CN113281744B - Time sequence InSAR method based on hypothesis test and self-adaptive deformation model - Google Patents
Time sequence InSAR method based on hypothesis test and self-adaptive deformation model Download PDFInfo
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Abstract
The invention provides a time sequence InSAR method based on hypothesis test and a self-adaptive deformation model, which comprises the following steps: acquiring a time sequence SAR image of a specific research area, and carrying out registration, differential interference and unwrapping on the SAR image to obtain an InSAR interference pair data set meeting a set time-space baseline threshold; converting the multi-main-image interference pattern into a single main-image time sequence phase to obtain observation data of hypothesis test; constructing a time-related cubic function and periodic function combination as an original deformation model, and converting the original deformation model into a multivariate linear model; performing hypothesis testing on the multivariate linear model parameters according to the observation data, and removing model parameters with insignificant hypothesis testing to obtain a final deformation model; establishing an observation equation among modeled time sequence deformation, terrain residual and observation data based on the deformation model and carrying out parameter calculation to obtain the terrain residual and deformation model parameters; and extracting terrain residual errors from the observation data, and removing atmospheric influences to obtain final time sequence deformation.
Description
Technical Field
The invention relates to the technical field of monitoring surface deformation, in particular to a time sequence InSAR method based on hypothesis testing and a self-adaptive deformation model.
Background
The Time-series Interferometric Synthetic Aperture Radar (TS-InSAR) technology is a surface deformation monitoring technology developed in recent years. The technology has the advantages of high spatial resolution, capability of monitoring large-range deformation for a long time and millimeter-scale accuracy. At present, the time sequence InSAR technology is widely applied to monitoring of various geological disasters (such as landslide displacement, urban surface subsidence, mining area subsidence, glacier movement, earthquake displacement, volcanic eruption and the like), and an effective decision basis is provided for prediction and early warning of related disasters by acquiring the change rule and trend of deformation on a time sequence. There are many timing InSAR methods, such as those based on Persistent Scatterers (PS), including PSI, PSP, etc.; a time sequence InSAR method based on a Distributed Scatterer (DS) includes SBAS-InSAR and the like; the timing InSAR method of fusing PS and DS includes SqueeSAR. The time sequence methods are different in observation point types and frames, but similar in basic principle, and all the observation point types and frames are used for calculating deformation model parameters and terrain residual error parameters by adopting model constraint after removing the flat land effect and the terrain phase. Wherein the phase contribution model of the terrain residual to the interferogram is known, and the deformation model is assumed based on a priori information. Therefore, the degree of coincidence between the assumed deformation model and the actual deformation determines the resolving precision of the deformation and the terrain residual error parameters, and further influences the time sequence deformation result.
However, most of the current time-series InSAR methods use simple functions (such as linear and periodic functions) as deformation models. Obviously, for long-time-sequence surface deformation with obvious nonlinear characteristics such as jump caused by mining area deformation, earthquake and the like, the coincidence degree is low, and even the deformation signal can be misinterpreted as a terrain residual signal. If a complex function model is directly adopted, parameter overfitting is easy to occur, and a calculation error is also caused.
Disclosure of Invention
The invention provides a time sequence InSAR method based on hypothesis test and a self-adaptive deformation model, and aims to solve the problem that a hypothesis deformation model is difficult to effectively fit real deformation under the traditional SBAS framework.
In order to achieve the above object, an embodiment of the present invention provides a time series InSAR method based on hypothesis testing and an adaptive deformation model, including:
step 2, converting the multi-main image interference pattern into a single main image time sequence phase to obtain observation data of hypothesis test;
step 3, constructing a time-related cubic function and periodic function combination as an original deformation model, redefining variables and writing the variables into a multivariate linear model;
step 4, performing hypothesis testing on the multivariate linear model parameters according to the observation data, eliminating model parameters which are not obvious in hypothesis testing to obtain a final deformation model, establishing an observation equation based on the deformation model, and performing parameter calculation to obtain a terrain residual error and deformation model parameters;
and 5, extracting terrain residual errors and deformation obtained by the hypothesis test model from the observed values, removing atmosphere and the like by performing space-time filtering on the residual phase of the observed values, and adding the filtered residual deformation and the deformation obtained by the hypothesis test model to obtain the final time sequence deformation.
