CN111366925A - SAR offset two-dimensional deformation time sequence calculation method and system - Google Patents

SAR offset two-dimensional deformation time sequence calculation method and system Download PDF

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CN111366925A
CN111366925A CN202010229326.7A CN202010229326A CN111366925A CN 111366925 A CN111366925 A CN 111366925A CN 202010229326 A CN202010229326 A CN 202010229326A CN 111366925 A CN111366925 A CN 111366925A
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dimensional deformation
time sequence
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slc image
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CN111366925B (en
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赵超英
王宝行
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Changan University
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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
    • 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
    • G01S13/9027—Pattern recognition for feature extraction

Abstract

The invention discloses a method and a system for calculating a two-dimensional deformation time sequence of SAR offset, which comprises the following steps: acquiring SLC images of a ground surface area to be monitored at different time points, and forming a group of SLC image pairs by the SLC images corresponding to every two different time points to obtain a plurality of groups of SLC image pairs; solving two-dimensional deformation data L of multiple SLC image pairs1(ii) a Establishing a complex linear model of the deformation of each monitoring point of the earth surface area to be monitored; solving to obtain a two-dimensional deformation time sequence X according to a minimization criterion of a complex number model1Estimated value X of(1)And X1Co-factor matrix of
Figure DDA0002428754050000011
And dynamically updating the two-dimensional deformation time sequence of the earth surface area to be monitored. According to the method, the complex model is established, the two-dimensional deformation time sequence is solved by adopting the sequential least square method, the deformation corresponding to each scene data can be dynamically updated under the condition of not losing the precision, the deformation time sequence is dynamically obtained at high precision, and meanwhile, the solution is carried outAnd the dynamic updating effect is good when a two-dimensional deformation sequence is calculated.

Description

SAR offset two-dimensional deformation time sequence calculation method and system
Technical Field
The invention belongs to the technical field of SAR dynamic data processing, relates to the field of two-dimensional deformation time sequence calculation, and particularly relates to a SAR offset two-dimensional deformation time sequence calculation method and system.
Background
With the development of earth observation technology, Synthetic Aperture Radar (SAR) technology has been widely applied to monitoring deformation such as earthquake, volcano, glacier, ground subsidence and landslide, and becomes one of the important technologies in the modern earth science.
In the aspect of time sequence SAR two-dimensional deformation estimation, at first, a cross-correlation technology is adopted for obtaining two-dimensional deformation in domestic and foreign researches, then a deformation time sequence is calculated by adopting least square, and distance direction and direction are respectively calculated. How to dynamically update the two-dimensional deformation time sequence of the newly observed data of each scene one by one with high precision does not yet come up with a feasible scheme, and particularly, the requirement is more urgent along with the shortening of the revisit period of the SAR data. Therefore, the existing SAR offset deformation time sequence estimation method cannot meet the requirement of dynamic disaster monitoring.
Disclosure of Invention
Aiming at the defects and shortcomings of the prior art, the invention provides a SAR offset two-dimensional deformation time sequence calculation method and a system, and solves the problem that the existing SAR offset deformation time sequence estimation method cannot meet the requirement of dynamic disaster monitoring.
