CN115629384A - Correction method of time sequence InSAR error and related equipment - Google Patents

Correction method of time sequence InSAR error and related equipment Download PDF

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CN115629384A
CN115629384A CN202211568937.XA CN202211568937A CN115629384A CN 115629384 A CN115629384 A CN 115629384A CN 202211568937 A CN202211568937 A CN 202211568937A CN 115629384 A CN115629384 A CN 115629384A
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insar
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time sequence
deformation
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CN115629384B (en
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刘计洪
胡俊
李志伟
朱建军
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Central South University
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    • 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
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    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
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Abstract

The invention provides a method for correcting a time sequence InSAR error and related equipment, wherein the method for correcting the time sequence InSAR error comprises the following steps: step 1, acquiring an InSAR time sequence phase of a research area; step 2, establishing a combined model for the space trend error, the terrain related error and the deformation signal in the InSAR time sequence phase based on the space-time characteristics of the multi-source signals, and solving model parameters in the combined model to obtain the space trend error and the terrain related error; step 3, subtracting the space trend error and the terrain related error from the InSAR time sequence phase to obtain the corrected InSAR time sequence deformation; the problem that various errors are easily affected by deformation or other error signals when being processed independently is effectively solved, accurate estimation of atmospheric delay and orbit errors is achieved, and accuracy and reliability of time sequence InSAR earth surface deformation measurement are remarkably improved.

Description

Correction method of time sequence InSAR error and related equipment
Technical Field
The invention relates to the technical field of surface deformation measurement, in particular to a method for correcting time sequence InSAR errors and related equipment.
Background
The time-series Synthetic Aperture Radar (SAR) interferometry can obtain the surface deformation result of a research area with long time series and high spatial resolution by analyzing a time-series SAR image, and provides important data support for interpretation, analysis and prevention of related geological disasters. However, due to the influence of factors such as atmospheric delay (including turbulent atmosphere and stratified atmosphere) and orbit errors, the deformation measurement accuracy of the time sequence InSAR technology is difficult to be effectively guaranteed, and further the subsequent application analysis is influenced. In the case where accurate external meteorological data (e.g., temperature, barometric pressure, etc.) or other geodetic data (e.g., global Navigation Satellite System (GNSS) Global Navigation System and leveling data) are available, atmospheric and orbital errors in the InSAR observations can be effectively attenuated. However, these external data are generally difficult to acquire, and error correction can be performed only based on different spatio-temporal characteristics of signals such as distortion, atmospheric delay, and track error in the InSAR observed value. For example, orbital errors can be modeled and corrected spatially using second order polynomials, layered atmospheres can be modeled and corrected by correlation analysis with terrain, and turbulent atmospheres can be suppressed by spatial and temporal filtering. Although the existing research has carried out relevant work for correcting and suppressing various errors, most of the research is to model and correct certain types of errors on the premise of assuming that other errors have small influence. However, in practical situations, orbit errors, turbulent atmosphere and stratified atmosphere often exist simultaneously, if only one type of errors are modeled and corrected, the correction accuracy is influenced by other error signals, and finally the reliability of the time sequence InSAR deformation measurement is reduced.
Disclosure of Invention
The invention provides a method for correcting time sequence InSAR errors and related equipment, and aims to solve the problem that various errors are easily affected by deformation or other error signals when being processed independently and improve the precision and reliability of time sequence InSAR deformation measurement.
In order to achieve the above object, the present invention provides a method for correcting timing InSAR errors, comprising:
step 1, acquiring an InSAR time sequence phase of an InSAR interferogram;
step 2, establishing a combined model for the spatial trend error, the terrain related error and the deformation signal in the InSAR time sequence phase based on the spatial-temporal characteristics of the multi-source signals, and solving model parameters in the combined model to obtain the spatial trend error and the terrain related error;
and 3, subtracting the space trend error and the terrain related error from the InSAR time sequence phase to obtain the corrected InSAR time sequence deformation.
Further, step 2 comprises:
modeling the spatial trend error by using a first-order polynomial to obtain a polynomial fitting coefficient equation;
characterizing the terrain related error by using a linear model to obtain a linear equation coefficient equation;
constructing a virtual observation equation for the deformation signal by utilizing a third-order polynomial function;
and (4) simultaneously establishing a polynomial fitting coefficient equation, a linear equation coefficient equation and a virtual observation equation to obtain a combined model.
Further, the model parameters in the joint model include time sequence deformation of all pixels, polynomial fitting coefficients of spatial trend errors at all pixels, and linear equation coefficients of terrain-related errors at all pixels.
Further, the step 2 further includes:
randomly selecting one pixel from all pixels as a target pixel;
at the moment of time
Figure 20214DEST_PATH_IMAGE001
By target pixel
Figure 468513DEST_PATH_IMAGE002
The center is taken as the size
Figure 513830DEST_PATH_IMAGE003
The polynomial fitting coefficient equation is established as follows:
Figure 174618DEST_PATH_IMAGE005
wherein,
Figure 520149DEST_PATH_IMAGE006
for an InSAR phase observation at each pixel within the window,
Figure 608190DEST_PATH_IMAGE007
for the phase of the deformation at each point,
Figure 406382DEST_PATH_IMAGE008
is composed of
Figure 870862DEST_PATH_IMAGE010
The integer number within the interval is such that,
Figure 805319DEST_PATH_IMAGE012
in order to have a terrain-dependent error phase,
Figure 329842DEST_PATH_IMAGE014
、
Figure 615330DEST_PATH_IMAGE015
、
Figure 617921DEST_PATH_IMAGE016
fitting coefficients for the polynomial;
vector the observed value in the above formula
Figure 672464DEST_PATH_IMAGE018
Incorporating the total observed value vector
Figure 367888DEST_PATH_IMAGE019
In (2), then the corresponding coefficient matrix
Figure 875093DEST_PATH_IMAGE020
Will increase
Figure 681375DEST_PATH_IMAGE022
Line, each line and the above formula medium observation value vector
Figure 590425DEST_PATH_IMAGE017
Corresponding to the elements of (2), most elements in each row are 0, and only correspond to the model parameter vector
Figure 191170DEST_PATH_IMAGE023
The column corresponding to the middle element is not 0, and the value is the matrix of the middle and coefficient in the above formula
Figure 454180DEST_PATH_IMAGE024
The corresponding element of the corresponding row.
