GNSS tropospheric zenith delay aided insar tropospheric delay correction method

Abstract

The application relates to an InSAR tropospheric delay correction method assisted by GNSS tropospheric zenith delay, which comprises the following steps: obtaining a tropospheric zenith delay product of a GNSS station, converting the product into a radar line-of-sight delay observation, constructing a joint correction model of tropospheric delay, representing the delay as a sum of an elevation-dependent vertical layering component, a distance-dependent turbulent signal component and a random error, adopting a least square configuration theory to jointly and iteratively determine a turbulent signal covariance function and a signal-to-noise variance component, solve a vertical layering model parameter and a turbulent estimation value at the station, estimate a tropospheric delay of each pixel of an interferogram in combination with the elevation and spatial correlation of an unmeasured point, and obtain a correction map. The application independently models based on external GNSS zenith delay products, does not depend on InSAR interference phases, can completely cover incoherent regions, avoids non-tropospheric error interference, and improves the precision and applicability of medium and long wave tropospheric delay correction.

Description

Technical Field

[0001] This invention relates to the field of synthetic aperture radar interferometry (InSAR) technology, and in particular to an InSAR tropospheric delay correction method assisted by GNSS tropospheric zenith delay. Background Technology

[0002] Interferometric Synthetic Aperture Radar (InSAR) is an important technique for monitoring surface deformation, but tropospheric delay is a key source of error, causing phase errors ranging from several centimeters to tens of centimeters, and its spatiotemporal variations are highly nonlinear. Traditional external meteorological model correction methods are insufficient in spatiotemporal resolution to accurately capture small-scale tropospheric fluctuations; while algorithmic corrections based on Synthetic Aperture Radar (SAR) data itself tend to weaken high-frequency deformation and topographically related deformation signals, exhibiting inherent limitations.

[0003] Tropospheric delay can be decomposed into a vertically layered component strongly correlated with terrain elevation and a turbulent component with stochastic characteristics. With the increasing density of Global Navigation Satellite System (GNSS) stations, high temporal resolution GNSS tropospheric zenith total delay (ZTD) products have made it possible to independently acquire atmospheric delay information, providing a new approach to correcting long-wavelength tropospheric delay in InSAR.

[0004] Existing GInSAR methods fuse GNSS and InSAR data, employing polynomial surface fitting to model tropospheric delay by substituting the difference between GNSS displacement and InSAR phase, thus suppressing long-wavelength spatial correlation errors in interferograms. However, this method is limited by the sparse distribution of GNSS stations, resulting in limited fitting capabilities for low-order polynomials and a tendency for overfitting with higher-order polynomials, particularly in complex terrain regions where it struggles to accurately describe vertical stratification and turbulence characteristics. Kriging and least-squares configurations avoid the parameterization constraints of polynomial models. Among these, the joint vertical stratification and turbulence correction model based on Lens Shading Correction (LSC) is particularly advanced: this model uses an elevation correlation function and a stochastic model to characterize vertical stratification delay and turbulence delay, respectively. It simultaneously estimates the vertical stratification model parameters and the turbulence delay values ​​of GNSS stations using least-squares configuration. Subsequently, leveraging the vertical stratification model and the signal cross-covariance matrix, it extrapolates both components to arbitrary pixels in the interferogram, more effectively compensating for mid- and long-wavelength tropospheric delays compared to GInSAR.

[0005] Nevertheless, the LSC method described above still directly equates the difference between GNSS displacement and InSAR phase to InSAR tropospheric delay when constructing corrections, assuming that the displacement measured by GNSS completely reflects the actual surface deformation. For GNSS stations deployed on bedrock, this assumption is not strictly valid, and the calculation process must rely on InSAR observations, inevitably subject to interference from non-tropospheric delay phases such as Digital Elevation Model (DEM) errors and ionospheric delay. Furthermore, it cannot be applied to phase correction in incoherent regions.

