High-precision earth surface deformation monitoring method based on data fusion
By iteratively updating the weights of InSAR and LiDAR data and optimizing data fusion, the monitoring accuracy problem of InSAR and LiDAR in areas with severe deformation is solved, and high-precision surface deformation monitoring is achieved.
Patent Information
- Application Number
- CN202510763244.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-09
- Publication Date
- 2025-09-12
AI Technical Summary
In the existing technology, InSAR and LiDAR have fusion errors in the data fusion process, making it difficult to achieve high-precision surface deformation monitoring in areas with severe deformation and limited coverage.
The weights of InSAR and LiDAR data are dynamically adjusted by iterative updating, and the data fusion is optimized through error propagation model and least square method to achieve the optimal fusion of InSAR and LiDAR data.
The accuracy of surface deformation monitoring has been improved, especially at the edge of subsidence and in areas of severe deformation. The overall advantages of InSAR and the local fine features of LiDAR have been maintained, which has improved the accuracy of monitoring results.
Smart Images
Figure CN120630179A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of geological deformation monitoring, and in particular to a high-precision surface deformation monitoring method using data fusion. Background Art
[0002] With the continuous development of earth observation technology, non-contact earth observation technology has become an important method for obtaining surface deformation due to its advantages such as large range and freedom from terrain and observation conditions. Among them, InSAR (Interferometric Synthetic Aperture Radar) and LiDAR (Light Detection and Reconnaissance) are widely used. InSAR and Ranging (LiDAR) are the two most widely used and effective technologies; there are significant differences between the two in spatial resolution, observation error and deformation extraction methods. InSAR has the ability to monitor a large area, but its monitoring accuracy decreases in areas with large deformation gradients (such as the edge of a subsidence), mainly due to the following limitations: reduced coherence: due to the drastic changes in the topography at the edge of the subsidence, the interference coherence of InSAR is reduced, resulting in an increase in phase unwrapping error; line of sight limitation: the LOS deformation measured by InSAR cannot directly reflect the three-dimensional deformation, and there is a large inversion error in areas with complex deformation directions (such as landslides and subsidence areas); high-precision data correction is difficult: although LiDAR data has high accuracy, its spatial coverage is limited, and traditional fusion methods often use fixed weight allocation, which is difficult to adjust adaptively; LiDAR can provide high-precision three-dimensional deformation data, but its coverage is small; therefore, how to dynamically allocate weights during the fusion process to optimize data fusion results has become an important research direction in the field of surface deformation monitoring. Summary of the Invention
[0003] The purpose of the present invention is to overcome the deficiencies in the above-mentioned prior art and provide a high-precision surface deformation monitoring method based on data fusion. The method adopts an iterative update method to dynamically adjust the weights, thereby facilitating the adjustment of the proportion of InSAR observation data and LiDAR observation data in the fusion, obtaining high-precision surface deformation monitoring results, avoiding the fusion error caused by static weights in traditional methods, and improving the surface monitoring accuracy.
[0004] To achieve the above-mentioned object, the technical solution adopted by the present invention is: a high-precision surface deformation monitoring method using data fusion, comprising: obtaining target data to be detected, wherein the target data includes InSAR observation data and LiDAR observation data; determining a unit weight variance based on the target data in combination with an error propagation model; updating the target data weight based on the unit weight variance, wherein the target data weight includes an InSAR data weight and a LiDAR data weight; and iterating the InSAR data weight and the LiDAR data weight respectively to obtain an optimal InSAR data weight and an optimal LiDAR data weight.
[0005] Preferably, the InSAR observation data is represented by the following formula:
[0006] L1=B1X+Δ1 (1)
[0007] Where: L1 is the InSAR deformation observation, B1 is the coefficient matrix of InSAR observation data, Δ1 is the measurement error of InSAR observation data, and X is the unknown surface deformation variable;
[0008] The LiDAR observation data is expressed by the following formula:
[0009] L2=B2X+Δ2 (2)
[0010] Where: L2 is the deformation observation of LiDAR, B2 is the coefficient matrix of LiDAR observation data, and Δ2 is the measurement error of LiDAR observation data.
[0011] Preferably, the error propagation model includes: constructing a normal equation based on minimizing the sum of squared errors; establishing a relationship between the observation residual and the unit weight variance based on the principle that the unit weight variances of different observations are equal; solving the unknown quantity based on the least squares method And calculate the observed residuals; substitute the observed residuals into the quadratic expectation formula to obtain the mathematical expectation of the weighted sum of squares of the residuals; determine the unit weight variance based on the mathematical expectation of the weighted sum of squares of the residuals.
[0012] Preferably, the minimizing the sum of squared errors to construct the normal equation includes: determining the objective function based on the observation model; solving the optimal parameter X based on the objective function to determine the normal equation.