Further, the step 2 further includes:
randomly selecting one pixel from all pixels as a target pixel;
at the moment of time
Figure 798574DEST_PATH_IMAGE001
By target pixel
Figure 562130DEST_PATH_IMAGE002
Is taken as the center and has the size of
Figure 599357DEST_PATH_IMAGE025
The linear equation coefficient equation is established:
Figure 81153DEST_PATH_IMAGE027
wherein,
Figure 229238DEST_PATH_IMAGE006
for an InSAR phase observation at each pixel within the window,
Figure 847301DEST_PATH_IMAGE007
in order to change the phase of the deformation,
Figure 321008DEST_PATH_IMAGE028
in order to trend the phase of the signal,
Figure 24522DEST_PATH_IMAGE029
is a window intervalThe number of the integers in (a) is,
Figure 710718DEST_PATH_IMAGE030
is a pixel
Figure 714446DEST_PATH_IMAGE002
And picture element
Figure 93475DEST_PATH_IMAGE031
The difference in elevation between the two,
Figure 284285DEST_PATH_IMAGE032
、
Figure 39751DEST_PATH_IMAGE033
is the coefficient of a linear equation;
vector the observed value in the above formula
Figure 366827DEST_PATH_IMAGE017
Incorporation of the Total observed value vector
Figure 916757DEST_PATH_IMAGE019
In (3), then the corresponding coefficient matrix
Figure 594863DEST_PATH_IMAGE020
Will increase
Figure 154021DEST_PATH_IMAGE021
Line, each line and the above formula medium observation value vector
Figure 601182DEST_PATH_IMAGE017
Corresponds to the elements of (1), most elements in each row are 0, and only correspond to the model parameter vector
Figure 56435DEST_PATH_IMAGE023
The corresponding column of the middle element is not 0, and the value is the coefficient matrix in the formula
Figure 221837DEST_PATH_IMAGE024
The corresponding element of the corresponding row.
Further, the step 2 further includes:
randomly selecting one pixel from all pixels as a target pixel;
at the moment of time
Figure 319106DEST_PATH_IMAGE001
By target pixel
Figure 886353DEST_PATH_IMAGE002
Taking a time window with the size as the center, and constructing a virtual observation equation as follows:
Figure 512507DEST_PATH_IMAGE034
wherein,
Figure 165205DEST_PATH_IMAGE035
is a variable of a parameter of the intermediate model,
Figure 63235DEST_PATH_IMAGE036
and with
Figure 219410DEST_PATH_IMAGE037
The difference between the values of the two values is equal to 0,
Figure 282044DEST_PATH_IMAGE038
in order to change the shape of the time sequence,
Figure 749934DEST_PATH_IMAGE039
to shape the time sequence
Figure 454585DEST_PATH_IMAGE040
The fitting value of the cubic polynomial of (c),
Figure 996425DEST_PATH_IMAGE041
、
Figure 229960DEST_PATH_IMAGE042
、
Figure 591671DEST_PATH_IMAGE043
are respectively the first
Figure 834434DEST_PATH_IMAGE044
Scene SAR image and second
Figure 965201DEST_PATH_IMAGE045
Time difference between scene SAR image moments
Figure 369637DEST_PATH_IMAGE046
Scene SAR image and scene SAR image
Figure 218645DEST_PATH_IMAGE045
Time difference between scene SAR image moments
Figure 999519DEST_PATH_IMAGE047
Scene SAR image and second
Figure 250372DEST_PATH_IMAGE045
The time difference between the moments of the scene SAR images,
Figure 825709DEST_PATH_IMAGE048
。
further, the step 2 further includes:
the additional virtual observation equation is established by using the prior information as follows:
Figure 162013DEST_PATH_IMAGE049
adding the virtual observation equation to the total observation vector
Figure 480999DEST_PATH_IMAGE019
And in the corresponding coefficient matrix
Figure 851937DEST_PATH_IMAGE020
Add one row in.
Further, the simultaneous polynomial fitting coefficient equation, the linear equation coefficient equation and the virtual observation equation obtain a combined model, which includes:
based on a polynomial fitting coefficient equation, a linear equation coefficient equation, a virtual observation equation and an additional virtual observation equation, establishing a combined model of a spatial trend error, a terrain correlation error and a deformation signal in an InSAR time sequence phase as follows:
Figure 598176DEST_PATH_IMAGE050
wherein,
Figure 156197DEST_PATH_IMAGE019
to be the total vector of observations,
Figure 278873DEST_PATH_IMAGE020
is a matrix of coefficients, and is,
Figure 507248DEST_PATH_IMAGE051
are model parameters.
The present invention also provides a computer-readable storage medium for storing a computer program for implementing the above-described method for correcting timing InSAR errors by executing the computer program.
The invention also provides a device for correcting the time sequence InSAR error, which is used for realizing the method for correcting the time sequence InSAR error and comprises the following steps:
a memory and a processor;
the memory is used for storing a computer program;
the processor is for executing the computer program stored by the memory.
