On-orbit moonlet uncontrolled geometric calibration method and system

Abstract

The invention provides an in-orbit moonlet uncontrolled geometric calibration method and system, and the method comprises the steps: S1, extracting a calibration control point according to an SAR image; s2, constructing a geometric calibration equation according to the calibration control points; s3, constructing a geometric calibration model based on the geometric calibration equation; s4, establishing a geometric calibration error model through the geometric calibration model so as to obtain a geometric calibration error parameter value; and S5, according to the error parameter value, compensating an imaging parameter of a satellite system, and completing on-orbit uncontrolled geometric parameter error calibration. According to the invention, the high-precision calibration control point with the positioning error less than 1m is adopted to replace the corner reflector, so that the outfield test cost can be reduced; the method is not only suitable for geometric calibration of single-satellite single-scene SAR images, but also suitable for geometric calibration of single-satellite multi-scene SAR images, especially for multiple on-orbit small satellites, the on-orbit test efficiency of the small satellites can be improved through the uncontrolled calibration method, and high-efficiency and low-cost geometric positioning is achieved.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace positioning technology, and in particular, relates to an uncontrolled geometric calibration method and system for an on-orbit small satellite. Background Art

[0002] Synthetic aperture radar, or SAR, is an active remote sensing technology that plays an important role in surveillance and reconnaissance, terrain mapping, disaster detection, and environmental monitoring. Compared with optical remote sensing, SAR can acquire images at all times of the day and in all weather conditions, even at night or during cloud cover.

[0003] In the demonstration of satellite-ground integration indicators, geometric positioning error is a very important indicator. If the geometric positioning accuracy of SAR images is poor, it will affect the application of SAR images. For example, in important target monitoring applications, geometric positioning errors affect the manual interpretation of targets; in terrain mapping applications, geometric positioning errors affect the accuracy of digital elevation models. Therefore, in order to improve the positioning accuracy of SAR images, geometric calibration is a very critical task and the key to achieving high-precision positioning of SAR images. The geometric on-orbit calibration method of large satellites in orbit usually uses the data of trihedral reflectors or active calibrators in the field for geometric calibration processing. For small satellites with a large number of on-orbit satellites, traditional geometric calibration methods are bound to reduce the efficiency of on-orbit testing of small satellites.

[0004] After searching, it is found that there are many invention patents and papers in China on the research of SAR geometric calibration methods. The specific situation is as follows:

[0005] Patent document CN114814755A discloses a SAR geometric calibration method and system, which was provided by Xing Tao and others from the Beijing Radio Measurement Institute. It uses an ideal slant range model and lacks actual on-orbit calibration verification. The application number of the patent is 202210463960.6.

[0006] Patent document CN107367716A discloses a high-precision SAR geometric calibration method, which was provided by Zhang Guo and others from Wuhan University. It takes into account the characteristics of time width and bandwidth and the influence of atmospheric propagation delay, and proposes a high-precision geometric calibration method based on automatic corner reflectors. However, this method is suitable for geometric calibration of single-view SAR images. The application number of the patent is 201710539627.8.

[0007] Patent document CN116520267A discloses a geometric calibration method for spaceborne SAR with additional control point geometric constraints. The solution was provided by Feng Yongjiu et al. from Tongji University. They proposed a geometric calibration method based on the geometric relationship of control points, but the method lacks research on geometric calibration without control points.

[0008] Patent document CN114594435A discloses a method for improving the geometric calibration and positioning accuracy of domestic civilian SAR satellites. The solution was provided by Shi Xiaoyu and others from the China Resources Satellite Center. It uses multiple views on the same track and multiple views on multiple tracks for verification, but lacks actual on-orbit geometric calibration results to support the method.

[0009] Patent document CN114942413A discloses a centimeter-level high-precision calibration method for multi-angle SAR slant range error based on a Luneberg sphere reflector. The solution was provided by Qiu Xiaolan and others from Suzhou Aerospace Information Research Institute. It uses a Luneberg sphere reflector device and is only suitable for geometric calibration of multi-angle modes of single-view SAR images.

[0010] The existing invention methods for the geometric calibration of single-view SAR images lack the support of actual on-orbit measured data calibration verification, and this problem needs to be solved urgently. Summary of the invention

[0011] In view of the defects in the prior art, the object of the present invention is to provide a method and system for uncontrolled geometric calibration of an on-orbit small satellite.

[0012] According to the present invention, a method for uncontrolled geometric calibration of an on-orbit small satellite is provided, comprising:

[0013] Step S1: extracting calibration control points based on SAR images;

[0014] Step S2: constructing a geometric calibration equation according to the calibration control points;

[0015] Step S3: constructing a geometric calibration model based on the geometric calibration equation;

[0016] Step S4: establishing a geometric calibration error model through the geometric calibration model, and then obtaining an error parameter value of the geometric calibration;

[0017] Step S5: Compensate the imaging parameters of the satellite system according to the error parameter value to complete the on-orbit uncontrolled geometric parameter error calibration.

