Dem error estimation method based on piecewise processing

Abstract

The application discloses a DEM error estimation method based on segmentation processing. The method acquires multi-temporal SAR images of a target area and performs time-series interference processing to obtain an interference phase sequence; interference phase sequences are divided into multiple candidate interference subsets in combination with scene constraint information, and effective interference subsets are screened according to vertical baseline distribution, interference coherence and local fitting residual; a joint observation equation of a DEM error term and a local deformation term is established for each effective interference subset to obtain DEM error candidate values, and a DEM error consensus subset is determined based on candidate value consistency, candidate value reliability and nonlinear deformation interference degree; and the DEM error candidate values in the consensus subset are weighted and fused to obtain DEM error estimation values of target pixels. The method can reduce the influence of nonlinear deformation residual and abnormal windows on DEM error estimation.

Description

Technical Field

[0001] This invention relates to the field of synthetic aperture radar interferometry technology, and in particular to a DEM error estimation method based on segmented processing. Background Technology

[0002] Synthetic Aperture Radar Interferometry (SAR) technology can acquire surface deformation information using multi-temporal SAR imagery. It boasts advantages such as wide coverage, short observation cycles, and all-weather operation, and has been widely applied in fields such as land subsidence, landslides, mining, urban construction, permafrost freeze-thaw monitoring, and geological disaster monitoring. Among these methods, the small baseline set temporal interferometry method, by constructing a small baseline interferometric network among multiple SAR images, can reduce the effects of spatiotemporal incoherence to a certain extent and invert the time series of surface deformation in the target area.

[0003] The main drawback of current technologies lies in their poor adaptability to nonlinear deformation, relying on the assumption of linear deformation. When surface deformation exhibits periodic, exponential, or complex nonlinear characteristics, the nonlinear deformation signal becomes mixed with phase residuals, leading to significant deviations in DEM error estimation. Furthermore, most actual surface deformations exhibit nonlinear evolution characteristics, making it difficult for traditional methods' global linear assumptions to accurately describe the true deformation process. Traditional methods also cannot effectively distinguish between DEM error signals and nonlinear deformation signals; the two are coupled in the phase equation, causing mutual interference in the estimation results. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a DEM error estimation method based on segmented processing, so as to solve the problem that the prior art is prone to misattributing deformation residuals into DEM error terms under nonlinear deformation and complex surface change conditions, which leads to unstable DEM error estimation results.

[0005] A DEM error estimation method based on segmented processing includes: Step 1: Acquire multi-temporal SAR images of the target area and perform temporal interferometry on the multi-temporal SAR images to obtain an interferometric phase sequence; Step 2: Obtain the scene constraint information corresponding to the target region, and divide the interference phase sequence according to multiple candidate time windows to obtain multiple candidate interference subsets; Step 3: Based on the vertical baseline distribution, interferometric coherence, local fitting residuals, and scene constraint information corresponding to each candidate interferometric subset, determine the effectiveness evaluation results of each candidate interferometric subset, and select the effective interferometric subsets based on the effectiveness evaluation results; Step 4: Establish a joint observation equation for the DEM error term and the local deformation term for each effective interference subset, solve for the corresponding DEM error candidate value, candidate value reliability and nonlinear deformation interference degree, and form a DEM error consensus subset; Step 5: Using the DEM error of the target pixel as the estimator, robust weighted fusion is performed based on the DEM error candidate values ​​in the DEM error consensus subset to obtain the estimated DEM error value of the target pixel.

[0006] As a preferred embodiment, the scene constraint information includes at least one of terrain geometry information, land cover information, and land change information.

[0007] As a preferred embodiment, the terrain geometry information includes at least one of slope, aspect, local incident angle, overlay risk, and shadow risk; the land cover information includes at least one of urban built-up areas, construction areas, bare land, mining areas, forests, farmland, water bodies, wetlands, and snow-covered areas; and the land change information includes at least one of SAR backscatter intensity change, interferometric coherence change, optical image texture change, vegetation index change, and building index change.