[0006] Chinese patent application publication number CN118584431A discloses an InSAR tropospheric delay correction method that takes into account the stochastic characteristics of the atmosphere. First, it generates differential interferograms using SAR imagery and extracts the phase of high-coherence points. Simultaneously, it calculates the zone-time delay (ZTD) of grid points based on ERA-5 meteorological reanalysis data, constructing a time-series Prophet negative exponential vertical profile model to achieve near-real-time estimation of ZTD at different elevations at any given time. Based on this, for each InSAR high-coherence point, it filters nearby ZTD samples by combining three-dimensional spatial distance, establishes a stochastic model based on minimum linear unbiased estimation, and predicts the tropospheric delay of high-coherence points point by point, converting it into phase correction values. However, this method relies entirely on InSAR observations, can only calculate for high-coherence points in the interferogram that meet the coherence threshold requirement, cannot correct the phase in decoherent regions, and is susceptible to interference from other error sources in the interferometric phase, limiting its applicability.

[0007] Given that organizations such as the International GNSS Service (IGS) can provide high temporal resolution GNSS ZTD products covering most of the world, there is an urgent need to develop a tropospheric delay correction method that can directly utilize these ZTD products and is completely independent of InSAR observations. This would overcome the limitations of existing methods, such as strong dependence on InSAR phase, susceptibility to non-tropospheric errors, and inability to handle decoherent regions, thereby improving the universality and reliability of atmospheric delay correction in InSAR deformation monitoring. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the prior art by providing a GNSS tropospheric zenith delay-assisted InSAR tropospheric delay correction method. This method aims to achieve accurate correction of long-wave delay in the troposphere of InSAR interferograms using GNSS tropospheric zenith delay products, without relying on InSAR interferometric phase observations, avoiding non-tropospheric error interference, and being applicable to decoherent regions.

[0009] The objective of this invention can be achieved through the following technical solutions: This invention provides a GNSS tropospheric zenith delay-assisted InSAR tropospheric delay correction method, comprising the following steps: The tropospheric zenith delay of multiple GNSS stations is obtained, and the zenith tropospheric delay of each GNSS station is converted into radar line-of-sight delay observations. A joint correction model for tropospheric delay is constructed, which models the radar line-of-sight delay observation as the sum of vertical layer delay components, turbulent delay components, and random errors. The vertical layer delay components adopt an elevation-related function model, and the turbulent delay components adopt a random signal model based on spatial distance. By using the least squares configuration, the function model of the vertical layer delay component is taken as the deterministic function part, and the turbulent delay component is taken as the random signal part. The observation equation is established, and the covariance function of the turbulent delay component and the variance components of the signal and noise are determined by iteration. The parameters of the vertical layer model and the turbulent signal estimate at the GNSS station are jointly solved. Based on the solved vertical stratification model parameters and turbulence signal estimates, combined with the elevation information of unmeasured points and their spatial correlation with measured points, the vertical stratification delay and turbulence delay at each pixel in the InSAR interferogram are estimated to obtain the InSAR tropospheric delay correction map.

[0010] As a preferred technical solution, the radar line-of-sight delay observation is calculated using the following formula: in, For the first Radar line-of-sight delay observations at GNSS stations For the first GNSS tropospheric delayed zenith observations from GNSS stations The incident angle of the SAR image.

[0011] As a preferred technical solution, the vertical layering delay component is: in, , Here are the parameters of the vertical layering model to be determined. For the first DEM elevation of GNSS stations This is the preset reference elevation.

[0012] As a preferred technical solution, the tropospheric delay joint correction model is as follows: in, For the first Radar line-of-sight delay observations at GNSS stations For the first Irregular turbulence components of a GNSS station For the first Random errors of GNSS stations.

