CN113742803A - Simulation analysis method for band-controlled geometric positioning precision of medium and high orbit SAR (synthetic aperture radar) satellite - Google Patents
Simulation analysis method for band-controlled geometric positioning precision of medium and high orbit SAR (synthetic aperture radar) satellite Download PDFInfo
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Abstract
The invention discloses a simulation analysis method for band-controlled geometric precision of a medium and high orbit SAR satellite. Simulating a medium-high orbit SAR satellite orbit by adopting STK software, and constructing a theoretical geometric relation between satellites and the ground by utilizing the simulated satellite position and speed and a ground control point; adding azimuth time error, target altitude error, Doppler center frequency error, slant range measurement error, satellite speed error, satellite position error and the like into RD model parameters in a single or combined mode according to simulation requirements to construct a virtual simulation satellite-ground geometric relation; carrying out uncontrolled geometric positioning calculation according to the simulated RD model, and carrying out comparative analysis on the geometric positioning calculation and ground control points; then, establishing and solving an affine transformation model by using the ground control points; compensating the RD model based on the affine transformation model; and finally, comparing and analyzing the geometric positioning accuracy of the SAR satellite under control.
Description
Technical Field
The invention belongs to the field of satellite image processing, and particularly relates to a geometric positioning accuracy simulation analysis method for a medium and high orbit spaceborne SAR satellite based on an RD model.
Background
At present, an in-orbit Synthetic Aperture Radar (SAR) satellite is in a low orbit, the replay period of the SAR satellite is generally longer, and the real-time observation requirement of a user on a specific area is difficult to meet. And the medium and high orbit SAR satellite can greatly improve the time resolution and the visible range of monitoring, and can quickly respond to an emergency by combining with a beam control technology. The medium and high orbit synthetic aperture radar has potential high resolution and wide swath capability and has important application prospect in national defense and economic construction.
The 2003 nasa (national aerironauties and space administration) first pre-researched and deployed the medium and high orbit SAR satellite plan, aiming to build a geological and topographic database of global hot spots and gradually implement a global seismic prediction and monitoring system. Subsequently, NASA combined with jet propulsion laboratory jrl (jet propulsion laboratory) performed a number of analyses of system performance and key-technology challenges. Units such as Beijing university of science and technology, Chinese academy electronics and the like in China have initial exploration in the aspects of medium and high orbit SAR system parameters, imaging processing, synchronization technology, orbit and the like. The research of medium and high orbit SAR satellites faces many technical difficulties, wherein the basic is also the geometric positioning accuracy of the SAR satellites most important. Although the SAR satellite is geometrically calibrated in the orbit debugging stage, some random errors still affect the geometric positioning accuracy. No matter the SAR satellite is in a low orbit or a medium and high orbit, the geometric positioning accuracy of the SAR satellite can be improved by compensating the geometric positioning model by utilizing the ground control point. Therefore, the simulation analysis of the geometric positioning accuracy of the medium and high orbit SAR satellite by using the ground control point is necessary.
In conclusion, aiming at the requirement of geometric positioning precision simulation of the medium and high orbit SAR satellite, an affine transformation model is established according to ground control points by establishing a theoretical geometric relation between satellites and ground and a virtual simulated geometric relation between satellites and ground, and a distance Doppler model is compensated based on the affine transformation model, so that the simulation analysis method for the band-controlled geometric positioning precision of the medium and high orbit SAR satellite is provided.
Disclosure of Invention
The invention provides an affine analysis method for band control geometric precision of a medium and high orbit SAR satellite aiming at the requirement of geometric positioning precision simulation of the medium and high orbit SAR satellite. The achievement of the invention can be applied to the fields of design and index demonstration of medium and high orbit SAR satellites.
