CN109254270A - A kind of spaceborne X-band interfering synthetic aperture radar calibrating method - Google Patents
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Abstract
The invention discloses a kind of spaceborne X-band interfering synthetic aperture radar calibrating methods, include the steps of determining that synthetic aperture radar three-dimensional reconstruction model waits for scaling parameter: baseline b, oblique square r, Doppler parameter f, interferometric phase；Coordinate system is established, spaceborne X-band synthetic aperture radar three-dimensional reconstruction model is constructed；The sensitivity coefficient to scaling parameter is calculated, spaceborne X-band synthetic aperture radar three-dimensional reconstruction model is solved；Spaceborne X-band synthetic aperture radar three-dimensional reconstruction model is improved using regularization method；It solves and improves spaceborne X-band synthetic aperture radar three-dimensional reconstruction model.Height accuracy and plane precision fundamentally improve the height accuracy and plane precision of the data that synthetic aperture radar obtains, provide the Law of DEM Data service of high quality.
Description
Technical Field
The invention belongs to the technical field of radar detection, and particularly relates to an interference calibration method for a satellite-borne X-band synthetic aperture radar.
Background
Digital Elevation Models (DEMs) play an increasingly important role in the fields of disaster monitoring, environmental planning, national economy, national defense and military and the like. The interferometric synthetic aperture radar technology has the advantages of being free of cloud and fog weather influence, being free of all-time and large-area imaging and the like, and is widely applied to obtaining global high-precision DEM data. Because the accuracy of the DEM obtained by the synthetic aperture radar technology is closely related to the accuracy of the interference parameters, in order to improve the DEM accuracy, a ground control point is required to perform error correction on various interference parameters, namely, interference calibration.
Because partial system parameter errors such as local oscillation errors and phase offset errors of SAR equipment can be corrected in a calibration stage in the SAR, the acquisition of high-precision DEM data depends on the index design of a synthetic aperture radar (synthetic aperture radar) platform on one hand. On the other hand, parameter errors such as a base line, an inclined distance, a platform position and a speed still influence the DEM precision in the DEM manufacturing process, the correction of the errors is an important means for the synthetic aperture radar to extract the high-precision DEM, and the acquisition of high-precision DEM data also depends on the guarantee of various calibration technologies to a great extent.
At present, the most common interference calibration method for the satellite-borne synthetic aperture radar is to establish a polynomial model to quickly correct interference parameter errors so as to improve DEM precision. However, the method can only improve the elevation accuracy of the DEM to a certain extent, and cannot evaluate the plane accuracy of the DEM. The main ideas of the currently most commonly used interference calibration method for the satellite-borne synthetic aperture radar are as follows: the method comprises the steps of firstly, systematically analyzing the influence of various interference parameters on DEM precision, then establishing a polynomial model based on corresponding errors according to the characteristics of the interference parameters, and then correcting the coarse DEM by using the polynomial models, thereby finally improving the DEM precision. The satellite-borne synthetic aperture radar interference calibration method based on error term analysis can improve elevation precision of DEM data, but the method ignores plane information of control points on one hand, and on the other hand, polynomial models are complex to build. It is difficult to obtain a large amount of calibration point data for an arbitrary area.
Disclosure of Invention
The invention aims to solve the problems and provide a satellite-borne X-band synthetic aperture radar interference calibration method, which comprises the following steps:
s1: determining undetermined calibration parameters of a three-dimensional reconstruction model of the synthetic aperture radar, including a baseline parameter b, a skew moment parameter r, a Doppler parameter f and an interference phase parameter
S2: establishing a TCN coordinate system for baseline parameter representation, a VPQ coordinate system for synthetic aperture radar three-dimensional reconstruction to perform view vector decomposition, and an XYZ coordinate system of a geocentric space rectangular coordinate system, and constructing a satellite-borne X-waveband synthetic aperture radar three-dimensional reconstruction model;
s3: calculating the sensitivity coefficient of the parameter to be calibrated, and solving a three-dimensional reconstruction model of the satellite-borne X-band synthetic aperture radar;
s4: improving a satellite-borne X-band synthetic aperture radar three-dimensional reconstruction model by adopting a regularization method;
s5: and solving the improved satellite-borne X-band synthetic aperture radar three-dimensional reconstruction model.