[0013] As a preferred technical solution, the process of jointly solving the parameters of the vertical layered model and the turbulence signal estimation at the GNSS station through least squares configuration includes the following steps: Establish observation equations ,in The observation vector is composed of line-of-sight delay observations from each GNSS station. The design matrix is ​​constructed based on the elevation difference. This is a parameter vector containing the parameters of the vertically hierarchical model. For turbulence signal vectors, This is the noise vector; According to the least squares allocation criterion Solving for the problem yields: Parameter estimation ; Signal Valuation ; in , The covariance matrix of the turbulence signal. Let be the covariance matrix of the noise. This represents the minimum value. This is a transpose.

[0014] As a preferred technical solution, the signal covariance matrix Noise covariance matrix , and These are the variance factors of the signal and noise, respectively. and These are the corresponding cofactor matrices; Estimating the total tropospheric delay at unmeasured points for: in, The design matrix is ​​constructed from the elevation information of unmeasured points. Let be the cross-covariance matrix between the measured point signals and the unmeasured point signals, and , The cross-factor matrix of the signal, This is the parameter vector for the vertically layered model.

[0015] As a preferred technical solution, the cofactor matrix Constructed using the following exponential covariance function: in, The interval distance is point and covariance; and The parameter to be estimated; The process of iteratively determining the covariance function of the turbulent delay signal includes the following steps: Step 1, Initialization Using an identity matrix, least squares estimation is used to determine the parameters of the vertical hierarchical model. ; Step 2, calculate the residuals Based on the variance and covariance of the residual statistical space, the exponential covariance function is fitted to obtain... and ; Step 3, using the obtained Update cofactor array ,in element at And repeat steps 1 and 2 until... and Stable, obtaining a definite cofactor matrix .

[0016] As a preferred technical solution, in step 2, the spatial variance is: in, For position The residual value at that point, The total number of GNSS stations; Given distance interval Inside The covariance of each measured point pair is: in, and Distance The residual value at that point, This represents the number of measured point pairs within a preset distance interval.

[0017] As a preferred technical solution, the variance components of signal and noise and The solution is obtained by iterative estimation of variance components, with the cofactor matrix fixed during the iteration process. And take the noise cofactor matrix For the identity matrix, the iterative equation is: in, To find the trace, , These are the variance factor estimates for the signal and noise, respectively.

[0018] As a preferred technical solution, the method is used for tropospheric delay correction of InSAR interferograms containing decoherent regions.

[0019] Compared with the prior art, the present invention has at least one of the following beneficial effects: (1) Get rid of dependence on InSAR observations themselves: Existing methods must rely on InSAR interferometric phase observations during the calculation process, which limits their applicability to the availability and quality of InSAR data and makes it impossible to implement correction independently. This invention directly uses publicly available GNSS tropospheric zenith delay products and projects them onto the radar line of sight as model input to establish a joint correction model that is completely independent of InSAR interferometric phase observations. This gets rid of dependence on InSAR observations themselves and makes the method an independent tropospheric delay correction tool. Its application is no longer limited by the presence or absence of InSAR images or the quality of coherence.

[0020] (2) Reduce the misjudgment rate of small bedrock deformation in GNSS: Traditional methods directly regard the difference between GNSS deformation and InSAR phase as InSAR tropospheric delay. This assumption is prone to introducing surface deformation signal contamination of atmospheric delay estimation. This invention directly models the amount of atmospheric delay reflected by GNSS ZTD products and decomposes it into two components: vertical stratification delay and turbulence delay, instead of fitting the difference between GNSS and InSAR observations. This avoids misjudging the small bedrock deformation contained in GNSS stations as tropospheric delay signals from the source of data, and achieves pure modeling and separation of the real atmospheric delay components.

