Error transfer modeling method for multi-orbit InSAR

Abstract

The invention discloses a multi-orbit InSAR error transfer modeling method, comprising: respectively obtaining multi-orbit surface LOS deformation and azimuth deformation; establishing the relationship between multi-orbit LOS deformation and azimuth deformation and surface three-dimensional deformation; establishing a deformation relationship equation group; establishing the relationship between the surface vertical, east-west and north-south directions and InSAR observations to obtain a relationship function; constructing a partial differential equation according to the relationship function; establishing a system error transfer model; constructing a comprehensive system error transfer model based on the system error transfer model and the system error caused by ignoring the north-south direction to solve the surface two-dimensional deformation algorithm; considering the correlation between multi-orbit InSAR observations and combining the random error of standard deviation evaluation, establishing a random error transfer model for the transmission of multi-orbit LOS and azimuth deformation errors to the surface three-dimensional deformation, and combining the system error and the random error transfer model to obtain the error transfer model of multi-orbit InSAR. The purpose of accurately calculating the surface three-dimensional deformation error is achieved.

Description

Technical Field

[0001] The invention relates to the field of microwave remote sensing measurement, and in particular to a multi-orbit InSAR error transfer modeling method. Background Art

[0002] Synthetic Aperture Radar Interferometry (InSAR) and Multiple-aperture SAR interferometry (MAI) are not restricted by weather conditions and can measure small-scale deformations in the LOS and azimuth directions of the surface over long distances without contact. They have the advantages of high spatial resolution, high accuracy, and wide monitoring area. The deformation in the LOS and azimuth directions alone cannot reflect the true surface deformation. The deformation in the three-dimensional directions, i.e., vertical, east-west, and north-south directions, can well assess the degree of surface deformation. At present, the method for solving the three-dimensional deformation of the surface is mainly to use the least squares method to jointly solve the LOS and azimuth deformations observed by multi-orbit InSAR. This method requires the decomposition of the LOS or azimuth deformations of at least three orbits, which means that the deformation errors in different LOS and azimuth directions will be transmitted to the three-dimensional deformation of the surface in different proportions. The sources of deformation errors in LOS and azimuth directions mainly include: phase decoherence, observation time asynchrony, satellite orbit and DEM inaccuracy, atmospheric troposphere and ionosphere delay, and SAR system noise. According to the error type, it can be divided into two categories: random error and systematic error. Among them, observation time asynchrony, satellite orbit and DEM inaccuracy, atmospheric ionosphere delay and layer delay mainly cause systematic errors; phase decoherence and atmospheric turbulence delay cause random errors. The existing technology has the problem of not being able to accurately calculate the three-dimensional deformation error of the surface. Summary of the invention

[0003] In order to solve the technical problems in the prior art, the present invention provides a multi-track InSAR error transfer modeling method. The method comprises the following contents:

[0004] A first aspect of the present invention provides a multi-orbit InSAR error transfer modeling method, comprising:

[0005] Obtain the LOS deformation and azimuth deformation of the multi-orbit surface respectively;

[0006] According to the geometric relationship of SAR sensor side-view imaging, the relationship between LOS deformation and azimuth deformation and the three-dimensional deformation of the surface is established;

[0007] The deformation relationship equations are established based on the approximately equal relationship between the LOS deformation and the vertical and east-west directions of the ground surface;

[0008] Based on the three-dimensional deformation of the surface and the deformation relationship equation group, the relationship between the surface vertical, east-west and north-south directions and InSAR observations is established to obtain the relationship function;

[0009] Construct partial differential equations based on relational functions;

[0010] A system error transmission model is established based on the relationship between the three-dimensional deformation of the surface and the partial differential equation;

[0011] A comprehensive error transfer model is constructed based on the system error transfer model and the system error caused by ignoring the north-south direction in solving the two-dimensional surface deformation algorithm;

[0012] Considering the correlation between multi-orbit InSAR observations and combining the random errors evaluated by standard deviation, a random error transfer model for the transmission of multi-orbit LOS and azimuth deformation errors to the three-dimensional surface deformation is established. The error transfer model of multi-orbit InSAR is obtained by combining the systematic error and random error transfer models.