Further, the step S2 includes:
s21: establishing a TCN coordinate system for baseline parameter representation, a VPQ coordinate system for synthetic aperture radar three-dimensional reconstruction to perform view vector decomposition, and an XYZ coordinate system of a geocentric space rectangular coordinate system, and setting: the initial value of the C direction baseline is bc0At a velocity vc0The initial value of the N-direction baseline is bn0An initial value of velocity vn0Initial skew moment of r0，f0、f1、f2The Doppler frequency is X, Y, Z direction components to a geocentric space rectangular coordinate system, S is a vector of a synthetic aperture radar antenna phase center in the geocentric space rectangular coordinate system, P is a position vector of a target point in the geocentric space rectangular coordinate system, and R is1Is the vector from S to the target point P; let v be the velocity of the target point in the rectangular coordinate system of the earth center space, and v be the components of the target point on the coordinate axisxi、vyi、vzi；
Calculating to obtain three-dimensional coordinates according to parameters to be calibrated;
[PxiPyiPzi]is a three-dimensional coordinate provided by the control point;
setting:
s22: synthetic aperture radar three-dimensional reconstruction model equation:
the equation of the three-dimensional reconstruction model is:
further, the sensitivity coefficient is a partial derivative of the three-dimensional reconstruction model to the parameter to be calibrated, and the method comprises the following steps:
s31: the baseline parameters comprise a parallel baseline and a vertical baseline, and are set as follows: parallel base lines are bv，Vertical base line of bpv，B is the base line vector of the coordinate system of the carrier, B is the base line vector of the space rectangular coordinate system, rvIs a unit visual vector projection component of the visual vector in the V-axis direction, rpIs a unit visual vector projection component of the visual vector in the P-axis direction, rqThe apparent vector component is projected in the unit of the apparent vector in the Q-axis direction, r0Is an initial skew moment, fdopIs the Doppler center frequency; s32: (1) and (3) performing partial derivation on the baseline parameters:
parallel baseline-to-baseline parameter derivation:
vertical baseline to baseline parameter derivation:
(2) and (3) solving the deviation of the initial skew moment parameters:
wherein the derivative of the unit vector of view projection component to the initial skew moment is:
(3) and (3) calculating the partial derivative of the Doppler frequency parameter:
(4) and (3) solving the partial derivative of the interference phase parameters:
further, the step S4 includes: setting: the matrix A is a sensitivity coefficient of the parameter to be calibrated to the three-dimensional coordinate, the curve curvature of the three-dimensional model equation is k (lambda), lambda is the optimal model parameter when the curve curvature of the three-dimensional model equation under the parameter to be calibrated is maximum, x is the solution of the improved regularization thought equation, I is a unit matrix, b is the solution of the original equation, and x is (A + lambda I)- 1b。
Further, the curvature of the three-dimensional model equation curve is as follows:
wherein u | | | xλ||，v＝||AxλB | |, where k (λ) is the maximum, the corresponding λ is the optimal model parameter.
The invention has the beneficial effects that: the invention effectively solves the problem that a large amount of calibration point data of any area is difficult to obtain; the phenomenon that the calibration model is failed to be solved due to the ill-condition of the sensitivity matrix is avoided; the interference calibration model is improved by the regularization method, so that accurate parameter correction values can be obtained under the condition of more calibration parameters, a reliable equation solution is obtained, the elevation precision and the plane precision of DEM data obtained by the synthetic aperture radar are fundamentally improved, and high-quality digital elevation model data service is provided.
Drawings
FIG. 1 is a flow chart of a satellite-borne X-band synthetic aperture radar interference calibration method.
Fig. 2 is a schematic diagram of a terrain mapping geometry of an on-board InSAR.