[0013] Preferably, the relationship between the observation residual and the unit weight variance is expressed by the following formula:
[0014]
[0015] Where: V1 is the InSAR observation residual vector, P1 is the weighting matrix, is the variance-covariance matrix of V1, and tr() represents the trace of the matrix.
[0016] Preferably, the least squares method is used to solve the unknown quantity And calculate the observation residual, which is expressed as follows:
[0017]
[0018] Where: V1 is the observation residual of InSAR observation data, V2 is the observation residual of LiDAR observation data, Indicates an unknown status.
[0019] Preferably, the mathematical expectation of the weighted sum of squares of the residuals includes the mathematical expectation of the weighted sum of squares of the residuals of InSAR and the mathematical expectation of the weighted sum of squares of the residuals of LiDAR.
[0020] The mathematical expectation of the weighted sum of squares of the InSAR residuals is expressed as follows:
[0021]
[0022] Where: n1 represents the matrix dimension when the InSAR observation system calculates the matrix trace;
[0023] The mathematical expectation of the weighted sum of squares of the LiDAR residuals is expressed as follows:
[0024]
[0025] Where n2 represents the matrix dimension when the LiDAR observation system calculates the matrix trace.
[0026] Preferably, the unit weight variance is expressed by the following formula:
[0027]
[0028] Where:
[0029] Preferably, the InSAR data weight and the LiDAR data weight are respectively expressed by the following formulas:
[0030]
[0031] Where: P1 (k) Indicates the InSAR data weight of the kth iteration, P1 (k+1) Indicates the weight of the InSAR data at the k+1th iteration, P2 (k) Indicates the weight of LiDAR data at iteration k, P2 (k+1)represents the weight of the LiDAR data at the k+1th iteration, σ1 represents the unit weight variance of the InSAR observation data, and σ2 represents the unit weight variance of the LiDAR observation data.
[0032] Compared with the prior art, the present invention has the following advantages:
[0033] 1. The present invention uses an iterative update method to dynamically adjust the weights, which facilitates the adjustment of the proportion of InSAR observation data and LiDAR observation data in the fusion, obtains high-precision surface deformation monitoring results, avoids the fusion error caused by static weights in traditional methods, and improves the surface monitoring accuracy.
[0034] 2. When calculating the weights, the present invention fully considers the spatial heterogeneity of InSAR and LiDAR observation errors, optimizes the error propagation model, and improves data fusion accuracy.
[0035] 3. The present invention optimizes the subsidence edge areas and areas with severe deformation, so that the fused deformation monitoring results can maintain the overall advantages of InSAR while retaining the local fine features of LiDAR, thereby improving the accuracy of surface monitoring.
[0036] The present invention is further described in detail below through the accompanying drawings and examples. BRIEF DESCRIPTION OF THE DRAWINGS
[0037] Figure 1 It is a schematic diagram of the process of the present invention. DETAILED DESCRIPTION
[0038] like Figure 1 As shown, the present invention discloses a high-precision surface deformation monitoring method using data fusion, comprising: acquiring target data to be detected, wherein the target data comprises InSAR observation data and LiDAR observation data; determining a unit weight variance based on the target data in combination with an error propagation model; updating target data weights based on the unit weight variance, wherein the target data weights comprise InSAR data weights and LiDAR data weights; and iterating the InSAR data weights and the LiDAR data weights respectively to obtain optimal InSAR data weights and optimal LiDAR data weights.
[0039] In this embodiment, due to the data monitoring characteristics of InSAR and LiDAR, InSAR data provides global constraints in areas with less deformation, ensuring the stability of deformation information over a large range. LiDAR data provides localized and refined information in areas with severe deformation, improving the deformation monitoring accuracy in boundary areas. The proportions of InSAR observation data and LiDAR observation data are adjusted through a weighting matrix. If the weight of InSAR observation data decreases, the proportion of InSAR observation data in the fusion is reduced; if the weight of LiDAR observation data decreases, the proportion of LiDAR observation data in the fusion is reduced. The weights of InSAR observation data and LiDAR observation data are iteratively adjusted to achieve optimal fusion of InSAR observation data and LiDAR observation data, thereby obtaining high-precision surface deformation monitoring results.
[0040] The InSAR observation data is expressed by the following formula:
[0041] L1=B1X+Δ1 (1)
[0042] Where: L1 is the InSAR deformation observation, B1 is the coefficient matrix of InSAR observation data, Δ1 is the measurement error of InSAR observation data, and X is the unknown surface deformation variable;
[0043] The LiDAR observation data is expressed by the following formula:
[0044] L2=B2X+Δ2 (2)
[0045] Where: L2 is the deformation observation of LiDAR, B2 is the coefficient matrix of LiDAR observation data, and Δ2 is the measurement error of LiDAR observation data.
