CN109254269A - A kind of Airborne Interferometric Synthetic Aperture calibrating method - Google Patents
A kind of Airborne Interferometric Synthetic Aperture calibrating method Download PDFInfo
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Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/40—Means for monitoring or calibrating
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
- G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
- G01S13/9021—SAR image post-processing techniques
- G01S13/9023—SAR image post-processing techniques combined with interferometric techniques
Abstract
The invention discloses a kind of Airborne Interferometric Synthetic Aperture calibrating methods, include the following steps: to observe Three-dimension Reconstruction Model, determine the undetermined parameter in carrier aircraft coordinate system, including Y-direction baseline component, Z-direction baseline component, interferometric phase, initial oblique distance, Doppler frequency；Interference calibration model is established based on least squares equation；The sensitivity coefficient of interferometric parameter is decomposed into three-dimensional coordinate to the local derviation of interferometric parameter by analyzing three-dimensional reconstruction model；Regularization parameter is found using regularization method, establishes parameters revision model；Propose the new general airborne InSAR calibration model based on Three-dimension Reconstruction Model, improve reliability and precision that InSAR extracts DEM, the parameters such as baseline, Doppler frequency, interferometric phase and oblique distance in model, each parameter is big to the sensitivity coefficient difference of positioning, to avoid sensitivity matrix morbid state from causing to resolve the phenomenon that failing, it introduces regularization method and improves interference calibration model, obtain accurate parameter corrected value, obtain reliable solution of equation.
Description
Technical field
The present invention relates to radar calibration field more particularly to a kind of Airborne Interferometric Synthetic Aperture calibrating methods.
Background technique
Since at the end of the 19th century, interference calibration is just widely used in correcting each system parameter error in InSAR mapping,
Lot of experiment validation has been obtained in terms of airborne InSAR interferometric parameter error correction.
1996, Madsen pointed out that signal multipath effect will increase phase error in interferometry, and then influences elevation
Measurement accuracy, the calibrating method based on interferometric phase can greatly reduce systematic error.1999, Geudtner et al. was analyzed
Then InSAR measurement of higher degree error source has carried out quantitative analysis to each error source using Sensitivity equation, started based on sensitivity
The interference calibrating method of equation is spent, and is widely used in airborne Interference calibration.The same year, Zink et al. to elevation susceptibility into
Row analysis, the error source baseline length of analyzing influence height reconstruction, baseline angle, phase, position of platform, oblique distance, last determines
Marking parameter is baseline length, inclination angle and phase, and is verified with SRTM-X data, is found to baseline length and baseline angle
Correct that precision is higher, and phase is taken second place, analysis main cause is that the sensitivity coefficient of baseline angle and phase is close, affects phase
The calculation accuracy of corrected value.2000, maximum likelihood method was introduced into interference scaling parameter estimation by Knedlik etc..The same year,
Mallorqui etc. carries out calibration processing to primary antenna position, time, phase, baseline length and inclination angle, analyzes control points layout
Influence to Matrix condition number.Be specifically divided into following 3 step: the DEM of first step simulation and control point are verified；Second step is used
Real terrain and control point data are verified；Third step carries out data verification with corner reflector point.Test result shows to control
Point, which lays situation, will affect the calibration results precision, it is indicated that it can be reduced Matrix condition number when scaling point is uniformly distributed in region,
Improve calculation accuracy.2001, Mallorqui compared the calibrating method based on phase and the calibration side based on Sensitivity equation
Method, simulation result show that the method based on Sensitivity equation is better than the method based on phase, but both when real data experiment
Without too big difference.Article is pointed out as much as possible calibrate more parameters in follow-up study simultaneously, improves calibration
Performance.