[0013] Optionally, the relationship between the LOS deformation and the azimuth deformation and the three-dimensional deformation of the ground surface is established based on the geometric relationship of the SAR sensor side imaging:

[0014]

[0015]

[0016] When the azimuthal deformation is obtained by MAI or OT technology, the above expression can be written as:

[0017]

[0018] Where Dl represents the deformation in the LOS direction;

[0019] Da represents the azimuthal deformation obtained by MAI or OT technique;

[0020] Du represents the vertical deformation of the surface;

[0021] De represents the east-west deformation of the ground;

[0022] Dn represents the ground deformation in the north-south direction;

[0023] The superscripts A and D indicate the data of ascending and descending orbits, respectively;

[0024] θ represents the radar satellite incident angle;

[0025] α represents the clockwise angle between the north direction and the flight direction of the radar satellite, i.e. the azimuth. The α value is obtained from the SAR data file.

[0026] Optionally, the deformation relationship equation group is established based on the approximately equal relationship between the LOS deformation and the vertical and east-west directions of the ground surface after ignoring the north-south deformation. The deformation relationship equation group is:

[0027]

[0028] Optionally, the relationship between the surface vertical, east-west and north-south directions and the InSAR observations is established based on the three-dimensional surface deformation and the deformation relationship equation group to obtain the relationship function, including:

[0029] Assuming that there are more than two tracks of InSAR observation data in the set area, the relationship function between the three-dimensional deformation of the surface and the InSAR measurement data is expressed as:

[0030]

[0031] In the formula, m represents the number of available LOS deformations in the study area;

[0032] n represents the number of azimuthal deformations available in the study area;

[0033] The three-dimensional deformation of the surface is obtained using the weighted least squares method and is expressed as:

[0034] D=(A T ·P·A) -1 ·A T ·P·L,

[0035] Where D represents the three-dimensional deformation of the surface.

[0036] A represents the relationship matrix between three-dimensional deformation, LOS direction and azimuth direction deformation when the three-dimensional deformation of the set area is obtained using m LOS direction data and n azimuth direction data.

[0037]

[0038] L represents the column matrix composed of LOS deformation and azimuth deformation

[0039] P represents the matrix composed of weights for each measurement.

[0040] Optionally, constructing a partial differential equation according to the relationship function includes:

[0041] The vertical, east-west and north-south directions have a linear relationship with the InSAR observations used, which can be expressed as:

[0042]

[0043] F1 represents the expression of vertical deformation with respect to the used LOS deformation and azimuth deformation;

[0044] F2 represents the expression of the east-west deformation with respect to the LOS deformation and azimuth deformation used;

[0045] F3 represents the expression of the north-south deformation with respect to the LOS deformation and azimuth deformation used;

[0046] Defining the system error using differential equations gives the partial differential equation:

[0047]

[0048] du is the vertical function increment, de is the east-west function increment, dn is the north-south function increment, d(l i ) and d(a v ) represent the differential components in the LOS direction and the azimuth direction, respectively, where i = 1,…,m; v = 1,…,n.

[0049] Optionally, the system error transmission model is established based on the three-dimensional deformation relationship of the surface and the partial differential equation, including: assuming that the system error of the k-th pixel point of the LOS measurement value is The systematic error of the kth pixel of the azimuth measurement value is The system error transmission model is:

[0050]

[0051] In the formula, represents the system error in the vertical direction, Systematic error in the east-west direction, Systematic error in the north-south direction, is the expression of the vertical deformation of the k-th pixel point with respect to the LOS direction and azimuth direction used; is the expression of the east-west deformation with respect to the k-th pixel deformation in the LOS and azimuth directions; is the expression of the north-south deformation with respect to the k-th pixel deformation in the LOS and azimuth directions used;

[0052] Assuming that each InSAR measurement data only has systematic errors, the systematic error transmission model is simplified to:

[0053]

[0054] In the formula, Indicates the systematic error in the three-dimensional deformation of the surface,

[0055] represents the systematic error in the LOS and azimuth measurements, and

[0056] B k represents the relationship matrix between the LOS and azimuth measurements and the three-dimensional deformation of the surface, and

[0057] It represents the system error transfer coefficient of each LOS direction in the vertical system error,

[0058] It represents the system error transfer coefficient in each direction of the vertical system error.

