Surface Deformation Monitoring Method and System Based on Backward Sequential Least Squares

Abstract

The present invention discloses a method and system for surface deformation monitoring based on backward sequential least squares. The method includes: determining the first deformation rate and the corresponding cofactor matrix for each time unit in the current time period of the monitoring area; determining multiple historical unwrapped interferograms corresponding to the SAR images in the historical time period of the monitoring area; using the backward sequential least squares method to determine the second deformation rate for each time unit in the historical time period and update the first deformation rate according to multiple first deformation rates, cofactor matrices, and multiple historical unwrapped interferograms; and determining the cumulative deformation between the current time period and the historical time period of the monitoring area according to multiple updated first deformation rates and multiple second deformation rates. The present invention can backwardly recover the deformation time series of historical time, the method is simple, and since less data needs to be stored during the calculation process, it can greatly save storage resources.

Description

Technical Field

[0001] The present invention discloses a method and system for monitoring surface deformation based on backward sequential least squares, specifically relating to a method and system for monitoring surface deformation of backward sequential least squares small baseline set InSAR for restoring historical sequential deformation, belonging to the technical field of surface deformation monitoring. Background Art

[0002] Affected by natural factors and human activities, the surface can produce deformations of different degrees, causing damage to surface buildings, threatening people's lives and safety, and causing economic losses. Rapid and accurate monitoring of surface deformation is crucial for the prevention, control and treatment of ground deformation disasters and the health and safety assessment of surface structures.

[0003] Interferometric Synthetic Aperture Radar (InSAR) is a ground observation technology that uses the phase difference of radar signals as the observation value. It has the advantages of high precision, high spatial resolution, wide monitoring range and low cost, and has been widely used in surface deformation monitoring such as urban subsidence, glacier movement, mining subsidence, volcanic eruption, landslide, debris flow, etc. Among them, the differential interferometry short baseline set time series analysis technology (Small Baseline Subset InSAR, SBAS-InSAR) in multi-temporal InSAR technology is an InSAR time series method based on multiple master images. It only uses interferometric pairs with short spatio-temporal baselines to extract surface deformation information. Because it generates a small baseline set by setting appropriate time and space baseline thresholds, suppressing the influence of decoherence, it has great application prospects in the field of large-area and long-time series ground subsidence monitoring.

[0004] At present, many SAR satellites have been launched by various countries around the world, which can provide a continuous stream of SAR data, and now it has entered the big data era of SAR. With the increase of SAR data and the need for dynamic monitoring of key monitoring targets, researchers have carried out research work on InSAR deformation dynamic monitoring. However, the current InSAR deformation dynamic monitoring all updates the deformation time series forward. Taking the use of SBAS-InSAR for deformation dynamic monitoring as an example, when new SAR data is obtained, it is necessary to perform repeated calculations in combination with historical SAR data to obtain the historical cumulative deformation time series. This method requires storing all the unwrapped interferograms during the calculation process, greatly occupying the storage resources of the computer. Summary of the Invention

[0005] The purpose of this application is to provide a method and system for monitoring surface deformation based on backward sequential least squares, so as to solve the technical problem in the prior art that when using SBAS-InSAR to solve the deformation time series, it is necessary to store all the unwrapped interferograms in the calculation process, which greatly occupies the storage resources of the computer.

[0006] The first aspect of the present invention provides a method for monitoring surface deformation based on backward sequential least squares, including:

[0007] Determine the first deformation rate and the corresponding cofactor matrix for each time unit in the current time period of the monitoring area;

[0008] Determine multiple historical unwrapped interferograms corresponding to the SAR images in the historical time period of the monitoring area;

[0009] According to the multiple first deformation rates, cofactor matrices and the multiple historical unwrapped interferograms, use the backward sequential least squares method to determine the second deformation rate for each time unit in the historical time period and update the first deformation rate;

[0010] According to the multiple updated first deformation rates and the multiple second deformation rates, determine the cumulative deformation between the current time period and the historical time period of the monitoring area.