The scheme of the invention has the following beneficial effects:
the method constructs a combined model of spatial trend errors, terrain related errors and deformation signals in the InSAR time sequence phase based on the time-space characteristics of multi-source signals such as deformation, atmospheric delay and orbit errors, effectively solves the problem that various errors are easily affected by deformation or other error signals when being processed independently, realizes accurate estimation of atmospheric delay and orbit errors, and obviously improves the precision and reliability of surface deformation measurement of the time sequence InSAR.
Other advantages of the present invention will be described in detail in the detailed description that follows.
Drawings
FIG. 1 is a flow diagram of an embodiment of the present invention;
fig. 2 is a comparison diagram of the InSAR time sequence deformation results at the funnel center obtained by different methods in the embodiment of the present invention.
Detailed Description
In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of description and simplification of description, but do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted", "connected" and "connected" are to be construed broadly, e.g., as being either a locked connection, a detachable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
In addition, the technical features involved in the different embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention provides a method for correcting time sequence InSAR errors and related equipment aiming at the existing problems.
Specifically, the embodiment of the invention performs combined correction on the time sequence InSAR atmospheric delay and the orbit errors, wherein the orbit errors are considered as low-frequency signals in space, and meanwhile, the turbulent atmospheric errors are in a small space range, such as 1 multiplied by 1km 2 It may also be considered a low frequency signal, and thus the orbit error and turbulent atmosphere are collectively referred to as a trend error in the embodiments of the present invention. For the spatial trend error at a certain pixel point, a polynomial fitting modeling can be performed by using observed values within a certain spatial range, such as 5 × 5 pixels. The layered atmosphere is mainly related to local terrains and is called as a terrain related error, for the terrain related error at a certain pixel point, linear fitting modeling can be performed on an InSAR observed value and the terrain within a certain spatial range, in addition, sudden events such as earthquakes and the like are eliminated, the deformation of the earth surface is a slowly-changing process in time under general conditions, time sequence earth surface deformation can be considered to meet a cubic equation related to time within a certain time range, the assumption is used as a priori constraint condition, and space-time unified modeling is performed on atmospheric delay errors, orbit errors and deformation signals in an InSAR time sequence phase, so that the problem that various errors are easily influenced by deformation or other error signals when being processed independently can be effectively avoided, and the precision and the reliability of time sequence InSAR deformation measurement are improved.
As shown in fig. 1, an embodiment of the present invention provides a method for correcting a timing InSAR error, including:
step 1, acquiring an InSAR time sequence phase of an InSAR interferogram;
step 2, establishing a combined model for the spatial trend error, the terrain related error and the deformation signal in the InSAR time sequence phase based on the spatial-temporal characteristics of the multi-source signals, and solving model parameters in the combined model to obtain the spatial trend error and the terrain related error;
and 3, subtracting the space trend error and the terrain related error from the InSAR time sequence phase to obtain the corrected InSAR time sequence deformation.
Specifically, the embodiment of the invention is Based on an SBAS (Satellite-Based Augmentation System) Satellite-Based Augmentation System or a SqueeSAR distribution permanent scatterer Satellite radar monitoring technical method, the orbit error and the atmospheric delay error in an InSAR interferogram do not need to be corrected until the InSAR time sequence phase is obtained, and the subsequent spatial trend error and terrain related error are corrected according to the InSAR time sequence phase.
The track error and the atmospheric delay error exist in the InSAR interferogram, and the essential reason is that the SAR images forming the interferogram contain the corresponding track error and the atmospheric delay error, so that the InSAR time sequence phase obtained based on the InSAR interferogram without track error and atmospheric delay error correction not only contains time sequence deformation but also contains the track error and the atmospheric delay error corresponding to each moment, and therefore, the method is more reasonable for directly carrying out corresponding error correction on the InSAR time sequence phase. Meanwhile, compared with an InSAR interferogram, the data volume of the InSAR time sequence phase can be greatly reduced, and the data processing efficiency is improved.
Specifically, step 2 in the embodiment of the present invention mainly considers the function model establishment in three aspects:
1, for a spatial trend error, in a small window range of 1km multiplied by 1km, modeling can be carried out by utilizing a first-order polynomial related to a position to obtain a polynomial fitting coefficient equation;
2, for terrain related errors, within a certain small window range, a linear model related to terrain can be used for characterization to obtain a linear equation coefficient equation;
for the deformation signal, in a certain space range, the deformation signal is often similar to the space trend error in terms of space characteristics, and the difference is that the deformation signal is also related in a certain time window, so that a virtual observation equation related to time sequence deformation can be established through a time-related third-order polynomial function, and further the virtual observation equation is combined with the function models in 1 and 2, so that the same modeling of space and time of the space trend error, the terrain related error and the time sequence deformation signal is realized.
In the embodiment of the present invention, it is assumed that there is an existing oneNInSAR time sequence phase of each time, the phase of each time isI×JThe size matrix, the model parameters to be solved in the combined model of the embodiment of the present invention include: time sequence deformation of all pixels
Figure 424389DEST_PATH_IMAGE052
Polynomial fitting coefficients of spatial trend errors at all pixels
Figure 735284DEST_PATH_IMAGE053
Coefficient of linear equation of terrain-dependent error at all pixels
Figure 396073DEST_PATH_IMAGE054
In which
Figure 476024DEST_PATH_IMAGE055
Is shown as
Figure 829645DEST_PATH_IMAGE056
At a time instant.
