CN104978761B - A kind of RPC models correction coefficient acquisition methods - Google Patents
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Abstract
The invention discloses a kind of RPC models correction coefficient acquisition methods, including Step 1: obtain RPC model coefficient solution matrixes according to mapping model and control point information；Step 2: the ridge estimaion based on L-curve；Step 3: carrying out composing modified iterative calculation to the ridge estimaion solution based on L-curve, the fixed number of iteration chooses wherein most accurate solution and is used as RPC model coefficient solutions；The present invention solves preliminary coefficient solution using the Biased estimator ridge estimaion based on L-curve, method Matrix condition number when to avoid directly resolving using least square method is too big, the coefficient matrix of normal equation morbid state is serious and leads to the defect of solution offset true value obtained, and assurance coefficient solution is stablized；The present invention is after using based on the ridge estimaion of L-curve, spectrum is carried out as iterative initial value to the coefficient solution acquired and corrects iteration, suitable initial value can greatly reduce iterations, and can effectively improve the accuracy of coefficient solution, both the speed for having improved solution in turn ensures the precision of solution.
Description
Technical field
The present invention relates to Radar Technology fields, specifically, referring to a kind of synthetic aperture radar (abbreviation SAR) slant-range image
The method that RPC (rational polynomial coefficient) model coefficient of geometric correction resolves.
Background technology
RPC models are a kind of geometrical models of general satellite remote-sensing image, are to make full use of satellite remote-sensing image subsidiary
Auxiliary parameter on the basis of, the broad sense sensor model that is fitted according to the stringent imaging geometry model of structure.It is reasonable
The theoretical of function model occurs very early, but when just having started to propose, because its in photogrammetric and remote sensing fields using less, therefore therewith
Relevant research is simultaneously few, and after IKONOS satellite launchs, RPC models receive more and more attention.International Photography measure with
Remote sensing association has set up the various aspects problems such as precision, the stability that task force is studied in relation to RPC models；RPC models are one
Imaging geometry model in kind mathematical meaning, RPC Model Independents can establish ground arbitrary system in sensor and platform
The relationship of system and image space, such as earth coordinates, geographic coordinate system, projected coordinate system etc..For synthetic aperture radar (SAR)
Image, when giving an appropriate number of control information, RPC models can obtain the very high fitting precision of tighter imaging model,
And it directly describes the correspondence between ground point and corresponding picpointed coordinate using mathematical model, and form is simple, calculates
It is efficient.Therefore the accurate quick resolving of RPC calibration model coefficients just has considerable meaning.
For RPC calibration models, when resolving coefficient using least square method, Matrix condition number is generally large, pathosis
It is more serious.The RPC coefficients solved at this time are inaccurate, cause to correct result and reality when carrying out geometric correction using RPC models
Position deviation is larger, seriously affects positioning accuracy.
Invention content
The purpose of the present invention is to solve the above problems, realize the energy under equation coefficient matrix pathosis serious situation
Enough coefficients for accurately obtaining RPC location models, the present invention are obtained according to practical point coordinates with corresponding SAR image picpointed coordinate first
RPC model coefficient solution matrixes；Then, RPC coefficients are calculated using the ridge estimaion based on L-curve, the ridge estimaion based on L-curve is
For a kind of improved Biased estimator of least-squares estimation the precision of equation solution is improved by improving the structure of method matrix
With stability to eliminate the pathosis of equation coefficient battle array, ensure that solution is stablized；Finally, it is by what is obtained based on L-curve ridge estimaion
Initial value of the number solution as Spectrum correction iteration, is iterated to calculate using Spectrum correction iteration, during search iteration when error minimum
Corresponding solution is used as RPC model coefficient solutions.
A kind of RPC models correction coefficient acquisition methods, including following steps：
Step 1: obtaining RPC model coefficient solution matrixes according to mapping model and control point information；
Step 2: solving ridge parameter k according to coefficient matrices A and disturbance term, ridge estimaion is carried out；
Step 3: carrying out composing modified iterative calculation to the ridge estimaion solution based on L-curve, the fixed number of iteration is chosen
Wherein most accurate solution is used as RPC model coefficient solutions；
The advantage of the invention is that：
(1) present invention is using the Biased estimator based on L-curve -- ridge estimaion solves preliminary coefficient solution, so as to avoid straight
The method Matrix condition number connect when being resolved using least square method is too big, and the coefficient matrix of normal equation morbid state is serious and causes the solution obtained inclined
The defect of true value is moved, assurance coefficient solution is stablized；
(2) present invention composes the coefficient solution acquired as iterative initial value after using based on the ridge estimaion of L-curve
Iteration is corrected, suitable initial value can greatly reduce iterations, and can effectively improve the accuracy of coefficient solution, both carry
The high speed solved, in turn ensures the precision of solution.