[0018] Preferably, in step S1:

[0019] Step S1.1: Obtain the geographic coordinates and pixel coordinates of the calibration control points on the optical image and the SAR image;

[0020] Step S1.2: Back-calculating the geographic coordinates into pixel coordinates through a range-Doppler model;

[0021] Step S1.3: Based on the pixel coordinates, the root mean square error model is used to evaluate the pixel mean error of each calibration control point in the azimuth and range directions, which is the geometric positioning error;

[0022] Step S1.4: Eliminate the calibration points whose geometric positioning error exceeds half a pixel, reselect the calibration control points, and re-execute step S1.1 until the calibration control points are extracted.

[0023] Preferably, in step S2, the geometric calibration equation is expressed as follows:

[0024]

[0025] Where R is the slant distance between the satellite and the scattering target; R sc =[X s Y s Z s ] T is the satellite position vector; R tc =[X t Y t Z t ] T is the position vector of the scattering target; f d is the Doppler frequency; λ is the radar wavelength; V sc =[V x V y V z ] T is the satellite's velocity vector; H t is the elevation of the target scatterer; R e With R p are the major and minor semi-axis of the Earth's reference ellipsoid, respectively;

[0026] In step S3, the mathematical expression of the geometric calibration model with respect to the slope distance is:

[0027] R=r0+m j ·j

[0028] Where R is the slant range, which is obtained based on the time difference between radar pulse transmission and reception, r0 is the initial slant range; m j is the pixel resolution in the range direction, j is the image column number; the symbol · represents the vector dot product;

[0029] The mathematical expression of the geometric calibration model with respect to the azimuth time is:

[0030] t=t0+t i ·i

[0031] Where t0 is the starting time of imaging; t i is the temporal resolution in azimuth, i is the image row number; the symbol · represents vector dot product.

[0032] Preferably, in step S4, the mathematical expression of the geometric calibration error model is:

[0033]

[0034] Wherein, ΔX represents the error matrix based on slant range and time; Δr0 represents the slant range error parameter; r0 is the initial slant range; Δt0 represents the time error parameter; t0 is the image starting time; represents the partial derivative law; F1 represents the conditional equation based on slant range; F2 represents the conditional equation based on Doppler; the symbol · represents vector dot product; (F1) represents the error of one observation value; (F2) represents the error of another observation value.

[0035] Preferably, in said step S5, said error parameter value, i.e., geometric calibration error parameter;

[0036] Step S5.1: Reading the initial values ​​of the imaging parameters according to the XML parameter header file of the SAR image; obtaining the estimated values ​​of the geometric parameter error terms through the geometric calibration error model according to the initial values ​​of the imaging parameters;

[0037] Step S5.2: using the estimated value as the initial value to iterate to the geometric calibration error model, and judging whether the geometric parameter error variation Δ is less than or equal to a threshold value; if the result is yes, the iteration converges, and the accumulated value of the current error parameter correction is recorded as the final geometric error parameter value, and the imaging parameters of the satellite system are compensated by the final geometric error parameter value; if the result is no, the iteration continues;

[0038] The initial values ​​of the imaging parameters include: r0, t0;

[0039] The threshold is 0.005.

[0040] According to the present invention, an on-orbit small satellite uncontrolled geometric calibration system is provided, comprising:

[0041] Module M1: Extract calibration control points based on SAR images;

[0042] Module M2: constructing a geometric calibration equation according to the calibration control points;

[0043] Module M3: Constructing geometric calibration model based on geometric calibration equation;

[0044] Module M4: establishing a geometric calibration error model through the geometric calibration model, and then obtaining an error parameter value of the geometric calibration;

[0045] Module M5: Compensate the imaging parameters of the satellite system according to the error parameter value to complete the on-orbit uncontrolled geometric parameter error calibration.

[0046] Preferably, in the module M1:

[0047] Module M1.1: Obtain the geographic coordinates and pixel coordinates of the calibration control points on the optical image and SAR image;

[0048] Module M1.2: Back-calculating the geographic coordinates into pixel coordinates through a range-Doppler model;

[0049] Module M1.3: Based on pixel coordinates, the root mean square error model is used to evaluate the pixel error in the azimuth and distance directions of each calibration control point, which is the geometric positioning error;

[0050] Module M1.4: Eliminate the calibration points whose geometric positioning error exceeds half a pixel, reselect the calibration control points, and re-execute module M1.1 until the calibration control points are extracted.