[0008] As a preferred embodiment, step 2 further includes: when the time window corresponding to the candidate interference subset spans changes in surface disturbance, splitting, eliminating, or reducing the weight of the candidate interference subset according to the occurrence time and disturbance intensity; wherein, the changes in surface disturbance include at least one of construction changes, mining changes, vegetation cover changes, water body range changes, snow cover changes, and coherence abrupt changes.

[0009] As a preferred embodiment, the nonlinear deformation interference degree is determined based on the local fitting residual corresponding to the effective interference subset, wherein the local fitting residual includes the phase residual remaining after fitting the local deformation term; wherein the nonlinear deformation interference degree is determined based on at least one of the following: the correlation between the local fitting residual and the vertical baseline sequence, the correlation between the local fitting residual and the time baseline sequence, and the second-order difference energy of the local fitting residual.

[0010] As a preferred embodiment, the DEM error consensus subset is determined as follows: using one of the multiple DEM error candidate values ​​or the statistical center obtained from multiple DEM error candidate values ​​as the candidate center, the deviation of each DEM error candidate value relative to the candidate center is calculated; the effective interference subsets whose deviations satisfy preset consistency conditions, whose candidate value reliability satisfies preset reliability conditions, and whose nonlinear deformation interference degree satisfies preset interference conditions are classified as the DEM error consensus subset.

[0011] As a preferred embodiment, the robust weighted fusion includes weighted fusion of DEM error candidate values, wherein the weights of the weighted fusion are determined based on at least one of the following: candidate value reliability, nonlinear deformation interference degree, coherence of candidate interference subsets, and effectiveness evaluation results of candidate interference subsets.

[0012] As a preferred embodiment, the length of the plurality of candidate time windows is 90 to 150 days. The advantages and beneficial effects of this invention are as follows: This invention divides the interferometric phase sequence into multiple candidate interferometric subsets according to time periods, and selects effective interferometric subsets by combining vertical baseline distribution, interferometric coherence, local fitting residuals, and scene constraint information. This avoids windows with insufficient baseline observability, poor coherence, or those affected by surface disturbances from directly participating in DEM error estimation. By jointly solving the DEM error term and local deformation term in each effective interferometric subset, and determining the DEM error consensus subset based on candidate value consistency, candidate value reliability, and nonlinear deformation interference, this invention can reduce the interference of nonlinear deformation residuals, atmospheric disturbances, and anomalous windows on the DEM error estimation results. Attached Figure Description

[0013] Figure 1 A schematic diagram is constructed for the simulation data. (a) is the simulated DEM error phase; (b) is the spatial distribution pattern of the simulated deformation; (c) is the simulated atmospheric delay phase; and (d) is the spatiotemporal baseline distribution of the interferometric pair.

[0014] Figure 2 To simulate the time evolution pattern of deformation, (a) represents linear deformation; (b) represents periodic deformation; (c) represents exponential deformation; and (d) represents complex deformation.

[0015] Figure 3 Examples of simulated interferograms generated under various deformation modes are shown, where (a) represents linear deformation; (b) represents periodic deformation; (c) represents exponential deformation; and (d) represents complex deformation.

[0016] Figure 4 The changes in RMSE of DEM error estimation under different time windows are: (a) linear deformation; (b) periodic deformation; (c) exponential deformation; and (d) complex deformation.

[0017] Figures 5 to 8The diagrams show a comparison of DEM error estimation results between the traditional method and the method of this invention under linear deformation, periodic deformation, exponential deformation, and complex deformation modes, respectively. Specifically, (a-1 to 4) represent the DEM error estimated by the traditional method; (b-1 to 4) represent the difference between the estimated result and the true value using the traditional method; (c-1 to 4) represent the statistical histograms of the residuals corresponding to figures (b-1 to 4); (d-1 to 4) represent the DEM error estimated by the method of this invention; (e-1 to 4) represent the difference between the estimated result and the true value using the method of this invention; and (f-1 to 4) represent the statistical histograms of the residuals corresponding to figures (e-1 to 4). Subplots 1 to 4 correspond to linear deformation, periodic deformation, exponential deformation, and complex deformation modes, respectively. Detailed Implementation

[0018] To enable those skilled in the art to better understand the present invention, the technical solution of the present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0019] This invention provides a DEM error estimation method based on segmented processing, comprising the following steps: Step 1: Acquire multi-temporal SAR images of the target area and perform temporal interferometry on the multi-temporal SAR images to obtain an interferometric phase sequence.