[0021] (3) It can be used for tropospheric delay correction of InSAR interferograms containing decoherent regions: Existing methods rely on InSAR observations, which inevitably suffer from non-tropospheric phase errors such as DEM residuals and ionospheric delay during calculation. Furthermore, they cannot correct decoherent regions in the interferogram. This invention only models based on ZTD and external DEM elevation information at GNSS stations and estimates the tropospheric delay of unmeasured points through the signal covariance function. The correction process does not introduce the phase value of the InSAR interferogram. Since the input source is pure, the model estimation result is naturally free from DEM errors and ionospheric interference in the InSAR phase. At the same time, the generated correction map is a continuous field based on spatial estimation, which can completely cover the decoherent region and realize the mid-to-long-wave tropospheric delay correction of the entire scale range of the interferogram.

[0022] (4) Reduce overfitting: In terms of fine modeling, polynomial surface fitting is difficult to accurately characterize the random characteristics of turbulent atmosphere, and high-order polynomials are prone to overfitting in sparse areas of the station. This invention adopts the least squares configuration theory, uses the vertical layer delay related to elevation as the function model, uses the irregular turbulent delay as the distance-based random signal model, and uses the exponential covariance function to fit the spatial correlation of turbulence. The weight of the adaptive balance signal and noise is estimated by the variance component, which is more in line with the physical characteristics of tropospheric delay. It can not only solve the elevation-related terms robustly, but also capture the irregular spatial fluctuations of atmospheric turbulence reasonably through the random signal terms, which significantly improves the estimation accuracy of medium and long wave tropospheric delay. Attached Figure Description

[0023] Figure 1 This is a flowchart of the InSAR tropospheric delay correction method assisted by GNSS tropospheric zenith delay in the embodiment; Figure 2 This is a schematic diagram of the calculation process for calculating the InSAR tropospheric delay correction on an epoch-by-epoch basis in the embodiment. Figure 3 This is a schematic diagram comparing the root mean square error of GNSS deformation and different InSAR deformation differences at 62 GNSS points in the example. Figure 4 This is a schematic diagram of the electronic device in the embodiment. Detailed Implementation

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0025] Example 1 To address the problems existing in the prior art, this embodiment provides a GNSS tropospheric zenith delay-assisted InSAR tropospheric delay correction method. It uses an elevation-related function model and a distance-related stochastic model to model the terrain-related vertical stratification delay component and the irregular turbulence delay component in the GNSS ZTD product, respectively. The stratification and turbulence delay components at the GNSS station are estimated by least squares configuration and variance component estimation criteria, and then extrapolated to other unobserved locations to establish a medium- and long-wave InSAR tropospheric delay correction map.

[0026] See Figure 1 The method includes the following steps: Step S1: The terrain-related vertical layering delay component and irregular turbulence delay component in the GNSS ZTD product are modeled using an elevation-related function model and a distance-related stochastic model, respectively. The layering and turbulence delay components at the GNSS station are estimated by least squares configuration and variance component estimation criteria, and then extrapolated to other unobserved locations to establish a medium- and long-wave InSAR tropospheric delay correction map.

[0027] By using equation (1) to... The zenith tropospheric delay projection of each GNSS station onto InSAR is the line of sight (LOS): In the formula, The incident angle of the SAR image; This is a GNSS observation of the tropospheric delayed zenith direction.

[0028] Step S2: Construct a joint correction model for tropospheric delay, modeling radar line-of-sight delay observations as the sum of vertical layered delay components, turbulent delay components, and random errors.

[0029] Considering the significant influence of turbulent components in the troposphere, which can be viewed as a stochastic function continuously varying with spatial distance, the vertical stratification is represented by an elevation function, conforming to the modeling requirements of least squares collocation theory. Therefore, a more comprehensive joint correction model for tropospheric errors is established, which can be described as... In the formula, For the first Radar line-of-sight delay observations at GNSS stations Represents irregular turbulent components; This indicates random errors such as decoherence noise and instrument noise. The DEM elevation of the observation point. For reference point elevation, and These are the parameters for the vertically layered model.

[0030] Step S3: Using least squares configuration, the function model of the vertical layer delay component is taken as the deterministic function part, and the turbulent delay component is taken as the random signal part. The observation equation is established, and the covariance function of the turbulent delay signal and the variance components of the signal and noise are determined by iteration. The parameters of the vertical layer model and the turbulent signal estimate at the GNSS station are jointly solved.