[0051] Preferably, in the module M2, the geometric calibration equation is expressed as follows:

[0052]

[0053] Where R is the slant distance between the satellite and the scattering target; R sc =[X s Y s Z s ] T is the satellite position vector; R tc =[X t Y t Z t ] T is the position vector of the scattering target; f d is the Doppler frequency; λ is the radar wavelength; V sc =[V x V y V z ] T is the satellite's velocity vector; H t is the elevation of the target scatterer; R e With R p are the major and minor semi-axis of the Earth's reference ellipsoid, respectively;

[0054] In the module M3, the mathematical expression of the geometric calibration model with respect to the slope distance is:

[0055] R=r0+m j ·j

[0056] Where R is the slant range, which is obtained based on the time difference between radar pulse transmission and reception, r0 is the initial slant range; m j is the pixel resolution in the range direction, j is the image column number; the symbol · represents the vector dot product;

[0057] The mathematical expression of the geometric calibration model with respect to the azimuth time is:

[0058] t=t0+t i ·i

[0059] Where t0 is the starting time of imaging; t i is the temporal resolution in azimuth, i is the image row number; the symbol · represents vector dot product.

[0060] Preferably, in the module M4, the mathematical expression of the geometric calibration error model is:

[0061]

[0062] Wherein, ΔX represents the error matrix based on slant range and time; Δr0 represents the slant range error parameter; r0 is the initial slant range; Δt0 represents the time error parameter; t0 is the image starting time; represents the partial derivative law; F1 represents the conditional equation based on slant range; F2 represents the conditional equation based on Doppler; the symbol · represents vector dot product; (F1) represents the error of one observation value; (F2) represents the error of another observation value.

[0063] Preferably, in the module M5, the error parameter value, i.e., the geometric calibration error parameter;

[0064] Module M5.1: Read the initial values ​​of imaging parameters according to the XML parameter header file of the SAR image; obtain the estimated values ​​of geometric parameter error terms through the geometric calibration error model according to the initial values ​​of imaging parameters;

[0065] Module M5.2: Iterate the estimated value as the initial value to the geometric calibration error model, and determine whether the geometric parameter error change Δ is less than or equal to a threshold value; if the result is yes, the iteration converges, and the accumulated value of the current error parameter correction is recorded as the final geometric error parameter value, and the imaging parameters of the satellite system are compensated by the final geometric error parameter value; if the result is no, continue the iteration;

[0066] The initial values ​​of the imaging parameters include: r0, t0;

[0067] The threshold is 0.005.

[0068] Compared with the prior art, the present invention has the following beneficial effects:

[0069] 1. The present invention adopts high-precision calibration control points with a positioning error of less than 1m to replace corner reflectors, which can reduce the cost of field tests. It is not only suitable for single-star single-scene SAR images, but also for the geometric calibration of single-star multi-scene SAR images, especially for multiple small satellites in orbit. The on-orbit test efficiency of small satellites can be improved through the uncontrolled calibration method, realizing high-efficiency and low-cost geometric positioning.

[0070] 2. The present invention compensates the calculated geometric parameter errors for the SAR images of the same source sensors, realizes on-orbit geometric calibration without control points, and can improve the on-orbit test efficiency for a large number of small satellites on-orbit, and can achieve high-precision and high-efficiency geometric calibration.

[0071] 3. The method of the present invention has been verified by on-orbit calibration tests of measured data from space-borne SAR satellites, specifically by geometric calibration verification of on-orbit data from the Gaofen-3 satellite, TerraSAR-X, TanDEM-X, etc. It can shorten the field calibration test cycle, reduce the field calibration test cost, and improve the on-orbit test efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0073] Figure 1 A schematic diagram of the process provided by the present invention;

[0074] Figure 2 The calibration control point distribution map based on the GF-3 SAR image provided by the present invention;

[0075] Figure 3 A distribution map of calibration control points based on TerraSAR-X images provided by the present invention;

[0076] Figure 4 This is the calibration control point distribution map of the TanDEM-X image provided by the present invention. DETAILED DESCRIPTION

[0077] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0078] Embodiment 1:

[0079] According to the present invention, a method and system for uncontrolled geometric calibration of an on-orbit small satellite are provided, the method comprising the following steps:

[0080] Step S1: Use corner reflectors or calibration control points to complete on-orbit geometric calibration.

[0081] The selection of the corner reflector or calibration control point mainly considers the terrain slope and the backscattering characteristics of the terrain surface. The terrain slope should be within a certain range to ensure that there will be no serious overlap and shadowing; the terrain should be selected as a flat area, and there should be no mountains with large elevation fluctuations within 500m around. In addition, the selection of calibration control points should also consider areas with obvious imaging features in SAR images, such as house corners, road intersections, etc. After selecting the calibration points, the accuracy of the control points should be improved.

[0082] Step S1.1: Select calibration control points on the optical image and the SAR image based on the above steps and principles, and obtain the geographic coordinates and pixel coordinates of the calibration control points;

[0083] Step S1.2: using the range-Doppler model to inversely calculate the geographic coordinates of the calibration point into pixel coordinates;

[0084] Step S1.3: Use the root mean square error model to evaluate the pixel error in the azimuth and range directions of each calibration point, which is the geometric positioning error.