Domestic airborne InSAR calibration is started late, and 2004, doctor Wang Yanping was in Madsen Orthogonal Decomposition (Madsen
Orthogonal Decomposition, MOD) plane wave model is replaced with spherical wave model on the basis of Three-dimension Reconstruction Model,
Modified MOD (Modified Madsen Orthogonal Decomposition, MMOD) Three-dimension Reconstruction Model is given,
Analyzed on the basis of MMOD Three-dimension Reconstruction Model initial oblique distance, interferometric phase, baseline length, azimuth of director from the gun, pitch angle and
Influence of the yaw angle to reconstruction accuracy, and the problem excessive for sensitivity matrix conditional number, analyze scaling point distribution
To the restraint condition of the calibration results.2008, common vetch etc. had studied the airborne calibrating method based on positive side perceived model, it is indicated that calibration
Carrier aircraft attitude error should be ignored in terms of parameter selection, it is not calibrated.In view of the angle of roll of baseline angle and carrier aircraft is to be superimposed upon
Together, due to being corrected to the angle of roll during SAR imaging early period, therefore, it is considered that baseline angle be it is stable,
Calibration processing is not carried out to it.Last interferometric parameter includes absolute time delay, phase bias and baseline length.2009,
It opens common vetch etc. and analyzes time delay, interferometric phase, baseline, yaw angle, the sensitivity of pitch angle, the angle of roll and carrier aircraft speed again
Degree, having chosen baseline, baseline angle and phase is scaling parameter.2010 Nian Jin states are prosperous etc. to construct a kind of consideration interferometric phase, base
New departure is calibrated in the interference of line length and inclination angle, it is therefore an objective to for domestic airborne InSAR calibration service.2010, the analysis such as common vetch
Sensitivity matrix and GCPs lay between relationship, it is indicated that GCP, which is laid, should select in same orientation, distance to cloth at equal intervals
It puts.When distance to when laying at equal intervals, laying for orientation influences less conditional number.2013, Mao Yongfei etc. calibrate in plane
On the basis of, propose the thought from three-dimensional perspective joint calibration, i.e., by interferometric phase, while obtaining the elevation and warp of target
The correction parameter of the plan-position of latitude form.2015 flowers put forth energy to construct the interference about airborne InSAR Three-dimension Reconstruction Model
Calibration model, using baseline length and inclination angle, phase, oblique distance and Doppler parameter as scaling parameter.
In general, airborne InSAR calibration is developed so far existing very perfect flow chart of data processing, the building of calibration model
Current three-dimensional reconstruction equation is developed to from high equation is surveyed, and scaling parameter mainly includes baseline length and inclination angle, interferometric phase, tiltedly
Away from and Doppler equation.But be only applicable to traditional baseline with the representation method of baseline length and inclination angle and lay mode, work as baseline
When laying diversification of forms, existing calibration model no longer has versatility.
Summary of the invention
The object of the invention is that devising a kind of Airborne Interferometric Synthetic Aperture calibration to solve the above-mentioned problems
Method.
The present invention through the following technical solutions to achieve the above objectives:
A kind of Airborne Interferometric Synthetic Aperture calibrating method, comprising:
S1: observation Three-dimension Reconstruction Model determines the undetermined parameter in carrier aircraft coordinate system, including Y-direction baseline component by、Z
Orienting line component bz, interferometric phaseInitial oblique distance r0, Doppler frequency fdop；
S2: interference calibration model, three-dimensional reconstruction equation are established based on least squares equation are as follows:
In above formula, v indicates the vector in velocity vector direction；B indicates the baseline vector under the rectangular coordinate system in space of the earth's core；
S3: the sensitivity coefficient of interferometric parameter can be decomposed into three-dimensional coordinate to interferometric parameter by analyzing three-dimensional reconstruction model
Local derviation；
S4: regularization parameter is found using regularization method, establishes parameters revision model.
Further, it in S2, usesIt indicates spin matrix, three-dimensional reconstruction equation can be simplified are as follows:
In above formula, FxIndicate the error of the target point X-coordinate of three-dimensional reconstruction equation inference and the X-coordinate of realistic objective；FyTable
Show the error of the target point Y coordinate of three-dimensional reconstruction equation inference and the Y coordinate of realistic objective；FzIndicate three-dimensional reconstruction equation inference
Target point Z coordinate and realistic objective Z coordinate error；Sx、Sy、SzPrimary antenna phase center is respectively indicated in the earth's core space
X-coordinate, Y coordinate in rectangular coordinate system, Z coordinate； Px、Py、PzTarget point P is respectively indicated in the rectangular coordinate system in space of the earth's core
X-coordinate, Y coordinate, Z coordinate；rv、rp、rqRespectively indicate unit projection component of the visual direction amount in V axis, P axis, Q axis direction；
Further, the least squares equation in S2 are as follows:
Simplify are as follows: V=A Δ x-l
In formula, matrixIndicate a parameter to three-dimensional coordinate
Susceptibility；
V=[vx1 vy1 vz1 ... vxn vyn vzn], indicate parameter value to be corrected；
In formulaIt is in the three-dimensional coordinate being calculated according to each interferometric parameter, [Pxi Pyi Pzi] it is the three of control point offer
Tie up coordinate.