In order to achieve the purpose, the invention adopts the following technical scheme:
a SAR offset two-dimensional deformation time sequence calculation method comprises the following steps:
step 1, acquiring SLC images of a ground surface area to be monitored at different time points, wherein the SLC images corresponding to every two different time points form a group of SLC image pairs to obtain a plurality of groups of SLC image pairs; solving two-dimensional deformation data L of multiple SLC image pairs1；
Step 2, establishing a complex linear model of the deformation of each monitoring point of the earth surface area to be monitored:
A1X1＝L1(1)
Figure BDA0002428754030000021
in the formula, A1Representing a design matrix; x1Representing a two-dimensional deformation time sequence of the monitoring points; m represents SLThe number of pairs of C images; n represents the number of SLC images;
step 3, solving according to the minimization criterion of the complex modulus to obtain a two-dimensional deformation time sequence X1Estimated value X of(1)And X1Co-factor matrix of
Figure BDA0002428754030000022
Step 4, dynamically updating the two-dimensional deformation time sequence of the earth surface area to be monitored:
step 4.1, when a new SLC image is added, the new SLC image is respectively grouped with the SLC image in the step 1 to form a plurality of groups of SLC images; solving two-dimensional deformation data L of multiple SLC image pairs2；
Step 4.2, establishing the following complex linear model for the deformation of each monitoring point of the earth surface area to be monitored:
Figure BDA0002428754030000023
in the formula, A2And B both represent a design matrix; n' represents the number of the updated SLC images; m' represents the number of SLC image pairs after update; x(2)Representing the updated two-dimensional deformation time sequence; y represents the accumulated deformation of the added SLC image at the corresponding time point;
step 4.3, solving by using a formula (4) to obtain X(2)And a combination of Y and Y, wherein,
Figure BDA0002428754030000031
in the formula, JxIs a gain matrix, QJIs X(2)A co-factor matrix of; b isTA transposed matrix representing B; qJ -1Represents QJThe inverse matrix of (d); p2Represents L2A priori information of.
Specifically, in step 1, the two-dimensional deformation data L of multiple SLC image pairs is obtained by using the intensity cross-correlation coefficient maximization method1。
Specifically, the step 3 specifically comprises: solving the two-dimensional deformation time sequence X of the monitoring points according to the formula (2) and the formula (3)1Estimated value X of(1)And X1Co-factor matrix of
Figure BDA0002428754030000032
X(1)＝(A1 TP1A1)-1A1 TP1L1(2)
Figure BDA0002428754030000033
In the formula, A1Representing a design matrix; m represents the number of SLC image pairs; n represents the number of SLC images; p1Represents L1Prior information of (2); a. the1 TIs represented by A1The transposed matrix of (2).
Specifically, in step 4.1, the two-dimensional deformation data L of multiple SLC image pairs is obtained by using the intensity cross-correlation coefficient maximization method2。
The invention also discloses a SAR offset two-dimensional deformation time sequence calculation system, which comprises:
the SLC image registration module is used for acquiring SLC images of the ground surface area to be monitored at different time points, and the SLC images corresponding to every two different time points form a group of SLC image pairs to obtain a plurality of groups of SLC image pairs; a two-dimensional deformation data acquisition module for obtaining two-dimensional deformation data L of multiple SLC image pairs1；
The stock data complex linear model establishing module is used for establishing a complex linear model of the deformation of each monitoring point of the earth surface area to be monitored:
A1X1＝L1(1)
Figure BDA0002428754030000041
in the formula, A1Representing a design matrix; x1Two indicating a monitoring pointA time sequence of dimensional deformation; m represents the number of SLC image pairs; n represents the number of SLC images;
the inventory data two-dimensional deformation time sequence acquisition module is used for solving by adopting a minimization criterion of a complex number module to obtain a two-dimensional deformation time sequence X1Estimated value X of(1)And X1Co-factor matrix of
Figure BDA0002428754030000042
Two-dimensional deformation time series update module includes:
the updated SLC image registration module is used for respectively grouping a new SLC image with the SLC image in the SLC image registration module to form a plurality of groups of SLC image pairs when a new SLC image is added; the updated two-dimensional deformation data acquisition module is used for obtaining the two-dimensional deformation data L of a plurality of groups of SLC image pairs2；
The updating data complex linear model establishing module is used for establishing the following complex linear model for the deformation of each monitoring point of the earth surface area to be monitored:
Figure BDA0002428754030000043
Figure BDA0002428754030000051
in the formula, A2And B both represent a design matrix; n' represents the number of the updated SLC images; m' represents the number of SLC image pairs after update; x(2)Representing the updated two-dimensional deformation time sequence; y represents the accumulated deformation of the added SLC image at the corresponding time point;
an update data two-dimensional deformation time sequence acquisition module for obtaining X by solving with a formula (4)(2)And a combination of Y and Y, wherein,
Figure BDA0002428754030000052
in the formula, JxIs a gain matrix，QJIs X(2)A co-factor matrix of; b isTA transposed matrix representing B; qJ -1Represents QJThe inverse matrix of (d); p2Represents L2Prior information of (2);
specifically, in the two-dimensional deformation data acquisition module, the two-dimensional deformation data L of a plurality of SLC image pairs is obtained by adopting an intensity cross-correlation coefficient maximization method1。
Specifically, the inventory data two-dimensional deformation time sequence acquisition module is specifically used for solving the two-dimensional deformation time sequence X of the monitoring point according to the formula (2) and the formula (3)1Estimated value X of(1)And X1Co-factor matrix of
Figure BDA0002428754030000053
X(1)＝(A1 TP1A1)-1A1 TP1L1(2)
Figure BDA0002428754030000054
In the formula, A1Representing a design matrix; m represents the number of SLC image pairs; n represents the number of SLC images; p1Represents L1Prior information of (2); a. the1 TIs represented by A1The transposed matrix of (2).
Specifically, in the updated SLC image registration module, a method of maximizing an intensity cross-correlation coefficient is used to obtain two-dimensional deformation data L of a plurality of SLC image pairs2。
Compared with the prior art, the invention has the beneficial effects that:
according to the method, the complex model is established, the two-dimensional deformation time sequence is solved by adopting the sequential least square method (namely the step 4.3), the deformation corresponding to each scene data can be dynamically updated under the condition of not losing the precision, the deformation time sequence is dynamically obtained at high precision, the two-dimensional deformation sequence is solved at the same time, and the dynamic updating effect is good.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a comparison of simulation results of the method of the present invention and a conventional least squares method, wherein (A) is an azimuth deformation time series without noise, (B) is a distance time series without noise, (C) is an azimuth time series with noise, and (D) is a distance time series with noise.
Fig. 3 is a real data coverage area of a UAV image provided by an embodiment of the present invention.
Fig. 4 is a graph of SAR offset configuration versus a vertical baseline and a time baseline in an embodiment of the present invention. Where the solid line represents the SLC image pair of archived data to calculate the offset and the dashed line represents the updated SLC image pair to calculate the offset.
FIG. 5 is a diagram illustrating dynamic estimation of real data two-dimensional time series deformation in an embodiment of the present invention; wherein (A) is a distance deformation time sequence, (B) is an orientation deformation time sequence, (C) is a difference value of the distance deformation time sequence and a traditional least square time sequence, and (D) is a difference value of the orientation deformation time sequence and the traditional least square time sequence.
FIG. 6 is a comparison graph of the dynamic deformation estimation of a certain monitoring point obtained by the least square method and the method of the present invention, wherein (A) is the distance deformation and (B) is the azimuth deformation.
The invention is described in detail below with reference to the drawings and the detailed description.
Detailed Description
In the present invention, a scene of SLC images is acquired at a time.
The invention discloses a SAR offset two-dimensional deformation calculation method, a flow chart of which is shown in figure 1, and the method specifically comprises the following steps:
step 1, acquiring SLC images of a ground surface area to be monitored at different time points, and generating a plurality of groups of SLC images by setting a time base line and a space base line, wherein the SLC images corresponding to every two different time points form a group of SLC image pairs to obtain a plurality of groups of SLC image pairs;
then, multiple groups are obtainedTwo-dimensional deformation data L of SLC image pair1(each SLC image corresponds to a two-dimensional deformation, preferably, the two-dimensional deformation data L of a plurality of SLC image pairs is obtained by adopting an intensity cross-correlation coefficient maximization method1. Two-dimensional deformation refers to the deformation of the offset in the distance and azimuth directions.