In order to achieve the above object, the present invention comprises the steps of:
s1: and simulating the medium and high orbit SAR satellite orbit. According to parameters such as a designed Satellite orbit long half shaft, orbit eccentricity, orbit inclination and the like, simulating a section of medium and high orbit SAR Satellite orbit by adopting a Satellite Tool Kit (STK), and calculating position coordinates (X, Y, Z) and speed coordinates (Vx, Vy, Vz) of the medium and high orbit SAR Satellite through an analysis function of the STK software;
s2: simulating an imaging area. Predicting the range of the radar beam covering the earth surface according to the simulated parameters of S1, the instantaneous position of the satellite and the view angle, and uniformly selecting a certain number of ground points (at least 9 points are suggested) in the imaging range as ground control points;
s3: and simulating a theoretical satellite-ground geometric imaging relation. Calculating the slant range, Doppler frequency and the like of the imaging moment by constructing a distance Doppler (RD) model by adopting the middle and high orbit satellite parameters simulated in S1 and the ground control point coordinates of the S2 prediction imaging range;
s4: and constructing a geometric positioning model in the virtual real imaging environment. Adding error parameters such as DEM elevation error, azimuth time synchronization error, slant range error, Doppler frequency error, satellite velocity error, satellite position error and the like into RD model parameters in S3 in a single or multiple combination form to construct a virtual simulated satellite-ground geometric relation;
s5: and (4) calculating the geometric positioning without control. Calculating the positions of 9 points on the SAR image by a theoretical geometric positioning model according to the ground control point coordinates of S2 and adopting the reverse calculation of the geometric model; calculating object space coordinates of the virtual real imaging environment by a geometric positioning model of the virtual real imaging environment according to image space coordinates corresponding to the 9 ground point coordinates and adopting geometric model forward calculation; comparing and analyzing the calculated ground point coordinates with the real ground control point coordinates in S2;
s6: and (5) constructing and solving an affine transformation model. Selecting at least 4 ground control points in S2, and solving an affine transformation model;
s7: and D model compensation based on an affine transformation model. Compensating the RD model by using the affine transformation model solved in the S7;
s8: and (4) carrying out geometric positioning calculation under control. After solving the affine transformation at S7, the ground control points (at least 5 points) in the other S2 are used as independent check points. And calculating object coordinates of the independent check points by using the compensated RD model in S7 and by adopting geometric model forward calculation according to the position coordinates on the SAR image, which are obtained by geometric inverse calculation of the check points in S5. And comparing and analyzing the real coordinates of the independent check points in S2;
s9: and (6) evaluating the precision. And comparing the uncontrolled geometric positioning precision error obtained by calculation in the S5 with the controlled geometric positioning precision error obtained by calculation in the S8, and analyzing and evaluating the controlled geometric positioning precision of the SAR satellite.
Further, step S1 includes the following steps:
(1) performing orbit simulation by using STK software according to parameters such as orbit semimajor axis, orbit eccentricity, orbit inclination angle and the like of the orbit of the SAR satellite with the medium and high orbit; the orbit equation is as follows:
wherein a is a semimajor axis, e is a major semiaxis, and f is a paraxial point angle.
(2) Satellite orbit data under a WGS84 coordinate system at a certain moment is taken as SAR satellite orbit data at the imaging moment, and a position vector and a velocity vector of a satellite are obtained, wherein a satellite position vector calculation formula is as follows:
in the formula, the coordinate component in the inertial system is shown, E is the eccentricity, E is the approximate point angle, and E is the semimajor axis;
the basic formula of the satellite velocity vector is as follows:
in the formula, E is a deviation angle, a is a major semi-axis, E is an eccentricity, and P and Q are coordinate components in an inertial system.
Further, step S2 includes the following steps:
(1) the satellite needs to continuously transmit or acquire relevant information with the ground during the orbit, and the imaging parameters of the medium and high orbit SAR are used for the satellite
The range and longitude and latitude of the coverage area can be expressed, the semi-central angle beta of the spherical crown surface is solved and calculated according to the following calculation formula, and then the following spherical trigonometric equation function formula is obtained according to the spherical geometrical relationship:
wherein, λ is longitude, and λ is longitude,
for geographical latitude, whenever the equation is satisfied
The set of points of (a) is the coverage area boundary.
(2) Ground points within the range of the earth's surface covered by the radar beam, optionally within the imaging range, are used as ground control point coordinates.
Further, step S3 includes the following steps:
(1) calculating the slope distance between the SAR satellite and the ground reference target at the imaging moment according to the position coordinates of the satellite orbit and the ground control point coordinates, and taking the slope distance as a true value of the slope distance;
(2) calculating the Doppler frequency between the SAR satellite and the ground reference surface target at the imaging moment by combining the speed information of the satellite orbit and the wavelength of the wave band, and taking the Doppler frequency as a true value of the Doppler frequency;
namely, the relationships (1) and (2) are as follows:
wherein (X, Y, Z) represents a ground point coordinate, ReAnd RpRespectively the major semi-axis and the minor semi-axis of the WGS84 ellipsoid, h is the elevation of the target point, RSOAnd VSORespectively the spatial position vector and the velocity vector, f, of the SAR satelliteDThe image element Doppler frequency of the SAR satellite image is shown, and lambda is the SAR electromagnetic wave wavelength.
Further, step S4 includes the following:
(1) and simulating satellite orbit errors. The error satellite speed difference and the satellite position error belong to random errors, are generated according to random numbers in statistical simulation, the satellite speed error and the satellite position error belong to non-uniform random number generation, and the satellite speed error and the satellite position error are calculated by adopting a truncation method.
The presence function M (·) satisfies the following condition:
in the formula, m (-) is also a density function, and a random variable Y having a density of m (-) can be easily generated.
② generating random variable Y-m (-) and random number V-U0, 1.