Further, the local derviation of interferometric parameter is indicated in S3 are as follows:
It further, include S31 in S3；
Local derviation is asked to indicate interferometric phase are as follows:
Local derviation is asked to indicate initial oblique distance are as follows:
To Doppler frequency fdopLocal derviation is asked to indicate are as follows:
It further, include S32 in S3, the calculating of VPQ coordinate system is related to the multiplication cross of baseline and speed, and baseline is sat by carrier aircraft
Mark system [Bx By Bz] to rectangular coordinate system in space [bx by bz] conversion formula are as follows:
[bx by bz]T=RmRf[Bx By Bz]T
It enablesAbove formula can be rewritten as:
The calculation that vector multiplication cross is decomposed are as follows:
VPQ coordinate system can rewrite matrix form by vector multiplication cross formula under airborne coordinate system are as follows:
Wherein
To ByLocal derviation is asked to indicate are as follows:
To BzLocal derviation is asked to indicate are as follows:
In above formula, B indicates the basic lineal vector of carrier aircraft coordinate system；The basic lineal vector of b representation space rectangular coordinate system； RmRfTable
Show carrier aircraft coordinate system to rectangular coordinate system in space transition matrix.
Further, in S4, the method for choosing regularization parameter is L-curve method.
The beneficial effects of the present invention are:
The new general airborne InSAR calibration model that the invention proposes a kind of based on Three-dimension Reconstruction Model, improves
InSAR extracts the reliability and precision of DEM, interferes in calibration model and is related to baseline, Doppler frequency, interferometric phase and oblique distance
Etc. parameters, and parameters differ greatly to the sensitivity coefficient of three-dimensional localization, and the morbid state of calibration matrix is interfered to restrict model
Calculation accuracy, in order to avoid sensitivity matrix morbid state causes calibration model to resolve the phenomenon that failing, present invention introduces be based on
The regularization method of ridge estimaion improves interference calibration model, it is ensured that under conditions of scaling parameter is more, obtains accurate ginseng
Number corrected value, obtains reliable solution of equation.
Detailed description of the invention
Fig. 1 is the curve graph of L in a kind of Airborne Interferometric Synthetic Aperture calibrating method of the present invention.
Specific embodiment
The present invention will be further explained below with reference to the attached drawings:
A kind of Airborne Interferometric Synthetic Aperture calibrating method, comprising:
S1: observation Three-dimension Reconstruction Model determines the undetermined parameter in carrier aircraft coordinate system, including Y-direction baseline component by、Z
Orienting line component bz, interferometric phaseInitial oblique distance r0, Doppler frequency fdop；
S2: interference calibration model, three-dimensional reconstruction equation are established based on least squares equation are as follows:
In above formula, v indicates the vector in velocity vector direction；B indicates the baseline vector under the rectangular coordinate system in space of the earth's core；
S3: the sensitivity coefficient of interferometric parameter can be decomposed into three-dimensional coordinate to interferometric parameter by analyzing three-dimensional reconstruction model
Local derviation；
S4: regularization parameter is found using regularization method, establishes parameters revision model.
Further, it in S2, usesIt indicates spin matrix, three-dimensional reconstruction equation can be simplified are as follows:
In above formula, FxIndicate the error of the target point X-coordinate of three-dimensional reconstruction equation inference and the X-coordinate of realistic objective；FyTable
Show the error of the target point Y coordinate of three-dimensional reconstruction equation inference and the Y coordinate of realistic objective；FzIndicate three-dimensional reconstruction equation inference
Target point Z coordinate and realistic objective Z coordinate error；Sx、Sy、SzPrimary antenna phase center is respectively indicated in the earth's core space
X-coordinate, Y coordinate in rectangular coordinate system, Z coordinate； Px、Py、PzTarget point P is respectively indicated in the rectangular coordinate system in space of the earth's core
X-coordinate, Y coordinate, Z coordinate；rv、rp、rqRespectively indicate unit projection component of the visual direction amount in V axis, P axis, Q axis direction；
Least squares equation in S2 are as follows:
Simplify are as follows: V=A Δ x-l
In formula, matrixIndicate a parameter to three-dimensional coordinate
Susceptibility；
V=[vx1 vy1 vz1 ... vxn vyn vzn], indicate parameter value to be corrected；
In formulaIt is in the three-dimensional coordinate being calculated according to each interferometric parameter, [Pxi Pyi Pzi] it is the three of control point offer
Tie up coordinate.