The scheme of the invention has the following beneficial effects:
the invention provides a time sequence InSAR method based on hypothesis test and a self-adaptive deformation model, which changes time sequence deformation without terrain residual error correction into an observed value; then, a deformation model is selected for the real deformation in a self-adaptive manner by using a hypothesis testing method; establishing an observation equation among modeled time sequence deformation, terrain residual error and observation data, and performing parameter calculation to obtain terrain residual error and deformation model parameters; and finally, removing influences of terrain residual error, atmosphere and the like to obtain a time sequence deformation quantity. The method avoids deformation model non-coincidence errors caused by a simple model and parameter overfitting caused by a complex function group through a hypothesis testing method, and improves parameter calculation precision in time sequence deformation. Meanwhile, the deformation model can be properly selected according to the place, and a good solution is provided for time sequence deformation monitoring of large-range and multi-type geological disaster areas.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 shows the time-series deformation accuracy obtained by the method of the present invention under the condition of different types of deformation of mining areas and different numbers of observation values of each group. Wherein the left graph is a plurality of deformation types of the mining area, and the right graph is a corresponding deformation error;
FIG. 3 is an interferogram and its components used in the simulation of the present invention, including (a) topographic residual phase, (b) morphic phase, (c) atmospheric phase, (d) random noise, (e) interferogram;
FIG. 4 is a diagram of terrain residuals obtained by different methods under different deformation types in a simulation experiment;
fig. 5 is a deformation residual statistical diagram obtained by different methods under different deformation types in a simulation experiment.
Detailed Description
In order to make the technical problems, technical solutions and advantages to be solved by the present invention clearer, specific embodiments will be described in detail below with reference to the accompanying drawings.
As shown in fig. 1, an embodiment of the present invention provides a time-series InSAR method based on hypothesis testing and an adaptive deformation model, including:
the method comprises the following steps of 1, obtaining a time sequence SAR image of a research area, realizing registration, differential interference and unwrapping of the SAR image of the same orbit based on the existing method, and obtaining an InSAR interference pair data set meeting a set space-time baseline threshold.
Step 2, converting the multi-main image interference pattern into a single main image time sequence phase
(x, y are the row and column numbers of any point on the image), and finally obtaining the observation data of hypothesis test.
The number of the obtained SAR images is N +1 scenes, interference pairs are selected according to a set space-time baseline threshold, and the number of the generated interference pairs is M. The resulting time-series phase is assumed to contain only the deformation signal, the terrain residual signal, and the atmospheric and incoherent noise phases are considered to be random in time-series. Furthermore, the terrain residual error can be solved on the basis of the assumed time sequence deformation model.
It should be noted that the real deformation is complex and variable, and is difficult to accurately describe with only one model in a long time sequence. In order to enable the assumed deformation model to better fit the real deformation, the invention considers grouping the observed values according to the time sequence, and simultaneously performs parameter significance hypothesis test on the assumed deformation model by combining the short time sequence deformation observed values in each group, thereby obtaining the self-adaptive time sequence deformation model. In a simulation experiment, deformation observation data of a mining area at 70 moments are simulated by taking a re-returning period (12 days) of the Sentinel-1SAR data of the European and vacant Bureau as a data sampling interval, and the time sequence deformation precision obtained by the method is further tested under the condition that the number of observation values of each group is different (see the attached figure 2 for details). According to simulation experiment results, fitting accuracy and equation complexity are comprehensively considered, and the method considers that each group contains 30 (1 year observation) observation values to be more appropriate. Meanwhile, in order to make the observed values of adjacent groups constrained with each other, when grouping, the two adjacent groups of observed values should be left with overlapped observed values(generally, 5 units are sufficient). Assuming that the time sequence is divided into J groups, the overlapping part has J-1, and the number of observed values of each group is n j The number of the overlapped observed values of the two adjacent groups of observed values is l r Then
And 3, taking the combination of the cubic function and the periodic function as an original deformation model. The following steps are all described by taking any point on the image as an example, so the column and row numbers are not marked.
Wherein k is j Is a constant term, v j Is the average velocity, a j Is the average acceleration, Δ a j Is the average acceleration rate, s j Is the coefficient of a sine function, c j Is a cosine function coefficient; t =365 days;
for the time-series deformation in the jth packet,
j =1, 2.. For the time corresponding to each observation value in the jth group, J is the number of observation value groups, n j The number of observed values in the jth group is;
order to
The original deformation model can be written as:
wherein k is j ,v j ,a j ,Δa j ,s j ,c j Is the model parameter to be solved.
In the step 4, the hypothesis test is performed in two steps: step 41, checking whether the model is valid; 42, on the premise that the model is effective, checking the significance of each parameter, then gradually removing non-significant parameters, and adaptively selecting a deformation model; if the individual point model is invalid, all parameters are used;
the model test assumes: h 0 :X＝[0,0,0,0,0] T ；
Wherein the content of the first and second substances,
p 0 j is the number of elements, p, in the unknown parameter vector X 0 j The initial values of (a) are 5,j =1,2., and J, J is the number of observation groups.