(2) Compensating for the simulated system error. The system errors influencing the geometric positioning comprise DEM elevation errors, azimuth time synchronization errors, slant range errors and Doppler frequency errors. The RD model with system error is related as follows:
in the formula, DEM error delta h, slope error delta R and Doppler frequency error delta f1Satellite position error Δ r, satellite velocity error Δ v, azimuth time synchronization error Δ f2。
Further, step S5 includes the following steps:
(1) inverse calculation of the geometric model: the method of indirect positioning is used and,
converting the ground control point coordinates in S2 into space rectangular coordinates (X, Y and Z) under a WGS-84 system to obtain a position vector and a velocity vector of a target point;
secondly, the middle line number of the SAR image is taken as an initial value, and the azimuth time t of the middle line number is calculated according to the corresponding relationi；
Utilizing azimuth time tiComputing t by interpolating orbit state dataiCorresponding satellite position vector sum RSOAnd velocity vector VSO；
Fourthly, R isSO、VSO、RtO、VtOSubstituting the obtained value into a formula (6) to obtain the slant range and the Doppler center frequency; then, the Doppler center frequency change rate is calculated by a numerical differentiation method by using the following formula,
dfdc＝(fdc-f′dc)/dt (9)
fifthly, according to the formula (9), f is calculateddcAnd fdc0The time difference dt of (d);
update time ti＝ti-1+dt；
Seventhly, updating and calculating fdcAnd fdc0；
Let us pass tiCalculating a line number; according to tiInterpolation of satellite position RSOAnd RtOThus, the skew distance is obtained; calculating a distance column number according to the relation between the Doppler center frequency and the slant distance, wherein the column number at the moment is the coordinate (i, j) of the target point in the SAR image plane;
(2) and (3) positive calculation of the geometric model:
calculating the slant range R and the Doppler center frequency f corresponding to the pixel according to a formula (8) and the row number (i, j) of the ground control point coordinate on the SAR image obtained by the inverse calculation of the geometric modeldc；
Calculating the space rectangular coordinate of the point by taking the coordinate of the central point of the SAR image as an initial value;
and thirdly, converting the spatial rectangular coordinate obtained by calculation into a geographic coordinate, namely a ground point coordinate corresponding to the SAR image pixel.
(3) And (3) calculating the error between the ground point coordinates obtained in the step (1) and the step (2) in the step (S5) and the reference target point in the step (S2), and counting the error. The formula is as follows:
where σ is the geometric positioning accuracy, σxFor geometric positioning accuracy in the along-the-track direction, σyFor geometric positioning accuracy in the vertical direction, σzThe geometric positioning accuracy of the radial position. Further, step S6 includes the following steps:
(1) the affine transformation model formula is constructed as follows:
wherein (Δ x, Δ y) is the difference between the measured coordinates and the real coordinates of the real ground control points on the image, i.e. the adjustment value, (r, c) is the row-column coordinates of the control points on the image; a isi，biIs the adjustment parameter of the image.
(2) Solving an affine transformation model: the parameters of the affine transformation are calculated using the 4 ground control points acquired in S2.
The error equation is:
V＝Bx-L，W (12)
in the formula (I), the compound is shown in the specification,
X＝[ai bj]and W is a weight matrix.
Secondly, according to the least square adjustment principle, an error equation can be transformed into a normal equation:
(BTB)X＝BTL
(13)
further, step S7 includes the following steps:
(1) let the SAR image have a distance pixel interval of mrThen the error equation of the slope distance in the RD model is:
ΔR＝mr× Δx (14)
(2) the satellite position will be biased.
The distance-direction time difference generated is as follows:
where Δ y is the azimuth pixel difference and PRF is the pulse repetition frequency of the satellite transmit signal.
② at time t1，t2，...tn+1At the interpolation node of (2), the satellite position coordinate is X1(t1)，X2(t2)、...Xt+1(tt+1) Etc., then the satellite coordinate error at that time is:
the satellite position at time Δ t obtained by the above equation (15) can be obtained by interpolating the equation in the direction X, Y, Z.
(3) When the geometric positioning of the SAR satellite deviates, a certain time deviation is generated, so that the Doppler center frequency generates an error.
The distance-direction time error equation generated is as follows:
in the formula, mrFor the range pixel spacing of the SAR image, Δ x is the range pixel difference, and c is the speed of light.
The error generated by the Doppler center frequency is:
Δf＝a0+a1(tsr+Δtsr-t0)+a2(tsr+Δtsr-t0)2+a3(tsr+Δtsr-t0)3+a4(tsr+Δtsr-t0)4(18) in the formula, a0，a1，a2，a3，a45 parameters, t, for the center frequency of DopplersrFor the fast time of the current pixel, t0Is the fast time that a pixel is in a close range.
Further, step S8 includes the following steps:
(1) and (5) performing positive calculation on the geometric model.
Calculating the slant range R and the Doppler center frequency f corresponding to the pixel according to the line and column numbers (i, j) of the independent check points on the SAR image obtained by the inverse calculation of the geometric model of the S5(1) and the RD model compensated by the S7 affine transformationdc；
Calculating the space rectangular coordinate of the point by taking the coordinate of the central point of the SAR image as an initial value;
and thirdly, converting the spatial rectangular coordinate obtained by calculation into a geographic coordinate, namely a ground point coordinate corresponding to the SAR image pixel.
(3) And (4) calculating the error between the ground point coordinates obtained in the step (1) of S8 and the ground control point coordinates of the step (S2), and counting the error. The formula is as follows:
where σ is the geometric positioning accuracy, σxFor geometric positioning accuracy in the along-the-track direction, σyFor geometric positioning accuracy in the vertical direction, σzThe geometric positioning accuracy of the radial position.