Step 2, a plurality of monitoring points are arranged on the surface area to be monitored and based on two-dimensional deformation data L1And establishing the following complex linear model for the deformation of each monitoring point:
A1X1＝L1(1)
Figure BDA0002428754030000071
in the formula, A1Representing a design matrix; x1Representing a two-dimensional deformation time sequence of the monitoring points; m represents the number of SLC image pairs; n represents the number of SLC images;
step 3, solving according to the minimization criterion of the complex modulus to obtain a two-dimensional deformation time sequence X1Estimated value X of(1)And X1Co-factor matrix of
Figure BDA0002428754030000072
The method specifically comprises the following steps:
one monitoring point corresponds to one two-dimensional deformation time sequence X1Solving the two-dimensional deformation time sequence X of the monitoring points according to the formula (2) and the formula (3)1Estimated value X of(1)And X1Co-factor matrix of
Figure BDA0002428754030000081
X(1)＝(A1 TP1A1)-1A1 TP1L1(2)
Figure BDA0002428754030000082
In the formula, A1Representing a design matrix; m represents SLC image pairThe number of (2); n represents the number of SLC images; p1Represents L1A priori information (i.e., precision information), P in the embodiment of the present invention1Is an identity matrix; a. the1 TIs represented by A1The transposed matrix of (2).
Step 4, dynamically updating deformation parameters of the earth surface area to be monitored:
step 4.1, when a new SLC image is added, according to the idea of step 1, grouping the new SLC image with the SLC image in step 1 by setting a time baseline and a space baseline, respectively, to form a plurality of SLC image pairs, wherein the time baseline in this step may be different from the time baseline in step 1;
solving two-dimensional deformation data L of multiple SLC image pairs2(ii) a Preferably, the two-dimensional deformation data L of a plurality of groups of SLC image pairs is obtained by adopting an intensity cross-correlation coefficient maximization method2。
Step 4.2, based on two-dimensional deformation data L2Establishing the following complex linear model for the deformation of each monitoring point of the earth surface area to be monitored:
Figure BDA0002428754030000083
in the formula, A2And B both represent a design matrix; n' represents the number of the updated SLC images; m' represents the number of SLC image pairs after update; x(2)Representing the updated two-dimensional deformation time sequence; y represents the accumulated deformation of the added SLC image at the corresponding time point;
step 4.3, considering X obtained in step 3(1)And co-factor matrix
Figure BDA0002428754030000091
Solving by using a formula (4) to obtain a two-dimensional deformation time sequence X(2)And the deformation Y is accumulated, and,
Figure BDA0002428754030000092
in the formula, JxIs a matrix of the gains that are,QJis X(2)A co-factor matrix of; b isTA transposed matrix representing B; qJ -1Represents QJThe inverse matrix of (d); p2Represents L2A priori information (i.e., precision information), P in the embodiment of the present invention2Is an identity matrix.
The invention also discloses a SAR offset two-dimensional deformation time sequence calculation system, which comprises:
the SLC image registration module is used for acquiring SLC images of the ground surface area to be monitored at different time points, and the SLC images corresponding to every two different time points form a group of SLC image pairs to obtain a plurality of groups of SLC image pairs;
a two-dimensional deformation data acquisition module for obtaining two-dimensional deformation data L of multiple SLC image pairs1(ii) a Preferably, the two-dimensional deformation data L of a plurality of groups of SLC image pairs is obtained by adopting an intensity cross-correlation coefficient maximization method1。
The stock data complex linear model establishing module is used for establishing a complex linear model of the deformation of each monitoring point of the earth surface area to be monitored:
A1X1＝L1(1)
Figure BDA0002428754030000101
in the formula, A1Representing a design matrix; x1Representing a two-dimensional deformation time sequence of the monitoring points; m represents the number of SLC image pairs; n represents the number of SLC images; the specific expression form of formula (1) is as described above.