Description of the drawings
Fig. 1 be the present invention establish spatial grid schematic diagram；
Fig. 2 is the simulating scenes schematic diagram of the present invention；
Fig. 3 is the present invention based on L-curve solution ridge parameter schematic diagram；
Fig. 4 is the Spectrum correction iteration schematic diagram of the present invention；
Fig. 5 is flow chart of the method for the present invention.
Specific implementation mode
Below in conjunction with drawings and examples, the present invention is described in further detail.
The present invention is a kind of RPC models correction coefficient acquisition methods, including following steps：
Step 1: obtaining RPC model coefficient solution matrixes according to mapping model and control point information.
Specially：
(a) spatial grid is established.As shown in Figure 1, for scene areas, image regular grid m × n, each net are initially set up
Point is uniformly distributed on image, and then space delamination establishes a three-dimensional article grid, and grid covers the sky on dimensional topography surface
Between range, elevation hierarchy number layer.
(b) control point is obtained.The picture point for corresponding to each site in spatial grid is calculated according to the tight imaging model of SAR image
Coordinate.There is N=m × n × layer control point at this time, by the tight imaging model of SAR image, using range Doppler algorithm
Calculate corresponding each mesh point (bi,li,hi) corresponding to the picpointed coordinate (r of SAR imagei,si), wherein (i=1,2 ..., N).
(c) normalized.By ground mesh point coordinate (bi,li,hi) and picpointed coordinate (ri,si) make normalizing according to the following formula
Change is handled, between standard to -0.5 and 0.5.
Obtain standardized ground coordinate (Bi,Li,Hi) and standardized SAR image coordinates (xi,yi)。bmax、lmax、
hmax、rmax、smaxRespectively control point longitude, latitude, height, maximum value from pixel distance to, orientation coordinate；bmin、lmin、
hmin、rmin、sminRespectively control point longitude, latitude, height, minimum value from pixel distance to, orientation coordinate
(d) according to control point ground coordinate (Bi,Li,Hi) and SAR image image coordinate (xi,yi) obtain solving coefficient matrix
A and observing matrix S.Using three rank RPC models, totally 78 parameters to be solved.A is the matrix of 2N × 78, and S is the array of 2N × 1,
The array that the coefficient X of demand solution is 78 × 1.
Coefficient matrices A is as follows：
SAR image picpointed coordinate battle array --- observing matrix S：
S=[y1 y2 … yn x1 x2 … xn]T (3)
Step 2: solving ridge parameter k according to coefficient matrices A and disturbance term, ridge estimaion is carried out.It adds and disturbs on observing matrix
Dynamic item obtains suitable ridge parameter using L-curve method, and obtaining coefficient using ridge estimaion method has inclined solution.
Specially：
(a) according to formula (4), disturbance term Δ, observing matrix S after being scrambled are added on observing matrix Sd, wherein Δ take
From the random number of normal distribution.For spaceborne model, variances sigma is added2It is 2 × 10-8Disturbance term.
Sd=S+ Δs (4)
(b) the determination ridge parameter of L-curve.L-curve solves the mathematical method that ridge parameter is comparative maturity, uses DTU herein
The regularization tool regtools for the Matlab language that university provides is resolved, and uses code
[U,sm, V] and=csvd (A)；
K=l_curve (U, sm,Sd)；
Obtained value k is L-curve curvature maximum, i.e. ridge parameter.
(c) it brings this ridge parameter value k into following formulas, carries out ridge estimaion：
It obtainsTo have inclined solution based on L-curve ridge estimaion.Wherein, the unit matrix that I is 78 × 78.
Step 3: carrying out composing modified iterative calculation to the ridge estimaion solution based on L-curve, the fixed number of iteration is chosen
Wherein most accurate solution is used as RPC model coefficient solutions.
Specially：
(a) first time iteration enables iterations k=1, has inclined solution by what the ridge estimaion based on L-curve obtainedAs repeatedly
The initial value in generationI.e.Bring following formula into：
Indicate the estimated value after kth time iteration.
(b) solution is obtainedThe coefficient solution of iteration is corrected as RPC models kth time spectrum；
(c) precision of control point is calculated.For all control points, corresponding each picpointed coordinate is calculated using this RPC model, is pressed
Formula (7) carries out renormalization, the actual image point coordinate (r ' that will be obtainedi,s′i) with the corresponding picpointed coordinate of tight imaging model
(ri,si) compare, planar pixel max value of error and planar pixel error mean square root are obtained, the coefficient of the secondary iteration result is recorded
Solution and pixel error；
Wherein, (r 'i,s′i) the actual image point coordinate that calculates of coefficient is taken off thus RPC model solutions.