The model parameters are solved by building a function model, whereby the model parameters in the built function model are solved
Figure 362258DEST_PATH_IMAGE057
Is of a size of
Figure 826737DEST_PATH_IMAGE058
(generally, the first scene image is selected as the reference image), the corresponding coefficient matrix
Figure 495616DEST_PATH_IMAGE020
Column number and model parameter vector of
Figure 285717DEST_PATH_IMAGE059
Are consistent in length. At this time, if the model parameter solution is required
Figure 305626DEST_PATH_IMAGE057
The key to constructing the coefficient matrix is
Figure 308217DEST_PATH_IMAGE020
Vector of sum observations
Figure 97181DEST_PATH_IMAGE019
。
Specifically, step 2 in the embodiment of the present invention further includes:
taking an example of arbitrarily selecting one pixel from all pixels as a target pixel, a specific process of establishing a coefficient matrix and an observed value vector related to the pixel model parameter at the moment is introduced.
First, a polynomial fitting coefficient equation of the spatial trend error is established
Figure 58184DEST_PATH_IMAGE060
Time of day, with target pixel
Figure 299810DEST_PATH_IMAGE061
Is taken as the center and has the size of
Figure 106091DEST_PATH_IMAGE062
The InSAR phase in the window can be regarded as the sum of the deformation phase, the space trend error phase and the terrain correlation error phase, wherein the model parameters in the window comprise the deformation phase of each pixel
Figure 15142DEST_PATH_IMAGE063
Topography dependent error phase
Figure 881467DEST_PATH_IMAGE064
And polynomial fitting coefficients of spatial trend error phase within the window
Figure 875967DEST_PATH_IMAGE065
In which
Figure 220361DEST_PATH_IMAGE066
Is composed of
Figure 983918DEST_PATH_IMAGE067
Integer within interval, therefore, inSAR phase observation for each pixel within the window
Figure 755565DEST_PATH_IMAGE068
Can be written as:
Figure 502941DEST_PATH_IMAGE069
（1）
in view of
Figure 651025DEST_PATH_IMAGE070
In time windows
Figure 269088DEST_PATH_IMAGE071
Each InSAR phase observation has:
Figure 477216DEST_PATH_IMAGE072
（2）
wherein,
Figure 443379DEST_PATH_IMAGE073
for the InSAR phase observation at each pixel within the window,
Figure 129575DEST_PATH_IMAGE074
for the phase of the deformation at each point,
Figure 867724DEST_PATH_IMAGE075
is composed of
Figure 981174DEST_PATH_IMAGE076
The integer number within the interval is such that,
Figure 171984DEST_PATH_IMAGE077
in order to have a terrain-dependent error phase,
Figure 927450DEST_PATH_IMAGE078
、
Figure 785685DEST_PATH_IMAGE079
、
Figure 335615DEST_PATH_IMAGE080
is a coefficient of a polynomial fit,Trepresenting a matrix transposition.
Vector of observed values in the above formula (2)
Figure 13721DEST_PATH_IMAGE081
Incorporating the total observed value vector
Figure 307299DEST_PATH_IMAGE082
In (2), then the corresponding coefficient matrix
Figure 754461DEST_PATH_IMAGE083
Will increase
Figure 475292DEST_PATH_IMAGE084
Lines, each line and the vector of observations in equation (2) above
Figure 640694DEST_PATH_IMAGE017
Corresponding to the elements of (2), most elements in each row are 0, and only correspond to the model parameter vector
Figure 472384DEST_PATH_IMAGE023
The column corresponding to the middle element is not 0, and the value is the matrix of coefficients in the above formula (2)
Figure 39632DEST_PATH_IMAGE024
The corresponding element of the corresponding row.
Specifically, step 2 in the embodiment of the present invention further includes:
establishing a linear fitting coefficient equation of the terrain-related errors in
Figure 931364DEST_PATH_IMAGE060
Time and target pixel
Figure 584062DEST_PATH_IMAGE061
Is taken as the center and has the size of
Figure 953864DEST_PATH_IMAGE085
The InSAR phase within the window can also be considered as the sum of the morphed phase, the trend phase, and the terrain-dependent phase, with the difference that the model parameters within the window include the morphed phase at each point
Figure 641197DEST_PATH_IMAGE086
Trend phase
Figure 703831DEST_PATH_IMAGE087
And linear fitting coefficients for terrain-dependent errors within the window
Figure 578246DEST_PATH_IMAGE088
Wherein
Figure 17318DEST_PATH_IMAGE089
is composed of
Figure 559158DEST_PATH_IMAGE090
Integer within the interval, thus, for InSAR phase observations at each pixel within the window
Figure 792693DEST_PATH_IMAGE091
Can be written as:
Figure 154404DEST_PATH_IMAGE092
（3）
in view of
Figure 134517DEST_PATH_IMAGE070
Common within a time window
Figure 530863DEST_PATH_IMAGE093
Each InSAR phase observation includes:
Figure 935300DEST_PATH_IMAGE094
（4）
wherein,
Figure 784307DEST_PATH_IMAGE095
for an InSAR phase observation at each pixel within the window,
Figure 299602DEST_PATH_IMAGE096
in order to change the phase of the deformation,
Figure 816034DEST_PATH_IMAGE097
in order to trend the phase of the signal,
Figure 391372DEST_PATH_IMAGE098
is an integer number within the window interval and,
Figure 727675DEST_PATH_IMAGE099
is a pixel
Figure 312240DEST_PATH_IMAGE100
And a pixel
Figure 417600DEST_PATH_IMAGE101
The difference in elevation between the two electrodes,
Figure 163839DEST_PATH_IMAGE102
、
Figure 987438DEST_PATH_IMAGE103
is the coefficient of a linear equation;
vector the observed values in the above formula (4)
Figure 110115DEST_PATH_IMAGE104
Incorporating the total observed value vector
Figure 69981DEST_PATH_IMAGE105
In (2), then the corresponding coefficient matrix
Figure 987121DEST_PATH_IMAGE106
Will increase
Figure 563596DEST_PATH_IMAGE107
Lines, each line and the vector of observations in equation (4) above
Figure 224385DEST_PATH_IMAGE104
Corresponds to the elements of (1), most elements in each row are 0, and only correspond to the model parameter vector
Figure 38757DEST_PATH_IMAGE023
The corresponding column of the middle element is not 0, and the value is the coefficient matrix in the above formula (4)
Figure 657957DEST_PATH_IMAGE024
The corresponding element of the corresponding row.