Detailed Description
The invention will be further described with reference to the accompanying drawings in which:
as shown in FIG. 1, the invention relates to an interference calibration method for a satellite-borne X-band synthetic aperture radar,
interference parameters related in the synthetic aperture radar three-dimensional reconstruction model mainly comprise a baseline, an inclined distance, Doppler frequency, a unwrapping phase, a main satellite position and a main satellite speed. The characteristics and error sources of the 6 parameters are analyzed by taking the system parameters of the TanDEM-X image as an example for a satellite-borne X-waveband SAR satellite platform as follows:
(1) error of base line
Studies have shown that the down-track baseline error in cross-track interferometry can be eliminated during the registration phase and therefore need not be considered. The interference base line is decomposed to a TCN coordinate system, and the T direction is consistent with the along-track direction, so that the component of the T direction is not required to be calibrated, and only the component of the base line in the C direction and the N direction is required to be calibrated. The baseline is a time-varying quantity, so that the baseline can be decomposed into a baseline initial value and a baseline rate related to time, and the change condition of the baseline is expressed by a first-order polynomial. In order to reduce the relative elevation error of the DEM in the TanDEM-X task, the set optimal baseline precision is 1 mm, the actual inter-satellite baseline measurement precision can only reach the magnitude of 2-4 mm, and the difference between the set baseline precision and the set baseline precision is certain. The baseline accuracy and the elevation measurement accuracy of the synthetic aperture radar are closely related and are parameters which need to be corrected.
(2) Skew error
The skew measurement is determined by calculating the time delay between the transmitted pulse and the received pulse. The influence of the skew error on the three-dimensional reconstruction accuracy is shown as the integral reduction or lifting in the skew direction, and the influence on the flat ground phase accuracy is shown. The slant range measurement error is mainly caused by radar timing system error, belongs to system error, and is determined as a parameter to be calibrated.
(3) Doppler parameter error
In the TanDEM-X mission, the doppler frequency has little effect on the X direction because in cross-track interferometry, the satellite is approximately perpendicular to the X direction when flying from north to south or from south to north. The doppler frequency mainly affects the measurement accuracy in the Y direction and the Z direction. Doppler coefficient f0、f1And f2The magnitude of the influence on the three-dimensional reconstruction precision is different. F at 0.001 Hz0、f1、f2The coefficient errors correspond to doppler frequency errors of 0.001 hz, 0.0038 hz and 11.027 hz, respectively. Therefore, the coefficient f2The influence on Doppler frequency is the largest, and the influence on three-dimensional reconstruction precision is more sensitive. In summary, a 0.1 hz doppler frequency error will cause a 0.1 m three-dimensional reconstruction error, and the doppler frequency has a large influence on the three-dimensional reconstruction accuracy and should be determined as a parameter to be calibrated.
(4) Interference phase error
Interferometric phase errors are another source of error in the three-dimensional reconstruction of synthetic aperture radar. The elevation error and the plane error of more than 1 meter can be generated by the phase error of about 10 degrees, and the influence on the plane positioning precision is larger. The interference phase error is equivalent to the influence of the baseline measurement error on the measurement precision, and when the baseline length is longer, the interference phase error plays a decisive role in the elevation measurement precision. The interference phase error comprises residual system error and random error introduced in the data processing process. The interference phase error is a main error source in the three-dimensional reconstruction process and should be determined as a parameter to be calibrated.
(5) Error in position of the main star
The absolute position of the satellite is calculated from the orbital data, and the orbital measurements are usually made by autonomous positioning of the satellite by a GPS receiver carried by the satellite. It has been found that the precise orbit determination error of the GPS is continuous: the track error under the short time scale changes linearly, and the change rate is very small; the orbit error at long time scales varies randomly. Since the acquisition time of a scene image is short, the position error of the main star can be regarded as a fixed value. Considering that the TanDEM-X system has higher absolute precision of orbit determination, the position error of the main satellite is not used as an interference calibration parameter.
(6) Error in speed of the main satellite
The satellite velocity can be obtained by solving the first-order partial derivative of satellite orbit data, and is closely related to the satellite orbit determination precision, so that the main satellite velocity error can also be regarded as a constant system error. The satellite speed precision determined by the double-frequency GPS technology in the TanDEM-X system is in a submillimeter level, and the influence of the main satellite speed error on the synthetic aperture radar system is small and can be ignored.
In summary, the baseline parameter, the initial slope, the doppler coefficient, and the interference phase are used as the parameters to be calibrated, i.e., the interference parameters.
