CN111562579B - MIMO InSAR phase unwrapping method based on integer programming model - Google Patents

MIMO InSAR phase unwrapping method based on integer programming model Download PDF

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CN111562579B
CN111562579B CN202010142065.5A CN202010142065A CN111562579B CN 111562579 B CN111562579 B CN 111562579B CN 202010142065 A CN202010142065 A CN 202010142065A CN 111562579 B CN111562579 B CN 111562579B
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CN111562579A (en
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刘辉
崔洪涛
宋惠静
王进涛
邵慧欢
崔红娅
吴永杰
李葛爽
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North China University of Water Resources and Electric Power
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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
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C5/00—Measuring height; Measuring distances transverse to line of sight; Levelling between separated points; Surveyors' levels

Abstract

The invention discloses a MIMO InSAR phase unwrapping method based on an integer programming model, which mainly comprises the following steps: (1) constructing an integer programming model according to the corresponding relation among the baseline ratio, the wavelength ratio and the elevation phase; (2) solving the minimum solution k satisfying the integer programming model by adopting a branch-and-bound methodi(i＝1,2,3,…,N2) (ii) a (3) Calculating a deblurring value d phi of interference phase differential at a corresponding pixel of the corresponding interferogrami(ii) a (4) Unwinding the seed at a given phase respectively
Figure DDA0002401396480000011
Micro-decomposing fuzzy value d phi of interference phase at all pixel positions in each interference patterniIntegrating according to a certain path to obtain the unwrapping result phi of each interference patterni(x, y). According to the invention, the target function and the constraint conditions thereof are constructed by analyzing the relation between the interference phase and the baseline and frequency, the MIMO InSAR phase unwrapping problem is converted into the linear programming expression and optimal value solving problem, the accurate and steady unwrapping of the MIMO InSAR interference phase is realized, and the elevation measurement performance and the mapping capability to complex terrain are improved.