The local derviation of interferometric parameter is indicated in S3 are as follows:
In formula, X is to scaling parameter.
It include S31 in S3；
To interferometric phaseLocal derviation is asked to indicate are as follows:
Wherein, unit visual direction amountIt is rightDerivative it is identical, be
To initial oblique distance r0Local derviation is asked to indicate are as follows:
Wherein, unit visual direction amountTo r0Derivative are as follows:
In formulaIt will be according to InSAR platform difference, in airborne InSAR system
To Doppler frequency fdopLocal derviation is asked to indicate are as follows:
Wherein, unit visual direction amountTo doppler centroid fdopDerivative are as follows:
In Three-dimension Reconstruction Model, the calculating of VPQ coordinate system is related to the multiplication cross of baseline and speed, base in airborne InSAR system
Line is located under carrier aircraft coordinate system, and speed indicates under space coordinates, therefore baseline need to be transformed into rectangular coordinate system in space
Lower to calculate, baseline is by carrier aircraft coordinate system [Bx By Bz] to rectangular coordinate system in space [bx by bz] conversion formula are as follows:
[bx by bz]T=RmRf[Bx By Bz]T
It enablesAbove formula can be rewritten as:
The calculation that vector multiplication cross is decomposed are as follows:
VPQ coordinate system can rewrite matrix form by vector multiplication cross formula under airborne coordinate system are as follows:
Wherein
To ByLocal derviation is asked to indicate are as follows:
Above formula is divided into two parts, i.e., spin matrix is to ByDerivativeWith visual direction amount to ByDerivativeUnit view
VectorTo ByDerivativeAre as follows:
Wherein
It enablesIt is calculated according to the Matrix Formula of VPQ coordinate system under airborne coordinate system:
Wherein
To BzLocal derviation is asked to indicate are as follows:
To BzSeek the formula of local derviationIt indicates are as follows:
Wherein
Unit visual direction amountTo BzDerivativeIt indicates are as follows:
Wherein
In above formula, B indicates the basic lineal vector of carrier aircraft coordinate system；The basic lineal vector of b representation space rectangular coordinate system； RmRfTable
Show carrier aircraft coordinate system to rectangular coordinate system in space transition matrix.
As shown in Figure 1,
In S4, the method for choosing regularization parameter is L-curve method.
Assuming that existing equation:
Ax=b
When λ ∈ (0, ∞), and all the points (log | | xλ||,log||Axλ- b | |) curve of a monotone decreasing is constituted, it is bent
The shape of line is as shown in Figure 1, commonly referred to as L-curve.L-curve is the full curve under logarithmic scale about parameter lambda, and L is bent
The regularization parameter that line selection takes is corresponding parameter lambda at L-curve maximum curvature.Maximum curvature calculation formula are as follows:
Wherein u=| | xλ| |, v=| | Axλ- b | |, when k (λ) maximum, corresponding λ is optimized parameter.
It obtains λ and can obtain most to approach to fit with former ill posed equation and determine equation, obtain regularization thought non trivial solution:
X=(A+ λ I)-1b
In formula, I is unit matrix.
Claims (7)
1. a kind of Airborne Interferometric Synthetic Aperture calibrating method, it is characterised in that: the following steps are included:
S1: observation Three-dimension Reconstruction Model determines the undetermined parameter in carrier aircraft coordinate system, including Y-direction baseline component by, Z-direction base
Line component bz, interferometric phaseInitial oblique distance r0, Doppler frequency fdop；
S2: interference calibration model, three-dimensional reconstruction equation are established based on least squares equation are as follows:
In above formula, v indicates the vector in velocity vector direction；B indicates the baseline vector under the rectangular coordinate system in space of the earth's core.
S3: the sensitivity coefficient of interferometric parameter can be decomposed into three-dimensional coordinate to the inclined of interferometric parameter by analyzing three-dimensional reconstruction model
It leads；
S4: regularization parameter is found using regularization method, establishes parameters revision model.