[0020] The target area refers to the geographical area within the common coverage of multi-temporal SAR images that requires DEM error estimation. It can be the area corresponding to the entire SAR image or a local monitoring area selected by the user, such as a land subsidence area, mining area, urban construction area, mountain excavation area or other areas with surface deformation; the target pixel is the pixel in the target area that participates in DEM error estimation.

[0021] Step 2: Obtain the scene constraint information corresponding to the target region, and divide the interferometric phase sequence according to multiple candidate time windows to obtain multiple candidate interferometric subsets. When the candidate time window length is too short, the number of available interferometric observations within the candidate interferometric subset is insufficient, and the separability between the DEM error term and the local deformation term is weak; when the candidate time window length is too long, the nonlinear deformation within the window is difficult to be fully expressed by the local linear deformation, and the nonlinear deformation residue easily affects the DEM error estimation. Therefore, there is an optimal range for the candidate time window length. In one specific embodiment, the candidate time window length is preferably 90 to 150 days, and more preferably 120 days.

[0022] In one implementation, the scene constraint information includes at least one of topographic geometry information, land cover information, and land surface change information. The topographic geometry information can be obtained from the DEM to be corrected, an existing reference DEM, SAR imaging geometric parameters, or a combination thereof, including at least one of slope, aspect, local incident angle, overlap risk, and shadow risk. The land cover information can be obtained from land cover data, multi-period optical remote sensing images, or SAR images, including at least one of urban built-up areas, construction areas, bare land, mining areas, forests, farmland, water bodies, wetlands, and snow-covered areas. The land surface change information can be obtained from multi-period SAR images, multi-period optical remote sensing images, or interferometric coherence sequences, including at least one of SAR backscatter intensity changes, interferometric coherence changes, optical image texture changes, vegetation index changes, and building index changes. This allows the selection of candidate interferometric subsets to no longer rely solely on the time window length and phase fitting results, but can further combine the topographic geometry conditions, land cover category, and temporal change status of the target area for judgment.

[0023] Step 3: Based on the vertical baseline distribution, interferometric coherence, local fitting residuals, and scenario constraint information corresponding to each candidate interferometric subset, determine the effectiveness evaluation results of each candidate interferometric subset, and select the effective interferometric subsets based on the effectiveness evaluation results.

[0024] Specifically, for each candidate interferometric subset, its baseline observability, coherence, local fitting residuals, and scene stability evaluation metrics are obtained. The baseline observability is determined based on the vertical baseline sequence of each interferometric pair within the candidate interferometric subset, including at least one of the vertical baseline range, vertical baseline variance, effective baseline number, and observation matrix condition number. The coherence is determined based on the interferometric coherence map obtained when each interferometric pair forms an interferogram, including at least one of the average coherence, median coherence, and low coherence proportion within the target pixel or its neighborhood. The local fitting residuals are obtained by jointly pre-fitting the DEM error term and local deformation term of the candidate interferometric subset, including at least one of the root mean square of the residuals, the correlation between the residuals and the vertical baseline sequence, the correlation between the residuals and the time baseline sequence, and the second-order difference energy of the residuals. The scene stability is determined based on the scene constraint information. The joint pre-fit is used to obtain the residual evaluation metrics of the candidate interferometric subset and is not used as the final DEM error estimation result.

[0025] When the above evaluation quantity meets the preset validity conditions, the corresponding candidate interference subset is determined as a valid interference subset; when the above evaluation quantity does not meet the preset validity conditions, the corresponding candidate interference subset is removed or its weight in subsequent participation in DEM error estimation is reduced.

[0026] Step 4: Establish a joint observation equation for the DEM error term and the local deformation term for each effective interference subset, solve for the corresponding DEM error candidate value, candidate value reliability and nonlinear deformation interference degree, and determine the DEM error consensus subset based on the consistency among multiple DEM error candidate values, the candidate value reliability and the nonlinear deformation interference degree.