[0085] Step S1.4: Eliminate the calibration points whose geometric positioning error exceeds half a pixel, then reselect the calibration points and repeat steps S1.1-S1.3. Specifically, one pixel is approximately equal to the resolution size, for example: the resolution is 2m, the positioning error does not exceed half a pixel, that is, the maximum positioning error is 1m, so the positioning control points exceeding 1m are eliminated.

[0086] Step S2: constructing geometric calibration equations, which mainly include the distance equation between the scattering target and the satellite, the Doppler equation for the relative motion between the satellite and the scattering target, and the earth ellipsoid equation.

[0087]

[0088] Where R is the slant distance between the satellite and the scattering target; R tc =[X t Y t Z t ] T is the position vector of the scattering target; R sc =[X s Y s Z s ] T is the satellite position vector; f d is the Doppler frequency; λ is the radar wavelength; V sc =[V x V y V z ] T ; is the satellite's velocity vector; H t is the elevation of the target scatterer; Re With R p They are the major and minor semi-axis of the Earth reference ellipsoid.

[0089] Step S3: According to the geometric calibration equation, the main factors affecting the geometric positioning accuracy of SAR images are slant range error, elevation error, azimuth time error, satellite position error, and satellite velocity error. Among them, the slant range error is related to the satellite position error and atmospheric delay error; the satellite position and velocity errors are also closely related to the azimuth time t. According to the experience of on-orbit calibration of previous models, the elevation accuracy of the field calibration point can reach the centimeter level, and the elevation error can be ignored here.

[0090] Based on the above analysis, the main factors affecting SAR geometric positioning error are slant range error and azimuth time error. Specifically, according to the geometric calibration equation, the slant range R is obtained by measuring the time difference between the radar pulse transmission and reception. The slant range error will cause the target's field of view position to move along the Doppler line, thereby generating a positioning error, which mainly affects the sampling position of the range echo window, resulting in inaccurate range positioning; the azimuth time is mainly reflected in the deviation between the satellite recursive orbit and the actual orbit, resulting in a deviation in the satellite imaging time, causing inaccurate image azimuth positioning.

[0091] Faced with multiple networked satellites in orbit, how to solve the geometric positioning errors of single-scene SAR images and multi-scene SAR images with high precision and efficiency is a key modeling goal of the present invention.

[0092] To solve this problem, the present invention proposes an on-orbit geometric calibration method without control points.

[0093] For SAR slant range imaging, the slant range is expressed as a linear function relationship with the initial slant range and the image pixel coordinate column value j. That is, the mathematical expression of the geometric calibration model for the slant range is:

[0094] R=r0+m j ·j

[0095] Where R is the slant range, which is obtained based on the time difference between radar pulse transmission and reception, r0 is the initial slant range; m j is the pixel resolution in the range direction; j is the image column number, r0, m j From the image parameter xml file, the symbol · represents vector dot product;

[0096] The azimuth time t represents a linear function relationship with the initial time and the image pixel coordinate row number i; that is, the mathematical expression of the geometric calibration model for the azimuth time is:

[0097] t=t0+t i ·i

[0098] Among them, t0 is the imaging start time; ti is the temporal resolution in azimuth, i is the image row number; the symbol · represents the vector dot product. i All come from the image parameter xml file.

[0099] Step S4: In the study of establishing a geometric calibration model, the conditional equation based on the slope range equation is expressed as follows:

[0100] F1(∑)=|R sc -R tc |-(r0+m j j)

[0101] Wherein, F1(∑) represents the conditional equation matrix based on the slant range error R, ∑ = |r0, t0|, and the symbol · represents vector dot product;

[0102] The conditional equation based on the Doppler equation is:

[0103]

[0104] In the study of establishing the geometric calibration model, the geometric parameter error term (Δr0, Δt0) is accurately estimated based on the nonlinear least squares method of the calibration control points. The mathematical expression of the established geometric calibration error model is:

[0105]

[0106] Wherein, ΔX represents the error matrix based on slant range and time; Δr0 represents the slant range error parameter; Δt0 represents the time error parameter; represents the partial derivative law; F1 represents the conditional equation based on slant range; F2 represents the conditional equation based on Doppler; the symbol · represents vector dot product; by substituting the approximate values ​​of each unknown parameter Σ=|r0t0| into the geometric calibration error model, one observation value error (F1) and another observation value error (F2) can be calculated.

[0107] Step S5: The geometric calibration error parameters are solved by adopting the principle of multiple iterations and gradual approximation.