Further, step S9 includes the following steps:
and comparing and analyzing the uncontrolled geometric positioning precision error obtained by calculation in the step S5 with the controlled geometric positioning precision error obtained by calculation in the step S8, and analyzing and evaluating the controlled geometric positioning precision. The root mean square error is used as an evaluation index of the geometric positioning accuracy. The root mean square error calculation formula is as follows:
where σ is the geometric positioning accuracy, σxFor geometric positioning accuracy in the along-the-track direction, σyFor geometric positioning accuracy in the vertical direction, σzThe geometric positioning accuracy of the radial position.
In view of the above, aiming at the requirement of geometric positioning accuracy simulation of the medium and high orbit SAR satellite, an affine transformation model is established according to ground control points by establishing a theoretical geometric relationship between satellites and the ground and a virtual simulated geometric relationship between the satellites and the ground, and a distance Doppler model is compensated based on the affine transformation model, so that a simulation analysis method for the band-controlled geometric positioning accuracy of the medium and high orbit SAR satellite is provided, and the simulation analysis method has certain significance for the deep research of the medium and high orbit SAR satellite.
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The description of the present disclosure will become apparent and readily understood in conjunction with the following drawings, in which:
fig. 1 is a flow chart of a simulation analysis method of band-controlled geometric positioning accuracy of a medium and high orbit SAR satellite according to the present invention.
Detailed Description
The method for simulation analysis of geometric positioning accuracy of medium and high orbit SAR satellites according to the present invention is explained in detail according to the steps shown in FIG. 1.
Step 1: and simulating the medium and high orbit SAR satellite orbit. The method comprises the following specific steps:
(1) performing orbit simulation by using STK software according to parameters such as orbit semimajor axis, orbit eccentricity, orbit inclination angle and the like of the orbit of the SAR satellite with the medium and high orbit; the orbit equation is as follows:
wherein a is a semimajor axis, e is a major semiaxis, and f is a paraxial point angle.
(2) Satellite orbit data under a WGS84 coordinate system at a certain moment is taken as SAR satellite orbit data at the imaging moment, and a position vector and a velocity vector of a satellite are obtained, wherein a satellite position vector calculation formula is as follows:
in the formula, the coordinate component in the inertial system is shown, E is the eccentricity, E is the approximate point angle, and E is the semimajor axis;
the basic formula of the satellite velocity vector is as follows:
in the formula, E is a deviation angle, a is a major semi-axis, E is an eccentricity, and P and Q are coordinate components in an inertial system.
Step 2: simulating an imaging area. The method comprises the following specific steps:
(1) the satellite needs to continuously transmit or acquire relevant information with the ground during the orbit, and the imaging parameters of the medium and high orbit SAR are used for the satellite
The range and longitude and latitude of the coverage area can be expressed, the semi-central angle beta of the spherical crown surface is solved and calculated according to the following calculation formula, and then the following spherical trigonometric equation function formula is obtained according to the spherical geometrical relationship:
wherein, λ is longitude, and λ is longitude,
for geographical latitude, whenever the equation is satisfied
The set of points of (a) is the coverage area boundary.
(2) In the range of the earth surface covered by the radar beam, the ground point in the optional imaging range is used as a real reference target point, and the coordinate of the ground point is the true value of the coordinate of the real reference target point.
And step 3: and simulating a theoretical satellite-ground geometric imaging relation. The method comprises the following specific steps:
(1) calculating the slope distance between the SAR satellite and the ground reference target at the imaging moment according to the position coordinates of the satellite orbit and the ground control point coordinates, and taking the slope distance as a true value of the slope distance;
(2) calculating the Doppler frequency between the SAR satellite and the ground reference surface target at the imaging moment by combining the speed information of the satellite orbit and the wavelength of the wave band, and taking the Doppler frequency as a true value of the Doppler frequency;
namely, the relationships (1) and (2) are as follows:
wherein (X, Y, Z) represents a ground point coordinate, ReAnd RpRespectively the major semi-axis and the minor semi-axis of the WGS84 ellipsoid, h is the elevation of the target point, RSOAnd VSORespectively the spatial position vector and the velocity vector, f, of the SAR satelliteDThe image element Doppler frequency of the SAR satellite image is shown, and lambda is the SAR electromagnetic wave wavelength.
And 4, step 4: and constructing a geometric positioning model in the virtual real imaging environment. The method comprises the following specific steps:
(1) and simulating satellite orbit errors. The error satellite speed difference and the satellite position error belong to random errors, are generated according to random numbers in statistical simulation, the satellite speed error and the satellite position error belong to non-uniform random number generation, and the satellite speed error and the satellite position error are calculated by adopting a truncation method.
The presence function M (·) satisfies the following condition:
in the formula, m (-) is also a density function, and a random variable Y having a density of m (-) can be easily generated.
② generating random variable Y-m (-) and random number V-U0, 1.