[0027] Specifically, for each effective subset of interferometry, the unwrapped phase, vertical baseline, and time interval corresponding to each interferometry pair within that subset are extracted, and a joint observation equation for the DEM error term and the local deformation term is established. This joint observation equation uses the unwrapped phase as the observed quantity, the DEM error parameter and the local deformation parameter as the parameters to be estimated, and the residual atmospheric phase, unwrapping error, and noise as the residual error term. For any interferometry pair, its observed phase is represented as the sum of the DEM error phase, the local deformation phase, and the residual error term; where the DEM error phase is determined by the vertical baseline corresponding to the interferometry pair and the DEM error parameter to be estimated, and the local deformation phase is determined by the time interval corresponding to the interferometry pair and the local deformation rate to be estimated.

[0028] Since the time window corresponding to the effective interferometric subset is short, the deformation of the target pixel within this time window can be approximated as local linear deformation. Therefore, the local deformation term is used as a parameter to be estimated in the joint observation equation, and is solved together with the DEM error parameter using least squares or weighted least squares. After solving, the DEM error parameter is used as a candidate value of the DEM error corresponding to the effective interferometric subset, and the reliability of the candidate value is determined based on at least one of the vertical baseline distribution, interferometric coherence, local fitting residual, and observation matrix condition number of the effective interferometric subset.

[0029] The nonlinear deformation interference degree is determined based on the local fitting residual corresponding to the effective interference subset, wherein the local fitting residual includes the phase residual remaining after fitting the local deformation term; wherein the nonlinear deformation interference degree is determined based on at least one of the following: the correlation between the local fitting residual and the vertical baseline sequence, the correlation between the local fitting residual and the time baseline sequence, and the second-order difference energy of the local fitting residual.

[0030] When determining the DEM error consensus subset, one of the multiple DEM error candidate values ​​or the statistical center obtained from multiple DEM error candidate values ​​is used as the candidate center, and the deviation of each DEM error candidate value relative to the candidate center is determined. The effective interference subset that satisfies the preset consistency condition, the candidate value reliability condition, and the nonlinear deformation interference degree condition is determined as the DEM error consensus subset.

[0031] Step 5: Using the DEM error of the target pixel as the estimator, robust weighted fusion is performed based on the DEM error candidate values ​​in the DEM error consensus subset to obtain the estimated DEM error value of the target pixel.

[0032] In one implementation, the robust weighted fusion includes weighted fusion of DEM error candidate values ​​in the DEM error consensus subset. The weights for the weighted fusion are determined based on at least one of the following: candidate value reliability, nonlinear deformation interference degree, coherence of the candidate interference subset, and effectiveness evaluation results of the candidate interference subset. This ensures that DEM error candidate values ​​with higher reliability and lower risk of nonlinear deformation interference have a larger weight in the final estimation, reducing the impact of DEM error candidate values ​​that are significantly affected by noise, decoherence, or nonlinear deformation residues on the final estimation result.

[0033] This embodiment reduces the impact of insufficient baseline observability, poor coherence, scene disturbances, or nonlinear deformation residues on DEM error estimation by evaluating the effectiveness of candidate interferometric subsets, screening for consistency of DEM error candidate values, and performing robust weighted fusion processing. This improves the stability and reliability of the target pixel DEM error estimation values.

[0034] This invention divides the interferometric phase sequence into multiple candidate interferometric subsets and selects effective interferometric subsets by combining vertical baseline distribution, interferometric coherence, local fitting residuals, and scene constraint information. This avoids windows with insufficient baseline observability, poor coherence, or those affected by surface disturbances from directly participating in DEM error estimation. By jointly solving the DEM error term and local deformation term in each effective interferometric subset, and determining the DEM error consensus subset based on candidate value consistency, candidate value reliability, and nonlinear deformation interference, this invention can reduce the interference of nonlinear deformation residuals, atmospheric disturbances, and anomalous windows on the DEM error estimation results.