[0011] Preferably, determining the first deformation rate and the corresponding cofactor matrix for each time unit in the current time period of the monitoring area specifically includes:

[0012] Determine multiple unwrapped interferograms corresponding to the SAR images in the current time period of the monitoring area;

[0013] According to the multiple unwrapped interferograms, use the SBAS-InSAR technology to determine the first deformation rate and the corresponding cofactor matrix for each time unit in the current time period of the monitoring area.

[0014] Preferably, determine the first deformation rate for each time unit in the current time period of the monitoring area according to the first formula, and the first formula is:

[0015] V1 = A1X1 - L1, P1

[0016] In the formula, V1 is the first residual vector, A1 is a design matrix of M1×N1, which is composed of multiple time units in the current time period, M1 is the number of the unwrapped interferograms, N1 is the number of the SAR images in the current time period, L1 is the vector composed of the differential interferometric phases of the unwrapped interferograms, P1 is the weight matrix corresponding to L1, and X1 is the vector composed of multiple first deformation rates, X1 = (A1 T P1A1)-1 A1 T P1L1。

[0017] Preferably, the cofactor matrix of the first deformation rate of each time unit in the monitoring area within the current time period is determined according to the second formula, and the second formula is:

[0018]

[0019] In the formula, is the cofactor matrix of X1, is the transpose matrix of A1.

[0020] Preferably, the second deformation rate of each time unit within the historical time period is determined according to the third formula, and the third formula is:

[0021]

[0022] In the formula, V2 is the second residual vector, Y is the vector composed of multiple second deformation rates, X1 is the vector composed of multiple first deformation rates, X2 is the vector after re-adjusting X1, that is, the updated first deformation rate, B is the coefficient matrix of Y, A2 is the coefficient matrix of X2, L2 is the vector composed of the differential interference phases of the historical unwrapped interferogram, and P2 is the weight matrix corresponding to L2.

[0023] Preferably, the adjustment criterion corresponding to the third formula is as the fourth formula, and the fourth formula is:

[0024]

[0025] In the formula, V2 is the second residual vector, X2 is the vector after re-adjusting X1, that is, the updated first deformation rate, P2 is the weight matrix corresponding to L2, is the cofactor matrix of X1.

[0026] Preferably, the normal equation matrix form corresponding to the fourth formula is as the fifth formula:

[0027]

[0028] In the formula, X1 is the vector composed of multiple first deformation rates, is the cofactor matrix of X1, X2 is the vector after re-adjusting X1, A2 is the coefficient of X2, L2 is the vector composed of the differential interference phases of the historical unwrapped interferogram, P2 is the weight matrix corresponding to L2, Y is the vector composed of multiple second deformation rates, B is the coefficient matrix of Y, and the solution of the fifth formula is as the sixth formula and the seventh formula, and the sixth formula is:

[0029]

[0030] The seventh formula is as follows:

[0031]

[0032] In the formula, N -1 is the inverse matrix of N, is the cofactor matrix of [Y X2] T Preferably, the block matrix of the eighth formula is used to solve the above-mentioned N

[0033] -1 and the eighth formula is as follows:

[0034]

[0035] In the formula,

[0036] Preferably, according to a plurality of updated first deformation rates and a plurality of second deformation rates, the cumulative deformation of the monitoring area between the current time period and the historical time period is determined, specifically including:

[0037] Integrating a plurality of updated first deformation rates and a plurality of second deformation rates in the time domain to obtain the cumulative deformation of the monitoring area between the current time period and the historical time period.