(2) Compensating for the simulated system error. The system errors influencing the geometric positioning comprise DEM elevation errors, azimuth time synchronization errors, slant range errors and Doppler frequency errors. The RD model with system error is related as follows:
in the formula, DEM error delta h, slope error delta R and Doppler frequency error delta f1Satellite position error Δ r, satellite velocity error Δ v, azimuth time synchronization error Δ f2。
And 5: and constructing a geometric positioning model in the virtual real imaging environment. The method comprises the following specific steps:
(1) inverse calculation of the geometric model: the method of indirect positioning is used and,
converting the ground control point coordinates in the step 2 into space rectangular coordinates (X, Y and Z) under a WGS-84 system to obtain a position vector and a velocity vector of a target point;
second, the middle line number of the SAR image is used as an initial value, and the direction of the middle line number is calculated according to the corresponding relationTime ti；
Utilizing azimuth time tiComputing t by interpolating orbit state dataiCorresponding satellite position vector sum RSOAnd velocity vector VSO；
Fourthly, R isSO、VSO、RtO、VtOSubstituting the obtained value into a formula (6) to obtain the slant range and the Doppler center frequency; then, the Doppler center frequency change rate is calculated by a numerical differentiation method by using the following formula,
dfdc＝(fdc-f′dc)/dt (9)
fifthly, according to the formula (9), f is calculateddcAnd fdc0The time difference dt of (d);
update time ti＝ti-1+dt；
Seventhly, updating and calculating fdcAnd fdc0；
Let us pass tiCalculating a line number; according to tiInterpolation of satellite position RSOAnd RtOThus, the skew distance is obtained; calculating a distance column number according to the relation between the Doppler center frequency and the slant distance, wherein the column number at the moment is the coordinate (i, j) of the target point in the SAR image plane;
(2) and (3) positive calculation of the geometric model:
obtaining row and column numbers (i, j) of the ground control points on the SAR image according to the inverse calculation of the geometric model, and calculating the corresponding slope distance R and Doppler center frequency f of the pixel according to a formula (8)dc；
Calculating the space rectangular coordinate of the point by taking the coordinate of the central point of the SAR image as an initial value;
and thirdly, converting the spatial rectangular coordinate obtained by calculation into a geographic coordinate, namely a ground point coordinate corresponding to the SAR image pixel.
(3) And (4) calculating the error between the ground point coordinates obtained in the step (5) through the steps (1) and (2) and the reference target point of S2, and counting the error. The formula is as follows:
where σ is the geometric positioning accuracy, σxFor geometric positioning accuracy in the along-the-track direction, σyFor geometric positioning accuracy in the vertical direction, σzThe geometric positioning accuracy of the radial position.
Step 6: and (5) constructing and solving an affine transformation model. The method comprises the following specific steps:
(1) the affine transformation model formula is constructed as follows:
wherein (Δ x, Δ y) is the difference between the measured coordinates and the real coordinates of the real ground control points on the image, i.e. the adjustment value, (r, c) is the row-column coordinates of the control points on the image; a isi，biIs the adjustment parameter of the image.
(2) Solving an affine transformation model: and (3) calculating parameters of affine transformation by using the 4 ground control points acquired in the step (2).
The error equation is:
V＝Bx-L，W (12)
in the formula (I), the compound is shown in the specification,
X＝[ai bj]and W is a weight matrix.
Secondly, according to the least square adjustment principle, an error equation can be transformed into a normal equation:
(BTB)X＝BTL
(13)
and 7: and D model compensation based on an affine transformation model. Simulating an imaging area. The method comprises the following specific steps:
(1) let the SAR image have a distance pixel interval of mrThen the error equation of the slope distance in the RD model is:
ΔR＝mr×Δx (14)
(2) the satellite position will be biased.
The distance-direction time difference generated is as follows:
where Δ y is the azimuth pixel difference and PRF is the pulse repetition frequency of the satellite transmit signal.
② at time t1，t2，...tn+1At the interpolation node of (2), the satellite position coordinate is X1(t1)，X2(t2)、...Xt+1(tt+1) Etc., then the satellite coordinate error at that time is:
the satellite position at time Δ t obtained by the above equation (15) can be obtained by interpolating the equation in the direction X, Y, Z.
(3) When the geometric positioning of the SAR satellite deviates, a certain time deviation is generated, so that the Doppler center frequency generates an error.
The distance-direction time error equation generated is as follows:
in the formula, mrFor the range pixel spacing of the SAR image, Δ x is the range pixel difference, and c is the speed of light.
The error generated by the Doppler center frequency is:
Δf＝a0+a1(tsr+Δtsr-t0)+a2(tsr+Δtsr-t0)2+a3(tsr+Δtsr-t0)3+a4(tsr+Δtsr-t0)4 (18)
in the formula, a0，a1，a2，a3，a45 parameters, t, for the center frequency of DopplersrFor the fast time of the current pixel, t0Is the fast time that a pixel is in a close range.
And 8: simulating an imaging area. And D model compensation based on an affine transformation model. The method comprises the following specific steps:
(1) and (5) performing positive calculation on the geometric model.