[0059] Represents the system error coefficient of each LOS direction in the east-west system error,

[0060] Represents the systematic error coefficient of each direction in the east-west systematic error,

[0061] Indicates the system error coefficient of each LOS direction in the north-south system error,

[0062] Represents the systematic error coefficient of each direction in the north-south systematic error,

[0063] i=1……m,v=1……n,m and n are both natural numbers;

[0064] The calculation method of the systematic error of the measured values ​​of j pixels in the set area transferred to the systematic error of the three-dimensional deformation of the surface is:

[0065]

[0066] Optionally, the comprehensive error transfer model is constructed based on the system error transfer model and the system error caused by ignoring the north-south direction in solving the two-dimensional deformation algorithm of the surface, including:

[0067] Assuming that only LOS data is used in solving the two-dimensional deformation of the surface, the coefficient matrix ignoring the north-south direction is:

[0068]

[0069] The coefficient matrix of the three-dimensional deformation of the surface and the LOS deformation of each orbit is:

[0070]

[0071] Ignoring the additional systematic error caused by the north-south algorithm is expressed as:

[0072]

[0073] In the formula, β u represents the vertical error coefficient,

[0074] β e represents the error coefficient in the east-west direction,

[0075] (x,:) represents all the values ​​in the xth row of the matrix, where x is 1, 2, or 3;

[0076] I m×1 represents the identity matrix of size m×1;

[0077] Represents the north-south deformation value of the k-th pixel;

[0078] Combining the system error transmission model and the additional system error, the comprehensive system error transmission model is constructed as follows:

[0079]

[0080] and Ignoring the north-south direction and solving the two-dimensional deformation will cause systematic errors in the vertical direction and the east-west direction respectively.

[0081] Optionally, the random error transfer model of the multi-orbit InSAR deformation errors in the LOS direction and azimuth direction is established by considering the correlation between the multi-orbit InSAR observations and combining the random errors evaluated by the standard deviation to obtain the random error transfer model of the multi-orbit InSAR, including:

[0082] The random error transmission model is expressed as:

[0083]

[0084] In the formula, Refers to the root mean square error of the vertical deformation of k pixels;

[0085] Refers to the root mean square error of the north-south deformation of k pixels;

[0086] Refers to the root mean square error of the east-west deformation of k pixels;

[0087] represents the root mean square error of the k-th pixel point in the i-th LOS direction;

[0088] represents the root mean square error of the i-th azimuth deformation of the k-th pixel;

[0089] R u , R n , R e Respectively represent the covariance between the random errors in each LOS direction and azimuth direction,

[0090]

[0091] The random error model is expressed as:

[0092]

[0093] In the formula, represents the random error of the three-dimensional deformation of the surface,

[0094] represents the covariance matrix of the random errors of multi-track measurements; and the calculation method is:

[0095]

[0096] The coherence coefficient of deformation errors in LOS and azimuth directions of different orbits, is the coherence coefficient of deformation error in LOS direction of different orbits;

[0097] is the coherence coefficient of the deformation error in different orbital azimuths.

[0098] According to a second aspect of the present invention, there is provided an electronic device, the electronic device comprising:

[0099] at least one processor; and,

[0100] a memory communicatively connected to the at least one processor; wherein,

[0101] The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute any modeling method described in the first aspect.

[0102] According to a third aspect of the present invention, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores computer instructions for causing a computer to execute any modeling method described in the first aspect.

[0103] A multi-orbit InSAR error transfer modeling method of the present invention establishes a random error transfer model and a systematic error transfer model for transferring deformation errors in the LOS direction and azimuth direction to three-dimensional deformation based on the random error transfer law and the systematic error transfer law, thereby achieving the purpose of accurately calculating the three-dimensional deformation error of the surface by using the systematic error and random error in the LOS direction and azimuth direction. BRIEF DESCRIPTION OF THE DRAWINGS

[0104] Figure 1 This is a flow chart of the multi-orbit InSAR error transfer modeling method disclosed in this embodiment. DETAILED DESCRIPTION

[0105] Various exemplary embodiments of the present invention will now be described in detail. This detailed description should not be considered as limiting the present invention, but should be understood as a more detailed description of certain aspects, features, and embodiments of the present invention.

[0106] It should be understood that the terms described in the present invention are only for describing special embodiments and are not intended to limit the present invention. In addition, for the numerical range in the present invention, it should be understood that the upper and lower limits of the scope and each intermediate value therebetween are specifically disclosed. Each smaller range between the intermediate value in any stated value or stated range and any other stated value or intermediate value in the described range is also included in the present invention. The upper and lower limits of these smaller ranges can be independently included or excluded in the scope.

[0107] Unless otherwise indicated, all technical and scientific terms used herein have the same meanings as those generally understood by those skilled in the art. Although the present invention describes only preferred methods and materials, any methods and materials similar or equivalent to those described herein may also be used in the implementation or testing of the present invention. All documents mentioned in this specification are incorporated by reference to disclose and describe the methods and / or materials associated with the documents. In the event of a conflict with any incorporated document, the content of this specification shall prevail.