The inventory data two-dimensional deformation time sequence acquisition module is used for solving by adopting a minimization criterion of a complex number module to obtain a two-dimensional deformation time sequence X1Estimated value X of(1)And X1Co-factor matrix of
Figure BDA0002428754030000102
Specifically, the method is used for solving the two-dimensional deformation time sequence X of the monitoring points according to the formula (2) and the formula (3)1Estimated value X of(1)And X1Co-factor matrix of
Figure BDA0002428754030000103
X(1)＝(A1 TP1A1)-1A1 TP1L1(2)
Figure BDA0002428754030000104
In the formula, A1Representing a design matrix; m represents the number of SLC image pairs; n represents the number of SLC images; p1Represents L1Prior information of (2); a. the1 TIs represented by A1The transposed matrix of (2).
Two-dimensional deformation time series update module includes:
the updated SLC image registration module is used for respectively grouping a new SLC image with the SLC image in the SLC image registration module to form a plurality of groups of SLC image pairs when a new SLC image is added;
the updated two-dimensional deformation data acquisition module is used for obtaining the two-dimensional deformation data L of a plurality of groups of SLC image pairs2(ii) a Preferably, the two-dimensional deformation data L of a plurality of groups of SLC image pairs is obtained by adopting an intensity cross-correlation coefficient maximization method2。
The updating data complex linear model establishing module is used for establishing the following complex linear model for the deformation of each monitoring point of the earth surface area to be monitored:
Figure BDA0002428754030000111
in the formula, A2And B both represent a design matrix; n' represents the number of the updated SLC images; m' represents the number of SLC image pairs after update; x(2)Representing the updated two-dimensional deformation time sequence; y represents the accumulated deformation of the added SLC image at the corresponding time point;
an update data two-dimensional deformation time sequence acquisition module for obtaining X by solving with a formula (4)(2)And a combination of Y and Y, wherein,
Figure BDA0002428754030000112
in the formula, JxIs a gain matrix, QJIs X(2)A co-factor matrix of; b isTA transposed matrix representing B; qJ -1Represents QJThe inverse matrix of (d); p2Represents L2Prior information of (2);
the invention also carries out simulation experiments on the calculation method and the traditional least square method, wherein the least square method respectively calculates the distance direction and the azimuth direction to finally obtain the two-dimensional deformation. The experimental result is shown in fig. 2, and it can be seen from the figure that the accuracy of the method of the present invention is consistent with the accuracy of the conventional least square method, but the method of the present invention can also realize dynamic update.
The following embodiments of the present invention are provided, and it should be noted that the present invention is not limited to the following embodiments, and all equivalent changes based on the technical solutions of the present invention are within the protection scope of the present invention.
Examples
In this embodiment, a region covering the Guizhou mining subsidence is selected as a ground surface region to be monitored, a collected UAV image is shown in FIG. 3, a real data coverage region of the UAV image can be seen, and collected data parameters are specifically shown in Table 1:
TABLE 1 SAR data parameters
Figure BDA0002428754030000121
In this embodiment, the foreground 7 scene data is the stock data, and X of the stock data is obtained through the steps 1 to 3(1)Sum co-factor matrix
Figure BDA0002428754030000122
Wherein, fig. 4 is a relationship diagram of the vertical baseline and the time baseline set when the SLC images are grouped, in the diagram, the circle of each line plus the point represents the time point, the line segment represents the number of the SLC images, it can be seen that, the front 7 scenes are numbersThe SLC images were formed in 8 sets, i.e., M-8 and N-7. In addition, P in the formula (2)1Is an identity matrix.
The dynamic update process of the present embodiment starts with the 8 th scene data and updates to the 16 th scene data in total, and SLC images of the 16 th scene data are shown in fig. 5 (a) and (B).