[0038] A second aspect of the present invention provides a method for monitoring surface deformation based on backward sequential least squares, including:

[0039] A first rate determination module, configured to determine the first deformation rate and the corresponding cofactor matrix of each time unit in the monitoring area within the current time period;

[0040] An interferogram determination module, configured to determine a plurality of historical unwrapped interferograms corresponding to the SAR images in the monitoring area within the historical time period;

[0041] A second rate determination and first rate update module, configured to determine the second deformation rate of each time unit within the historical time period and update the first deformation rate by using the backward sequential least squares method according to a plurality of the first deformation rates, the cofactor matrix, and the plurality of historical unwrapped interferograms;

[0042] A deformation determination module, configured to determine the cumulative deformation of the monitoring area between the current time period and the historical time period according to a plurality of updated first deformation rates and a plurality of second deformation rates.

[0043] The method and system for surface deformation monitoring based on backward sequential least squares of the present invention have the following beneficial effects compared with the prior art:

[0044] For the method and system of the present invention, only historical unwrapped interferograms are required, and combined with the first deformation rate and its cofactor matrix of each time unit within the current time period, the deformation time series of historical time can be restored backward. The method is simple, and since only the first deformation rate, cofactor matrix, and historical unwrapped interferograms need to be stored during the calculation process, compared with the SBAS-InSAR technology that needs to store all unwrapped interferograms, it can greatly save storage resources.

[0045] In addition, when solving the normal equation coefficient matrix of sequential least squares, the present invention uses block matrix inversion to reduce the order of the calculated matrix and improve the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a schematic flow chart of the method for surface deformation monitoring based on backward sequential least squares in an embodiment of the present invention;

[0047] Figure 2 It is a detailed flow chart of the method for surface deformation monitoring based on backward sequential least squares in an embodiment of the present invention;

[0048] Figure 3 It is a schematic structural diagram of the system for surface deformation monitoring based on backward sequential least squares in an embodiment of the present invention;

[0049] Figure 4 It is the calculation results of three deformation models, namely linear model, trigonometric function model, and quadratic function model, without adding noise in an embodiment of the present invention. (a), (d), (g) are respectively the simulated deformation time series; (b), (e), (h) are respectively the calculation results of SBAS-InSAR, and (c), (f), (i) are respectively the calculation results of backward sequential least squares small baseline set InSAR;

[0050] Figure 5 It is the calculation results of three deformation models, namely linear model, trigonometric function model, and quadratic function model, with adding noise in an embodiment of the present invention. (a), (d), (g) are respectively the simulated deformation time series; (b), (e), (h) are respectively the calculation results of SBAS-InSAR, and (c), (f), (i) are respectively the calculation results of backward sequential least squares small baseline set InSAR;

[0051] Figure 6 It is the deformation time series calculated by SBAS-InSAR in an embodiment of the present invention;

[0052] Figure 7 This is the deformation time series obtained from the first solution of the backward sequential least squares small baseline set InSAR in the embodiment of the present invention;

[0053] Figure 8 This is the deformation time series obtained from the second solution of the backward sequential least squares small baseline set InSAR in the embodiment of the present invention;

[0054] Figure 9 This is the histogram of the difference between the results of the backward sequential least squares small baseline set InSAR and the SBAS-InSAR results in the embodiment of the present invention;

[0055] Figure 10 is Figure 8 The deformation time series of point P1 in, where (a) is the solution result of SBAS-InSAR; (b) is the solution result of the backward sequential least squares small baseline set InSAR;

[0056] Figure 11 In the embodiment of the present invention Figure 8 The deformation time series of point P2 in, where (a) is the solution result of SBAS-InSAR; (b) is the solution result of the backward sequential least squares small baseline set InSAR.

[0057] In the figure, 101 is the first rate determination module; 102 is the interferogram determination module; 103 is the second rate determination and first rate update module; 104 is the deformation determination module. Detailed implementation manners

[0058] In the following description, specific details such as specific system structures and technologies are presented for the purpose of illustration rather than limitation, so as to thoroughly understand the embodiments of the present invention. However, those skilled in the art should clearly understand that the present invention can also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid unnecessary details from interfering with the description of the present invention.