[0046] The error random model is:
[0047]
[0048] Where: P1 is the weighting matrix of InSAR observation data, P2 is the weighting matrix of LiDAR observation data, is the unit weight variance of InSAR observation data, is the unit weight variance of LiDAR observation data.
[0049] The error components in formula (1) and formula (2) are expressed as observation residuals, that is, Δ1 = V1, Δ2 = V2, and the observation model can be obtained as follows:
[0050] L1=B1X+V1 (5)
[0051] L2=B2X+V2 (6)
[0052] Since the error levels of InSAR observation data and LiDAR observation data are different, the weighted least squares method is used for data fusion to minimize the sum of squared errors:
[0053] min(L-BX) T P(L-BX)(7)
[0054] The normal equation is constructed based on the minimization of the sum of squared errors, including:
[0055] Determine the objective function based on the observation model;
[0056] The objective function is expressed as follows:
[0057] J=(L-BX) T P(L-BX) (8)
[0058] Solve for the optimal parameter X based on the objective function and determine the normal equation.
[0059] The normal equation is expressed as follows:
[0060] (B T PB)X=B T PL (9)
[0061] Transform formula (9) to obtain:
[0062] (B T PB)XB T PL=0 (10)
[0063] Where: B is the coefficient matrix containing InSAR observation data and LiDAR observation data, P is the weighting matrix containing InSAR observation data and LiDAR observation data;
[0064] in:
[0065] Let N = B T PB; W = B T PL, then formula (10) can be transformed into:
[0066]
[0067] but:
[0068] From formula (11), we can get:
[0069]
[0070] Based on the principle that the unit weight variances of different observations are equal, the relationship between the observation residuals and the unit weight variances is established;
[0071] The relationship between the observed residuals and the unit weight variance is expressed as follows:
[0072]
[0073] Where: V1 is the InSAR observation residual vector, P1 is the weighting matrix, is the variance-covariance matrix of V1, and tr() represents the trace of the matrix.
[0074] Solving unknown quantities based on the least squares method And calculate the observation residual, which is expressed as follows:
[0075]
[0076] Where: V1 is the observation residual of InSAR observation data, V2 is the observation residual of LiDAR observation data, Indicates an unknown status.
[0077] Combine formula (14) and formula (15) into a matrix form:
[0078]
[0079] From formula (16), we know that:
[0080]
[0081] Combining equations (11) and (12), equation (17) can be expressed as:
[0082]
[0083] According to the covariance propagation law, calculate the variance of V1:
[0084]
[0085] According to linear transformation, the basic form of formula (18) can be expressed as:
[0086] V=AX+BY (20)
[0087] Its covariance propagation law is:
[0088] D V =AD X A T +BD Y B T (twenty one)
[0089] Assuming that X and Y are uncorrelated, the two parts can be directly added together, combined with formula (20):
[0090]
[0091] X=L1
[0092] Y=L2
[0093] According to the covariance propagation law, equation (21) can be expressed as:
[0094]
[0095] Combined with the error random model, formula (22) can be expressed as:
[0096]
[0097] Substituting the observed residuals into the quadratic expectation formula, we can obtain the mathematical expectation of the weighted sum of squares of the residuals. Substituting formula (23) into formula (13), we can obtain:
[0098]
[0099] Where:
[0100] Using the normal matrix N = N1 + N2, then:
[0101] N -1 =(N1+N2) -1 (25)
[0102] Since N -1 Approximately satisfied: N1N -1 +N2N -1 =I, then:
[0103]
[0104] Where n1 is the matrix dimension when the InSAR observation system calculates the matrix trace.
[0105] The mathematical expectation of the weighted sum of squares of the residuals includes the mathematical expectation of the weighted sum of squares of the residuals of InSAR and the mathematical expectation of the weighted sum of squares of the residuals of LiDAR.
[0106] Combining equations (24) to (27), the mathematical expectation of the weighted sum of squares of the InSAR residuals is expressed as follows:
[0107]
[0108] Where: n1 represents the matrix dimension when the InSAR observation system calculates the matrix trace;
[0109] Similarly, the mathematical expectation of the weighted sum of squares of the LiDAR residuals is expressed as follows:
[0110]
[0111] Where n2 represents the matrix dimension when the LiDAR observation system calculates the matrix trace.
[0112] The unit weight variance is determined based on the mathematical expectation of the weighted sum of squares of the residuals.
[0113] Remove the expectation from Equation (28) and Equation (29), and replace the unit weight variance with Rewritten as an estimator but:
[0114]
[0115] Formula (30) and Formula (31) are written in matrix form, and the unit weight variance is expressed as follows:
[0116]
[0117] but:
[0118]
[0119] Where:
[0120] The InSAR data weight and LiDAR data weight are respectively expressed by the following formulas:
[0121]
[0122] Where: P1 (k) Indicates the InSAR data weight of the kth iteration, P1 (k+1) Indicates the weight of the InSAR data at the k+1th iteration, P2 (k) Indicates the weight of LiDAR data at iteration k, P2 (k+1) represents the weight of the LiDAR data at the k+1th iteration, σ1 represents the unit weight variance of the InSAR observation data, and σ2 represents the unit weight variance of the LiDAR observation data.
