CN111398956B - Multi-base high-ratio space-borne SAR three-dimensional positioning RD equation optimization weight distribution method - Google Patents
Multi-base high-ratio space-borne SAR three-dimensional positioning RD equation optimization weight distribution method Download PDFInfo
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Abstract
The invention discloses a multi-base-height-ratio satellite-borne SAR three-dimensional positioning RD equation optimal weight allocation method, which is characterized in that an RD equation set under a multi-base-height-ratio condition is constructed based on an RD model; converting an RD equation set under the condition of multiple base height ratios into a matrix form by using a Gauss Newton method; calculating a normalization part and an empirical weighting part of a linear equation according to the matrix coefficients, the RD model and the earth ellipsoid equation, and determining a weight distribution matrix; calculating the increment of each iteration step according to the weight distribution matrix, and updating the geographic space coordinates of the target point; and repeating iteration updating until iteration meets the judgment and stop condition, and obtaining a final three-dimensional positioning result. The method can not only keep the direct relevance between the model and the error source and facilitate the subsequent error analysis, but also solve the problems of inaccuracy and instability under the condition of multi-base-height ratio.
Description
Technical Field
The invention relates to a three-dimensional positioning technology of a satellite-borne synthetic aperture radar image, in particular to a multi-base high-ratio satellite-borne SAR three-dimensional positioning RD equation optimization weight distribution method.
Background
Three-dimensional positioning and geocoding of each pixel point in a satellite-borne Synthetic Aperture Radar (SAR) image are important bases of SAR image application. The single SAR image needs the support of an earth equation and a DEM library when the three-dimensional position is obtained, and the multi-angle SAR image of the same scene is obtained by observing at two or more angles, the three-dimensional position of an image target point can be obtained by solving in a form of a simultaneous positioning equation, and the principle is shown in figure 1. Compared with two-scene SAR three-dimensional positioning, the multi-base-height SAR three-dimensional positioning formed by a plurality of SAR images has more positioning equations than satellite-borne SAR three-dimensional positioning, and the three-dimensional positioning precision is higher.
The SAR image geometric positioning model mainly comprises two main types, namely a strict geometric model and a universal geometric model. The rigorous geometric model mainly refers to the range-doppler location model (RD model) originally proposed by Brown [1Brown, w.e. "Applications of SEASAT SAR digital correlated imaging for sea ice dynamics". am geops Union Spring meeting.baltimore: ieee.vol.29.1981 ]. The general geometric Model mainly refers to a rational polynomial system digital-analog Model (RPC Model), which is extended from the optical geometric positioning field to the SAR field by Zhang et al [2Zhang, Guo, et. "Evaluation of the RPC Model for space borne SAR image." Photogrammetric Engineering & Remote sensing76.6(2010):727 + 733. ]. The RPC model has the advantages of independence from system parameters and uniform form, and is widely applied to three-dimensional positioning under the condition of the base-height ratio. However, the solution of the RPC model parameters firstly requires establishing geospatial coordinates and corresponding image coordinates of a plurality of virtual target points using a rigorous geometric model, and then fitting the model parameters of the RPC model according to the coordinates of the target points, that is, the RPC model is essentially a fitting of the rigorous geometric model, but the specific physical meaning of each parameter in the model is not clear at this time, so that the method loses the direct association between the model and an error source, and is difficult to perform error analysis directly through the RPC model. If the RPC model in the method is directly replaced by the RD model for solving, the distance equation of the RD model describes the distance between the phase center of the radar antenna and the target point at the imaging moment, and the Doppler equation describes the Doppler frequency shift phenomenon generated by the relative motion between the phase center of the radar antenna and the target point, the two expressions have completely different physical meanings, and simultaneously, the size of each parameter and the size of the error in the RD model are different greatly, so that the two equations are far apart in value and are not beneficial to equation solving, and particularly, the solving result is very unstable and the error is large under the condition of multi-base high ratio. In summary, the existing method is difficult to consider both the physical meaning of the model and the accuracy of the solution under the condition of multi-base high ratio.
Disclosure of Invention
The invention aims to provide a multi-base high-ratio satellite-borne SAR three-dimensional positioning RD equation optimal weight distribution method.