[0035] Furthermore, in step 2, when the time window corresponding to the candidate interference subset spans changes in surface disturbance, the candidate interference subset is split, eliminated, or has its weight reduced according to the occurrence time and intensity of the changes in surface disturbance; wherein, the changes in surface disturbance include at least one of construction changes, mining changes, vegetation cover changes, water body range changes, snow cover changes, and coherence abrupt changes.

[0036] This embodiment eliminates the need for the sliding window to mechanically span the entire time series, instead avoiding or mitigating periods of significant surface state change. When candidate interferometric subsets span disturbances such as construction, mining, vegetation cover, water bodies, snow cover, or abrupt changes in coherence, the phase changes within this window may simultaneously include multiple factors such as DEM error, true surface deformation, changes in scattering centers, and coherence degradation. Directly incorporating these factors into DEM error estimation can easily lead to misattribution of true surface changes or anomalous phase residuals into the DEM error term. By splitting, eliminating, or reducing the weight of candidate interferometric subsets according to the timing and intensity of the disturbance, interference from cross-disturbance windows on DEM error candidate values ​​can be reduced. This makes the interferometric subsets entering the subsequent joint observation equation and consensus subset selection closer to a local stable state, thereby improving the robustness of the DEM error estimation results.

[0037] This invention introduces scene constraints, candidate interferometric subset validity evaluation, and DEM error consensus subset determination mechanisms into the DEM error estimation process of temporal InSAR. This allows DEM error estimation to move beyond relying solely on fixed time windows or single deformation models. Instead, it first selects effective interferometric subsets with good baseline observability, coherence stability, and local deformation expressibility from multiple candidate time windows. Then, it uses the consistency among the DEM error candidate values ​​obtained from multiple effective interferometric subsets to identify reliable observation results. This reduces the interference of nonlinear deformation residuals, atmospheric disturbances, unwrapping errors, land cover changes, and human construction disturbances on DEM error estimation, and minimizes the impact of anomalous windows on the final results.

[0038] refer to Figure 1 , 2 The simulated data shown illustrates how this invention uses simulated data to verify its method. The simulated data is constructed based on the imaging time and baseline distribution of Sentinel-1 time-series data from the Lanzhou area from October 2020 to February 2023. Four surface deformation modes—linear, periodic, exponential, and complex deformation—were simulated, and DEM errors ranging from 50m to +50m and atmospheric delay phase were superimposed on these models to synthesize 316 interferometric pairs, as shown in the attached figure. Figure 3 As shown in the diagram, linear deformation is used to characterize the stable deformation process that is easily adapted to the traditional SBAS-InSAR method; periodic deformation, exponential deformation, and complex deformation are used to simulate nonlinear deformation processes that may occur in scenarios such as permafrost freeze-thaw, groundwater extraction subsidence, mining area subsidence, or fill consolidation. The superimposed atmospheric delay phase is used to simulate atmospheric phase disturbances in real InSAR observations, avoiding overly idealized simulation data and verifying the stability of the proposed method for DEM error estimation in the presence of actual observational interference.

[0039] First, we tested DEM error estimation for four deformation modes using different time window lengths (60 to 360 days). Then, we evaluated the accuracy of DEM error estimation for different time window lengths or different methods using RMSE. The results are attached. Figure 4 As shown, the results indicate that statistical analysis of DEM error estimation results under different time window lengths reveals that when the window length increases from 60 days to the range of 90 to 150 days, the RMSE decreases in most deformation modes; however, as the window length continues to increase, the RMSE increases in some nonlinear deformation modes. The RMSE variation trends corresponding to different deformation modes are as follows: Figure 4 The results shown are accurate.

[0040] Based on the above analysis, a time window of 120 days is used to compare the traditional overall estimation method with the estimation method of this invention. (See attached...) Figure 5-8 As shown, under linear deformation modes, the two methods exhibit comparable accuracy, with residuals ranging from -3m to 3m. The RMSE of the traditional method is 0.78m, while that of this method is 0.89m, indicating similar accuracy. However, under periodic, exponential, and complex deformation modes, the residual range of the piecewise DEM estimation by this method narrows to -4m to 4m, with root mean square errors of 0.98m, 1.00m, and 0.98m, respectively. In contrast, the residual ranges of the traditional method reach -8~8m, -15~15m, and -13~13m, respectively, with RMSEs as high as 1.94m, 4.11m, and 3.62m, representing an accuracy improvement of up to 75%. Simulation experiments confirm the significant advantages of the method of this invention under nonlinear deformation scenarios.