Calculating the slant range R and the Doppler center frequency f corresponding to the pixel according to the line number (i, j) of the independent check point on the SAR image obtained by the inverse calculation of the geometric model in the step 5(1) and the RD model after the affine transformation compensation in the step 7dc；
Calculating the space rectangular coordinate of the point by taking the coordinate of the central point of the SAR image as an initial value;
and thirdly, converting the spatial rectangular coordinate obtained by calculation into a geographic coordinate, namely a ground point coordinate corresponding to the SAR image pixel.
(3) And (3) calculating the error between the ground point coordinates obtained in the step (8) and the step (1) and the ground control point coordinates in the step (2), and counting the error. The formula is as follows:
where σ is the geometric positioning accuracy, σxFor geometric positioning accuracy in the along-the-track direction, σyFor geometric positioning accuracy in the vertical direction, σzThe geometric positioning accuracy of the radial position.
And step 9: and (6) evaluating the precision. Simulating an imaging area. The method comprises the following specific steps:
and (4) comparing and analyzing the uncontrolled geometric positioning precision error obtained by calculation in the step (5) with the controlled geometric positioning precision error obtained by calculation in the step (8), and analyzing and evaluating the controlled geometric positioning precision. The root mean square error is used as an evaluation index of the geometric positioning accuracy. The root mean square error calculation formula is as follows:
where σ is the geometric positioning accuracy, σxFor geometric positioning accuracy in the along-the-track direction, σyFor geometric positioning accuracy in the vertical direction, σzThe geometric positioning accuracy of the radial position.
The invention discloses a simulation analysis method for band-controlled geometric positioning accuracy of a medium and high orbit SAR (synthetic aperture radar) satellite. The method has the characteristic of virtual simulation, and can provide reference basis for geometric positioning precision analysis of the medium and high orbit SAR satellite.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (10)
1. A simulation analysis method for band-controlled geometric positioning accuracy of medium and high orbit SAR satellites is characterized by comprising the following steps:
s1: and simulating the medium and high orbit SAR satellite orbit. According to parameters such as a designed Satellite orbit long half shaft, orbit eccentricity, orbit inclination and the like, simulating a section of medium and high orbit SAR Satellite orbit by adopting a Satellite Tool Kit (STK), and calculating position coordinates (X, Y, Z) and speed coordinates (Vx, Vy, Vz) of the medium and high orbit SAR Satellite through an analysis function of the STK software;
s2: simulating an imaging area. Predicting the range of the radar beam covering the earth surface according to the simulated parameters of S1, the instantaneous position of the satellite and the view angle, and uniformly selecting a certain number of ground points (at least 9 points are suggested) in the imaging range as ground control points;
s3: and simulating a theoretical satellite-ground geometric imaging relation. Calculating the slant range, Doppler frequency and the like of the imaging moment by constructing a distance Doppler (RD) model by adopting the middle and high orbit satellite parameters simulated in S1 and the ground control point coordinates of the S2 prediction imaging range;
s4: and constructing a geometric positioning model in the virtual real imaging environment. Adding error parameters such as DEM elevation error, azimuth time synchronization error, slant range error, Doppler frequency error, satellite velocity error, satellite position error and the like into RD model parameters in S3 in a single or multiple combination form to construct a virtual simulated satellite-ground geometric relation;
s5: and (4) calculating the geometric positioning without control. Calculating the positions of 9 points on the SAR image by a theoretical geometric positioning model according to the ground control point coordinates of S2 and adopting the reverse calculation of the geometric model; calculating object space coordinates of the virtual real imaging environment by a geometric positioning model of the virtual real imaging environment according to image space coordinates corresponding to the 9 ground point coordinates and adopting geometric model forward calculation; comparing and analyzing the ground point coordinates obtained by calculation with the real ground control point coordinates in S2;
s6: and (5) constructing and solving an affine transformation model. Selecting at least 4 ground control points in S2, and solving an affine transformation model;
s7: and D model compensation based on an affine transformation model. Compensating the RD model by using the affine transformation model solved in the S7, and improving the geometric positioning accuracy of the RD model;
s8: and (4) carrying out geometric positioning calculation under control. After solving the affine transformation at S7, the ground control point coordinates (at least 5 points) in the other S2 are used as independent check points. And calculating object coordinates of the independent check points by using the compensated RD model in S7 and by adopting geometric model forward calculation according to the position coordinates on the SAR image, which are obtained by geometric inverse calculation of the check points in S5. And comparing and analyzing the real coordinates of the independent check points in S2;
s9: and (6) evaluating the precision. And comparing the uncontrolled geometric positioning precision error obtained by calculation in the S5 with the controlled geometric positioning precision error obtained by calculation in the S8, and analyzing and evaluating the controlled geometric positioning precision of the SAR satellite.
2. The simulation analysis method for geometric positioning accuracy of medium and high orbit SAR satellite according to claim 1, wherein the step S1 comprises the following steps:
(1) performing orbit simulation by using STK software according to parameters such as orbit semimajor axis, orbit eccentricity, orbit inclination angle and the like of the orbit of the SAR satellite with the medium and high orbit; the orbit equation is as follows:
wherein a is a semimajor axis, e is a major semiaxis, and f is a paraxial point angle.