[0059] Existing InSAR deformation dynamic monitoring all updates the deformation time series forward. After obtaining the deformation time series of a certain period, in order to more accurately describe the deformation characteristics of the deformed body, it is necessary to update the deformation time series backward, that is, there is a need to restore the historical deformation time series before this period. Therefore, the present invention aims to restore the deformation time series in the historical period on the basis of obtaining a certain deformation time series, so as to realize long-time series monitoring of key monitoring targets.

[0060] The first aspect of the present invention provides a surface deformation monitoring method based on backward sequential least squares, as shown in Figure 1 and Figure 2 shown, including:

[0061] Step 1: Determine the first deformation rate and the corresponding co-factor matrix of each time unit in the monitoring area in the current time period, specifically including:

[0062] Step 1.1: Determine multiple unwrapped interferograms corresponding to the SAR images of the monitoring area in the current time period.

[0063] In the embodiment of the present invention, it is assumed that in the current time period In the SAR image processing system, N1+1 scenes of SLC images are collected (single-view complex SLC images refer to SAR images formed by only one section of synthetic aperture length), and then the SLC images are registered with the master and slave images, and a small baseline set is generated according to the spatial and temporal baseline thresholds. Then, the differential interferogram is generated by combining the external digital elevation model (DEM) data, and then the differential interferogram is phase filtered to suppress the influence of noise, and then the interferogram is phase unwrapped to obtain M1 unwrapped interferograms, where:

[0064]

[0065] In order to improve the accuracy of the unwrapped interferogram, it is necessary to perform error correction on the unwrapped interferogram. In the embodiment of the present invention, the unwrapped interferogram is corrected for orbit error, atmospheric delay error, and DEM error, thereby reducing the interference of these error terms and obtaining an error-corrected M1-amplitude unwrapped interferogram. The unwrapped interferograms involved in the following of the present invention are all error-corrected unwrapped interferograms.

[0066] Step 1.2: Based on multiple unwrapped interferograms, use SBAS-InSAR technology to determine the first deformation rate and the corresponding cofactor matrix of each time unit in the monitoring area within the current time period.

[0067] SBAS-InSAR technology is a commonly used multi-primary image MT-InSAR (multi-temporal InSAR) technology. By selecting appropriate spatial baseline and time baseline thresholds to form a differential interferometer pair, the influence of decoherence caused by long time baseline and spatial baseline is suppressed. This embodiment uses differential interferometry short baseline set timing analysis technology (Small BaselineSubset InSAR, SBAS-InSAR) to determine the first deformation rate and the corresponding cofactor matrix of each time unit in the monitoring area in the current time period. Specifically:

[0068] In time period t i ~t i+1 The deformation rate v(Δt i ) is an unknown number, and the differential interferometric phase δφ after removing the DEM error and atmospheric delay errori If (i = 1, …, M1) are the observables, then the function model for the SBAS-InSAR technique to first obtain the deformation time series is as follows:

[0069] V1 = A1X1 - L1, P1 (2)

[0070] In the formula, V1 is the first residual vector, A1 is the design matrix of M1×N1, which is composed of multiple time units within the current time period, M1 is the number of unwrapped interferograms, N1 is the number of SAR images within the current time period, X1 is the vector composed of multiple first deformation rates, L1 is the vector composed of the differential interferometric phases of the unwrapped interferograms, and P1 is the weight matrix corresponding to L1. Specifically:

[0071]

[0072]

[0073]

[0074] A1 is the design matrix of M1×N1, which can be determined by the time baselines of the generated small baseline set interferometric pairs. X1 is the parameter to be estimated, L1 is the observation vector, V1 is the first residual vector, and P1 is the weight matrix corresponding to the observation vector L1. For formula (2), the optimal solution can be obtained using the least squares criterion:

[0075] X1 = (A1 T P1A1) -1 A1 T P1L1 (6)

[0076]

[0077]

[0078] In the formula, is the cofactor matrix of X1, representing the relative accuracy of the deformation rates in different time periods in the solution, is the transpose matrix of A1. Finally, integrating the deformation rates in different time periods in the time domain can obtain the time series of the cumulative deformation displacement.