[0123] like The InSAR data error is large, and its weight needs to be reduced, that is, P1 becomes smaller and P2 becomes larger;
[0124] like The LiDAR data error is large, and its weight needs to be reduced, that is, P2 becomes smaller and P1 becomes larger.
[0125] By iteratively calculating P1 and P2, when the unit weight variance and When convergence occurs, the optimal weights of P1 and P2 are obtained. If the unit weight variance and satisfy Or if the number of iterations reaches the set threshold, the iteration is stopped.
[0126] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any way. Any simple modification, change and equivalent structural transformation made to the above embodiment based on the technical essence of the present invention shall still fall within the scope of protection of the technical solution of the present invention.
Claims
1. A high-precision surface deformation monitoring method based on data fusion, characterized in that: include: Acquiring target data to be detected, wherein the target data includes InSAR observation data and LiDAR observation data; Determining a unit weight variance based on the target data and in combination with an error propagation model; Based on the unit weight variance, updating the target data weight, the target data weight including the InSAR data weight and the LiDAR data weight; The InSAR data weight and LiDAR data weight are iterated separately to obtain the optimal InSAR data weight and the optimal LiDAR data weight.
2. A high-precision surface deformation monitoring method using data fusion according to claim 1, characterized in that: The InSAR observation data is expressed by the following formula: L1=B1X+Δ1 (1) Where: L1 is the InSAR deformation observation, B1 is the coefficient matrix of InSAR observation data, Δ1 is the measurement error of InSAR observation data, and X is the unknown surface deformation variable; The LiDAR observation data is expressed by the following formula: L2=B2X+Δ2 (2) Where: L2 is the deformation observation of LiDAR, B2 is the coefficient matrix of LiDAR observation data, and Δ2 is the measurement error of LiDAR observation data.
3. A high-precision surface deformation monitoring method using data fusion according to claim 1, characterized in that: The error propagation model includes: Construct normal equations based on minimizing the sum of squared errors; Based on the principle that the unit weight variances of different observations are equal, the relationship between the observation residuals and the unit weight variances is established; Solving unknown quantities based on the least squares method and calculate the observation residuals; Substitute the observed residuals into the quadratic expectation formula to obtain the mathematical expectation of the weighted sum of squares of the residuals; The unit weight variance is determined based on the mathematical expectation of the weighted sum of squares of the residuals.
4. A high-precision surface deformation monitoring method using data fusion according to claim 3, characterized in that: The normal equations constructed by minimizing the sum of squared errors include: Determine the objective function based on the observation model; Solve for the optimal parameter X based on the objective function and determine the normal equation.
5. A high-precision surface deformation monitoring method using data fusion according to claim 3, characterized in that: The relationship between the observed residuals and the unit weight variance is expressed as follows: Where: V1 is the InSAR observation residual vector, P1 is the weighting matrix, is the variance-covariance matrix of V1, and tr() represents the trace of the matrix.
6. A high-precision surface deformation monitoring method using data fusion according to claim 3, characterized in that: The least square method is used to solve the unknown And calculate the observation residual, which is expressed as follows: Where: V1 is the observation residual of InSAR observation data, V2 is the observation residual of LiDAR observation data, Indicates an unknown status.
7. A high-precision surface deformation monitoring method using data fusion according to claim 3, characterized in that: The mathematical expectation of the weighted sum of squares of the residuals includes the mathematical expectation of the weighted sum of squares of the residuals of InSAR and the mathematical expectation of the weighted sum of squares of the residuals of LiDAR. The mathematical expectation of the weighted sum of squares of the InSAR residuals is expressed as follows: Where: n1 represents the matrix dimension when the InSAR observation system calculates the matrix trace; The mathematical expectation of the weighted sum of squares of the LiDAR residuals is expressed as follows: Where n2 represents the matrix dimension when the LiDAR observation system calculates the matrix trace.
8. A high-precision surface deformation monitoring method using data fusion according to claim 3, characterized in that: The unit weight variance is expressed as follows: Where:
9. A high-precision surface deformation monitoring method using data fusion according to claim 1, characterized in that: The InSAR data weight and LiDAR data weight are respectively expressed by the following formulas: Where: represents the InSAR data weight of the kth iteration, represents the InSAR data weight of the k+1th iteration, represents the LiDAR data weight of iteration k, represents the weight of the LiDAR data at the k+1th iteration, σ1 represents the unit weight variance of the InSAR observation data, and σ2 represents the unit weight variance of the LiDAR observation data.