Setting an initial value b of a C-direction baseline of a TCN coordinate systemc0And velocity vc0N direction baseline initial value bn0And velocity vn0Initial slope distance r0Doppler coefficient f0、f1And f2Interference phaseLet the baseline component be b and the velocity be v, letThenThree-dimensional coordinates obtained according to each interference parameter; [ P ]xiPyiPzi]For three-dimensional coordinates of control points, PxRepresenting the X coordinate of the target point P in the rectangular coordinate system of the geocentric space; pyRepresenting the Y coordinate of the target point P in the rectangular coordinate system of the geocentric space; pzAnd represents the Z coordinate of the target point P in the rectangular coordinate system of the earth-center space.
Setting the matrix A as the sensitivity of each parameter to be calibrated to the three-dimensional coordinate, and correcting the system parameter
By usingRepresenting a rotation matrixThe synthetic aperture radar three-dimensional reconstruction model equation can be simplified as follows:
the above formula can be rewritten as:
and setting V as the parameter value to be corrected. V ═ Vx1vy1vz1... vxnvynvzn]。
The error equation of the three-dimensional reconstruction model is:
the above equation can be simplified as: v ═ a Δ x-l; v is the parameter value to be corrected. Matrix A:
setting X as a parameter to be calibrated, and decomposing the sensitivity coefficient of the interference parameter into partial derivatives of the interference parameter by three-dimensional coordinates:
(1) and (3) performing bias derivation on the baseline:
let B be the baseline vector of the coordinate system of the carrier, B be the baseline vector of the rectangular coordinate system of the space,are all rotation matrices. The baseline in the TCN coordinate system is then expressed as:
the base line is defined by TCN coordinate system BtBcBn]TGo to the space rectangular coordinate system [ b ]xbybz]TThe baseline conversion formula is:
according to the vector cross multiplication principle, a matrix for converting the TCN coordinate system into the geocentric space rectangular coordinate system can be obtainedThe detailed expression of (c):
wherein:
the baseline conversion formula is then expressed as:
similarly, the detailed expression of the VPQ coordinate system calculated according to the vector cross-product formula is as follows:
wherein:
[pxpypz]the derivative to the baseline parameter is:
[qxqyqz]the derivative to the baseline parameter is:
parallel base lines bvCan be expressed as:
the derivative of the parallel baseline to the baseline parameter is then:
perpendicular base line bpvFrom parallel base line bvThe base line b forms a right-angle triangle relation and satisfies the following relation:
the derivative of the vertical baseline to the baseline parameter is:
① pairs of Bc0、Bn0Derivative of (a):
with x representing Bc0And Bn0The unit apparent vector isThree-dimensional coordinate pair Bc0、Bn0The derivative of (d) is expressed as:
wherein the unit visual vectorTo Bc0、Bn0Derivative of (2)Expressed as:
rotation matrix pair Bc0、Bn0Derivation:
expressed as:
② pairs vc0、vn0Derivative of (2)
The parameter v is denoted by xc0、vn0. Three-dimensional coordinate pair vc0、vn0The derivative of (d) can be expressed as:
wherein the unit visual vectorFor vc0、vn0Derivative of (2)Expressed as:
rotation matrixFor vc0、vn0The derivative of (d) can be expressed as:
(2) calculating the initial skew deviation
Initial slope distance r0The derivative to three-dimensional localization is expressed as:
wherein the unit visual vectorTo r0The derivative of (c) is:
in the above formulaAccording to differences of synthetic aperture radar platforms, in satellite-borne synthetic aperture radar system
(3) Derivation of Doppler frequency
The doppler coefficients provided by different SAR systems may vary, and the partial derivative of the TanDEM-X satellite doppler coefficient may be represented by the following equation:
where i is 0, 1, 2, R1Is the distance from the target point to the phase center of the main antenna. Unit apparent vectorTo fiThe derivative of (c) is:
the derivative of the Doppler coefficient is different and should be changed according to the actual data format, TanDEM-X dataExpressed as:
wherein t represents the time corresponding to the corresponding pixel coordinate.
(4) Derivation of interference phase
To interference phaseAnd (5) calculating a partial derivative to obtain:
wherein,
fig. 2 shows the basic principle of acquiring DEM by InSAR, S1 and S2 respectively show the phase centers of the main and auxiliary antennas,the vector of the phase center of the main and auxiliary antennas in the geocentric space rectangular coordinate system,is the position vector of the target point P in the geocentric space rectangular coordinate system,vectors from S1 and S2 to the target point P, respectively.