[0031] Solving equation (2) using least squares collocation, the first two terms, i.e. and Process it as a function model and design the matrix. Irregular turbulent components Incorporating random signal terms Random error term The least squares collocation function model can be expressed as: In the formula, For observation vectors; For designing the matrix; For parameter vectors; Given the signal vector at the measured point, its expected value is... covariance matrix ; For the observed noise vector, its expectation covariance matrix ; and They are respectively and variance factor and This is the corresponding cofactor matrix.

[0032] According to the least squares allocation valuation criterion: Solving equation (4) yields... in .

[0033] Estimation of turbulent components at unmeasured points for: Total delay estimate considering vertical stratification contribution for in This is the cross-covariance matrix between the measured points and the unmeasured points. For the corresponding cofactor matrix; This is the parameter vector for the vertically layered model; The elevation correlation design matrix is ​​calculated for the DEM of unmeasured points.

[0034] This completes the establishment of the corrected model. Solving the above model requires knowing the cofactor matrix of the stochastic model. In reality, the factor matrix Since it is unknown, it is often constructed by choosing a reasonable covariance fitting function. The exponential function, which is widely used in InSAR, is chosen: In the formula, The interval distance is point and covariance; and The parameters to be estimated are calculated through the following steps: (1) Least squares estimation function model parameters During the first calculation, Take it as the identity matrix; (2) Calculate the residuals The variance and covariance of spatial correlation are calculated to describe the spatial variation characteristics of the turbulent components. The spatial variance... Given distance interval Within range The statistical value of the covariance between each measured point pair is in It is the position information of the pixels. The non-negative covariance elements are selected from the statistics to fit the equation (9). and ; midpoint and Corresponding cofactor components ; (3) Repeat steps (1) and (2) until and Stability, determining the cofactor matrix of the stochastic model Similarly, the mutual factor matrix can be determined. .

[0035] Finally, the variance component estimation method is used to determine and The corresponding iterative form is: In the formula, This represents the trace operation. ; , , In actual calculations, in equation (11) It has been fixed. Take it as the identity matrix. and express and The estimate.

[0036] Step S4: Based on the solved vertical stratification model parameters and turbulence signal estimates, combined with the elevation information of unmeasured points and their spatial correlation with measured points, estimate the vertical stratification delay and turbulence delay at each pixel in the InSAR interferogram to obtain the InSAR tropospheric delay correction map.

[0037] For details, see Figure 2 To calculate the InSAR tropospheric delay correction on an epoch-by-epoch basis, the input data first includes normalized DEM data of the target area and GNSS tropospheric data. The modeling and calculation process involves first constructing the least squares residual. ,in for The observation vectors of the GNSS observation error equations are then used to calculate the cofactor matrix. ,Pick Solve using equation (5) and Calculate the new residual Then, iterative calculations are performed based on variance component estimation. and ,judge If not, solve again. and Then it enters a new round of iteration; if so, the final parameters are obtained. , , , and .

[0038] To verify the performance of the joint correction method in correcting long-wavelength tropospheric delays in InSAR, 151 Sentinel-1A / B down-orbit imagery scenes covering the Hawaiian Islands were selected (data acquired from May 24, 2020 to January 6, 2024). The islands are located in the tropical Pacific climate zone, characterized by abundant moisture, significant topographic relief, and elevations exceeding 4000 m. This complex topography and high humidity environment result in significant tropospheric delays in the interferometric phase, including irregular turbulence and topographically related vertical stratification delays. The Sentinel-1 SAR satellite acquired data for the islands at 16:16 UTC. Correspondingly, 151 GNSS ZTD products at 16:15 UTC were downloaded.