(e) it enables k values add 1, next iteration is carried out, using the coefficient solution of last iteration as the iterative initial value of current iterationBring formula (6) into；
(f) (b)~(e) is repeated, until iteration M times；
(g) the coefficient solution solved as RPC models that planar pixel error is minimum in M iteration is selected.
Finally, the method is obtained into geometric correction of the RPC models for whole picture SAR images, you can realize and be based on RPC models
SAR image quick high accuracy geometric correction.
Embodiment：
A kind of RPC models correction coefficient calculating method of the present invention, specific embodiment are：
Step 1: writing out RPC model coefficient solution matrixes according to mapping model：
(a) spatial grid is established.Simulating scenes aircraft altitude 500Km as shown in Figure 2, using 45 ° of positive side view pitch angle,
Scene size is 4000m × 6000m, azimuth resolution 1m, range resolution 1.5m, first with certain grid size
11 × 11 establish image regular grid, and each site is uniformly distributed on image, and then space delamination establishes a three-dimensional article grid
Net, grid cover the spatial dimension on dimensional topography surface, and elevation hierarchy number layer is 11.
(b) control point is obtained.Each site in corresponding spatial grid, which is calculated, according to tight imaging model calculates corresponding picture
Point coordinates.Having N=1331 control point at this time, pass through the tight imaging model of SAR image --- range Doppler algorithm calculates
Corresponding each mesh point (bi,li,hi) corresponding to the picpointed coordinate (r of SAR imagei,si), wherein (i=1,2 ..., 1331).
(d) normalized.By topocentric coordinates (bi,li,hi) and picpointed coordinate (ri,si) normalized according to formula (1)
Processing, between standard to -0.5 and 0.5.Obtain standardized ground coordinate (Bi,Li,Hi) and standardized SAR image coordinates
(xi,yi), wherein (i=1,2 ..., 1331).
(e) it is write out according to (2), (3) formula form according to RPC models and control point information and solves coefficient matrices A and observation square
Battle array S.Using three rank RPC models, totally 78 parameters to be solved.The matrix that A is 2662 × 78, the array that S is 2662 × 1, demand
The array that the coefficient X of solution is 78 × 1.
Step 2: solving ridge parameter k according to coefficient matrices A and disturbance term, ridge estimaion is carried out.Disturbance is added on observing matrix
, suitable ridge parameter is obtained using L-curve method, obtaining coefficient using ridge estimaion method has inclined solution：
(a) according to formula (4), disturbance term Δ, observing matrix S after being scrambled are added on observing matrix Sd, wherein Δ take
From the random number of normal distribution.For spaceborne model, variances sigma is added2It is 2 × 10-8Disturbance term.
(b) the determination ridge parameter of L-curve.L-curve solves the mathematical method that ridge parameter is comparative maturity, uses DTU herein
The regularization tool regtools for the Matlab language that university provides is resolved, and uses code
[U,sm, V] and=csvd (A)；
K=l_curve (U, sm,Sd)；
L-curve figure is as shown in figure 3, obtain being ridge parameter at maximum curvature, ridge parameter k=1.4223 × 10 at this time-6。
(c) it brings this ridge parameter value k into formulas (5), carries out ridge estimaion.
It obtainsInclined solution is as had based on L-curve ridge estimaion.
Step 3: carrying out composing modified iterative calculation to the ridge estimaion solution based on L-curve, the fixed number of iteration is chosen
Wherein most accurate solution is RPC model coefficient solutions.Specially：
(a) first time iteration enables iterations k=1, has inclined solution by what the ridge estimaion based on L-curve obtainedAs repeatedly
The initial value in generationI.e.Bring formula (6) into
(b) solution is obtainedThe coefficient solution of iteration is corrected as RPC models kth time spectrum；
(c) precision of control point is calculated.For all control points, corresponding each picpointed coordinate is calculated using this RPC model, is pressed
Formula (7) carries out renormalization, the actual image point coordinate (r ' that will be obtainedi,s′i) with the corresponding picpointed coordinate of tight imaging model
(ri,si) compare, planar pixel max value of error and planar pixel error mean square root are obtained, the coefficient of the secondary iteration result is recorded
Solution and pixel error；
(e) it enables k values add 1, next iteration is carried out, using the coefficient solution of last iteration as the iterative initial value of current iterationBring formula (6) into；
(f) (b)~(e) is repeated, until iteration 120 times；
(g) the coefficient solution solved as RPC models that planar pixel error is minimum in 120 iteration is selected.