The technical solution for realizing the purpose of the invention is as follows: a multi-base-height ratio satellite-borne SAR three-dimensional positioning RD equation optimal weight distribution method comprises the following steps:
the first step is as follows: constructing an RD equation set under the condition of multiple base height ratios based on the RD model;
the second step is that: converting an RD equation set under the condition of multiple base height ratios into a matrix form by using a Gauss Newton method;
the third step: calculating a normalization part and an empirical weighting part of a linear equation according to the matrix coefficients, the RD model and the earth ellipsoid equation, and determining a weight distribution matrix;
the fourth step: calculating the increment of each iteration step according to the weight distribution matrix, and updating the geographic space coordinates of the target point;
the fifth step: and repeating the fourth step until the iteration meets the judgment and stop condition, and obtaining the final three-dimensional positioning result.
Compared with the prior art, the invention has the following remarkable advantages: 1) the RD equations are adopted to carry out multi-base high-ratio SAR three-dimensional positioning solution, the numerical dimensions of the linear equation set are changed by a normalization weight allocation method, compared with the traditional RD equations simultaneous solution, the solution error of the RD model under the condition of multi-base high-ratio is greatly reduced, and compared with the traditional RPC model method, the physical meaning of the model is kept and the solution accuracy is ensured; 2) an empirical weight matching part is introduced into the weight matching strategy, and the distance between the single-scene solution result and the average solution result is used for measuring the reliability of the corresponding equation of each scene image, so that the calculation precision is improved.
Drawings
Fig. 1 is a schematic diagram of three-dimensional positioning of a stereo SAR, wherein (a) is a schematic diagram of single-baseline three-dimensional positioning, and (b) is a schematic diagram of multi-baseline three-dimensional positioning.
FIG. 2 is a flow chart of a multi-base-height ratio space-borne SAR three-dimensional positioning RD equation optimization weight distribution method.
Detailed Description
The invention will be further described with reference to the accompanying drawings and specific embodiments.
As shown in fig. 2, the multi-base-to-high-ratio space-borne SAR three-dimensional positioning RD equation optimization weight allocation method includes the following steps:
the first step is as follows: constructing an RD equation set under the condition of multiple base height ratios based on the RD model;
according to the RD model, the following two equations can be listed for each SAR image:
wherein f isi1(X, Y, Z) and fi2(X, Y, Z) respectively represents a distance equation and a Doppler equation listed according to the ith scene image, (X, Y, Z) are geographical space coordinates of a target point to be solved, and (X)Si,YSi,ZSi) Satellite position, R, being the moment of imagingiTarget point slope distance, V, at the moment of imagingXi,VYi,VZiFor the velocity components of the satellite in three directions at the moment of imaging, fDiDoppler center frequency, λ, used for imagingiIs the wavelength of the radar transmitted signal.
Under the condition of multi-base height ratio, if there are n scenes, the equation system as the formula (2) can be listed, and the following is rewritten:
the second step is that: for the nonlinear equation set of the formula (2), a gauss-newton method can be used for iterative solution, and the iterative initial value can use a simultaneous solution result of an RD model of a single scene image and an earth ellipsoid equation. In each iteration, the above equation set is linearized, i.e. taylor expansion is performed, and its linear terms are taken and written in matrix form as follows:
A·x＝b(3)
wherein
Wherein (X)(k),Y(k),Z(k)) Is the target point geospatial coordinates in the kth iteration. (Δ X, Δ Y, Δ Z) represents the increment in the target point geospatial coordinates in three directions in the kth iteration.
The third step: calculating a weight distribution matrix
The weighting matrix P is a diagonal matrix with each diagonal element being Pj＝tjEjIt consists of two parts: normalized part tjAnd an empirically weighted part Ej。
The normalization part is the normalization of the current linear equation when A is ═ A1,A2,...,A2n]T,b＝[b1,b2,...,b2n]TThen t isjThe expression is as follows:
wherein A isj＝[aj1,aj2,aj3]，||Aj||2＝aj1 2+aj2 2+aj3 2. Therefore, the value of the normalization part is different in each step of iteration and is uniform to the numerical dimension of the current equation.
And the experience weighting part calculates the positioning result of the single-scene image of each scene image by a simultaneous RD model and an earth ellipsoid equation, wherein the simultaneous equation set is expressed as:
wherein R iseIs the mean equatorial radius of the earth, RpThe polar radius of the earth ellipsoid and h are the elevations of the target points, and when the elevations are unknown, the reference elevations of the area can be used for replacing the reference elevations.
Similarly, n positioning results generated by n scene images can be obtained. Let n positioning results corresponding to n scene images be
Then, an average value of the positioning results is obtained according to the n positioning results, as follows:
then, calculating the distance between the positioning result of each scene image and the mean value, and further obtaining the empirical weight distribution coefficient E of the distance equation and the Doppler equation corresponding to the ith scene image2i,E2i-1The following were used:
it can be seen that the empirical weighting term actually measures the reliability of the scene image information through the distance between the single scene image positioning result and the positioning average value, the reliability is lower when the distance between the single scene positioning result and the average positioning result is larger, and the reliability is higher when the distance is smaller. Moreover, the empirical weight distribution item is independent of the number of iteration steps and only needs to be calculated once.