[0079] Step 2: Determine multiple historical unwrapped interferograms corresponding to the SAR images in the monitoring area during the historical time period.

[0080] In the embodiments of the present invention, a new unwrapped interferogram related to the historical time to be restored is generated, denoted as the historical unwrapped interferogram. The SAR images within the historical time period to be restored are registered with the master image, a new interferometric pair is generated according to the spatial and temporal baseline thresholds, and a new differential interferogram is generated in combination with external DEM data. Then, phase filtering and phase unwrapping are performed on the newly generated interferogram to obtain the newly generated historical unwrapped interferogram.

[0081] Then, error correction is performed on the newly generated historical unwrapped interferogram. Specifically: orbit error, atmospheric delay error, and DEM error correction are performed on the newly generated historical unwrapped interferogram, so as to reduce the interference of these error terms.

[0082] Step 3: According to multiple first deformation rates, covariance matrices, and multiple historical unwrapped interferograms, the second deformation rate of each time unit within the historical time period is determined by using the backward sequential least squares method, and the first deformation rate is updated. Specifically:

[0083] When it is necessary to restore the deformation time series of the historical time period, the backward sequential least squares can be used to perform backward calculation, estimate the historical deformation time series to be restored, and update the estimated deformation time series. Assume that it is necessary to perform backward calculation of the deformation time series at N2 time points backward based on time t k That is, obtain the cumulative deformation time series of the moment t i (i = k - N2, k - N2 + 1, …, k, k + 1, … k + N1 + 1, k > N2) relative to the moment Then, only according to M2 unwrapped interferograms related to the time points before time t k and the deformation rates of different time periods calculated previously, the deformation rates of all time periods can be restored by using the sequential adjustment method.

[0084] In the embodiments of the present invention, the adjustment function model is:

[0085]

[0086] In the formula, V2 is the second residual vector, Y is the vector composed of multiple second deformation rates, X2 is the vector after re-adjusting X1, that is, the updated first deformation rate, B is the coefficient matrix of Y, A2 is the coefficient matrix of X2, L2 is the vector composed of the differential interference phases of the historical unwrapped interferogram, and P2 is the weight matrix corresponding to L2. Specifically:

[0087]

[0088] Y is the vector composed of the deformation rates of the historical time period to be restored, X2 is the value after re-adjusting X1, B and A2 are the coefficients corresponding to the parameters Y and X2 respectively, and L2 is the observation vector, which is composed of the values related to the moment tk The differential interferometric phase related to the previous time point, which has removed the DEM error and atmospheric delay error, constitutes P2 as the weight matrix of the observation vector L2, and V2 as the second residual vector. The adjustment result X1 obtained in step 1.2 can be regarded as the prior information of the parameter X2 to be estimated this time. Therefore, both X2 and V2 follow a normal distribution and are independent of each other, that is

[0089]

[0090]

[0091] Cov(V2,X2) = 0 (11)

[0092] In the formula, is the variance of unit weight. For equation (9), its adjustment criterion is:

[0093]

[0094] Let Then

[0095]

[0096] That is

[0097]

[0098] Transposing both sides simultaneously, we get

[0099]

[0100] That is

[0101]

[0102] Let

[0103]

[0104]

[0105] Then equation (16) can be written as

[0106]

[0107] For the inversion of matrix N, the inversion of block matrices can be used to improve the calculation efficiency. According to the block matrix inversion formula, we have

[0108]

[0109] Among them, Therefore, the solution of equation (18) is

[0110]

[0111]

[0112] The variance of unit weight of this adjustment is

[0113]

[0114] Among them, M1 is the number of interferograms in the first estimation, M2 is the number of interferograms in the second estimation, and N1 + N2 is the total number of parameters in this estimation. Then the variance of the estimated parameters is

[0115]

[0116] Step 4: Determine the cumulative deformation of the monitoring area between the current time period and the historical time period according to the updated multiple first deformation rates and multiple second deformation rates.

