse repetition frequency, the delay time and Doppler frequency are converted into specific pixel coordinates of the radar image to obtain the mapping relationship.

[0047] As an example, the relative two-way slant distance from the center of the imaging region can be used. Joint envelope and phase compensation are performed on the entire scene (lunar imaging region), and the residual two-way slant range at any point P (non-center point) in the scene is calculated. It can be represented as:

[0048]

[0049] Where, r pn With r cn These are the coefficients of each term in the two-way slant distance between point P and the scene center, respectively. This represents the constant term at point P. Ideally, this refers to the delay t and Doppler frequency f at each point in the scene. d They can be represented as follows:

[0050]

[0051] in, Let represent the coefficients of the first-order term at the center point and point P, respectively, and λ represent the signal wavelength. Converting the delay time and Doppler frequency into delay-Doppler domain image coordinates can be expressed as:

[0052]

[0053] Where mod() represents the modulo operation, f s f is the range sampling rate. p Where A is the pulse repetition frequency, Asize is the number of azimuth units, and Rsize is the number of range units.

[0054] Please continue reading. Figure 3 and Figure 4 Next, an initial RPC model is constructed based on the mapping relationship. Using the RPC model to implement full-scene coordinate projection can protect sensitive information such as the position and parameters of the transmitting and receiving radars, and provide a basis for subsequent compensation for positioning deviations introduced by uncalibrated bistatic system errors.

[0055] In some embodiments, multiple uniformly distributed elevation layers can be established based on the elevation range of the lunar imaging region, with uniformly distributed lunar geographic coordinate points set on each elevation layer. Delayed-Doppler image coordinate points corresponding to each lunar geographic coordinate point in each elevation layer are determined according to the mapping relationship. Rational polynomial coefficients are fitted based on the coordinate pairs formed by each lunar geographic coordinate point and its corresponding delayed-Doppler image coordinate point to obtain an initial rational polynomial coefficient model.

[0056] As an example, based on the elevation range of the imaging area provided by the DEM, m uniformly distributed elevation layers are established, and each layer is set with n×n uniformly distributed lunar geographic coordinate points (lat). i ,lon j ,h k ). lat i ,lon j ,h k These represent latitude, longitude, and altitude, respectively.

[0057] Next, the lunar geographic coordinates (lat) are calculated based on the precise delayed Doppler information calculation model. i,lon j ,h k The corresponding delay-Doppler domain image coordinates (x) p ,y q ).

[0058] Based on the n×n×m sets of coordinate pairs, the RPC coefficients can be fitted:

[0059]

[0060] Where, N x D x N y D y These are polynomials defined by RPC coefficients. Let N... x For example:

[0061]

[0062] Where a1~a 20 Let D be the RPC coefficients of this polynomial. Similarly, D x N y D y Each of these can be defined by 20 different RPC coefficients. It should be noted that 20 here is just an example and does not constitute a limitation on the number of RPC coefficients.

[0063] Then, based on the RPC model and the DEM data of the imaging scene, the projection of the entire scene from the delay-Doppler domain image coordinates to the lunar geographic coordinates is realized to obtain preliminary geometric correction results.

[0064] Please continue reading. Figure 3 and Figure 4 Next, based on the system error analysis results of the ground-based bistatic radar, an affine transformation correction system error is constructed to achieve affine transformation coefficient fitting, and finally, geometric correction for the entire scene is realized.

[0065] In some embodiments, the time synchronization error and center frequency error of the ground-based bistatic radar can be determined, and the time synchronization error and center frequency error constitute the system error. Then, the echo signal model under the influence of the system error is determined. After range compression, joint correction of envelope and phase, and azimuth-to-Fourier transform, the echo signal model is obtained, and the delay-Doppler domain echo signal model characterizes the analysis results.

[0066] As an example, the errors of a bistatic SAR system mainly include time synchronization error Δt(η) and center frequency error. The two can be expressed in the following ways:

[0067]

[0068]

[0069] Where t0 is the fixed time deviation of the transceiver radar power-on time. For linear time deviation caused by inconsistent clock frequencies, n prt (η) represents the random time error following a normal distribution; Δf c To fix the center frequency deviation, The stable phase error has a mean of 0. This is a non-stationary phase error.