It should be noted that, since the spatial dimensions of the spatial trend error and the terrain-related error are generally different, for example, the spatial dimension for modeling the terrain-related error is often related to the actual terrain, and the spatial dimension of the spatial trend error is often in a larger range, the window size model parameters in the process of establishing the above equations (2) and (4) are more extensive
Figure 190569DEST_PATH_IMAGE108
Are generally different. Further, as can be seen from equations (2) and (4), the observed value vectors in the two types of equations
Figure 389470DEST_PATH_IMAGE109
And
Figure 323928DEST_PATH_IMAGE110
will contain the same observed value, that is to say, for one observed value in InSAR time sequence phase
Figure 114029DEST_PATH_IMAGE111
May be in the final observation vector
Figure 868358DEST_PATH_IMAGE112
Multiple times. And when the trend phase in the window is modeled in the formula (1), the reference point of the space position is the target pixel
Figure 136529DEST_PATH_IMAGE100
In this case, the constant term in the polynomial coefficient is the trend phase value at the pixel, and the target pixel
Figure 188143DEST_PATH_IMAGE100
The trend phase of (b) may also appear as a model parameter in an equation established at other pixel, namely equation (2); similarly, when the terrain related error in the window is modeled in the formula (3), the reference point of the elevation is the target pixel
Figure 617987DEST_PATH_IMAGE100
The elevation of the target pixel, in which case the constant term in the linear equation coefficient is the terrain related error value of the pixel, and the target pixel
Figure 125192DEST_PATH_IMAGE113
The terrain-related error at (a) may also appear as a model parameter in the equations established at other picture elements, i.e., equation (4). From the analysis, it can be seen that the formulas (2) and (4) established for different pixels contain model parameters of other pixels, so that the model parameter solution of each pixel cannot be performed pixel by pixel, only one large-scale function model about all model parameters at all moments and all pixels can be established, then the model parameters are integrally solved, and the solved model parameters are space trend errors and terrain related errors.
Specifically, step 2 in the embodiment of the present invention further includes:
and (3) assuming that the time sequence deformation is fitted through a cubic polynomial in a certain time window range, namely providing an external constraint condition for the time sequence deformation, and establishing a virtual observation equation related to the time sequence deformation. In general, the virtual observation equation is in the form of "0= coefficient matrix × model parameter vector". For time-series deformation, the model parameter vector is the time-series deformation, so the key point for constructing the virtual observation equation is how to determine a corresponding coefficient matrix according to external constraint conditions.
At the moment of time
Figure 931474DEST_PATH_IMAGE070
By target pixel
Figure 840524DEST_PATH_IMAGE113
The process of constructing the virtual observation equation is described as follows:
first, with the time of day
Figure 706849DEST_PATH_IMAGE070
As a center, take the size of
Figure 435770DEST_PATH_IMAGE114
Time window of
Figure 45743DEST_PATH_IMAGE115
Then the corresponding model parameter (time series deformation) vector is
Figure 74879DEST_PATH_IMAGE116
. When the temperature is higher than the set temperature
Figure 908843DEST_PATH_IMAGE117
When known, the following relationships exist:
Figure 452957DEST_PATH_IMAGE118
（5）
coefficient matrix
Figure 601041DEST_PATH_IMAGE119
In the step (1), the first step,
Figure 219104DEST_PATH_IMAGE120
、
Figure 958390DEST_PATH_IMAGE121
、
Figure 661904DEST_PATH_IMAGE122
are respectively the first
Figure 879259DEST_PATH_IMAGE123
Scene SAR image and second
Figure 351829DEST_PATH_IMAGE124
Time difference between scene SAR image moments
Figure 733787DEST_PATH_IMAGE125
Scene SAR image and second
Figure 190176DEST_PATH_IMAGE124
Time difference between scene SAR image moments
Figure 680063DEST_PATH_IMAGE126
Scene SAR image and second
Figure 272719DEST_PATH_IMAGE124
The time difference between scene SAR image moments, constant terms in cubic polynomial coefficients are
Figure 822649DEST_PATH_IMAGE070
Deformation corresponding to the moment. Due to the coefficient matrix
Figure 500755DEST_PATH_IMAGE119
Is known, then based on the least square method can obtain
Figure 794333DEST_PATH_IMAGE127
（6）
Further, the time sequence deformation can be obtained
Figure 241495DEST_PATH_IMAGE128
Fitting value of cubic polynomial
Figure 962326DEST_PATH_IMAGE129
Is composed of
Figure 393307DEST_PATH_IMAGE130
（7）
In the formula,
Figure 224997DEST_PATH_IMAGE131
and
Figure 526665DEST_PATH_IMAGE132
are all known quantities.