[0108] Step S5.1: First, read the initial values ​​of imaging parameters r0 and t0 according to the image XML parameter header file;

[0109] Step S5.2: constructing a geometric calibration error model according to step S4, thereby obtaining a first estimate of the geometric parameter error term;

[0110] Step S5.3: The estimated value is used as the initial value of the next iteration. After multiple iterations, the error change Δ of the geometric parameter gradually tends to be stable, that is, the error change Δ≤0.005;

[0111] Step S5.4: If the correction amount of the geometric calibration parameter is less than a given threshold, the iteration converges, and the accumulated parameter correction amount is the final error parameter value of the geometric calibration.

[0112] Step S6: Substitute the solved geometric error parameters (Δr0, Δt0) into the azimuth time and range slant range parameter items of the ground system, and automatically compensate them to the system imaging parameters in the synthetic aperture radar satellite to achieve on-orbit uncontrolled geometric parameter error calibration.

[0113] In addition, if the accuracy of geometric calibration without control points is to be verified, a small number of calibration check points are selected according to step S1, and the root mean square error model is used to perform geometric accuracy verification.

[0114] Embodiment 2:

[0115] Embodiment 2 is a preferred example of Embodiment 1, and is used to illustrate the present invention in more detail.

[0116] In other words, the present invention also provides an on-orbit small satellite uncontrolled geometric calibration system, which can be implemented by executing the process steps of the on-orbit small satellite uncontrolled geometric calibration method, that is, those skilled in the art can understand the on-orbit small satellite uncontrolled geometric calibration method as a preferred implementation of the on-orbit small satellite uncontrolled geometric calibration system.

[0117] The present invention also provides an uncontrolled geometric calibration system for an on-orbit small satellite, comprising:

[0118] Module M1: Extract calibration control points based on SAR images;

[0119] Module M2: constructing a geometric calibration equation according to the calibration control points;

[0120] Module M3: Constructing geometric calibration model based on geometric calibration equation;

[0121] Module M4: establishing a geometric calibration error model through the geometric calibration model, and then obtaining an error parameter value of the geometric calibration;

[0122] Module M5: Compensate the imaging parameters of the satellite system according to the error parameter value to complete the on-orbit uncontrolled geometric parameter error calibration.

[0123] Embodiment 3:

[0124] Embodiment 3 is a preferred example of Embodiment 1, and is used to illustrate the present invention in more detail.

[0125] In order to solve the above problems existing in the prior art, the present invention adopts and designs an uncontrolled geometric calibration method for small satellites in orbit, which mainly selects high-precision calibration points with positioning errors less than 1m through SAR images, completes the on-orbit calibration of geometric parameter errors by establishing a geometric calibration model, and substitutes the calibrated geometric parameter errors into other images of the same source sensor SAR satellite to achieve on-orbit geometric calibration without control points. The present invention uses calibration control points instead of corner reflectors to reduce the cost of field tests; the uncontrolled geometric calibration method of the present invention can improve the on-orbit test efficiency for small satellites with a large number of on-orbit satellites. In addition, the method of the present invention has been fully verified by the geometric calibration of on-orbit data of Gaofen-3 satellites, TerraSAR-X, TanDEM-X, etc.

[0126] like Figure 1 As shown, this embodiment provides an uncontrolled geometric calibration method and system for an on-orbit small satellite, including the following steps:

[0127] Step S1: extracting calibration control points from SAR images;

[0128] Step S2: constructing geometric calibration equations;

[0129] Step S3: Geometric calibration error source analysis;

[0130] Step S4: Establishing a geometric calibration model;

[0131] Step S5: Calculate the geometric calibration error; compare the error to other SAR images of the same sensor;

[0132] Step S6: Complete on-orbit uncontrolled geometric calibration (verification).

[0133] Furthermore, in step S1, corner reflectors or calibration control points are selected to complete the on-orbit geometric calibration. The selection of corner reflectors or calibration control points mainly considers the terrain slope and the backscattering characteristics of the terrain surface. The terrain slope should be within a certain range to ensure that no serious overlap and shadowing will occur; specifically, the terrain is selected as a flat area, and there should be no mountains with large elevation fluctuations within 500m around. In addition, the selection of calibration control points must also consider areas with obvious imaging features in SAR images, such as house corners, road intersections, etc. After selecting the calibration control points, take the following steps to improve the accuracy of the control points.

[0134] Step S1.1: Select calibration control points on the optical image and the SAR image based on the above steps and principles, and obtain the geographic coordinates and pixel coordinates of the calibration control points;

[0135] Step S1.2: using the range-Doppler model to inversely calculate the geographic coordinates of the calibration point into pixel coordinates;

[0136] Step S1.3: Use the root mean square error model to evaluate the pixel error in the azimuth and range directions of each calibration point, which is the geometric positioning error.

[0137] Step S1.4: Eliminate the calibration points whose geometric positioning error exceeds half a pixel, then reselect the calibration points and repeat steps S1.1-S1.3. Specifically, one pixel is approximately equal to the resolution size, for example: the resolution is 2m, the positioning error does not exceed half a pixel, that is, the maximum positioning error is 1m, so the positioning control points exceeding 1m are eliminated.