Finally, the normalized part is multiplied by the empirical weighting part correspondingly to obtain the final weighting matrix P, which is expressed as the following formula (8).
In the above, i represents the image number, j represents the equation number, and the relationship between i and j is:
indicating rounding.
The fourth step: the increment of each iteration is calculated and the coordinates are updated as follows:
the above equation is an iterative formula after weighting, and it can be seen that since the normalization part is different in each iteration step, the weight matrix P is also dynamically adjusted in each iteration step to adapt to the jacobian matrices of different numerical dimensions.
The fifth step: when the iteration meets the judgment and stop condition, for example, the iteration number reaches the set maximum iteration number (such as 500) or the iteration increment | | X(k),Y(k),Z(k)If the | | is smaller than the set minimum value (such as 0.001), the iteration is finished, and the final three-dimensional positioning result is output.
According to the method, optimal weight allocation is carried out based on the RD model, so that the direct relevance between the model and an error source can be reserved, the subsequent error analysis is facilitated, and the problems of inaccuracy and instability in solution under the condition of multi-base high ratio are solved.
Examples
To verify the validity of the inventive scheme, the following simulation experiment was performed.
4 scenes of GF-3 satellite images observed at different angles are selected in the XX area, and the image information is shown in the following table 1. The 4 scene images all contain observation information of a certain corner reflector in the XX area, and the accurate geographic coordinates of the corner reflector are obtained through field measurement and are used as the basis for judging the positioning result.
TABLE 1 GF-3 satellite image information used in this experiment
| Numbering | Mode(s) | Angle of incidence |
| 1 | UFS | -43.28° |
| 2 | FS2 | 24.71° |
| 3 | UFS | -18.68° |
| 4 | UFS | 41.1° |
According to the method of the invention and the traditional methods of RD model multi-view simultaneous solution and RPC model multi-view simultaneous solution, 2-view, 3-view and 4-view images are selected to carry out three-dimensional positioning solution on the corner reflector. The results of the solution are shown in table 2. It can be seen that compared with the RPC model method, when the number of images is increased, i.e. the multi-base-height ratio is increased, the resolving error of the conventional RD model becomes very large and unstable. According to the method provided by the invention, the resolving error equivalent to the multi-scene simultaneous accuracy of the RPC model is obtained by optimizing the weight distribution under the condition of multi-base-to-height ratio. Compared with the conventional RPC model, the method has the advantages that the physical model of SAR positioning is reserved, the direct relation between the system parameters and the positioning result is established, and the influence of the system parameter errors on the positioning result is conveniently analyzed. Therefore, the method provided by the invention has the advantages of taking into account the two aspects of the physical meaning of the model and the accuracy of the resolving.
TABLE 2XX area actual data calculation error contrast (unit: meter)
| Two scenes | 1,2 | 1,3 | 1,4 | 2,3 | 2,4 | 3,4 |
| RPC model | 36.3060 | 31.3300 | 42.6376 | 28.0017 | 31.7564 | 32.7101 |
| RD model | 34.9670 | 30.8154 | 42.6167 | 28.2500 | 31.7321 | 32.6266 |
| The method of the invention | 36.4228 | 29.7951 | 41.6087 | 28.0709 | 31.7576 | 32.8642 |
| Three scenes | 1,2,3 | 1,2,4 | 1,3,4 | 2,3,4 | ||
| RPC model | 29.4950 | 40.6460 | 32.5352 | 31.9361 | ||
| RD model | 130.0138 | 213.5915 | 175.2347 | 182.7927 | ||
| The method of the invention | 29.8009 | 41.5410 | 31.7376 | 30.8332 | ||
| Four scenes | 1,2,3,4 | |||||
| RPC model | 32.1624 | |||||
| RD model | 185.7101 | |||||
| The method of the invention | 31.5459 |
Claims (6)
1. A multi-base-height ratio satellite-borne SAR three-dimensional positioning RD equation optimization weight distribution method is characterized by comprising the following steps:
the first step is as follows: constructing an RD equation set under the condition of multiple base height ratios based on the RD model;
the second step is that: converting an RD equation set under the condition of multiple base height ratios into a matrix form by using a Gauss Newton method;
the third step: calculating a normalization part and an experience weighting part of a linear equation according to the matrix coefficient, the RD model and the earth ellipsoid equation, and determining a weight distribution matrix;
the fourth step: calculating the increment of each iteration step according to the weight distribution matrix, and updating the geographic space coordinates of the target point;
the fifth step: and repeating the fourth step until the iteration meets the judgment and stop condition, and obtaining the final three-dimensional positioning result.