The vector expression of the target point P under the geocentric space rectangular coordinate system is as follows:
in the formula (f)dopIs the Doppler center frequency;is the satellite velocity vector; λ is the radar wavelength; r1The distance from a target point to the phase center of the main antenna; r2The distance from the auxiliary antenna to the target point; phi is a winding phase; k is the whole cycle number of the interference phase;is the absolute interference phase; the repetitive track interference pattern Q is 2, and the dual antenna interference pattern Q is 1.
And solving the InSAR three-dimensional reconstruction model by using a view vector orthogonal decomposition method. Firstly, look vectorDecomposing the coordinate system into a moving coordinate system, and then converting the apparent vector under the moving coordinate system into a geocentric space rectangular coordinate system. The vector expression above can be converted into:
in the formula,the function of the method is to convert the visual vector under the VPQ coordinate system into a geocentric space rectangular coordinate system.Indicating the apparent vectorUnit vector in V-axis, P-axis, Q-axis directions:
rvrepresents the unit projection of the view vector in the V-axis direction, and the expression is:
rpis a unit projection component of the view vector in the P-axis direction, which can be expressed as:
in the formula, the component of the base line resolved into the velocity direction isThe component of the baseline resolved to perpendicular to the direction of velocity isThe symbols have the same meanings as above.
rqCan be expressed as:
rqthe calculation of the middle sign and the sign is related to the flight direction and the left side and the right side during InSAR imaging.
Unite rv、rp、rqThe expression, the unit projection component of the view vector in the VPQ moving coordinate system is:
and substituting the above expression into the transformed vector expression to obtain a complete expression of the three-dimensional reconstruction model:
when solving Δ x using least squares, it is necessary to solve for ATAnd (4) carrying out PA inverse matrix. The matrix a represents the sensitivity of each system parameter to three-dimensional coordinates. Because the sensitivity of each interference parameter is not in the same order, the matrix has a small value in a certain column and a large value in the certain column. In this case, A of the compositionTThe PA has the problem of matrix singularity, and the condition number of the matrix can even reach 1026The magnitude of the equation is seriously influenced on the equation resolving precision. In view of this, the present invention adopts a regularization method of an L-curve to solve this problem: and by selecting the regularization parameters, utilizing the regularization parameters to reform the A matrix, and then solving the inverse matrix to finally obtain the solution closest to the original equation.
The L curve is a continuous curve related to a parameter lambda under a logarithmic scale, and the regularization parameter selected by the L curve is the parameter lambda corresponding to the maximum curvature of the L curve. The maximum curvature calculation formula is set as:
wherein u | | | xλ||，v＝||AxλB | |, where k (λ) is the maximum, the corresponding λ is the optimal parameter.
Solution of the final equation: x ═ a + λ I)-1b。
The invention effectively solves the problem that a large amount of calibration point data of any area is difficult to obtain; the phenomenon that the calibration model is failed to be solved due to the ill-condition of the sensitivity matrix is avoided; the interference calibration model is improved by the regularization method, so that accurate parameter correction values can be obtained under the condition of more calibration parameters, a reliable equation solution is obtained, the elevation precision and the plane precision of DEM data obtained by the synthetic aperture radar are fundamentally improved, and high-quality digital elevation model data service is provided.
The technical solution of the present invention is not limited to the limitations of the above specific embodiments, and all technical modifications made according to the technical solution of the present invention fall within the protection scope of the present invention.
Claims (5)
1. A satellite-borne X-band synthetic aperture radar interference calibration method is characterized by comprising the following steps:
s1: determining undetermined calibration parameters of a three-dimensional reconstruction model of the synthetic aperture radar, including a baseline parameter b, a skew moment parameter r, a Doppler parameter f and an interference phase parameter
S2: establishing a TCN coordinate system for baseline parameter representation, a VPQ coordinate system for synthetic aperture radar three-dimensional reconstruction to perform view vector decomposition, and an XYZ coordinate system of a geocentric space rectangular coordinate system, and constructing a satellite-borne X-waveband synthetic aperture radar three-dimensional reconstruction model;
s3: calculating the sensitivity coefficient of the parameter to be calibrated, and solving a three-dimensional reconstruction model of the satellite-borne X-band synthetic aperture radar;
s4: improving a satellite-borne X-band synthetic aperture radar three-dimensional reconstruction model by adopting a regularization method;
s5: and solving the improved satellite-borne X-band synthetic aperture radar three-dimensional reconstruction model.