[0108] The study area of ​​this embodiment is the set area.

[0109] like Figure 1 As shown, a multi-orbit InSAR error transfer modeling method includes:

[0110] Step S1, using InSAR technology, SBAS-InSAR, MAI and OT technology to obtain the LOS deformation of the surface.

[0111] Specifically, based on DInSAR, MAI and OT technologies, SARspace software can be used to obtain geocoded LOS and azimuth deformation maps, where geocoding refers to converting the radar image coordinate system to the Universal Transverse Mercator (UTM) coordinate system.

[0112] Step S2: According to the geometric relationship of the SAR sensor side imaging, the relationship between the LOS and azimuth deformations and the three-dimensional deformation is established as follows:

[0113]

[0114]

[0115] In formulas (1) and (2), Dl represents the deformation in the line of sight; Da represents the azimuth deformation value obtained by MAI or OT technology; Du represents the vertical deformation of the ground surface; De represents the east-west deformation value of the ground; Dn represents the north-south deformation value of the ground; θ represents the incident angle of the radar satellite; α represents the clockwise angle between the north direction and the flight direction of the radar satellite, and its value is obtained from the SAR data file.

[0116] Step S3, based on the approximate relationship between the LOS deformation ignoring the north-south direction and the vertical direction and the east-west direction of the surface, a deformation relationship equation group is established, and the deformation relationship equation is:

[0117]

[0118] In formula (3), Dl represents the deformation value in the LOS direction; the superscripts A and D represent the data of ascending and descending orbits, respectively.

[0119] Step S4, the specific process of obtaining the three-dimensional deformation of the ground surface in the vertical direction, east-west direction, and north-south direction is as follows:

[0120] Assuming that there are more than two tracks of InSAR observation data in the study area, the three-dimensional deformation of the surface can be expressed as:

[0121]

[0122] In formula (4), m represents the number of available LOS directions in the study area; n represents the number of available azimuth directions in the study area;

[0123] The method of obtaining the three-dimensional deformation of the surface using the weighted least squares method is as follows:

[0124] D=(A T ·P·A) -1·A T ·P·L (5)

[0125] In formula (5), represents the three-dimensional deformation of the surface; A represents the three-dimensional deformation and relationship matrix when the three-dimensional deformation of the study area is obtained using m LOS data and n azimuth data, and L represents the column matrix composed of the LOS data and azimuth deformation used, P represents a diagonal matrix consisting of the weights of each measurement.

[0126] The LOS deformation obtained in the study area and the azimuth deformation obtained by MAI and OT technology are substituted into the equation, and each pixel point is traversed to obtain the vertical, east-west, and north-south deformations of the entire study area.

[0127] Step S5: construct a differential equation based on the established relationship between the vertical, east-west, north-south directions of the surface and the InSAR observations used:

[0128] The vertical direction, east-west direction, and vertical direction have a linear relationship with the InSAR observations used, as described below:

[0129]

[0130] In formula (6), F1 represents the expression of vertical deformation with respect to the used LOS deformation and azimuth deformation; F2 represents the expression of east-west deformation with respect to the used LOS deformation and azimuth deformation; F3 represents the expression of north-south deformation with respect to the used LOS deformation and azimuth deformation.

[0131] Because du, de, and dn are all multivariate linear functions, their systematic errors can be defined by partial differential equations:

[0132]

[0133] du is the vertical function increment, de is the east-west function increment, dn is the north-south function increment, d(l i ) and d(a v ) represent the differential components in the LOS direction and the azimuth direction, respectively, where i = 1,…,m; v = 1,…,n.

[0134] Step S6: The specific process of establishing the system error transfer model according to the differential equation of the three-dimensional deformation of the surface and the InSAR observation quantity used:

[0135] Assume that the systematic error of the kth pixel of each LOS measurement value and azimuth measurement value is Then the system error transmission model is written as:

[0136]

[0137] In formula (8) represents the system error in the vertical direction, represents the systematic error in the east-west direction, Represents the systematic error in the north-south direction.