Starting from scene 8, the two-dimensional deformation time sequence of each scene data is obtained through calculation in step 4. Fig. 4 also shows the form of a group of update data, such as the 8 th scene data, and the image pairs formed by the 7 th scene stock data are 2 groups, i.e., M '2 and N' 8; as for the 16 th scene data, the image pairs formed with the previous 15 scenes are 2 groups, i.e., M '2 and N' 16; as shown in dashed lines in fig. 4. In addition, P in the present embodiment2Is an identity matrix.
The two-dimensional deformation time-series results of the 16-scene data are shown in fig. 5 and 6, in which (a) is a distance direction deformation time-series and (B) is an azimuth direction deformation time-series in fig. 5. FIG. 6 is a dynamic deformation of a certain monitoring point.
The present invention also compares the two-dimensional deformation time-series and dynamic deformation structure of the present embodiment with the results obtained by the conventional least-squares method, as shown in fig. 5 (C), fig. (D), and fig. 6. (C) Is the difference between the distance deformation time series and the traditional least square time series, and (D) is the difference between the azimuth deformation time series and the traditional least square time series. It can be seen that the precision of the result of this embodiment is consistent with that of the conventional least square method, and this embodiment can also realize dynamic real-time update.

Claims (8)

1. A SAR offset two-dimensional deformation time sequence calculation method is characterized by comprising the following steps:
step 1, acquiring SLC images of a ground surface area to be monitored at different time points, wherein the SLC images corresponding to every two different time points form a group of SLC image pairs to obtain a plurality of groups of SLC image pairs; solving two-dimensional deformation data L of multiple SLC image pairs1；
Step 2, establishing a complex linear model of the deformation of each monitoring point of the earth surface area to be monitored:
A1X1＝L1(1)
Figure FDA0002428754020000011
in the formula, A1Representing a design matrix; x1Representing a two-dimensional deformation time sequence of the monitoring points; m represents the number of SLC image pairs; n represents the number of SLC images;
step 3, solving according to the minimization criterion of the complex modulus to obtain a two-dimensional deformation time sequence X1Estimated value X of(1)And X1Co-factor matrix of
Figure FDA0002428754020000013
Step 4, dynamically updating the two-dimensional deformation time sequence of the earth surface area to be monitored:
step 4.1, when a new SLC image is added, the new SLC image is respectively grouped with the SLC image in the step 1 to form a plurality of groups of SLC images; solving two-dimensional deformation data L of multiple SLC image pairs2；
Step 4.2, establishing the following complex linear model for the deformation of each monitoring point of the earth surface area to be monitored:
Figure FDA0002428754020000012
Figure FDA0002428754020000021
in the formula, A2And B both represent a design matrix; n' represents the number of the updated SLC images; m' represents the number of SLC image pairs after update; x(2)Representing the updated two-dimensional deformation time sequence; y represents the accumulated deformation of the added SLC image at the corresponding time point;
step 4.3, solving by using a formula (4) to obtain X(2)And a combination of Y and Y, wherein,
Figure FDA0002428754020000022
Figure FDA0002428754020000023
Figure FDA0002428754020000024
in the formula, JxIs a gain matrix, QJIs X(2)A co-factor matrix of; b isTA transposed matrix representing B; qJ -1Represents QJThe inverse matrix of (d); p2Represents L2A priori information of.
2. The SAR offset two-dimensional deformation time sequence calculation method of claim 1, characterized in that in step 1, the two-dimensional deformation data L of multiple SLC image pairs is obtained by adopting an intensity cross-correlation coefficient maximization method1。
3. The SAR offset two-dimensional deformation time sequence calculation method of claim 1, wherein the step 3 specifically comprises: solving the two-dimensional deformation time sequence X of the monitoring points according to the formula (2) and the formula (3)1Estimated value X of(1)And X1Co-factor matrix of
Figure FDA0002428754020000025
X(1)＝(A1 TP1A1)-1A1 TP1L1(2)
Figure FDA0002428754020000026
In the formula, A1Representing a design matrix; m represents the number of SLC image pairs; n represents the number of SLC images; p1Represents L1Prior information of (2); a. the1 TIs represented by A1The transposed matrix of (2).