[0138] Furthermore, in step S2, a geometric calibration equation is constructed, including: a distance equation between the scattering target and the satellite, a Doppler equation for the relative motion between the satellite and the scattering target, and an earth ellipsoid equation.

[0139]

[0140] Where R is the slant distance between the satellite and the scattering target; R tc =[X t Y t Z t ] T is the position vector of the scattering target; R sc =[X s Y s Z s ] T is the satellite position vector, the superscript T indicates the transposed sign; f d is the Doppler frequency; λ is the radar wavelength; V sc =[V x V y V z ] T is the satellite's velocity vector; H t is the elevation of the target scatterer; R e and R p They are the major and minor semi-axis of the Earth reference ellipsoid.

[0141] Furthermore, in step S3, according to the geometric calibration equation, the main factors affecting the geometric positioning accuracy of the SAR image are slant range error, elevation error, azimuth time error, satellite position error, and satellite velocity error. Among them, the slant range error is related to the satellite position error and the atmospheric delay error; the satellite position and velocity errors are also closely related to the azimuth time t. According to the experience of on-orbit calibration of previous models, the elevation accuracy of the field calibration point can reach the centimeter level, and the elevation error can be ignored here. Based on the above analysis, the main factors affecting the SAR geometric positioning error are the slant range error and the azimuth time error.

[0142] Furthermore, in step S3, the slant range R is obtained by measuring the time difference between the radar pulse transmission and reception. The slant range error will cause the target's field of view position to move along the Doppler line, thereby generating a positioning error. For SAR slant range imaging, the slant range is expressed as a linear function relationship with the initial slant range and the image pixel coordinate column value j:

[0143] R=r0+m j ·j

[0144] Where r0 is the initial slant distance; m j is the pixel resolution in the range direction; j is the image column number, and r0, m j From the image parameter xml file, the symbol · represents vector dot product;

[0145] In step S3, the azimuth time t can be expressed as a linear function relationship with the initial time and the image pixel coordinate row number i:

[0146] t=t0+t i ·i

[0147] Where t0 is the starting time of imaging; t i is the azimuth time resolution; i is the image row number. In step S3, t0 and t i All of them come from the image parameter xml file, and the symbol · represents vector dot product.

[0148] Furthermore, in the step S4, in the study of establishing a geometric calibration model, the conditional equation based on the slope range equation is:

[0149] F1(∑)=|R sc -R tc |-(r0+m j j)

[0150] Where F1(∑) represents the conditional equation matrix based on the slope range error R, and the symbol · represents the vector dot product;

[0151] The conditional equation based on the Doppler equation is:

[0152]

[0153] In step S4, in the study of establishing a geometric calibration model, the geometric parameter error term (Δr0, Δt0) is accurately estimated based on the nonlinear least squares method of the calibration control points. The mathematical expression of the established geometric calibration error model is:

[0154]

[0155] Wherein, ΔX represents the error matrix based on slant range and time; Δr0 represents the slant range error parameter; Δt0 represents the time error parameter; represents the partial derivative law; F1 represents the conditional equation based on slant range; F2 represents the conditional equation based on Doppler; the symbol · represents vector dot multiplication; by substituting the approximate values ​​of each unknown parameter ∑ = |r0t0| into the geometric calibration error model, one observation value error (F1) and another observation value error (F2) can be calculated.

[0156] Furthermore, in step S5, the geometric calibration error parameter is solved by adopting the principle of multiple iterations and gradual approximation, and the specific steps include:

[0157] Step S5.1: Read the initial values ​​of imaging parameters r0 and t0 according to the image xml parameter header file;

[0158] Step S5.2: constructing a geometric calibration error model according to step S4, thereby obtaining a first estimate of the geometric parameter error term;

[0159] Step S5.3: The estimated value is used as the initial value of the next iteration. After multiple iterations, the error change Δ of the geometric parameter gradually tends to be stable, that is, the error change Δ≤0.005;

[0160] Step S5.4: If the correction amount of the geometric calibration parameter is less than a given threshold, the iteration converges, and the accumulated parameter correction amount is the final error parameter value of the geometric calibration.

[0161] Furthermore, the error parameters (Δr0, Δt0) calculated in step S6 are substituted into the ground system azimuth time and range slant range parameter items, and automatically compensated to the system imaging parameters in the synthetic aperture radar radar satellite, so as to realize the on-orbit uncontrolled geometric parameter error calibration. In addition, if the accuracy of the uncontrolled point geometric calibration is to be verified, a small number of calibration check points are selected according to step S1, and the root mean square error model is used to verify the geometric accuracy.