2. The method according to claim 1, wherein the step S2 includes:
s21: establishing a TCN coordinate system for baseline parameter representation, a VPQ coordinate system for synthetic aperture radar three-dimensional reconstruction to perform view vector decomposition, and an XYZ coordinate system of a geocentric space rectangular coordinate system, and setting: the initial value of the C direction baseline is bc0At a velocity vc0The initial value of the N-direction baseline is bn0An initial value of velocity vn0Initial skew moment of r0，f0、f1、f2The Doppler frequency is X, Y, Z direction components to a geocentric space rectangular coordinate system, S is a vector of a synthetic aperture radar antenna phase center in the geocentric space rectangular coordinate system, P is a position vector of a target point in the geocentric space rectangular coordinate system, and R is1Is the vector from S to the target point P; let v be the velocity of the target point in the rectangular coordinate system of the earth center space, and v be the components of the target point on the coordinate axisxi、vyi、vzi；
Is to calculate the three-dimensional coordinate according to the parameter to be calibrated,
[PxiPyiPzi]is a three-dimensional coordinate provided by the control point;
setting:
s22: synthetic aperture radar three-dimensional reconstruction model equation:
the equation of the three-dimensional reconstruction model is:
3. the method according to claim 1, wherein the sensitivity coefficient is a partial derivative of a parameter to be calibrated of the three-dimensional reconstruction model, and the method comprises the following steps:
s31: the baseline parameters comprise a parallel baseline and a vertical baseline, and are set as follows: parallel base lines are bv，Vertical base line of bpv，B is the base line vector of the coordinate system of the carrier, B is the base line vector of the space rectangular coordinate system, rvIs a unit visual vector projection component of the visual vector in the V-axis direction, rpIs a unit visual vector projection component of the visual vector in the P-axis direction, rqThe apparent vector component is projected in the unit of the apparent vector in the Q-axis direction, r0Is an initial skew moment, fdopIs the Doppler center frequency;
s32: (1) and (3) performing partial derivation on the baseline parameters:
parallel baseline-to-baseline parameter derivation:
vertical baseline to baseline parameter derivation:
(2) and (3) solving the deviation of the initial skew moment parameters:
wherein the derivative of the unit vector of view projection component to the initial skew moment is:
(3) and (3) calculating the partial derivative of the Doppler frequency parameter:
(4) and (3) solving the partial derivative of the interference phase parameters:
4. the method according to claim 1, wherein the step S4 includes: setting: the matrix A is a sensitivity coefficient of the parameter to be calibrated to the three-dimensional coordinate, the curve curvature of the three-dimensional model equation is k (lambda), lambda is the optimal model parameter when the curve curvature of the three-dimensional model equation under the parameter to be calibrated is maximum, x is the solution of the improved regularization thought equation, I is a unit matrix, b is the solution of the original equation, and x is (A + lambda I)-1b。
5. The spaceborne X-band synthetic aperture radar interferometric calibration method according to claim 4, characterized in that the curvature of the three-dimensional model equation is as follows:
wherein u | | | xλ||，v＝||AxλB | |, where k (λ) is the maximum, the corresponding λ is the optimal model parameter.
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| CN110907932A (en) * | 2019-11-26 | 2020-03-24 | 上海卫星工程研究所 | Distributed InSAR satellite height measurement precision influence factor analysis method and system |
| CN111239736A (en) * | 2020-03-19 | 2020-06-05 | 中南大学 | Single-baseline-based surface elevation correction method, device, equipment and storage medium |
| CN111812645A (en) * | 2020-06-10 | 2020-10-23 | 西南交通大学 | Satellite interferometry method for deformation of frozen soil in season |
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| CN111239736A (en) * | 2020-03-19 | 2020-06-05 | 中南大学 | Single-baseline-based surface elevation correction method, device, equipment and storage medium |
| CN111812645A (en) * | 2020-06-10 | 2020-10-23 | 西南交通大学 | Satellite interferometry method for deformation of frozen soil in season |
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