4. The SAR offset two-dimensional deformation time sequence calculation method of claim 1, characterized in that in step 4.1, the two-dimensional deformation data L of multiple SLC image pairs is obtained by adopting an intensity cross-correlation coefficient maximization method2。
5. A SAR offset two-dimensional deformation time sequence calculation system is characterized by comprising:
the SLC image registration module is used for acquiring SLC images of the ground surface area to be monitored at different time points, and the SLC images corresponding to every two different time points form a group of SLC image pairs to obtain a plurality of groups of SLC image pairs; a two-dimensional deformation data acquisition module for obtaining two-dimensional deformation data L of multiple SLC image pairs1；
The stock data complex linear model establishing module is used for establishing a complex linear model of the deformation of each monitoring point of the earth surface area to be monitored:
A1X1＝L1(1)
Figure FDA0002428754020000031
in the formula, A1Representing a design matrix; x1Representing a two-dimensional deformation time sequence of the monitoring points; m represents the number of SLC image pairs; n represents the number of SLC images;
the inventory data two-dimensional deformation time sequence acquisition module is used for solving by adopting a minimization criterion of a complex number module to obtain a two-dimensional deformation time sequence X1Estimated value X of(1)And X1Co-factor matrix of
Figure FDA0002428754020000032
Two-dimensional deformation time series update module includes:
an updated SLC image registration module for adding one image at a timeSetting the new SLC image with the SLC image in the SLC image registration module to form multiple SLC image pairs; the updated two-dimensional deformation data acquisition module is used for obtaining the two-dimensional deformation data L of a plurality of groups of SLC image pairs2；
The updating data complex linear model establishing module is used for establishing the following complex linear model for the deformation of each monitoring point of the earth surface area to be monitored:
Figure FDA0002428754020000041
Figure FDA0002428754020000042
in the formula, A2And B both represent a design matrix; n' represents the number of the updated SLC images; m' represents the number of SLC image pairs after update; x(2)Representing the updated two-dimensional deformation time sequence; y represents the accumulated deformation of the added SLC image at the corresponding time point;
an update data two-dimensional deformation time sequence acquisition module for obtaining X by solving with a formula (4)(2)And a combination of Y and Y, wherein,
Figure FDA0002428754020000043
Figure FDA0002428754020000044
Figure FDA0002428754020000045
in the formula, JxIs a gain matrix, QJIs X(2)A co-factor matrix of; b isTA transposed matrix representing B; qJ -1Represents QJThe inverse matrix of (d); p2Represents L2A priori information of.
6. The SAR offset two-dimensional deformation time sequence calculation system of claim 5, wherein in the two-dimensional deformation data acquisition module, the two-dimensional deformation data L of a plurality of SLC image pairs is obtained by adopting a strength cross correlation coefficient maximization method1。
7. The SAR offset two-dimensional deformation time sequence calculation system of claim 5, characterized in that the stock data two-dimensional deformation time sequence acquisition module is specifically used for solving the two-dimensional deformation time sequence X of the monitoring point according to the formula (2) and the formula (3)1Estimated value X of(1)And X1Co-factor matrix of
Figure FDA0002428754020000051
X(1)＝(A1 TP1A1)-1A1 TP1L1(2)
Figure FDA0002428754020000052
In the formula, A1Representing a design matrix; m represents the number of SLC image pairs; n represents the number of SLC images; p1Represents L1Prior information of (2); a. the1 TIs represented by A1The transposed matrix of (2).
8. The SAR offset two-dimensional deformation timing sequence calculation system of claim 5, wherein in the updated SLC image registration module, the two-dimensional deformation data L of a plurality of SLC image pairs is obtained by adopting an intensity cross-correlation coefficient maximization method2。
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