[0039] Small baseline interferograms were constructed using ISCE2 software, with a maximum temporal baseline threshold of 72 days and a spatial baseline threshold of 250 m. Topographic phase was simulated and removed using 30 m resolution DEM data released by the European Space Agency, while satellite orbital errors were corrected using precise orbital ephemeris. Phase unwrapping was performed using multi-look processing with an azimuth:range ratio of 25:5 and Goldstein adaptive filtering to suppress local noise. The phase time series was calculated using coherence-weighted least squares. Residual DEM errors were corrected using spatial baseline-related parameter estimation, and long-wavelength phase caused by solid tide variations was subtracted using the open-source software pySolid. Since the Sentinel imagery is a C-band observation, the ionospheric delay has a relatively small impact and is negligible.

[0040] Two interferogram corrections with a 12-day interval were used as comparative examples. The comparison methods were PyAPS and ICAMS methods based on ERA5 observations, and GACOS methods based on ERA5 and GNSS ZTD observations, with observation periods of 20220303-20220315 and 20230930-20231012, respectively. According to the results, the correction results of this invention have the least residual delay, especially in areas with dense GNSS stations.

[0041] A cumulative time series comparison experiment was conducted in a densely populated GNSS area. All data were referenced to the same time period, with the observation periods being: 20190729-20190810, 20190729-20190909, 20190729-20191102, 20190729-2019122, and 20190729-20200107. Based on the results, this invention can clearly show two volcano-related deformations within the region, consistent with GNSS observations.

[0042] See Figure 3The root mean square error (RMSE) of GNSS deformation at 62 GNSS points was compared with the differences in InSAR deformation. The RMSE calculated by this invention is generally smaller than the other four results, with a mean of 1.1 cm.

[0043] Example 2 Based on Embodiment 1, this embodiment provides an electronic device, including: one or more processors and a memory, wherein the memory stores one or more programs, and the one or more programs include instructions for executing the GNSS tropospheric zenith delay-assisted InSAR tropospheric delay correction method as described in Embodiment 1.

[0044] like Figure 4 At the hardware level, the electronic device includes a processor, internal bus, network interface, memory, and non-volatile memory, and may also include other hardware required for the business operations. The processor reads the corresponding computer program from the non-volatile memory into memory and then runs it to achieve the above-mentioned functions. Figure 1 The method described herein. Of course, in addition to software implementation, this invention does not exclude other implementation methods, such as logic devices or a combination of hardware and software, etc. That is to say, the execution subject of the following processing flow is not limited to each logic unit, but can also be hardware or logic devices.

[0045] Memory may include non-persistent storage in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0046] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0047] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0048] This invention can be described in the general context of computer-executable instructions, such as program modules, that are executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform a specific task or implement a specific abstract data type. This invention can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0049] The various embodiments in this invention are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments.

[0050] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A GNSS tropospheric zenith delay-assisted InSAR tropospheric delay correction method, characterized in that, The steps include the following: The tropospheric zenith delay of multiple GNSS stations is obtained, and the zenith tropospheric delay of each GNSS station is converted into radar line-of-sight delay observations. A joint correction model for tropospheric delay is constructed, which models the radar line-of-sight delay observation as the sum of vertical layer delay components, turbulent delay components, and random errors. The vertical layer delay components adopt an elevation-related function model, and the turbulent delay components adopt a random signal model based on spatial distance. By using the least squares configuration, the function model of the vertical layer delay component is taken as the deterministic function part, and the turbulent delay component is taken as the random signal part. The observation equation is established, and the covariance function of the turbulent delay component and the variance components of the signal and noise are determined by iteration. The parameters of the vertical layer model and the turbulent signal estimate at the GNSS station are jointly solved. Based on the solved vertical stratification model parameters and turbulence signal estimates, combined with the elevation information of unmeasured points and their spatial correlation with measured points, the vertical stratification delay and turbulence delay at each pixel in the InSAR interferogram are estimated to obtain the InSAR tropospheric delay correction map.