[0138] Assuming that there are only systematic errors in each InSAR measurement data, the systematic error transfer model is simplified to:

[0139]

[0140] In formula (9), Indicates the systematic error in the three-dimensional deformation of the surface, represents the systematic error in the LOS and azimuth measurements, and B k represents the relationship matrix between the LOS and azimuth measurements and the three-dimensional deformation of the surface, and It represents the system error transfer coefficient of each LOS direction in the vertical system error, It represents the system error transfer coefficient in each direction of the vertical system error. It represents the system error transfer coefficient of each LOS direction in the east-west system error, It represents the system error transfer coefficient of each direction in the east-west system error, Indicates the system error coefficient of each LOS direction in the north-south system error, Represents the systematic error coefficient of each direction in the north-south systematic error,

[0141] The calculation method of the systematic error of the measured value of j pixel points in the study area transferred to the systematic error of the three-dimensional deformation of the surface is:

[0142]

[0143] Step S7, modeling the additional systematic error caused by the algorithm for solving the two-dimensional deformation of the surface in the north-south direction and providing a specific process of a comprehensive systematic error transmission model suitable for this algorithm:

[0144] Assuming that only LOS data is used in solving the two-dimensional deformation of the surface, the coefficient matrix ignoring the north-south direction is:

[0145]

[0146] The coefficient matrix of the three-dimensional deformation of the surface and the LOS deformation of each orbit is:

[0147]

[0148] The additional systematic error is expressed as:

[0149]

[0150]

[0151]

[0152] In formula (13), β u Indicates the vertical error coefficient; β e represents the error coefficient in the east-west direction; (x,:) represents all the values ​​in the xth row of the matrix; I m×1 represents the identity matrix of size m×1; Indicates the north-south deformation value of the k-th pixel.

[0153] The comprehensive system error transmission model and the additional system error model define the comprehensive system error transmission model as:

[0154]

[0155] Step S8: Specific process of using standard deviation to evaluate random errors and establish a random error transfer model for transferring multi-track LOS and azimuth deformation errors to ground three-dimensional deformation:

[0156]

[0157] In formula (17), u Refers to the root mean square error of vertical deformation; σ e The root mean square error of the north-south deformation; σ n Refers to the root mean square error of east-west deformation; represents the root mean square error of the i-th LOS deformation; represents the root mean square error of the i-th azimuth deformation; R u , R n , R e Represent the covariance between the random errors in each LOS direction and azimuth direction respectively.

[0158]

[0159] The random error model can be expressed as:

[0160]

[0161]

[0162]

[0163] In formula (19), represents the random error of the three-dimensional deformation of the surface, The covariance matrix representing the random errors of multi-orbit measurements.

[0164] The transfer model of the LOS deformation error of the multi-orbit InSAR of this embodiment to the three-dimensional deformation is achieved by using the InSAR technology and the time-series InSAR technology to obtain the LOS deformation of the surface, and using the MAI and OT technologies to obtain the azimuth deformation of the study area; according to the geometric relationship of the SAR sensor side-view imaging, a group of equations for the relationship between the LOS and azimuth deformations and the three-dimensional deformation of the surface is established; when the north-south solution is ignored to establish the approximate relationship between the LOS direction and the vertical direction and the east-west direction of the surface, the relationship equation is rewritten into a matrix form; the least squares method is used to solve the vertical, east-west, and north-south directions of the surface. Deformation; According to the deformation relationship equation group established based on the approximate relationship between LOS deformation and the vertical and east-west directions of the surface, the vertical and east-west deformation of the surface is solved by the least squares method, and the systematic errors in the vertical and east-west directions caused by ignoring the north-south solution method are modeled; the corresponding expressions of the two-dimensional surface deformation and the LOS deformation are inferred, and a two-dimensional system error transmission model and a random error transmission model are established according to the error transmission law; the corresponding expressions of the three-dimensional surface deformation and the LOS and azimuth directions are inferred, and a three-dimensional system error transmission model and a random error transmission model are established according to the error transmission law.

[0165] This embodiment establishes a model for the systematic error caused by ignoring the north-south direction. In the application of ignoring the north-south direction to obtain the surface deformation, the vertical and east-west accuracy can be improved. At the same time, it plays a guiding role in the application of ignoring the north-south direction to solve the two-dimensional shape of the surface, and improves the application prospects of this method. At the same time, this application establishes a model for the manifestation of the errors in the LOS direction and the azimuth direction in the three-dimensional deformation components of the surface, provides a method for studying how to improve the monitoring accuracy of the three-dimensional deformation of the surface, and provides a new solution for studying the monitoring accuracy evaluation method.

[0166] The electronic device disclosed in this embodiment includes a memory and a processor. The memory is used to store non-temporary computer-readable instructions. Specifically, the memory may include one or more computer program products, and the computer program product may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may, for example, include a random access memory (RAM) and / or a cache memory (cache), etc. The non-volatile memory may, for example, include a read-only memory (ROM), a hard disk, a flash memory, etc.