[0117] In the embodiment of the present invention, the updated multiple first deformation rates and multiple second deformation rates are integrated in the time domain to obtain the cumulative deformation of the monitoring area between the current time period and the historical time period.

[0118] The second aspect of the present invention provides a surface deformation monitoring system based on backward sequential least squares, as Figure 3 shown, including a first rate determination module 101, an interferogram determination module 102, a second rate determination and first rate update module 103, and a deformation determination module 104.

[0119] Among them, the first rate determination module 101 is used to determine the first deformation rate of each time unit in the current time period of the monitoring area and the corresponding cofactor matrix;

[0120] The interferogram determination module 102 is used to determine multiple historical unwrapped interferograms corresponding to the SAR images in the historical time period of the monitoring area;

[0121] The second rate determination and first rate update module 103 is used to determine the second deformation rate of each time unit in the historical time period and update the first deformation rate by using the backward sequential least squares method according to the multiple first deformation rates, the corresponding cofactor matrix, and the multiple historical unwrapped interferograms;

[0122] The deformation determination module 104 is used to determine the cumulative deformation of the monitoring area between the current time period and the historical time period according to the updated multiple first deformation rates and multiple second deformation rates.

[0123] The method and system of the present invention will be described in more specific embodiments below.

[0124] 1. Simulation data experiment

[0125] To compare the results of the method of the present invention with the results of SBAS-InSAR solution, deformation time series solution experiments of three deformation models, namely, a linear model, a trigonometric function model, and a quadratic function model, were respectively simulated under the conditions of noiseless and noisy addition. As Figure 4 shown, the interferometric phases of 84 interferometric pairs generated from 30 SLC data collected under three deformation models were simulated, and the deformation time series were calculated from these interferometric phases. The method of the present invention was solved in three times to sequentially recover all the deformation time series. First, the deformation time series of the 21st to 30th time points were obtained by the first solution using the SBAS-InSAR method, and then the deformation time series of the historical times of the 11th to 20th and the 1st to 10th were recovered by the backward sequential least squares solution respectively. From Figure 4 it can be seen that under the condition of noiseless, the solution results of the backward sequential least squares small baseline set InSAR of the present invention are completely consistent with the results of SBAS-InSAR solution. The deformation time series solution results of the three deformation models, namely, the linear model, the trigonometric function model, and the quadratic function model, under the condition of noisy addition are as Figure 5 shown. After adding random noise obeying N(0, 1.5 2 ) to these three different deformation models, the solution results of the backward sequential least squares small baseline set InSAR of the present invention are also completely consistent with the results of SBAS-InSAR solution, but there are slight differences from the true deformation. In addition, the mean square error of unit weight of SBAS-InSAR and the backward sequential least squares small baseline set InSAR was also calculated. For the deformation of the linear model, after adding noise, the mean square error of unit weight of the SBAS-InSAR solution is 1.59 mm, and the mean square error of unit weight of the backward sequential least squares small baseline set InSAR of the present invention after the first solution, the second, and the third backward sequential least squares solutions are 1.60 mm, 1.48 mm, and 1.59 mm respectively. For the deformation of the trigonometric function model, after adding noise, the mean square error of unit weight of the SBAS-InSAR solution is 1.79 mm, and the mean square error of unit weight of the backward sequential least squares small baseline set InSAR of the present invention after the first solution, the second, and the third backward sequential least squares solutions are 1.15 mm, 1.81 mm, and 1.79 mm respectively. For the deformation of the quadratic function model, after adding noise, the mean square error of unit weight of the SBAS-InSAR solution is 1.61 mm, and the mean square error of unit weight of the backward sequential least squares small baseline set InSAR of the present invention after the first solution, the second, and the third backward sequential least squares solutions are 1.77 mm, 1.57 mm, and 1.61 mm respectively. The final adjusted mean square error of unit weight of the backward sequential least squares small baseline set InSAR of the present invention is also consistent with the mean square error of unit weight of SBAS-InSAR.