2. The InSAR tropospheric delay correction method with GNSS tropospheric zenith delay assistance according to claim 1, characterized in that, The radar line-of-sight delay observation is calculated using the following formula: in, For the first Radar line-of-sight delay observations at GNSS stations For the first GNSS tropospheric delayed zenith direction observations from GNSS stations The incident angle of the SAR image.

3. The InSAR tropospheric delay correction method with GNSS tropospheric zenith delay assistance according to claim 1, characterized in that, The vertical layer delay component is: in, , Here are the parameters of the vertical layering model to be determined. For the first DEM elevation of GNSS stations This is the preset reference elevation.

4. The InSAR tropospheric delay correction method with GNSS tropospheric zenith delay assistance according to claim 3, characterized in that, The joint correction model for tropospheric delay is as follows: in, For the first Radar line-of-sight delay observations at GNSS stations For the first Irregular turbulence components of GNSS stations For the first Random errors of GNSS stations.

5. The InSAR tropospheric delay correction method with GNSS tropospheric zenith delay assistance according to claim 1, characterized in that, The process of jointly solving the parameters of the vertical hierarchical model and the turbulence signal estimate at the GNSS station using least squares configuration includes the following steps: Establish observation equations ,in The observation vector is composed of line-of-sight delay observations from each GNSS station. The design matrix is ​​constructed based on the elevation difference. This is a parameter vector containing the parameters of the vertically hierarchical model. For turbulence signal vectors, This is the noise vector; According to the least squares allocation criterion Solving for the problem yields: Parameter estimation ; Signal Valuation ; in , The covariance matrix of the turbulence signal. Let be the covariance matrix of the noise. This represents the minimum value. This is a transpose.

6. The InSAR tropospheric delay correction method with GNSS tropospheric zenith delay assistance according to claim 5, characterized in that, Signal covariance matrix Noise covariance matrix , and These are the variance factors of the signal and noise, respectively. and These are the corresponding cofactor matrices; Estimating the total tropospheric delay at unmeasured points for: in, The design matrix is ​​constructed from the elevation information of unmeasured points. Let be the cross-covariance matrix between the measured point signals and the unmeasured point signals, and , The cross-factor matrix of the signal, This is the parameter vector for the vertically layered model.

7. The InSAR tropospheric delay correction method with GNSS tropospheric zenith delay assistance according to claim 6, characterized in that, The cofactor matrix Constructed using the following exponential covariance function: in, The interval distance is point and covariance; and The parameter to be estimated; The process of iteratively determining the covariance function of the turbulent delay signal includes the following steps: Step 1, Initialization Using an identity matrix, least squares estimation is used to determine the parameters of the vertical hierarchical model. ; Step 2, calculate the residuals Based on the variance and covariance of the residual statistical space, the exponential covariance function is fitted to obtain... and ; Step 3, using the obtained Update cofactor array ,in element at And repeat steps 1 and 2 until... and Stable, obtaining a definite cofactor matrix .

8. The InSAR tropospheric delay correction method with GNSS tropospheric zenith delay assistance according to claim 7, characterized in that, In step 2, the spatial variance is: in, For position The residual value at that point, The total number of GNSS stations; Given distance interval Inside The covariance of each measured point pair is: in, and Distance The residual value at that point, This represents the number of measured point pairs within a preset distance interval.

9. The InSAR tropospheric delay correction method with GNSS tropospheric zenith delay assistance according to claim 8, characterized in that, Variance components of signal and noise and The solution is obtained by iterative estimation of variance components, with the cofactor matrix fixed during the iteration process. And take the noise cofactor matrix For the identity matrix, the iterative equation is: in, To find the trace, , These are the variance factor estimates for the signal and noise, respectively.

10. A GNSS tropospheric zenith delay-assisted InSAR tropospheric delay correction method according to claim 1, characterized in that, The method is used for tropospheric delay correction of InSAR interferograms containing decoherent regions.

Images