[0070] Under the influence of systematic errors, the echo signal model can be expressed as:

[0071]

[0072] Where σ is the scattering coefficient, w r and w a Let k be the range and azimuth envelopes, τ and η be the range fast time and azimuth slow time, and k be the range and azimuth fast time. r f is the signal modulation frequency, λ is the signal wavelength, and f c The signal center frequency.

[0073] After range compression, joint correction of envelope and phase, and azimuth-to-Fourier transform, the delay-Doppler domain echo signal model can be expressed as:

[0074]

[0075] in, The resulting phase error in the frequency domain, ΔR e (f a ) is ΔR e (η)=(r p0 -r c0 +r p1 t0)+(r p1 (α+1)-r c1 The frequency domain expression of η (ignoring the influence of second-order and higher-order small quantities), Δt(f a Let Δt(η) be the frequency domain expression. The Doppler frequency shift Δf caused by systematic errors is mainly manifested as follows:

[0076]

[0077] Where α is the frequency inconsistency coefficient between the transmitting and receiving radar clocks.

[0078] Therefore, the errors of the bistatic SAR system will introduce spatially variable Doppler frequency shifts, resulting in spatially variable geometric distortions in the preliminary geometric correction results.

[0079] Next, based on the analysis results, an affine transformation is added to the initial rational polynomial coefficient model to obtain an improved rational polynomial coefficient model. In some embodiments, the matching error between the preliminary geometric correction results and the optical digital orthophoto image at each coordinate point can be obtained. Then, the least squares method is used to solve for the correction parameters corresponding to the matching errors in the range and azimuth directions to obtain the affine transformation coefficients. Next, based on the affine transformation coefficients, the system error correction values ​​in each direction are determined, and the system error correction values ​​are added to the initial rational polynomial coefficient model to obtain the improved rational polynomial coefficient model.

[0080] As an example, constructing an improved RPC model supported by affine transformations can be represented as:

[0081]

[0082]

[0083] Where n0+n1x+n2y and m0+m1x+m2y are the system error correction values ​​in the x and y directions, respectively.

[0084] In some embodiments, a photo-radar image matching algorithm based on an improved phase-consistency model can be used to obtain the matching error between the preliminary geometric correction result and the optical DOM. , .

[0085] Next, the least squares method is used to solve for the affine transformation coefficients:

[0086]

[0087]

[0088] The coefficients of the affine transformation are:

[0089]

[0090]

[0091] Then, based on the improved RPC model, the delayed-Doppler domain image results are projected back onto the lunar geographic coordinate system to achieve the final geometric correction.

[0092] Based on the above embodiments, this invention designs a two-way slant range model for lunar imaging using ground-based bistatic SAR based on ephemeris and lunar DEM data. This model achieves accurate calculation of delayed Doppler information and solves the problem of inaccurate geometric description of Earth-Moon observations. This invention also designs a coordinate projection and geometric correction method based on the RPC model, enabling direct transformation of the imaging scene from the delayed-Doppler domain to lunar geographic coordinates, avoiding the high dependence of geometric correction results on the accuracy of physical parameters. Furthermore, based on a system error analysis model, this invention uses affine transformation to improve the RPC model and establishes a method for correcting positioning deviations introduced by bistatic system errors, effectively improving the geometric correction accuracy of lunar surface SAR images.

[0093] Based on the above-mentioned geometric correction method for lunar imaging using ground-based bistatic radar, this invention also provides a geometric correction device for lunar imaging using ground-based bistatic radar. The following will be combined with... Figure 5 The device is described in detail.

[0094] Figure 5 A schematic block diagram of a ground-based bistatic radar lunar imaging geometric correction device according to an embodiment of the present invention is shown. Figure 5 As shown, the ground-based bistatic radar lunar imaging geometric correction device 500 of this embodiment includes a determination module 510, a first correction module 520, and a second correction module 530.

[0095] The determination module 510 can be used to construct a two-way slant range model based on the geometric relationship between the ground-based bistatic radar and the lunar imaging area, and to determine the mapping relationship between the lunar geographic coordinate system and the delayed-Doppler coordinate system based on the two-way slant range model. In one embodiment, the determination module 510 can be used to perform the operation S210 described above, which will not be repeated here.