2. a kind of Airborne Interferometric Synthetic Aperture calibrating method according to claim 1, it is characterised in that: the S2
In, it usesIt indicates spin matrix, three-dimensional reconstruction equation can be simplified are as follows:
In above formula, FxIndicate the error of the target point X-coordinate of three-dimensional reconstruction equation inference and the X-coordinate of realistic objective；FyIndicate three
Tie up the error of the Y coordinate of target point Y coordinate and realistic objective that Reconstructed equation derives；FzIndicate the mesh of three-dimensional reconstruction equation inference
The error of the Z coordinate of punctuate Z coordinate and realistic objective；Sx、Sy、SzPrimary antenna phase center is respectively indicated in the earth's core space right-angle
X-coordinate, Y coordinate in coordinate system, Z coordinate；Px、Py、PzX of the target point P in the rectangular coordinate system in space of the earth's core is respectively indicated to sit
Mark, Y coordinate, Z coordinate；rv、rp、rqRespectively indicate unit projection component of the visual direction amount in V axis, P axis, Q axis direction.
3. a kind of Airborne Interferometric Synthetic Aperture calibrating method according to claim 2, it is characterised in that: in the S2
Least squares equation are as follows:
Simplify are as follows: V=A Δ x-l
In formula, matrixIndicate a parameter to the sensitivity of three-dimensional coordinate
Degree；
V=[vx1 vy1 vz1 ... vxn vyn vzn], indicate parameter value to be corrected；
In formulaIt is in the three-dimensional coordinate being calculated according to each interferometric parameter, [Pxi Pyi Pzi] it is the three of control point offer
Tie up coordinate.
4. a kind of Airborne Interferometric Synthetic Aperture calibrating method according to claim 3, it is characterised in that: in the S3
The local derviation of interferometric parameter is indicated are as follows:
。
5. a kind of Airborne Interferometric Synthetic Aperture calibrating method according to claim 4, it is characterised in that: in the S3
Including S31；
Local derviation is asked to indicate interferometric phase are as follows:
Local derviation is asked to indicate initial oblique distance are as follows:
To Doppler frequency fdopLocal derviation is asked to indicate are as follows:
。
6. a kind of Airborne Interferometric Synthetic Aperture calibrating method according to claim 4, it is characterised in that: in the S3
Including S32, the calculating of VPQ coordinate system is related to the multiplication cross of baseline and speed, and baseline is by carrier aircraft coordinate system [Bx By Bz] straight to space
Angular coordinate system [bx by bz] conversion formula are as follows:
[bx by bz]T=RmRf[Bx By Bz]T
It enablesAbove formula can be rewritten as:
The calculation that vector multiplication cross is decomposed are as follows:
VPQ coordinate system can rewrite matrix form by vector multiplication cross formula under airborne coordinate system are as follows:
Wherein
To ByLocal derviation is asked to indicate are as follows:
To BzLocal derviation is asked to indicate are as follows:
In above formula, B indicates the basic lineal vector of carrier aircraft coordinate system；The basic lineal vector of b representation space rectangular coordinate system；RmRfIt indicates to carry
Transition matrix of the machine coordinate system to rectangular coordinate system in space.
7. a kind of Airborne Interferometric Synthetic Aperture calibrating method according to claim 1, it is characterised in that: the S4
In, the method for choosing regularization parameter is L-curve method.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112305510A (en) * | 2020-09-22 | 2021-02-02 | 江苏师范大学 | DEM matching-based synthetic aperture radar image geometric calibration method |
| CN117687028A (en) * | 2024-02-02 | 2024-03-12 | 中国科学院空天信息创新研究院 | Carrier platform three-dimensional positioning method based on interference SAR fringe pattern matching |
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| EP1959270A1 (en) * | 2007-02-15 | 2008-08-20 | Selex Sensors and Airborne Systems Limited | Improved synthetic aperture radar technique |
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| EP1959270A1 (en) * | 2007-02-15 | 2008-08-20 | Selex Sensors and Airborne Systems Limited | Improved synthetic aperture radar technique |
| CN103207388A (en) * | 2013-03-26 | 2013-07-17 | 中国科学院电子学研究所 | Method for calibrating airborne interference synthesis aperture radar (SAR) under squint condition |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112305510A (en) * | 2020-09-22 | 2021-02-02 | 江苏师范大学 | DEM matching-based synthetic aperture radar image geometric calibration method |
| CN117687028A (en) * | 2024-02-02 | 2024-03-12 | 中国科学院空天信息创新研究院 | Carrier platform three-dimensional positioning method based on interference SAR fringe pattern matching |
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