[0126] 2. Real data experiment

[0127] The research area selected for this experiment is the Heifangtai area in Yongjing County, Linxia Hui Autonomous Prefecture, Gansu Province. The data used are 44 interferograms generated from 19 descending-track TerraSAR-X data in the Heifangtai area from January 24, 2016 to November 5, 2016. The deformation time series of the Heifangtai area are obtained by using SBAS-InSAR and the backward sequential least squares small baseline set InSAR of the present invention respectively. Among them, the backward sequential least squares small baseline set InSAR first calculates the deformation time series of the latter 10 time points from June 15, 2016 to November 5, 2016, and then uses the backward sequential least squares to recover the deformation time series of the previous 9 time points from January 24, 2016 to June 15, 2016. The deformation time series results obtained by SBAS-InSAR are as Figure 6 shown, and the deformation time series results calculated by the backward sequential least squares small baseline set InSAR of the present invention are as Figure 7 、 Figure 8 shown. In order to compare the differences between the deformation time series results calculated by the backward sequential least squares small baseline set InSAR of the present invention and the results calculated by SBAS-InSAR, the time series results are also differenced, and the statistical histogram of the differences is plotted as Figure 9 shown. In order to further compare the differences between the results calculated by SBAS-InSAR and the backward sequential least squares small baseline set InSAR, the deformation time series of two unstable points P1 and P2 in the deformation area in Figure 8 are extracted as Figure 10 、 Figure 11 shown. It can be seen from the deformation time series of these two unstable points P1 and P2 that the results calculated by the backward sequential least squares small baseline set InSAR are completely consistent with the results of SBAS-InSAR, and the backward sequential least squares small baseline set InSAR can be used to recover the historical deformation time series.

[0128] For the surface deformation monitoring method and system based on backward sequential least squares of the present invention, only the newly generated unwrapped interferogram after error correction is required, and then combined with the solution and its cofactor matrix calculated last time, the deformation time series of historical time can be recovered backward;

[0129] When the present invention uses the backward sequential least squares small baseline set InSAR technology to recover the deformation time series of historical time, the data that need to be stored are the previous solution, cofactor matrix, and the newly generated unwrapped interferogram. Compared with the SBAS-InSAR technology that needs to store all the unwrapped interferograms, the storage resources can be greatly saved.

[0130] The present invention uses the backward sequential least squares small baseline set InSAR technology. When solving the coefficient matrix of the normal equation, the inverse of the block matrix is used to reduce the order of the calculated matrix and improve the calculation efficiency.

[0131] As described above, only several embodiments of the present application are shown, and there is no any form of limitation to the present application. Although the present application is disclosed by the preferred embodiments as above, it is not used to limit the present application. Any technical personnel familiar with the profession, within the scope of the technical solution of the present application, making some changes or modifications by using the disclosed technical content are equivalent to the equivalent implementation cases and all belong to the scope of the technical solution.

Claims

1. A ground deformation monitoring method based on backward sequential least squares, characterized in that, Including: Determine the first deformation rate and the corresponding cofactor matrix for each time unit in the current time period of the monitoring area; Determine multiple historical unwrapped interferograms corresponding to the SAR images in the historical time period of the monitoring area; According to the multiple first deformation rates, cofactor matrices, and the multiple historical unwrapped interferograms, use the backward sequential least squares method to determine the second deformation rate for each time unit in the historical time period and update the first deformation rate; According to the multiple updated first deformation rates and the multiple second deformation rates, determine the cumulative deformation between the current time period and the historical time period of the monitoring area; Determine the first deformation rate and the corresponding cofactor matrix for each time unit in the current time period of the monitoring area, specifically including: Determine multiple unwrapped interferograms corresponding to the SAR images in the current time period of the monitoring area; According to the multiple unwrapped interferograms, use the SBAS-InSAR technology to determine the first deformation rate and the corresponding cofactor matrix for each time unit in the current time period of the monitoring area; Determine the first deformation rate for each time unit in the current time period of the monitoring area according to the first formula, and the first formula is: V1 = A1X1 - L1, P1 Wherein, V1 is the first residual vector, A1 is a design matrix of M1×N1, which is composed of multiple time units within the current time period, M1 is the number of the unwrapped interferograms, N1 is the number of the SAR images within the current time period, L1 is a vector composed of the differential interference phases of the unwrapped interferograms, P1 is the weight matrix corresponding to L1, X1 is a vector composed of multiple said first deformation rates, and X1 = (A1 T P1A1) -1 A1 T P1L1; Determine the cofactor matrix of the first deformation rate for each time unit in the current time period of the monitoring area according to the second formula, and the second formula is: In the formula, is the cofactor matrix of X1, is the transposed matrix of A1.