2. The multi-base-height-ratio space-borne SAR three-dimensional positioning RD equation optimal weight allocation method according to claim 1, characterized in that in the first step, the specific method for constructing the RD equation set under the condition of multi-base-height ratio is as follows:
according to the RD model, the following two equations can be listed for each SAR image:
wherein f isi1(X, Y, Z) and fi2(X, Y, Z) respectively represents a distance equation and a Doppler equation listed according to the ith scene image, (X, Y, Z) are geographical space coordinates of a target point to be solved, and (X)Si,YSi,ZSi) Satellite position, R, being the moment of imagingiTarget point slope distance, V, at the moment of imagingXi,VYi,VZiFor the velocity components of the satellite in three directions at the moment of imaging, fDiDoppler center frequency, λ, used for imagingiA wavelength of a signal transmitted for the radar;
under the condition of multiple base height ratio, if there are n scene images, the equation set as the formula (2) can be listed as follows:
3. the multi-base-height-ratio satellite-borne SAR three-dimensional positioning RD equation optimization weight distribution method according to claim 2, characterized in that in the second step, the RD equation set under the condition of multi-base-height ratio is converted into an iterative matrix form, that is, Taylor expansion is performed on the equation set, and a linear term is taken and written into the matrix form as follows:
A·Δx＝b (3)
wherein
Wherein (X)(k),Y(k),Z(k)) For the target point geospatial coordinates in the kth iteration, (Δ X, Δ Y, Δ Z) represents the increment of the target point geospatial coordinates in three directions.
4. The multi-base-high-ratio space-borne SAR three-dimensional positioning RD equation optimization weight distribution method as claimed in claim 3, wherein in the third step, the weight distribution matrix P is a diagonal matrix, and each diagonal element is Pj＝tjEjWherein t isjAs a normalizing part, EjAn experience weighting section;
the normalization part is the normalization of the current linear equation when A is ═ A1,A2,...,A2n]T,b＝[b1,b2,...,b2n]TThen t isjThe expression is as follows:
wherein A isj＝[aj1,aj2,aj3]，||Aj||2＝aj1 2+aj2 2+aj3 2；
Therefore, the value of the normalization part is different in each iteration step, and the numerical dimensions of the current equation are unified;
the empirical weighting part firstly calculates the positioning result of the single scene image of each scene image by a simultaneous RD model and an earth ellipsoid equation, and the simultaneous equation system is expressed as:
wherein R iseIs the mean equatorial radius of the earth, RpThe polar radius of an ellipsoid of the earth is adopted, h is the elevation of a target point, and when the elevation is unknown, the reference elevation of the area is used for replacing the target point;
let n positioning results corresponding to n scene images be
Then, an average value of the positioning results is obtained according to the n positioning results, as follows:
finally, calculating the distance between the positioning result of each scene image and the mean value, and further obtaining the empirical weight distribution coefficient E of the distance equation and the Doppler equation corresponding to the ith scene image2i,E2i-1The following were used:
it can be seen that the empirical weighting item actually measures the reliability of the scene image information through the distance between the single scene image positioning result and the positioning average value, the greater the distance between the single scene positioning result and the average positioning result, the lower the reliability, and the smaller the distance, the higher the reliability, and the empirical weighting item is unrelated to the number of iteration steps and only needs to be calculated once;
finally, the normalized part is multiplied by the empirical weighting part correspondingly to obtain the final weighting matrix P, which is expressed as the following formula (8).
In the above, i represents the image number, j represents the equation number, i andthe relationship of j is:
indicating rounding.
5. The multi-base-height-ratio space-borne SAR three-dimensional positioning RD equation optimization weight allocation method according to claim 4, wherein in the fourth step, the specific method for calculating the increment of each iteration step and updating the geographic space coordinates of the target point comprises the following steps:
the above equation is an iterative formula after weighting, and it can be seen that since the normalization part is different in each iteration step, the weight matrix P is also dynamically adjusted in each iteration step to adapt to the jacobian matrices of different numerical dimensions.
6. The multi-base-height-ratio satellite-borne SAR three-dimensional positioning RD equation optimization weight distribution method according to claim 1, characterized in that in the fifth step, the judgment and stop condition is that the iteration number reaches the set maximum iteration number or the iteration increment is smaller than the set minimum value.
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