[0167] The processor may be a central processing unit (CPU) or other forms of processing units having data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions. In one embodiment of the present disclosure, the processor is used to run the computer-readable instructions stored in the memory, so that the electronic device performs all or part of the steps of the multi-orbit InSAR error transfer modeling method of each embodiment of the present disclosure.

[0168] Those skilled in the art should be able to understand that in order to solve the technical problem of how to obtain a good user experience, the present embodiment may also include well-known structures such as a communication bus and an interface, and these well-known structures should also be included in the protection scope of the present disclosure.

[0169] Electronic devices may include processing devices (e.g., central processing units, graphics processing units, etc.), which may perform various appropriate actions and processes according to programs stored in a read-only memory (ROM) or programs loaded from a storage device into a random access memory (RAM). In RAM, various programs and data required for the operation of the electronic device are also stored. The processing device, ROM, and RAM are connected to each other via a bus. An input / output (I / O) interface is also connected to the bus.

[0170] Typically, the following devices can be connected to the I / O interface: input devices such as sensors or visual information acquisition devices; output devices such as display screens; storage devices such as tapes, hard disks, etc.; and communication devices. The communication device can allow the electronic device to communicate with other devices (such as edge computing devices) wirelessly or by wire to exchange data. However, it should be understood that it is not required to implement or have all the devices shown. More or fewer devices may be implemented or provided instead.

[0171] In particular, according to an embodiment of the present disclosure, the process described above with reference to the flowchart can be implemented as a computer software program. For example, an embodiment of the present disclosure includes a computer program product, which includes a computer program carried on a non-transitory computer-readable medium, and the computer program contains program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network through a communication device, or installed from a storage device, or installed from a ROM. When the computer program is executed by a processing device, all or part of the steps of the multi-orbit InSAR error transfer modeling method of an embodiment of the present disclosure are executed.

[0172] For detailed description of this embodiment, reference may be made to the corresponding descriptions in the aforementioned embodiments, which will not be repeated here.

[0173] The computer-readable storage medium according to the embodiment of the present disclosure stores non-transitory computer-readable instructions. When the non-transitory computer-readable instructions are executed by a processor, all or part of the steps of the multi-orbit InSAR error transfer modeling method of each embodiment of the present disclosure are executed.

[0174] The above-mentioned computer-readable storage media include, but are not limited to: optical storage media (e.g., CD-ROM and DVD), magneto-optical storage media (e.g., MO), magnetic storage media (e.g., magnetic tape or mobile hard disk), media with built-in rewritable non-volatile memory (e.g., memory card) and media with built-in ROM (e.g., ROM box).

[0175] For detailed description of this embodiment, reference may be made to the corresponding descriptions in the aforementioned embodiments, which will not be repeated here.

[0176] The basic principles of the present disclosure are described above in conjunction with specific embodiments. However, it should be noted that the advantages, strengths, effects, etc. mentioned in the present disclosure are only examples and not limitations, and it cannot be considered that these advantages, strengths, effects, etc. are required by each embodiment of the present disclosure. In addition, the specific details disclosed above are only for the purpose of illustration and ease of understanding, and are not limitations. The above details do not limit the present disclosure to the necessity of adopting the above specific details to be implemented.

[0177] In the present disclosure, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply that there is any such actual relationship or order between these entities or operations. The block diagrams of the devices, devices, equipment, and systems involved in the present disclosure are only illustrative examples and are not intended to require or imply that they must be connected, arranged, and configured in the manner shown in the block diagram. As will be appreciated by those skilled in the art, these devices, devices, equipment, and systems can be connected, arranged, and configured in any manner. Words such as "including", "comprising", "having", etc. are open words, referring to "including but not limited to", and can be used interchangeably with them. The words "or" and "and" used here refer to the words "and / or" and can be used interchangeably with them, unless the context clearly indicates otherwise. The words "such as" used here refer to the phrase "such as but not limited to", and can be used interchangeably with them.

[0178] Additionally, as used herein, "or" used in a list of items beginning with "at least one" indicates a separate list, so that, for example, a list of "at least one of A, B, or C" means A or B or C, or AB or AC or BC, or ABC (i.e., A and B and C). Furthermore, the word "exemplary" does not mean that the example described is preferred or better than other examples.

[0179] It should also be noted that in the system and method of the present disclosure, each component or each step can be decomposed and / or recombined. Such decomposition and / or recombination should be regarded as equivalent solutions of the present disclosure.