2. The ground deformation monitoring method based on backward sequential least squares according to claim 1, wherein Determine the second deformation rate for each time unit in the historical time period according to the third formula, and the third formula is: In the formula, V2 is the second residual vector, Y is the vector composed of the multiple second deformation rates, X1 is the vector composed of the multiple first deformation rates, X2 is the vector after re-adjustment of X1, that is, the updated first deformation rate, B is the coefficient matrix of Y, A2 is the coefficient matrix of X2, L2 is the vector composed of the differential interference phases of the historical unwrapped interferograms, and P2 is the weight matrix corresponding to L2.

3. The ground deformation monitoring method based on backward sequential least squares according to claim 2, characterized in that, The adjustment criterion corresponding to the third formula is as the fourth formula, and the fourth formula is: In the formula, V2 is the second residual vector, X2 is the vector after re-adjusting X1, that is, the updated first deformation rate, and P2 is the weight matrix corresponding to L2. It is the cofactor matrix of X1.

4. The ground deformation monitoring method based on backward sequential least squares according to claim 3, characterized in that The normal equation matrix form corresponding to the fourth formula is as the fifth formula: In the formula, X1 is a vector composed of multiple said first deformation rates, Q X1 is the cofactor matrix of X1, X2 is the vector after readjustment of X1, A2 is the coefficient of X2, L2 is the vector composed of the differential interference phases of the historical unwrapped interferograms, P2 is the weight matrix corresponding to L2, Y is the vector composed of multiple said second deformation rates, B is the coefficient matrix of Y, and the solution of the fifth formula is as shown in the sixth and seventh formulas. The sixth formula is: The seventh formula is: where N -1 is the inverse matrix of N, is the cofactor matrix of [Y X2] T .

5. The ground deformation monitoring method based on backward sequential least squares according to claim 4, characterized in that Solve the N using the block matrix of the eighth formula -1 , and the eighth formula is: In the formula, 6. The method for monitoring surface deformation based on backward sequential least squares according to claim 1, wherein, According to the multiple updated first deformation rates and the multiple second deformation rates, determine the cumulative deformation between the current time period and the historical time period of the monitoring area, specifically including: Integrate the multiple updated first deformation rates and the multiple second deformation rates in the time domain to obtain the cumulative deformation between the current time period and the historical time period of the monitoring area.

7. A land surface deformation monitoring system based on backward sequential least squares using the land surface deformation monitoring method based on backward sequential least squares according to any one of claims 1-6, characterized in that, Including: The first rate determination module is used to determine the first deformation rate and the corresponding cofactor matrix for each time unit in the current time period of the monitoring area; The interferogram determination module is used to determine multiple historical unwrapped interferograms corresponding to the SAR images in the historical time period of the monitoring area; The second rate determination and first rate update module, which is used to determine the second deformation rate of each time unit within the historical time period and update the first deformation rate by using the backward sequential least squares method according to the multiple first deformation rates, the covariance matrix, and the multiple historical unwrapped interferograms; The deformation determination module, which is used to determine the cumulative deformation of the monitoring area between the current time period and the historical time period according to the multiple updated first deformation rates and the multiple second deformation rates.

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