(2) Satellite orbit data under a WGS84 coordinate system at a certain moment is taken as SAR satellite orbit data at the imaging moment, and a position vector and a velocity vector of a satellite are obtained, wherein a satellite position vector calculation formula is as follows:
in the formula, the coordinate component in the inertial system is shown, E is the eccentricity, E is the approximate point angle, and E is the semimajor axis;
the basic formula of the satellite velocity vector is as follows:
in the formula, E is a deviation angle, a is a major semi-axis, E is an eccentricity, and P and Q are coordinate components in an inertial system.
3. The simulation analysis method for geometric positioning accuracy of medium and high orbit SAR satellite according to claim 1, wherein the step S2 comprises the following steps:
(1) the satellite needs to continuously transmit or acquire relevant information with the ground during the orbit, and the imaging parameters of the medium and high orbit SAR are used for the satellite
The range and longitude and latitude of the coverage area can be expressed, the semi-central angle beta of the spherical crown surface is solved and calculated according to the following calculation formula, and then the following spherical trigonometric equation function formula is obtained according to the spherical geometrical relationship:
wherein, λ is longitude, and λ is longitude,
for geographical latitude, whenever the equation is satisfied
The set of points of (a) is the coverage area boundary.
(2) Ground points within the range of the earth's surface covered by the radar beam, optionally within the imaging range, are used as ground control point coordinates.
4. The simulation analysis method for geometric positioning accuracy of medium and high orbit SAR satellite according to claim 1, wherein the step S3 comprises the following steps:
(1) calculating the slope distance between the SAR satellite and the ground reference target at the imaging moment according to the position coordinates of the satellite orbit and the ground control point coordinates, and taking the slope distance as a true value of the slope distance;
(2) calculating the Doppler frequency between the SAR satellite and the ground reference surface target at the imaging moment by combining the speed information of the satellite orbit and the wavelength of the wave band, and taking the Doppler frequency as a true value of the Doppler frequency;
namely, the relationships (1) and (2) are as follows:
wherein (X, Y, Z) represents a ground point coordinate, ReAnd RpRespectively the major semi-axis and the minor semi-axis of the WGS84 ellipsoid, h is the elevation of the target point, RSOAnd VSORespectively the spatial position vector and the velocity vector, f, of the SAR satelliteDThe image element Doppler frequency of the SAR satellite image is shown, and lambda is the SAR electromagnetic wave wavelength.
5. The simulation analysis method for geometric positioning accuracy of medium and high orbit SAR satellite according to claim 1, wherein the step S4 comprises the following steps:
(1) and simulating satellite orbit errors. The error satellite speed difference and the satellite position error belong to random errors, are generated according to random numbers in statistical simulation, the satellite speed error and the satellite position error belong to non-uniform random number generation, and the satellite speed error and the satellite position error are calculated by adopting a truncation method.
The presence function M (·) satisfies the following condition:
in the formula, m (-) is also a density function, and a random variable Y having a density of m (-) can be easily generated.
② generating random variable Y-m (-) and random number V-U0, 1.
(2) Compensating for the simulated system error. The system errors influencing the geometric positioning comprise DEM elevation errors, azimuth time synchronization errors, slant range errors and Doppler frequency errors. The RD model with system error is related as follows:
in the formula, DEM error Δ h, slope error Δ R, Doppler frequencyRate error Δ f1Satellite position error Δ r, satellite velocity error Δ v, azimuth time synchronization error Δ f2。
6. The simulation analysis method for geometric positioning accuracy of medium and high orbit SAR satellite according to claim 1, wherein the step S5 comprises the following steps:
(1) inverse calculation of the geometric model: the method of indirect positioning is used and,
converting the ground control point coordinates in S2 into space rectangular coordinates (X, Y and Z) under a WGS-84 system to obtain a position vector and a velocity vector of a target point;
secondly, the middle line number of the SAR image is taken as an initial value, and the azimuth time t of the middle line number is calculated according to the corresponding relationi；
Utilizing azimuth time tiComputing t by interpolating orbit state dataiCorresponding satellite position vector sum RSOAnd velocity vector VSO；
Fourthly, R isSO、VSO、RtO、VtOSubstituting the obtained value into a formula (6) to obtain the slant range and the Doppler center frequency; then, the Doppler center frequency change rate is calculated by a numerical differentiation method by using the following formula,
dfdc＝(fdc-f′dc)/dt (9)
fifthly, according to the formula (9), f is calculateddcAnd fdc0The time difference dt of (d);
update time ti＝ti-1+dt；
Seventhly, updating and calculating fdcAnd fdc0；
Let us pass tiCalculating a line number; according to tiInterpolation of satellite position RSOAnd RtOThus, the skew distance is obtained; calculating a distance column number according to the relation between the Doppler center frequency and the slant distance, wherein the column number at the moment is the coordinate (i, j) of the target point in the SAR image plane;
(2) and (3) positive calculation of the geometric model:
obtained by inverse calculation of the geometric modelThe row number and column number (i, j) of the ground control point coordinate on the SAR image, and the slant range R and the Doppler center frequency f corresponding to the pixel are calculated according to a formula (8)dc；
Calculating the space rectangular coordinate of the point by taking the coordinate of the central point of the SAR image as an initial value;
and thirdly, converting the spatial rectangular coordinate obtained by calculation into a geographic coordinate, namely a ground point coordinate corresponding to the SAR image pixel.