[0180] Various changes, substitutions, and modifications of the techniques described herein may be made without departing from the teachings defined by the appended claims. Furthermore, the scope of the claims of the present disclosure is not limited to the specific aspects of the processes, machines, manufactures, compositions of events, means, methods, and actions described above. Currently existing or later to be developed processes, machines, manufactures, compositions of events, means, methods, or actions that perform substantially the same functions or achieve substantially the same results as the corresponding aspects described herein may be utilized. Thus, the appended claims include such processes, machines, manufactures, compositions of events, means, methods, or actions within their scope.

[0181] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use the present disclosure. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other aspects without departing from the scope of the present disclosure. Therefore, the present disclosure is not intended to be limited to the aspects shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

[0182] The above description has been given for the purpose of illustration and description. In addition, this description is not intended to limit the embodiments of the present disclosure to the forms disclosed herein. Although multiple example aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, changes, additions and sub-combinations thereof.

Claims

1. A multi-orbit InSAR error propagation modeling method, characterized in that: include: Obtain the LOS deformation and azimuth deformation of the multi-orbit surface respectively; According to the geometric relationship of SAR sensor side-view imaging, the relationship between LOS deformation and azimuth deformation and the three-dimensional deformation of the surface is established; The deformation relationship equations are established based on the approximately equal relationship between the LOS deformation and the vertical and east-west directions of the ground surface; Based on the three-dimensional deformation of the surface and the deformation relationship equation group, the relationship between the surface vertical, east-west and north-south directions and InSAR observations is established to obtain the relationship function; Construct partial differential equations based on relational functions; A system error transmission model is established based on the relationship between the three-dimensional deformation of the surface and the partial differential equation; A comprehensive error transfer model is constructed based on the system error transfer model and the system error caused by ignoring the north-south direction in solving the two-dimensional surface deformation algorithm; Considering the correlation between multi-orbit InSAR observations and combining the random errors evaluated by standard deviation, a random error transmission model of multi-orbit LOS and azimuth deformation errors to the three-dimensional surface deformation is established. The error transmission model of multi-orbit InSAR is obtained by combining the systematic error and random error transmission models.

2. The multi-orbit InSAR error transfer modeling method according to claim 1, characterized in that: According to the geometric relationship of the SAR sensor side imaging, the relationship between the LOS deformation and the azimuth deformation and the three-dimensional deformation of the surface is established as follows: When the azimuthal deformation is obtained by MAI or OT technology, the above expression can be written as: Where Dl represents the deformation in the LOS direction; Da represents the azimuthal deformation obtained by MAI or OT technique; Du represents the vertical deformation of the surface; De represents the east-west deformation of the ground; Dn represents the ground deformation in the north-south direction; The superscripts A and D indicate the data of ascending and descending orbits, respectively; θ represents the radar satellite incident angle; α represents the clockwise angle between the north direction and the flight direction of the radar satellite, i.e. the azimuth. The α value is obtained from the SAR data file.

3. The multi-orbit InSAR error transfer modeling method according to claim 2, characterized in that: According to the approximately equal relationship between LOS deformation and the vertical and east-west directions of the ground surface after ignoring the north-south deformation, the deformation relationship equation group is established. The deformation relationship equation group is:

4. The multi-orbit InSAR error transfer modeling method according to claim 3, characterized in that: Based on the three-dimensional deformation of the surface and the deformation relationship equation group, the relationship between the surface vertical, east-west and north-south directions and the InSAR observations is established to obtain the relationship function, including: Assuming that there are more than two tracks of InSAR observation data in the study area, the relationship function between the three-dimensional deformation of the surface and the InSAR measurement data is expressed as: In the formula, m represents the number of available LOS deformations in the study area; n represents the number of azimuthal deformations available in the study area; The three-dimensional deformation of the surface is obtained using the weighted least squares method and is expressed as: D=(A T ·P·A) -1 ·A T ·P·L, Where D represents the three-dimensional deformation of the surface. A represents the relationship matrix between three-dimensional deformation, LOS direction and azimuth direction deformation when the three-dimensional deformation of the set area is obtained using m LOS direction data and n azimuth direction data. L represents the column matrix composed of LOS deformation and azimuth deformation, P represents the matrix composed of weights for each measurement.

5. The multi-orbit InSAR error transfer modeling method according to claim 4, characterized in that: The constructing of the partial differential equation according to the relational function comprises: The vertical, east-west and north-south directions have a linear relationship with the InSAR observations used, which can be expressed as: F1 represents the expression of vertical deformation with respect to the used LOS deformation and azimuth deformation; F2 represents the expression of the east-west deformation with respect to the LOS deformation and azimuth deformation used; F3 represents the expression of the north-south deformation with respect to the LOS deformation and azimuth deformation used; Defining the system error using differential equations gives the partial differential equation: du is the vertical function increment, de is the east-west function increment, dn is the north-south function increment, d(l i ) and d(a v ) represent the differential components in the LOS direction and the azimuth direction, respectively, where i = 1,…,m; v = 1,…,n.