[0096] The first correction module 520 can be used to construct an initial rational polynomial coefficient model based on the mapping relationship, and use the initial rational polynomial coefficient model to project the delayed Doppler domain image results acquired by the ground-based bistatic radar onto the lunar geographic coordinate system to obtain preliminary geometric correction results. In one embodiment, the first correction module 520 can be used to perform the operation S220 described above, which will not be repeated here.

[0097] The second correction module 530 can be used to analyze the system error of the ground-based bistatic radar. Based on the analysis results, an affine transformation is added to the initial rational polynomial coefficient model to obtain an improved rational polynomial coefficient model. Then, based on the improved rational polynomial coefficient model, the delayed Doppler domain image results are projected again onto the lunar geographic coordinate system to obtain the final geometric correction result. In one embodiment, the second correction module 530 can be used to perform the operation S230 described above, which will not be repeated here.

[0098] Please refer to the previous text for details on the relevant content, which will not be repeated here.

[0099] According to embodiments of the present invention, any plurality of the above modules can be combined into one module, or any one of the modules can be split into multiple modules. Alternatively, at least a portion of the functionality of one or more of these modules can be combined with at least a portion of the functionality of other modules and implemented in one module. According to embodiments of the present invention, at least one of the above modules can be at least partially implemented as hardware circuitry, such as a field-programmable gate array (FPGA), a programmable logic array (PLA), a system-on-a-chip, a system-on-a-substrate, a system-on-package, an application-specific integrated circuit (ASIC), or implemented in hardware or firmware by any other reasonable means of integrating or packaging the circuitry, or implemented in any one of software, hardware, and firmware methods, or in a suitable combination of any of these. Alternatively, at least one of the above modules can be at least partially implemented as a computer program module, which, when run, can perform corresponding functions.

[0100] Figure 6 A block diagram of an electronic device suitable for implementing a ground-based bistatic radar lunar imaging geometric correction method according to an embodiment of the present invention is shown schematically.

[0101] like Figure 6 As shown, an electronic device 600 according to an embodiment of the present invention includes a processor 601, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 602 or a program loaded from a storage portion 608 into a random access memory (RAM) 603. The processor 601 may include, for example, a general-purpose microprocessor (e.g., a CPU), an instruction set processor and / or an associated chipset and / or a special-purpose microprocessor (e.g., an application-specific integrated circuit (ASIC)), etc. The processor 601 may also include onboard memory for caching purposes. The processor 601 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of the present invention.

[0102] RAM 603 stores various programs and data required for the operation of electronic device 600. Processor 601, ROM 602, and RAM 603 are interconnected via bus 604. Processor 601 executes various operations of the method flow according to embodiments of the present invention by executing programs in ROM 602 and / or RAM 603. It should be noted that programs may also be stored in one or more memories other than ROM 602 and RAM 603. Processor 601 may also execute various operations of the method flow according to embodiments of the present invention by executing programs stored in one or more memories.

[0103] According to an embodiment of the present invention, the electronic device 600 may further include an input / output (I / O) interface 605, which is also connected to a bus 604. The electronic device 600 may also include one or more of the following components connected to the input / output (I / O) interface 605: an input section 606 including a keyboard, mouse, etc.; an output section 607 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and a speaker, etc.; a storage section 608 including a hard disk, etc.; and a communication section 609 including a network interface card such as a LAN card, modem, etc. The communication section 609 performs communication processing via a network such as the Internet. A drive 610 is also connected to the input / output (I / O) interface 605 as needed. A removable medium 611, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on the drive 610 as needed so that computer programs read from it can be installed into the storage section 608 as needed.

[0104] The present invention also provides a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into the device / apparatus / system. The computer-readable storage medium carries one or more programs, which, when executed, implement the method according to the embodiments of the present invention.

[0105] According to embodiments of the present invention, a computer-readable storage medium may be a non-volatile computer-readable storage medium, such as including, but not limited to: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In the present invention, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. For example, according to embodiments of the present invention, a computer-readable storage medium may include ROM 602 and / or RAM 603 and / or one or more memories other than ROM 602 and RAM 603 described above.