[0162] Furthermore, in the steps, calibration control points with positioning errors less than 1m are used instead of corner reflectors, which can reduce the cost of field tests. The calculated geometric parameter errors are automatically compensated for the SAR images of the same source sensors, so as to realize the geometric parameter calibration of small satellites without control points on orbit and improve the efficiency of on-orbit testing. At present, the method of the present invention has been verified by geometric calibration of data without control points such as Gaofen-3, TerraSAR-X, and TanDEM-X on orbit.

[0163] Attached Figure 2 is a calibration point distribution map based on GF-3 SAR images provided by an implementation example of the present invention, Figure 3is a calibration point distribution map based on TerraSAR-X images provided by an implementation case of the present invention, Figure 4 It is a calibration point distribution map based on TanDEM-X image provided by the implementation case of the present invention.

[0164] In the embodiment of the present invention, the effect of the present invention is further described below in combination with the on-orbit GF-3 data, TerraSAR-X data, and TanDEM-X data. Table 1 shows the SAR image imaging parameters in the embodiment.

[0165]

[0166]

[0167] Table 1 On-orbit SAR image imaging parameters in the embodiment

[0168] According to the SAR image data given in Table 1, calibration control points are selected and the accuracy is improved. According to the method proposed in the present invention, a geometric calibration model is established. The geometric parameter error term (Δr0, Δt0) is accurately estimated based on the nonlinear least squares method of the calibration control points to obtain the geometric parameter error correction. The geometric parameter error is substituted into other SAR images of the same source sensor to perform geometric calibration without control points. The indirect geometric positioning algorithm is used to evaluate the geometric positioning error after calibration.

[0169]

[0170] Table 2 Geometric parameter error estimation and positioning accuracy evaluation of on-orbit data of the embodiment

[0171] Table 2 shows the geometric parameter error correction calculated by the method of the present invention based on SAR data of different sensors in the embodiment. The geometric positioning error without control points is evaluated by the indirect geometric positioning algorithm. The calibrated geometric positioning accuracy is better than 5.08m, about 1.5 pixels, which meets the use requirements.

[0172] Those skilled in the art may understand this embodiment as a more specific description of Embodiment 1 and Embodiment 2.

[0173] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0174] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A method for uncontrolled geometric calibration of an on-orbit small satellite, characterized in that: include: Step S1: extracting calibration control points based on SAR images; Step S2: constructing a geometric calibration equation according to the calibration control points; Step S3: constructing a geometric calibration model based on the geometric calibration equation; Step S4: establishing a geometric calibration error model through the geometric calibration model, and then obtaining an error parameter value of the geometric calibration; Step S5: Compensate the imaging parameters of the satellite system according to the error parameter value to complete the on-orbit uncontrolled geometric parameter error calibration.

2. The method for uncontrolled geometric calibration of an on-orbit small satellite according to claim 1, characterized in that: In step S1: Step S1.1: Obtain the geographic coordinates and pixel coordinates of the calibration control points on the optical image and the SAR image; Step S1.2: Back-calculating the geographic coordinates into pixel coordinates through a range-Doppler model; Step S1.3: Based on the pixel coordinates, the root mean square error model is used to evaluate the pixel mean error of each calibration control point in the azimuth and range directions, which is the geometric positioning error; Step S1.4: Eliminate the calibration points whose geometric positioning error exceeds half a pixel, reselect the calibration control points, and re-execute step S1.1 until the calibration control points are extracted.

3. The method for uncontrolled geometric calibration of an on-orbit small satellite according to claim 1, characterized in that: In step S2, the geometric calibration equation is expressed as follows: Where R is the slant distance between the satellite and the scattering target; R sc =[X s Y s Z s ] T is the satellite position vector; R tc =[X t Y t Z t ] T is the position vector of the scattering target; f d is the Doppler frequency; λ is the radar wavelength; V sc =[V x V y V z ] T is the satellite's velocity vector; H t is the elevation of the target scatterer; R e With R p are the major and minor semi-axis of the Earth's reference ellipsoid, respectively; In step S3, the mathematical expression of the geometric calibration model with respect to the slope distance is: R=r0+m j ·j Where R is the slant range, which is obtained based on the time difference between radar pulse transmission and reception, r0 is the initial slant range; m j is the pixel resolution in the range direction, j is the image column number; the symbol · represents the vector dot product; The mathematical expression of the geometric calibration model with respect to the azimuth time is: t=t0+t i ·i Where t0 is the starting time of imaging; t i is the temporal resolution in azimuth, i is the image row number; the symbol · represents vector dot product.

4. The method for uncontrolled geometric calibration of an on-orbit small satellite according to claim 3, characterized in that: In step S4, the mathematical expression of the geometric calibration error model is: Wherein, ΔX represents the error matrix based on slant range and time; Δr0 represents the slant range error parameter; r0 is the initial slant range; Δt0 represents the time error parameter; t0 is the image starting time; represents the partial derivative law; F1 represents the conditional equation based on slant range; F2 represents the conditional equation based on Doppler; the symbol · represents vector dot product; (F1) represents the error of one observation value; (F2) represents the error of another observation value.