Description

MIMO InSAR phase unwrapping method based on integer programming model
Technical Field
The invention relates to a MIMO InSAR phase unwrapping method based on an integer programming model, and belongs to the technical field of radar interferometry.
Background
Synthetic Aperture Radars (SAR) obtain two-dimensional high-resolution images by transmitting broadband signals and projecting three-dimensional information of a spatial target onto an azimuth-distance plane by using a Synthetic Aperture technology. The Synthetic aperture radar interferometry (InSAR) technology developed on the basis can quickly acquire a digital elevation model all day long and all weather, and has important application value in topographic map surveying and updating of areas seriously affected by cloud, rain and fog haze all year round.
The traditional single-baseline and single-frequency InSAR system is difficult to play a role in surveying and mapping of a complex terrain area, is limited by system complexity and cost factors, and the number of independent observation channels provided by the conventional multi-channel InSAR system is limited.
In order to solve the problem, a MIMO InSAR phase unwrapping method based on an integer programming model is provided, the number of independent observation channels of an InSAR system is greatly increased under the condition that the working frequency or observation array elements are not increased by adopting the MIMO InSAR phase unwrapping technology, the high precision of a high-frequency interference diagram and the easy resolvability of a low-frequency interference diagram are fully utilized, the unwrapping problems of frequency spectrum aliasing and phase undersampling positions are solved, and the elevation measurement performance and the surveying and mapping capacity of complex terrains are improved.
Disclosure of Invention
In view of the above, the present invention aims to provide a theory and a method for MIMO InSAR phase unwrapping using integer programming, which transform the MIMO InSAR phase unwrapping problem into the linear programming expression and optimum value solution problem by analyzing the relationship between the interference phase and the baseline and frequency to construct an objective function and its constraint conditions, thereby realizing accurate and robust unwrapping of the MIMO InSAR interference phase, and improving the elevation measurement performance and the mapping capability to complex terrain.
In order to achieve the above object, the present invention provides: the MIMO InSAR phase unwrapping method based on the integer programming model mainly comprises the following steps:
step R1, constructing an integer programming model according to the corresponding relation among the baseline ratio, the wavelength ratio and the elevation phase;
step R2, solving the minimum solution k meeting the integer programming model by adopting a branch-and-bound methodi(i＝1,2,3,···,N2)；
Step R3, calculating the ambiguity resolving value d phi of the interference phase differential at the corresponding pixel of the corresponding interferogrami；
Step R4, respectively unwinding the seed at a given phase
Figure GDA0003448020630000021
Micro-decomposing fuzzy value d phi of interference phase at all pixel positions in each interference patterniIntegrating according to a certain path to obtain the unwrapping result phi of each interference patterni(x,y)；
In the above method for MIMO InSAR phase unwrapping based on integer programming model, in step R1, N obtained by the MIMO InSAR system is used2The SAR images are accurately registered, and the land flattening effect is removed according to a base line ratio B1:B2:···:BNAnd wavelength ratio lambda1:λ2:···:λNObtaining the corresponding relationship of elevation phase
Figure GDA0003448020630000022
Wherein the least common multiple of the base line is
Figure GDA0003448020630000023
The least common multiple of the wavelength is
Figure GDA0003448020630000024
Figure GDA0003448020630000025
Is the interference phase differential; k is a radical ofiIs composed of
Figure GDA0003448020630000026
And:
Figure GDA0003448020630000031
according to the formula (1) and the formula (2), the MIMO InSAR phase unwrapping problem can be converted into an integer programming model:
Figure GDA0003448020630000032
Figure GDA0003448020630000033
in the above method for MIMO InSAR phase unwrapping based on integer programming model, in step R2, the integer programming problem described in equation (3) is solved by using branch-and-bound method, and a solution satisfying S minimum can be obtained: k is a radical ofi(i＝1,2,3,···,N2) The method comprises the following specific steps:
step 1, solving a linear plan S corresponding to the integer plan, if the S has no feasible solution, the integer plan also has no feasible solution, and stopping calculation; if the optimal solution of the S is an integer solution, the solution is the optimal solution of the integer programming, and the calculation is stopped; if the optimal solution of the S is not an integer solution, turning to the step 2;
step 2, branching: optionally selecting a variable not meeting an integer condition in the optimal solution of S
Figure GDA0003448020630000034
Has a value of (B)-1b)i，[(B-1b)]Is less than (B)-1b)iIs used to construct two constraints
Figure GDA0003448020630000035
And
Figure GDA0003448020630000036
adding the two constraint conditions to the constraint conditions of the question S respectively to form two sub-questions S1And S2And solve for S1And S2；
And step 3, delimitation: getThe maximum target value in the integer solution is the lower limit of the limit value T, and if no integer solution exists in the calculation, S is set to infinity; checking for branches SiIf its optimal solution is not an integer solution, and SiIf > T, repeat step 2, if SiT is less than or equal to T, then SiNo longer branched;
and 4, repeating the steps 2-3 until all branches can not be solved again, wherein the integer solution corresponding to the threshold value T is the optimal solution of the original problem.
The method for MIMO InSAR phase unwrapping based on integer programming model as described above, in the step R3, according to ki(i＝1,2,3,···,N2) Obtaining the ambiguity resolving value d phi of the interference phase differential at the corresponding pixel of each interference patterni；