Iteration result is as shown in figure 4, minimum value occurs in planar pixel error when iteration 27 times, maximum planes picture at this time
Plain error is 7.463 × 10-5(pixel), planar pixel error mean square root are 8.936 × 10-6(pixel).
The coefficient solution of RPC models at this time is：
| Parameter | Parameter value | Parameter | Parameter value | Parameter | Parameter value | Parameter | Parameter value |
| a1 | 2.4728×10-10 | b1 | 1.0 | c1 | -0.00044 | d1 | 1.0 |
| a2 | 1.0000 | b2 | -7.0555×10-9 | c2 | 9.0781×10-10 | d2 | -1.6590×10-8 |
| a3 | 7.7819×10-9 | b3 | 6.4544×10-9 | c3 | 0.85726 | d3 | -0.00099 |
| a4 | 4.3161×10-9 | b4 | -2.1382×10-9 | c4 | -0.14273 | d4 | -0.00049 |
| a5 | -2.5335×10-8 | b5 | 0.001728 | c5 | 4.8404×10-8 | d5 | -9.6292×10-5 |
| a6 | 2.5194×10-9 | b6 | -0.001894 | c6 | 0.00171 | d6 | 1.9935×10-5 |
| a7 | -1.2790×10-9 | b7 | -0.001182 | c7 | 0.000141 | d7 | 4.6279×10-5 |
| a8 | 1.0518×10-8 | b8 | -6.4026×10-9 | c8 | -2.2383×10-8 | d8 | -4.4966×10-7 |
| a9 | 1.8197×10-10 | b9 | 2.9093×10-9 | c9 | 2.2712×10-9 | d9 | -1.9204×10-6 |
| a10 | 7.3325×10-9 | b10 | -8.9065×10-9 | c10 | 0.000578 | d10 | -0.00016 |
| a11 | 0.00172 | b11 | -3.3797×10-8 | c11 | -2.4977×10-8 | d11 | 2.6525×10-8 |
| a12 | -1.5333×10-8 | b12 | 1.0204×10-7 | c12 | -9.2948×10-7 | d12 | -3.855×10-7 |
| a13 | -2.5409×10-8 | b13 | -3.5426×10-8 | c13 | -6.5783×10-6 | d13 | 2.0196×10-8 |
| a14 | 8.3624×10-9 | b14 | -1.0464×10-7 | c14 | -8.2542×10-5 | d14 | 3.4465×10-7 |
| a15 | -2.9601×10-9 | b15 | 3.6440×10-8 | c15 | 1.3744×10-5 | d15 | 1.7869×10-7 |
| a16 | -0.001894 | b16 | -2.7518×10-8 | c16 | -3.6686×10-7 | d16 | -1.1218×10-7 |
| a17 | 1.4497×10-8 | b17 | 5.1330×10-8 | c17 | -0.00015 | d17 | 4.9148×10-7 |
| a18 | -0.001182 | b18 | -6.2083×10-8 | c18 | 2.9018×10-7 | d18 | 4.8155×10-8 |
| a19 | -2.1027×10-8 | b19 | 4.335×10-8 | c19 | 6.3651×10-5 | d19 | 2.6649×10-7 |
| a20 | 8.2075×10-9 | b20 | -7.0852×10-9 | c20 | -1.5918×10-6 | d20 | -3.0417×10-9 |
Wherein, a1,a1,…a20、b1,b1,…b20Respectively molecule of the distance to pixel coordinate RPC models, denominator coefficients；
c1,c1,…c20、d1,d1,…d20The respectively molecule of orientation pixel coordinate RPC models, denominator coefficients
Finally, the RPC models of this coefficient solution can be used for the SAR image geometric correction of this scene, you can realization to be based on
The quick high accuracy geometric correction of RPC models.
Present invention is generally directed to satellite-borne SAR image RPC model geometric correction coefficient solution process, realize in equation coefficient square
The coefficient of RPC location models can be accurately obtained under battle array pathosis serious situation.First according to practical point coordinates and corresponding SAR
Image picpointed coordinate writes out RPC model coefficient solution matrixes；Then, ridge parameter is calculated using L-curve method, ridge estimaion calculates
RPC coefficients have inclined solution；Finally, it is iterated to calculate using Spectrum correction iteration, it is corresponding when error minimum during search iteration
Solution is used as coefficient solution, to obtain the most accurate solution of RPC coefficients.Based on the ridge estimaion of L-curve for least-squares estimation
A kind of improved Biased estimator improves the precision and stability of equation solution to the side of elimination by improving the structure of method matrix
The pathosis of journey factor arrays ensures that solution is stablized, gives one suitable initial value of Spectrum correction iteration, both improved the speed of solution
Degree, in turn ensures the precision of solution；The experiment proves that the correctness of this method, and can make control point location under the spaceborne model
Precision reaches 10-5Magnitude.