In theory, it is possible to use,
Figure 418398DEST_PATH_IMAGE133
and
Figure 71096DEST_PATH_IMAGE134
the difference is equal to 0, then there is
Figure 706477DEST_PATH_IMAGE135
（8）
Wherein,
Figure 128231DEST_PATH_IMAGE136
for the intermediate model parameter variables, the model parameters,
Figure 190865DEST_PATH_IMAGE137
and
Figure 330859DEST_PATH_IMAGE138
the difference between the values of the two values is equal to 0,
Figure 504352DEST_PATH_IMAGE139
in order to change the shape of the time sequence,
Figure 780612DEST_PATH_IMAGE140
to shape the time sequence
Figure 14147DEST_PATH_IMAGE141
The fitting value of the cubic polynomial of (c),
Figure 641438DEST_PATH_IMAGE120
、
Figure 618621DEST_PATH_IMAGE121
、
Figure 14967DEST_PATH_IMAGE122
are respectively the first
Figure 419404DEST_PATH_IMAGE123
Scene SAR image and scene SAR image
Figure 2832DEST_PATH_IMAGE124
Time difference between scene SAR image moments
Figure 69793DEST_PATH_IMAGE125
Scene SAR image and second
Figure 320646DEST_PATH_IMAGE124
Time difference between scene SAR image moments
Figure 895984DEST_PATH_IMAGE126
Scene SAR image and scene SAR image
Figure 966708DEST_PATH_IMAGE124
The time difference between the moments of the scene SAR images,
Figure 551273DEST_PATH_IMAGE142
。
equation (8) is the time in the method of the present invention
Figure 656632DEST_PATH_IMAGE060
Target pixel
Figure 402871DEST_PATH_IMAGE113
And (4) constructing a virtual observation equation. For each moment of each pixel, the formula (A)8) When in the observation vector
Figure 226471DEST_PATH_IMAGE019
Add a 0 value element to the corresponding coefficient matrix
Figure 349148DEST_PATH_IMAGE020
A row is added, and the elements in the row corresponding to the model parameters in the formula (8) are the corresponding elements of the coefficient matrix in the formula (8). It can be seen that, in the modeling process in the similar space and the virtual observation equation in time, for a certain moment, the model parameters of the pixels corresponding to other moments are also included, so that the model parameters at all moments need to be modeled and solved simultaneously.
In addition to the three equation establishment methods described above, additional virtual observation equations may also be established, typically using other a priori information. For example, in some research areas, the deformation range is often smaller than the coverage range of the whole SAR image, so there is a far-field area, which is considered as the far-field area without surface deformation, that is:
Figure 574593DEST_PATH_IMAGE143
（9）
similar to equation (8), the above-mentioned virtual observation equation can also be added to the final model parameter solution function model (i.e. the model
Figure 757312DEST_PATH_IMAGE144
). This kind of a priori assumption condition is often true because in the process of InSAR data processing, it is inevitable to perform spatial phase unwrapping with a certain point as a reference point in space, that is, the measurement result of the InSAR data itself is a relative result. For a target research area, some areas are manually selected based on prior information, and the deformation of the areas is assumed to be 0, so that the reliability of the combined model in the embodiment of the invention can be further improved.
Based on the formulas (2) and (4)The parameters for solving the model can be obtained from (8) and (9)
Figure 802629DEST_PATH_IMAGE051
Vector of observed values of
Figure 463417DEST_PATH_IMAGE019
Sum coefficient matrix
Figure 543369DEST_PATH_IMAGE020
Wherein
Figure 896990DEST_PATH_IMAGE145
Satisfies the following formula
Figure 429602DEST_PATH_IMAGE146
（10）
Equation (10) is a combined model of the spatial trend error, the terrain-related error and the deformation signal in the built InSAR time sequence phase, wherein,
Figure 894082DEST_PATH_IMAGE019
to be the total vector of observations,
Figure 828540DEST_PATH_IMAGE020
in the form of a matrix of coefficients,
Figure 353062DEST_PATH_IMAGE051
are model parameters.
Specifically, in the embodiment of the present invention, the coefficient matrix in the formula (10) is used
Figure 372970DEST_PATH_IMAGE020
Is a large coefficient matrix, so the existing sparse least square iterative algorithm is adopted to carry out the step 3 on the model parameters
Figure 641141DEST_PATH_IMAGE051
Solving is carried out, and the model parameters in the formula (10) are quickly and accurately solved through the lsmr function in the matlab to obtainTo the corresponding spatial trend error and terrain-related error at each pixel at each instant in time.
Specifically, in step 4, the spatial trend error and the terrain correlation error are subtracted from the original InSAR time sequence phase, so that the corrected high-precision InSAR time sequence deformation is obtained.
In summary, based on the conventional method for obtaining the timing phase of the InSAR, the embodiments of the present invention consider that, within a certain spatial range (e.g., 1km × 1 km), the turbulent atmosphere and the orbit error can be modeled by using a first-order polynomial related to the position; the method can utilize the relation between the layered atmosphere and the local terrain to carry out linear modeling; within a certain time range (such as 1 month), most of the surface deformation can be regarded as a time-dependent smoothing process, and a time-dependent cubic function can be used for fitting; in the InSAR image, the deformation of the far field area is equal to 0, and the prior information can be used as a constraint condition for auxiliary modeling. Based on the 4 kinds of prior information, the invention realizes the combined modeling of different signals such as deformation, atmospheric delay, orbital error and the like in the InSAR time sequence phase, and on the basis, the solution is carried out by using a sparse least square iterative algorithm, so that the high-precision estimation and correction of the atmospheric delay and the orbital error in the InSAR time sequence phase can be realized, and the measurement precision of the InSAR time sequence deformation is further obviously improved; the method breaks through the idea of independently processing various errors by the traditional method, fully considers the time-space characteristics of multi-source signals, and greatly enriches the theory and method system of time sequence InSAR earth surface deformation measurement.