[0106] Embodiments of the present invention also include a computer program product comprising a computer program containing program code for performing the methods shown in the flowchart. When the computer program product is run on a computer system, the program code enables the computer system to implement the ground-based bistatic radar lunar imaging geometric correction method provided in the embodiments of the present invention.

[0107] When the computer program is executed by the processor 601, it performs the functions defined in the system / apparatus of this invention. According to embodiments of the invention, the systems, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0108] In one embodiment, the computer program may rely on a tangible storage medium such as an optical storage device or a magnetic storage device. In another embodiment, the computer program may also be transmitted and distributed in the form of signals over a network medium, and downloaded and installed via the communication section 609, and / or installed from the removable medium 611. The program code contained in the computer program can be transmitted using any suitable network medium, including but not limited to: wireless, wired, etc., or any suitable combination thereof.

[0109] In such an embodiment, the computer program can be downloaded and installed from a network via the communication section 609, and / or installed from the removable medium 611. When the computer program is executed by the processor 601, it performs the functions defined in the system of this embodiment of the invention. According to embodiments of the invention, the systems, devices, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0110] According to embodiments of the present invention, program code for executing the computer programs provided in the embodiments of the present invention can be written in any combination of one or more programming languages. Specifically, these computational programs can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. Programming languages ​​include, but are not limited to, languages ​​such as Java, C++, Python, "C", or similar programming languages. The program code can be executed entirely on the user's computing device, partially on the user's device, partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0111] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0112] Those skilled in the art will understand that the features described in the various embodiments of the present invention can be combined and / or combined in various ways, even if such combinations or combinations are not explicitly described in the present invention. In particular, the features described in the various embodiments of the present invention can be combined and / or combined in various ways without departing from the spirit and teachings of the present invention. All such combinations and / or combinations fall within the scope of the present invention.

[0113] The embodiments of the present invention have been described above. However, these embodiments are merely illustrative and not intended to limit the scope of the invention. Although various embodiments have been described above, this does not mean that the measures in the various embodiments cannot be used advantageously in combination. Various substitutions and modifications can be made by those skilled in the art without departing from the scope of the invention, and all such substitutions and modifications should fall within the scope of the invention.

Claims

1. A method for correcting the geometry of a lunar imaging bistatic radar based on the ground, characterized in that, include: A two-way slant range model is constructed based on the geometric relationship between the ground-based bistatic radar and the lunar imaging area. The mapping relationship between the lunar geographic coordinate system and the delayed-Doppler coordinate system is determined based on the two-way slant range model. Based on the mapping relationship, an initial rational polynomial coefficient model is constructed, and the delayed Doppler domain image results acquired by the ground-based bistatic radar are projected onto the lunar geographic coordinate system using the initial rational polynomial coefficient model to obtain preliminary geometric correction results. The system error of the ground-based bistatic radar is analyzed. Based on the analysis results, an affine transformation is added to the initial rational polynomial coefficient model to obtain an improved rational polynomial coefficient model. Based on the improved rational polynomial coefficient model, the delayed Doppler domain image results are projected again onto the lunar geographic coordinate system to obtain the final geometric correction result. The step of adding an affine transformation to the initial rational polynomial coefficient model based on the analysis results to obtain an improved rational polynomial coefficient model includes: obtaining the matching error of each coordinate point between the preliminary geometric correction result and the optical digital orthophoto; solving for the correction parameters corresponding to the matching errors in the range and azimuth directions using the least squares method to obtain the affine transformation coefficients; determining the system error correction value in each direction based on the affine transformation coefficients, and adding the system error correction value to the initial rational polynomial coefficient model to obtain the improved rational polynomial coefficient model.

2. The geometric correction method according to claim 1, characterized in that, The construction of the two-way slant range model based on the geometric relationship between the ground-based bistatic radar and the lunar imaging region includes: Based on radar ephemeris, lunar digital elevation model and single-way optical time correction, the transmission slant range corresponding to a specified time and the receiving slant range corresponding to the specified time after the delay are determined. The transmission slant range and the receiving slant range are added together to obtain the two-way slant range at the specified time. The two-way slant distance model is obtained by fitting a polynomial to the two-way slant distance at different times.