Figure GDA0003448020630000041
In the method for MIMO InSAR phase unwrapping based on integer programming model as described above, in the step R4, the seeds are unwrapped with the given phases respectively
Figure GDA0003448020630000042
Micro-decomposing fuzzy value d phi of interference phase at all pixel positions in each interference patterniIntegrating according to a certain path to obtain the unwrapping result phi of each interference patterni(x,y)；
Figure GDA0003448020630000043
Compared with the prior art, the invention has the following advantages:
the invention provides an MIMO InSAR phase unwrapping method based on an integer programming model, which is characterized in that a target function and constraint conditions thereof are constructed by analyzing the relation between an interference phase and a baseline and frequency, the MIMOInSAR phase unwrapping problem is converted into a linear programming expression and optimum value solving problem, the accurate and steady unwrapping of the MIMOInSAR interference phase is realized, and the elevation measurement performance and the mapping capability to complex terrain are improved.
Drawings
Fig. 1 is a phase unwrapping flow chart of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings
Referring to fig. 1, the present invention provides a method of: the MIMO InSAR phase unwrapping method based on the integer programming model mainly comprises the following steps:
step R1, constructing an integer programming model according to the corresponding relation among the baseline ratio, the wavelength ratio and the elevation phase;
step R2, solving the minimum solution k meeting the integer programming model by adopting a branch-and-bound methodi(i＝1,2,3,···,N2)；
Step R3, calculating the ambiguity resolving value d phi of the interference phase differential at the corresponding pixel of the corresponding interferogrami；
Step R4, respectively unwinding the seed at a given phase
Figure GDA0003448020630000051
Micro-decomposing fuzzy value d phi of interference phase at all pixel positions in each interference patterniIntegrating according to a certain path to obtain the unwrapping result phi of each interference patterni(x,y)；
In the above method for MIMO InSAR phase unwrapping based on integer programming model, in step R1, N obtained by the MIMO InSAR system is used2The SAR images are accurately registered, and the land flattening effect is removed according to a base line ratio B1:B2:···:BNAnd wavelength ratio lambda1:λ2:···:λNObtaining the corresponding relationship of elevation phase
Figure GDA0003448020630000052
Wherein the least common multiple of the base line is
Figure GDA0003448020630000053
Wavelength of lightHas a least common multiple of
Figure GDA0003448020630000054
Figure GDA0003448020630000055
Is the interference phase differential; k is a radical ofiIs composed of
Figure GDA0003448020630000056
And:
Figure GDA0003448020630000057
according to the formula (1) and the formula (2), the MIMO InSAR phase unwrapping problem can be converted into an integer programming model:
Figure GDA0003448020630000061
Figure GDA0003448020630000062
in the above method for MIMO InSAR phase unwrapping based on integer programming model, in step R2, the integer programming problem described in equation (3) is solved by using branch-and-bound method, and a solution satisfying S minimum can be obtained: k is a radical ofi(i＝1,2,3,···,N2) The method comprises the following specific steps:
step 1, solving a linear plan S corresponding to the integer plan, if the S has no feasible solution, the integer plan also has no feasible solution, and stopping calculation; if the optimal solution of the S is an integer solution, the solution is the optimal solution of the integer programming, and the calculation is stopped; if the optimal solution of the S is not an integer solution, turning to the step 2;
step 2, branching: optionally selecting a variable not meeting an integer condition in the optimal solution of S
Figure GDA0003448020630000063
Has a value of (B)-1b)i，[(B-1b)]Is less than (B)-1b)iIs used to construct two constraints
Figure GDA0003448020630000064
And
Figure GDA0003448020630000065
adding the two constraint conditions to the constraint conditions of the question S respectively to form two sub-questions S1And S2And solve for S1And S2；
And step 3, delimitation: taking the maximum target value in the integer solution as the lower bound of a limit value T, and if no integer solution exists in the calculation, taking S-infinity; checking for branches SiIf its optimal solution is not an integer solution, and SiIf > T, repeat step 2, if SiT is less than or equal to T, then SiNo longer branched;
and 4, repeating the steps 2-3 until all branches can not be solved again, wherein the integer solution corresponding to the threshold value T is the optimal solution of the original problem.
The method for MIMO InSAR phase unwrapping based on integer programming model as described above, in the step R3, according to ki(i＝1,2,3,···,N2) Obtaining the ambiguity resolving value d phi of the interference phase differential at the corresponding pixel of each interference patterni；
Figure GDA0003448020630000071
In the method for MIMO InSAR phase unwrapping based on integer programming model as described above, in the step R4, the seeds are unwrapped with the given phases respectively
Figure GDA0003448020630000072
Micro-decomposing fuzzy value d phi of interference phase at all pixel positions in each interference patterniIntegrating according to a certain path to obtain the unwrapping result phi of each interference patterni(x,y)；
Figure GDA0003448020630000073
Compared with the prior art, the invention has the following advantages:
the MIMO InSAR phase unwrapping method based on the integer programming model provided by the invention is described in detail above; to sum up, the content of the present specification should not be construed as limiting the invention, since the scope of the application and the detailed description of the invention may vary according to the concept of the embodiment of the present invention.