The following simulation experiments further illustrate the embodiments of the present invention:
InSAR time sequence deformation at 22 moments is obtained through simulation by an SBAS method, the space size of a deformation field is 600 x 600 pixels, and the spatial resolution of each pixel is 100m x 100m. Wherein the deformation is characterized by funnel shape in space, and the change trend of each point in time is logarithmic, i.e. the deformation is characterized by
Figure 695684DEST_PATH_IMAGE147
Deformation of
Figure 125529DEST_PATH_IMAGE148
In units of meters, time
Figure 632733DEST_PATH_IMAGE149
Represents the time difference relative to a reference time in days; the orbit error in the whole deformation field range at each moment is simulated, wherein the maximum magnitude of the orbit error is 10 radians (about 4.4 centimeters for a c wave band), and the orbit error shows that the three-dimensional trend direction is random at each moment in space; the turbulence atmospheric error at each moment can be simulated by using a fractal function with a fractal dimension of 2.2, and the maximum magnitude is 10 radians; regarding the layered exhaust steam related to the terrain, considering that the proportionality coefficients between the layered atmosphere and the terrain are possibly inconsistent in different regions of the space, the proportionality coefficients between the layered atmosphere phase and the terrain in different regions of the space are simulated by using a fractal function with a fractal dimension of 2.2 in a simulation experiment, and then the layered atmosphere component in the simulation data is obtained by multiplying the proportionality coefficient obtained through simulation by real DEM Data (DEM) global Digital Elevation data; and adding the simulated InSAR time sequence deformation, the orbit error, the turbulent atmosphere and the layered atmosphere to obtain the InSAR time sequence phase used by the simulation test.
In order to compare the advantages of the embodiment of the invention, the simulated InSAR time sequence phase is used as an observed value, and the method provided by the embodiment of the invention and the traditional method are respectively utilized to correct the atmospheric delay error and the orbit error in the InSAR time sequence phase. The conventional method is that in the whole image, a deformation region is masked, a trend phase and a terrain-related phase are jointly modeled and solved by using a non-deformation region, and then the trend phase and the terrain-related phase of the deformation region are forward calculated by using model parameters obtained by solving, so that the correction of related errors in the whole image can be realized, and as shown in fig. 2, the InSAR time sequence deformation results obtained by different methods at the center of a funnel show that the method provided by the embodiment of the invention is more accurate than the InSAR time sequence deformation results obtained by the conventional method.
The embodiment of the invention also provides a computer-readable storage medium for storing a computer program and implementing the method for correcting the timing InSAR error by executing the computer program.
The embodiment of the invention also provides a device for correcting the time sequence InSAR error, which is used for realizing the method for correcting the time sequence InSAR error and comprises the following steps:
a memory and a processor;
the memory is used for storing a computer program;
the processor is for executing the computer program stored by the memory.
While the foregoing is directed to the preferred embodiment of the present invention, it will be appreciated by those skilled in the art that various changes and modifications may be made therein without departing from the principles of the invention as set forth in the appended claims.

Claims (10)

1. A method for correcting time sequence InSAR errors is characterized by comprising the following steps:
step 1, acquiring an InSAR time sequence phase of an InSAR interferogram;
step 2, establishing a combined model for the spatial trend error, the terrain related error and the deformation signal in the InSAR time sequence phase based on the space-time characteristics of the multi-source signals, and solving model parameters in the combined model to obtain the spatial trend error and the terrain related error;
and 3, removing the space trend error and the terrain related error in the InSAR time sequence phase to obtain the corrected InSAR time sequence deformation.
2. The method for correcting timing InSAR error according to claim 1, wherein the step 2 further comprises:
modeling the space trend error by using a first-order polynomial to obtain a polynomial fitting coefficient equation;
characterizing the terrain related error by using a linear model to obtain a linear equation coefficient equation;
constructing a virtual observation equation for the deformation signal by utilizing a third-order polynomial function;
and simultaneously establishing the polynomial fitting coefficient equation, the linear equation coefficient equation and the virtual observation equation to obtain a combined model.
3. The method for correcting the timing InSAR error according to claim 2, wherein the model parameters in the joint model include timing deformation of all pixels, polynomial fitting coefficients of spatial trend errors at all pixels, and linear equation coefficients of terrain-related errors at all pixels.
4. The method for correcting timing InSAR error according to claim 3, wherein the step 2 further comprises:
randomly selecting one pixel from all pixels as a target pixel;
at the moment of time
Figure 796490DEST_PATH_IMAGE001
With the target pixel
Figure 120155DEST_PATH_IMAGE002
Is taken as the center and has the size of
Figure 368734DEST_PATH_IMAGE003
The polynomial fitting coefficient equation is established as follows:
Figure 704556DEST_PATH_IMAGE004
wherein,
Figure 987770DEST_PATH_IMAGE005
for an InSAR phase observation at each pixel within the window,
Figure 747915DEST_PATH_IMAGE006
for the phase of the deformation at each point,
Figure 483790DEST_PATH_IMAGE007
is composed of
Figure 151532DEST_PATH_IMAGE008
The number of integers in the interval (a) is,
Figure 554831DEST_PATH_IMAGE009
in order for the terrain-dependent error phase to be,
Figure 17037DEST_PATH_IMAGE010
、
Figure 505787DEST_PATH_IMAGE011
、
Figure 711640DEST_PATH_IMAGE012
fitting coefficients for the polynomial;
vector the observed values in the above equation
Figure 703867DEST_PATH_IMAGE013
Incorporating the total observed value vector
Figure 868132DEST_PATH_IMAGE014
In (3), then the corresponding coefficient matrix
Figure 578599DEST_PATH_IMAGE015
Will increase
Figure 588143DEST_PATH_IMAGE016
Line, each line and the above formula medium observation value vector
Figure 700456DEST_PATH_IMAGE013
Corresponding to the elements of (2), most elements in each row are 0, and only correspond to the model parameter vector
Figure 770043DEST_PATH_IMAGE017
The column corresponding to the middle element is not 0, and the value is the matrix of the middle and coefficient in the above formula
Figure 967806DEST_PATH_IMAGE018
The corresponding element of the corresponding row.