5. The method for uncontrolled geometric calibration of an on-orbit small satellite according to claim 4, characterized in that: In the step S5, the error parameter value is a geometric calibration error parameter; Step S5.1: Reading the initial values ​​of the imaging parameters according to the XML parameter header file of the SAR image; obtaining the estimated values ​​of the geometric parameter error terms through the geometric calibration error model according to the initial values ​​of the imaging parameters; Step S5.2: using the estimated value as an initial value to iterate the geometric calibration error model, and determining whether the geometric parameter error variation Δ is less than or equal to a threshold; If the result is yes, the iteration converges, the accumulated value of the current error parameter correction is recorded as the final geometric error parameter value, and the imaging parameters of the satellite system are compensated by the final geometric error parameter value; If the result is no, continue iterating; The initial values ​​of the imaging parameters include: r0, t0; The threshold is 0.

005.

6. An uncontrolled geometric calibration system for small satellites on orbit, characterized in that: include: Module M1: Extract calibration control points based on SAR images; Module M2: constructing a geometric calibration equation according to the calibration control points; Module M3: Constructing geometric calibration model based on geometric calibration equation; Module M4: establishing a geometric calibration error model through the geometric calibration model, and then obtaining an error parameter value of the geometric calibration; Module M5: Compensate the imaging parameters of the satellite system according to the error parameter value to complete the on-orbit uncontrolled geometric parameter error calibration.

7. The uncontrolled geometric calibration system for small satellites on orbit according to claim 6, characterized in that: In the module M1: Module M1.1: Obtain the geographic coordinates and pixel coordinates of the calibration control points on the optical image and SAR image; Module M1.2: Back-calculating the geographic coordinates into pixel coordinates through a range-Doppler model; Module M1.3: Based on pixel coordinates, the root mean square error model is used to evaluate the pixel error in the azimuth and distance directions of each calibration control point, which is the geometric positioning error; Module M1.4: Eliminate the calibration points whose geometric positioning error exceeds half a pixel, reselect the calibration control points, and re-execute module M1.1 until the calibration control points are extracted.

8. The uncontrolled geometric calibration system for small satellites on orbit according to claim 6, characterized in that: In the module M2, the geometric calibration equation is expressed as follows: Where R is the slant distance between the satellite and the scattering target; R sc =[X s Y s Z s ] T is the satellite position vector; R tc =[X t Y t Z t ] T is the position vector of the scattering target; f d is the Doppler frequency; λ is the radar wavelength; V sc =[V x V y V z ] T is the satellite's velocity vector; H t is the elevation of the target scatterer; R e With R p are the major and minor semi-axis of the Earth's reference ellipsoid, respectively; In the module M3, the mathematical expression of the geometric calibration model with respect to the slope distance is: R=r0+m j ·j Where R is the slant range, which is obtained based on the time difference between radar pulse transmission and reception, r0 is the initial slant range; m j is the pixel resolution in the range direction, j is the image column number; the symbol · represents the vector dot product; The mathematical expression of the geometric calibration model with respect to the azimuth time is: t=t0+t i ·i Where t0 is the starting time of imaging; t i is the temporal resolution in azimuth, i is the image row number; the symbol · represents vector dot product.

9. The uncontrolled geometric calibration system for small satellites on orbit according to claim 8, characterized in that: In the module M4, the mathematical expression of the geometric calibration error model is: Wherein, ΔX represents the error matrix based on slant range and time; Δr0 represents the slant range error parameter; r0 is the initial slant range; Δt0 represents the time error parameter; t0 is the image starting time; represents the partial derivative law; F1 represents the conditional equation based on slant range; F2 represents the conditional equation based on Doppler; the symbol · represents vector dot product; (F1) represents the error of one observation value; (F2) represents the error of another observation value.

10. The uncontrolled geometric calibration system for small satellites on orbit according to claim 9, characterized in that: In the module M5, the error parameter value, i.e., the geometric calibration error parameter; Module M5.1: Read the initial values ​​of imaging parameters according to the XML parameter header file of the SAR image; obtain the estimated values ​​of geometric parameter error terms through the geometric calibration error model according to the initial values ​​of imaging parameters; Module M5.2: Iterate the estimated value as the initial value to the geometric calibration error model to determine whether the geometric parameter error change Δ is less than or equal to a threshold; If the result is yes, the iteration converges, the accumulated value of the current error parameter correction is recorded as the final geometric error parameter value, and the imaging parameters of the satellite system are compensated by the final geometric error parameter value; If the result is no, continue iterating; The initial values ​​of the imaging parameters include: r0, t0; The threshold is 0.005.

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