[0041] The present invention has been described above by way of example. It should be noted that any simple modifications, alterations or other equivalent substitutions that can be made by those skilled in the art without creative effort without departing from the core of the present invention fall within the protection scope of the present invention.

Claims

1. A DEM error estimation method based on segmented processing, characterized in that, include: Step 1: Acquire multi-temporal SAR images of the target area and perform temporal interferometry on the multi-temporal SAR images to obtain an interferometric phase sequence; Step 2: Obtain the scene constraint information corresponding to the target region, and divide the interference phase sequence according to multiple candidate time windows to obtain multiple candidate interference subsets; Step 3: Based on the vertical baseline distribution, interferometric coherence, local fitting residuals, and scene constraint information corresponding to each candidate interferometric subset, determine the effectiveness evaluation results of each candidate interferometric subset, and select the effective interferometric subsets based on the effectiveness evaluation results; Step 4: Establish a joint observation equation for the DEM error term and the local deformation term for each effective interference subset, solve for the corresponding DEM error candidate value, candidate value reliability and nonlinear deformation interference degree, and form a DEM error consensus subset; Step 5: Using the DEM error of the target pixel as the estimator, robust weighted fusion is performed based on the DEM error candidate values ​​in the DEM error consensus subset to obtain the estimated DEM error value of the target pixel.

2. The DEM error estimation method based on segmented processing according to claim 1, characterized in that, The scene constraint information includes at least one of terrain geometry information, land cover information, and land surface change information.

3. The DEM error estimation method based on segmented processing according to claim 2, characterized in that, The topographic geometry information includes at least one of slope, aspect, local incident angle, overlay risk, and shadow risk; the land cover information includes at least one of urban built-up areas, construction areas, bare land, mining areas, forests, farmland, water bodies, wetlands, and snow-covered areas; the land change information includes at least one of SAR backscatter intensity change, interferometric coherence change, optical image texture change, vegetation index change, and building index change.

4. The DEM error estimation method based on segmented processing according to claim 1, characterized in that, Step 2 further includes: when the time window corresponding to the candidate interference subset spans changes in surface disturbance, the candidate interference subset is split, eliminated, or its weight is reduced according to the occurrence time and disturbance intensity; wherein, the changes in surface disturbance include at least one of construction changes, mining changes, vegetation cover changes, water body range changes, snow cover changes, and coherence abrupt changes.

5. The DEM error estimation method based on segmented processing according to claim 1, characterized in that, The nonlinear deformation interference degree is determined based on the local fitting residual corresponding to the effective interference subset, wherein the local fitting residual includes the phase residual remaining after fitting the local deformation term; wherein the nonlinear deformation interference degree is determined based on at least one of the following: the correlation between the local fitting residual and the vertical baseline sequence, the correlation between the local fitting residual and the time baseline sequence, and the second-order difference energy of the local fitting residual.

6. The DEM error estimation method based on segmented processing according to claim 1, characterized in that, The DEM error consensus subset is determined as follows: using one of the multiple DEM error candidate values ​​or the statistical center obtained from multiple DEM error candidate values ​​as the candidate center, the deviation of each DEM error candidate value relative to the candidate center is calculated; the effective interference subset that satisfies the preset consistency condition, the candidate value reliability condition, and the nonlinear deformation interference degree condition is classified as the DEM error consensus subset.

7. The DEM error estimation method based on segmented processing according to claim 1, characterized in that, The robust weighted fusion includes weighted fusion of DEM error candidate values, wherein the weights of the weighted fusion are determined based on at least one of the following: candidate value reliability, nonlinear deformation interference degree, coherence of candidate interference subsets, and effectiveness evaluation results of candidate interference subsets.

8. The DEM error estimation method based on segmented processing according to claim 1, characterized in that, The length of the multiple candidate time windows ranges from 90 days to 150 days.

Images