Claims (4)

1. The invention provides a MIMO InSAR phase unwrapping method based on an integer programming model, which is characterized by mainly comprising the following steps:
step R1, constructing an integer programming model according to the corresponding relation among the baseline ratio, the wavelength ratio and the elevation phase;
step R2, solving the minimum solution k meeting the integer programming model by adopting a branch-and-bound methodi(i＝1,2,3,···,N2)；
Step R3, calculating the ambiguity resolving value d phi of the interference phase differential at the corresponding pixel of the corresponding interferogrami；
Step R4, respectively unwinding the seed at a given phase
Figure FDA0003448020620000011
Micro-decomposing fuzzy value d phi of interference phase at all pixel positions in each interference patterniIntegrating according to a certain path to obtain the unwrapping result phi of each interference patterni(x,y)；
In the step R1, obtaining N of the MIMO InSAR system2The SAR images are accurately registered, and the land flattening effect is removed according to a base line ratio B1:B2:···:BNAnd wavelength ratio lambda1:λ2:···:λNObtaining the corresponding relationship of elevation phase
Figure FDA0003448020620000012
Wherein the least common multiple of the base line is
Figure FDA0003448020620000013
The least common multiple of the wavelength is
Figure FDA0003448020620000014
Is the interference phase differential; k is a radical ofiIs composed of
Figure FDA0003448020620000015
And:
Figure FDA0003448020620000016
according to the formula (1) and the formula (2), the MIMO InSAR phase unwrapping problem can be converted into an integer programming model:
Figure FDA0003448020620000021
2. the integer programming model-based MIMO InSAR phase unwrapping method of claim 1, wherein in the step R2, the integer programming problem described by the equation (3) is solved by using a branch-and-bound method, such that a solution satisfying S-min is obtained: k is a radical ofi(i＝1,2,3,···,N2) The method comprises the following specific steps:
step 1, solving a linear plan S corresponding to the integer plan, if the S has no feasible solution, the integer plan also has no feasible solution, and stopping calculation; if the optimal solution of the S is an integer solution, the solution is the optimal solution of the integer programming, and the calculation is stopped; if the optimal solution of the S is not an integer solution, turning to the step 2;
step 2, branching: optionally selecting a variable not meeting an integer condition in the optimal solution of S
Figure FDA0003448020620000022
Has a value of (B)-1b)i，[(B- 1b)]Is less than (B)-1b)iIs used to construct two constraints
Figure FDA0003448020620000023
And
Figure FDA0003448020620000024
adding the two constraint conditions to the constraint conditions of the question S respectively to form two sub-questions S1And S2And solve for S1And S2；
And step 3, delimitation: taking the maximum target value in the integer solution as the lower bound of a limit value T, and if no integer solution exists in the calculation, taking S-infinity; checking for branches SiIf its optimal solution is not an integer solution, and SiIf > T, repeat step 2, if SiT is less than or equal to T, then SiNo longer branched;
and 4, repeating the steps 2-3 until all branches can not be solved again, wherein the integer solution corresponding to the threshold value T is the optimal solution of the original problem.
3. The integer programming model based MIMO InSAR phase unwrapping method according to claim 2, wherein in the step R3, according to ki(i＝1,2,3,···,N2) Obtaining the ambiguity resolving value d phi of the interference phase differential at the corresponding pixel of each interference patterni；
Figure FDA0003448020620000031
4. The integer programming model based MIMO InSAR phase unwrapping method according to claim 3, wherein in the step R4, the seeds are unwrapped with a given phase respectively
Figure FDA0003448020620000032
Micro-decomposing fuzzy value d phi of interference phase at all pixel positions in each interference patterniIntegrating according to a certain path to obtain the unwrapping result phi of each interference patterni(x,y)；
Figure FDA0003448020620000033
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