(3) And (3) calculating the error between the ground point coordinates obtained in the step (1) and the step (2) in the step (S5) and the reference target point in the step (S2), and counting the error. The formula is as follows:
where σ is the geometric positioning accuracy, σxFor geometric positioning accuracy in the along-the-track direction, σyFor geometric positioning accuracy in the vertical direction, σzThe geometric positioning accuracy of the radial position.
7. The simulation analysis method for geometric positioning accuracy of medium and high orbit SAR satellite according to claim 1, wherein the step S6 comprises the following steps:
(1) the affine transformation model formula is constructed as follows:
wherein (Δ x, Δ y) is the difference between the measured coordinates and the real coordinates of the real ground control points on the image, i.e. the adjustment value, (r, c) is the row-column coordinates of the control points on the image; a isi，biIs the adjustment parameter of the image.
(2) Solving an affine transformation model: the parameters of the affine transformation are calculated using the 4 ground control points acquired in S2.
The error equation is:
V＝Bx-L,W (12)
in the formula (I), the compound is shown in the specification,
X＝[ai bj]and W is a weight matrix.
Secondly, according to the least square adjustment principle, an error equation can be transformed into a normal equation:
(BTB)X＝BTL (13)
8. the simulation analysis method for geometric positioning accuracy of medium and high orbit SAR satellite according to claim 1, wherein the step S7 comprises the following steps:
(1) let the SAR image have a distance pixel interval of mrThen the error equation of the slope distance in the RD model is:
ΔR＝mr×Δx (14)
(2) the satellite position will be biased.
The distance-direction time difference generated is as follows:
where Δ y is the azimuth pixel difference and PRF is the pulse repetition frequency of the satellite transmit signal.
② at time t1，t2，…tn+1At the interpolation node of (2), the satellite position coordinate is X1(t1)，X2(t2)、…Xt+1(tt+1) Etc., then the satellite coordinate error at that time is:
the satellite position at time Δ t obtained by the above equation (15) can be obtained by interpolating the equation in the direction X, Y, Z.
(3) When the geometric positioning of the SAR satellite deviates, a certain time deviation is generated, so that the Doppler center frequency generates an error.
The distance-direction time error equation generated is as follows:
in the formula, mrFor the range pixel spacing of the SAR image, Δ x is the range pixel difference, and c is the speed of light.
The error generated by the Doppler center frequency is:
Δf＝a0+a1(tsr+Δtsr-t0)+a2(tsr+Δtsr-t0)2+a3(tsr+Δtsr-t0)3+a4(tsr+Δtsr-t0)4 (18)
in the formula, a0,a1,a2,a3,a45 parameters, t, for the center frequency of DopplersrFor the fast time of the current pixel, t0Is the fast time that a pixel is in a close range.
9. The simulation analysis method for geometric positioning accuracy of medium and high orbit SAR satellite according to claim 1, wherein the step S8 comprises the following steps:
1) and (5) performing positive calculation on the geometric model.
Calculating the slant range R and the Doppler center frequency f corresponding to the pixel according to the line and column numbers (i, j) of the independent check points on the SAR image obtained by the inverse calculation of the geometric model of the S5(1) and the RD model compensated by the S7 affine transformationdc；
Calculating the space rectangular coordinate of the point by taking the coordinate of the central point of the SAR image as an initial value;
and thirdly, converting the spatial rectangular coordinate obtained by calculation into a geographic coordinate, namely a ground point coordinate corresponding to the SAR image pixel.
(3) And (4) calculating the error between the ground point coordinates obtained in the step (1) of S8 and the ground control point coordinates of the step (S2), and counting the error. The formula is as follows:
where σ is the geometric positioning accuracy, σxFor geometric positioning accuracy in the along-the-track direction, σyFor geometric positioning accuracy in the vertical direction, σzThe geometric positioning accuracy of the radial position.
10. The simulation analysis method for geometric positioning accuracy of medium and high orbit SAR satellite according to claim 1, wherein the step S9 comprises the following steps:
(1) and comparing and analyzing the uncontrolled geometric positioning precision error obtained by calculation in the step S5 with the controlled geometric positioning precision error obtained by calculation in the step S8, and analyzing and evaluating the controlled geometric positioning precision. The root mean square error is used as an evaluation index of the geometric positioning accuracy. The root mean square error calculation formula is as follows:
where σ is the geometric positioning accuracy, σxFor geometric positioning accuracy in the along-the-track direction, σyFor geometric positioning accuracy in the vertical direction, σzThe geometric positioning accuracy of the radial position.
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