Claims (1)
1. a kind of RPC models correction coefficient acquisition methods, including following steps：
Step 1: obtaining RPC model coefficient solution matrixes according to mapping model and control point information；
Specially：
(a) spatial grid is established；
For scene areas, image regular grid m × n is initially set up, each site is uniformly distributed on image, then space delamination
Three-dimensional article grid is established, grid covers the spatial dimension on dimensional topography surface, elevation hierarchy number layer；
(b) control point is obtained；
Equipped with N=m × n × layer control point, by the tight imaging model of SAR image, using the resolving of range Doppler algorithm
Go out corresponding each mesh point (bi,li,hi) corresponding to the picpointed coordinate (r of SAR imagei,si), wherein i=1,2 ..., N；
(c) normalized；
By ground mesh point coordinate (bi,li,hi) and picpointed coordinate (ri,si) make normalized, standard to -0.5 according to the following formula
And between 0.5；
Obtain standardized ground coordinate (Bi,Li,Hi) and standardized SAR image coordinates (xi,yi)；bmax、lmax、hmax、
rmax、smaxRespectively control point longitude, latitude, height, maximum value from pixel distance to, orientation coordinate；bmin、lmin、hmin、
rmin、sminRespectively control point longitude, latitude, height, minimum value from pixel distance to, orientation coordinate
(d) according to control point ground coordinate (Bi,Li,Hi) and SAR image image coordinate (xi,yi) obtain solve coefficient matrices A and
Observing matrix S；
Using three rank RPC models, totally 78 parameters to be solved；A is the matrix of 2N × 78, and L is the array of 2N × 1, demand solution
The array that coefficient X is 78 × 1；
Coefficient matrices A is as follows：
Observing matrix S：
S=[y1 y2 … yn x1 x2 … xn]T (3)
Step 2: solving ridge parameter k according to coefficient matrices A and disturbance term, ridge estimaion is carried out；
Specially：
(a) according to formula (4), disturbance term Δ, observing matrix S after being scrambled are added on observing matrix Sd, wherein Δ obey normal state
The random number of distribution adds variances sigma for spaceborne model2It is 2 × 10-8Disturbance term；
Sd=S+ Δs (4)
(b) the ridge parameter k of L-curve is determined；
(c) it brings this ridge parameter value k into following formulas, carries out ridge estimaion：
It obtainsTo have inclined solution based on L-curve ridge estimaion；Wherein, the unit matrix that I is 78 × 78；
Step 3: carrying out composing modified iterative calculation to the ridge estimaion solution based on L-curve, the fixed number of iteration is chosen wherein
Most accurate solution is used as RPC model coefficient solutions；
Specially：
(a) first time iteration enables iterations k=1, has inclined solution by what the ridge estimaion based on L-curve obtainedAs iteration
Initial valueI.e.Bring following formula into：
Indicate the estimated value after kth time iteration；
(b) solution is obtainedThe coefficient solution of iteration is corrected as RPC models kth time spectrum；
(c) precision of control point is calculated；For all control points, corresponding each picpointed coordinate is calculated using RPC models, by formula (7)
Carry out renormalization, the actual image point coordinate (r ' that will be obtainedi,s′i) picpointed coordinate (r corresponding with tight imaging modeli,si)
Compare, obtain planar pixel max value of error and planar pixel error mean square root, record the secondary iteration result coefficient solution and
Pixel error；
Wherein, (r 'i,s′i) it is the actual image point coordinate that RPC model solutions calculate；
(e) it enables k values add 1, next iteration is carried out, using the coefficient solution of last iteration as the iterative initial value of current iteration
Bring formula (6) into；
(f) (b)~(e) is repeated, until iteration M times；
(g) the coefficient solution solved as RPC models that planar pixel error is minimum in M iteration is selected；
Geometric correction of the RPC models for whole picture SAR images will be obtained, realizes the SAR image quick high accuracy based on RPC models
Geometric correction.
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Application publication date: 20151014 Assignee: SPACETY Co.,Ltd. (CHANGSHA) Assignor: BEIHANG University Contract record no.: X2023990000783 Denomination of invention: A Method for Obtaining Correction Coefficients of RPC Models Granted publication date: 20180824 License type: Common License Record date: 20230829 |