5. The method for correcting timing InSAR error according to claim 4, wherein said step 2 further comprises:
randomly selecting one pixel from all pixels as a target pixel;
at the moment of time
Figure 781041DEST_PATH_IMAGE001
With the target pixel
Figure 744931DEST_PATH_IMAGE002
Is taken as the center and has the size of
Figure 250998DEST_PATH_IMAGE019
The linear equation coefficient equation is established:
Figure 670478DEST_PATH_IMAGE020
wherein,
Figure 21825DEST_PATH_IMAGE005
for an InSAR phase observation at each pixel within the window,
Figure 108730DEST_PATH_IMAGE006
in order to change the phase of the deformation,
Figure 520120DEST_PATH_IMAGE021
in order to trend the phase of the signal,
Figure 692475DEST_PATH_IMAGE022
is an integer number within the window interval and,
Figure 581934DEST_PATH_IMAGE023
is a pixel
Figure 523345DEST_PATH_IMAGE002
And a pixel
Figure 777740DEST_PATH_IMAGE024
The difference in elevation between the two electrodes,
Figure 171812DEST_PATH_IMAGE025
、
Figure 864962DEST_PATH_IMAGE026
is the coefficient of a linear equation;
vector the observed value in the above formula
Figure 129721DEST_PATH_IMAGE013
Incorporation of the Total observed value vector
Figure 882913DEST_PATH_IMAGE014
In (2), then the corresponding coefficient matrix
Figure 778930DEST_PATH_IMAGE015
Will increase
Figure 275770DEST_PATH_IMAGE016
Lines, each line and the observed value vector in the above formula
Figure 395036DEST_PATH_IMAGE013
Corresponding to the elements of (2), most elements in each row are 0, and only correspond to the model parameter vector
Figure 53551DEST_PATH_IMAGE017
The corresponding column of the middle element is not 0, and the value is the coefficient moment in the formulaMatrix of
Figure 422215DEST_PATH_IMAGE018
The corresponding element of the corresponding row.
6. The method for correcting timing InSAR error according to claim 5, characterized in that said step 2 further includes:
randomly selecting one pixel from all pixels as a target pixel;
at the moment of time
Figure 926009DEST_PATH_IMAGE001
With the target pixel
Figure 962098DEST_PATH_IMAGE002
Taking a time window with the size as the center, and constructing a virtual observation equation as follows:
Figure 791514DEST_PATH_IMAGE027
wherein,
Figure 913053DEST_PATH_IMAGE028
，
Figure 751696DEST_PATH_IMAGE029
for the intermediate model parameter variables, the model parameters,
Figure 111134DEST_PATH_IMAGE030
and
Figure 642609DEST_PATH_IMAGE031
the difference between the values of the two values is equal to 0,
Figure 454707DEST_PATH_IMAGE032
in order to change the shape of the time sequence,
Figure 362620DEST_PATH_IMAGE033
to shape the time sequence
Figure 310985DEST_PATH_IMAGE034
The fitting value of the cubic polynomial of (c),
Figure 744853DEST_PATH_IMAGE035
、
Figure 309826DEST_PATH_IMAGE036
、
Figure 755851DEST_PATH_IMAGE037
are respectively the first
Figure 89880DEST_PATH_IMAGE038
Scene SAR image and scene SAR image
Figure 166421DEST_PATH_IMAGE040
Time difference between scene SAR image moments
Figure 218690DEST_PATH_IMAGE041
Scene SAR image and second
Figure 937248DEST_PATH_IMAGE040
Time difference between scene SAR image moments
Figure 656942DEST_PATH_IMAGE042
Scene SAR image and second
Figure 435542DEST_PATH_IMAGE043
The time difference between the scene SAR image instants,
Figure 240687DEST_PATH_IMAGE044
。
7. the method for correcting timing InSAR error according to claim 6, wherein the step 2 further comprises:
the additional virtual observation equation is established by using the prior information as follows:
Figure 762935DEST_PATH_IMAGE045
adding the virtual observation equation to the total observation vector
Figure 71557DEST_PATH_IMAGE014
And in the corresponding coefficient matrix
Figure 286638DEST_PATH_IMAGE015
Add one row in.
8. The method for correcting timing InSAR error according to claim 7, wherein the simultaneous fitting of the polynomial fitting coefficient equation, linear equation coefficient equation and virtual observation equation to obtain a combined model comprises:
based on the polynomial fitting coefficient equation, the linear equation coefficient equation, the virtual observation equation and the additional virtual observation equation, establishing a combined model of the space trend error, the terrain correlation error and the deformation signal in the InSAR time sequence phase as follows:
Figure 313500DEST_PATH_IMAGE046
wherein,
Figure 639439DEST_PATH_IMAGE014
to be the total vector of observations,
Figure 802567DEST_PATH_IMAGE015
in the form of a matrix of coefficients,
Figure 188549DEST_PATH_IMAGE047
are model parameters.
9. A computer-readable storage medium storing a computer program for implementing the method for correcting timing InSAR error of any one of claims 1 to 8 by executing the computer program.
10. A correction device for timing InSAR errors, for implementing the correction method for timing InSAR errors according to any one of claims 1 to 8, characterized in that it comprises:
a memory and a processor;
the memory is used for storing a computer program;
the processor is configured to execute the computer program stored by the memory.
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