6. The multi-orbit InSAR error transfer modeling method according to claim 5, characterized in that: The system error transmission model is established based on the three-dimensional deformation relationship of the surface and the partial differential equation, including: assuming that the system error of the k-th pixel point of the LOS measurement value is The systematic error of the kth pixel of the azimuth measurement value is The system error transmission model is: In the formula, represents the system error in the vertical direction, Systematic error in the east-west direction, Systematic error in the north-south direction, is the expression of the vertical deformation of the k-th pixel point with respect to the LOS direction and azimuth direction used; is the expression of the east-west deformation with respect to the k-th pixel deformation in the LOS and azimuth directions; is the expression of the north-south deformation with respect to the k-th pixel deformation in the LOS and azimuth directions used; Assuming that each InSAR measurement data only has systematic errors, the systematic error transmission model is simplified to: In the formula, Indicates the systematic error in the three-dimensional deformation of the surface, represents the systematic error in the LOS and azimuth measurements, and B k represents the relationship matrix between the LOS and azimuth measurements and the three-dimensional deformation of the surface, and It represents the system error transfer coefficient of each LOS direction in the vertical system error, It represents the system error transfer coefficient in each direction of the vertical system error. It represents the system error transfer coefficient of each LOS direction in the east-west system error, Represents the systematic error coefficient of each direction in the east-west systematic error, Represents the system error coefficient of each LOS direction in the north-south system error, Represents the systematic error coefficient of each direction in the north-south systematic error, i=1……m,v=1……n,m and n are both natural numbers; The calculation method of the systematic error of the measured values ​​of j pixels in the set area transferred to the systematic error of the three-dimensional deformation of the surface is:

7. The multi-orbit InSAR error transfer modeling method according to claim 6, characterized in that: The comprehensive error transfer model is constructed based on the system error transfer model and the system error caused by ignoring the north-south direction to solve the two-dimensional deformation algorithm of the surface, including: Assuming that only LOS data is used in solving the two-dimensional deformation of the surface, the coefficient matrix ignoring the north-south direction is: The coefficient matrix of the three-dimensional deformation of the surface and the LOS deformation of each orbit is: Ignoring the additional systematic error caused by the north-south algorithm is expressed as: In the formula, β u represents the vertical error coefficient, β e represents the error coefficient in the east-west direction, (x,:) represents all the values ​​in the xth row of the matrix, where x is 1, 2, or 3; I m×1 represents the identity matrix of size m×1; Represents the north-south deformation value of the k-th pixel; Combining the system error transmission model and the additional system error, the comprehensive system error transmission model is constructed as follows: and Ignoring the north-south direction and solving the two-dimensional deformation will cause systematic errors in the vertical direction and the east-west direction respectively.

8. The multi-orbit InSAR error transfer modeling method according to claim 7, characterized in that: The random error transmission model of the multi-orbit InSAR is established by considering the correlation between the multi-orbit InSAR observations and combining the random errors evaluated by the standard deviation, and the random error transmission model of the multi-orbit LOS and azimuth deformation errors is transmitted to the three-dimensional deformation of the surface, and the random error transmission model of the multi-orbit InSAR is obtained, including: The random error transmission model is expressed as: In the formula, Refers to the root mean square error of the vertical deformation of k pixels; Refers to the root mean square error of the north-south deformation of k pixels; Refers to the root mean square error of the east-west deformation of k pixels; represents the root mean square error of the k-th pixel point in the i-th LOS direction; represents the root mean square error of the i-th azimuth deformation of the k-th pixel; R u , R n , R e Respectively represent the covariance between the random errors in each LOS direction and azimuth direction, The random error model is expressed as: In the formula, represents the random error of the three-dimensional deformation of the surface, represents the covariance matrix of the random errors of multi-track measurements; and the calculation method is: The coherence coefficient of deformation errors in LOS and azimuth directions of different orbits, is the coherence coefficient of deformation error in LOS direction of different orbits; is the coherence coefficient of the deformation error in different orbital azimuths.

9. An electronic device, characterized in that: The electronic device comprises: at least one processor; and, a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the modeling method described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a computer to execute the modeling method described in any one of claims 1-8.

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