3. The geometric correction method according to claim 2, characterized in that, The determination of the mapping relationship between the lunar geographic coordinate system and the delayed-Doppler coordinate system based on the two-way slant range model includes: The polynomial coefficients of the center point and any non-center point of the lunar imaging region are determined using the two-way slant distance model. Based on their respective polynomial coefficients, the residual two-way slant distance of the arbitrary non-center point relative to the center point is determined; Extract the constant term and the difference between the coefficients of the first term from the coefficients of the residual two-way slant distance, and determine the delay time and Doppler frequency of the arbitrary non-center point in the delay-Doppler coordinate system based on the constant term and the difference between the coefficients of the first term; Based on the radar range sampling rate and pulse repetition frequency, the delay time and Doppler frequency are converted into specific pixel coordinates of the radar image to obtain the mapping relationship.

4. The geometric correction method according to claim 1, characterized in that, The construction of the initial rational polynomial coefficient model based on the mapping relationship includes: Based on the elevation range of the lunar imaging area, multiple uniformly distributed elevation layers are established, and lunar geographic coordinate points are set uniformly on each elevation layer. Based on the mapping relationship, determine the delayed-Doppler image coordinates corresponding to each lunar geographic coordinate point of each elevation layer; Based on the coordinate pairs consisting of each lunar geographic coordinate point and the corresponding delayed-Doppler image coordinate point, rational polynomial coefficients are fitted to obtain the initial rational polynomial coefficient model.

5. The geometric correction method according to claim 1, characterized in that, The analysis of the system error of the ground-based bistatic radar includes: The time synchronization error and center frequency error of the ground-based bistatic radar are determined, and the time synchronization error and center frequency error constitute the system error. The echo signal model under the influence of the system error is determined. After the echo signal model is subjected to range compression, joint correction of envelope and phase, and azimuth Fourier transform, the delay-Doppler domain echo signal model is obtained. The delay-Doppler domain echo signal model characterizes the analysis results.

6. The geometric correction method according to claim 1, characterized in that, The matching error of each coordinate point between the obtained preliminary geometric correction result and the optical digital orthophoto image includes: The matching error of each coordinate point between the preliminary geometric correction result and the optical digital orthophoto image is obtained using a light-radar image matching algorithm based on an improved phase-consistency model.

7. A ground-based bistatic radar lunar imaging geometric correction device, characterized in that, include: The determination module is used to construct a two-way slant range model based on the geometric relationship between the ground-based bistatic radar and the lunar imaging area, and to determine the mapping relationship between the lunar geographic coordinate system and the delayed-Doppler coordinate system based on the two-way slant range model. The first correction module is used to construct an initial rational polynomial coefficient model based on the mapping relationship, and to project the delayed Doppler domain image results acquired by the ground-based bistatic radar onto the lunar geographic coordinate system using the initial rational polynomial coefficient model to obtain preliminary geometric correction results. The second correction module is used to analyze the system error of the ground-based bistatic radar. Based on the analysis results, an affine transformation is added to the initial rational polynomial coefficient model to obtain an improved rational polynomial coefficient model. Based on the improved rational polynomial coefficient model, the delayed Doppler domain image result is projected again onto the lunar geographic coordinate system to obtain the final geometric correction result. The step of adding an affine transformation to the initial rational polynomial coefficient model based on the analysis results to obtain an improved rational polynomial coefficient model includes: obtaining the matching error of each coordinate point between the preliminary geometric correction result and the optical digital orthophoto; solving for the correction parameters corresponding to the matching errors in the range and azimuth directions using the least squares method to obtain the affine transformation coefficients; determining the system error correction value in each direction based on the affine transformation coefficients, and adding the system error correction value to the initial rational polynomial coefficient model to obtain the improved rational polynomial coefficient model.

8. An electronic device, characterized in that, include: One or more processors; Storage device for storing one or more programs. Wherein, when the one or more programs are executed by the one or more processors, the one or more processors perform the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program or instructions stored thereon, characterized in that, When the computer program or instructions are executed by a processor, they implement the steps of the method according to any one of claims 1 to 6.

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