If it accepts H 0 Linear regression was considered not significant; otherwise, the linear regression is considered to be obvious, and the model is effective;
when H is present 0 When it is established, there are
The rejection region is F > F alpha (p) 0 j ,n j -p 0 j -1) when the model is valid;
wherein the content of the first and second substances,
the observed quantity of the ith time of the jth group,
solved for the model
The values of the fit are determined,
is the average of the j-th group of observations, n j Is the number of observations in group j, p 0 j Is the number of elements in the unknown parameter vector X, alpha is the significance level and the value is 0.99;
parameter testing hypothesis:
if it accepts H 0 Then consider the u-th parameter in X
The effect is not significant, and the parameters should be
Removing the model; if it refuses H 0 Then, it represents the u-th parameter in X
The effect is significant and should be preserved.
When H is present 0 When it is established, have
The rejection region is
The parameter is significant, and is reserved;
wherein the content of the first and second substances,
is an estimate of the jth parameter of the jth group, Q = ((B) j ) T B j ) -1 ，
p j The number of parameters of the deformation model after hypothesis testing is shown; q. q.s uu The u +1 th row and the u +1 th column element of Q,
for the ith observation of the jth group,
is composed of
Fitting value of n j In the jth groupNumber of observations of p 0 j Is the number of elements in the unknown parameter vector X, alpha is the significance level and the value is 0.99;
according to the method, the deformation model suitable for the observed value can be obtained by removing the insignificant parameters
Wherein the content of the first and second substances,
p j the number of parameters of the deformation model after hypothesis testing is shown.
Step 4 also includes that in order to make the model parameters of two adjacent groups mutually constrained, the observed values of each group are connected through an overlapping part to form an integral observation equation. Thus, the observation equations are divided into two categories, the first category being the internal observation equations of each set, and the second category being the observation equations of the overlapping portions of two adjacent sets. Meanwhile, in consideration of the fact that the contribution of a terrain residual error phase in a time sequence phase is less than that of a deformation quantity, the phase difference value of adjacent moments is used as the observation value of the part to improve the occupation ratio of the terrain residual error phase and improve the parameter resolving precision.
The first type of observation equation has the atmosphere delay error and the phase loss noise error in the InSAR observation value as random noise
Wherein the content of the first and second substances,
for the jth group of adjacent time instant phase difference vectors,
for the distortion value vector for the jth group of neighboring time instants,
the phase contribution vector of the interference pair to the terrain residual for the jth set of virtual adjacent time instants.
And substituting the terrain residual error model and the deformation model after hypothesis testing into:
wherein the content of the first and second substances,
representing the phase observations of group j, n j Representing the number of observed values;
for the coefficients of the deformation model parameters at the ith time in the jth group after hypothesis testing,
for corresponding deformation model parameters, p j The number of the parameters;
is the vertical baseline of the ith moment image in the jth group relative to the initial reference moment image; i =1, 2.. The nj, J =1, 2.. The J, J is the number of groups, dz is the terrain residual value to be solved, λ, r, θ respectively represent the transmitted signal wavelength, the slope distance between the sensor and the ground point and the sensor incidence angle, and the observation equations share the same
And (4) respectively.
In the second type of observation equation, two adjacent groups of observation values have overlapping moments, and the observation values of the part are equal under the condition of two adjacent groups of deformation model parameters, so that the following results are obtained:
wherein r is 1, 2.., J-1, l r The number of the r-th overlapped part observation values is 5,j =1,2,. And J is the grouping number of the observation values. Such observation equations are common
A plurality of;
integrating the two types of observed values into the same matrix, the observation equation is as follows:
solving by using a least square method to obtain a parameter [ X ] of deformation and terrain residual error to be solved 1 ,X 2 ...,X J ,dz] T
And 5, extracting terrain residual errors and deformation obtained by the hypothesis test model from the observed values, removing atmosphere and the like by performing space-time filtering on the residual phase of the observed values, and adding the filtered residual deformation and the deformation obtained by the hypothesis test model to obtain the final time sequence deformation.
The effects of the invention can be further illustrated by the following simulation experiments, the simulation data describing: (1) according to the characteristics of the existing SAR satellite, imaging geometric parameters and time space baseline configuration of SAR data are obtained through simulation; (2) simulating and generating surface deformation caused by underground fluid change in a certain area (image size is 200 pixels x 200 pixels), and projecting the surface deformation in the LOS direction; taking the data as the spatial characteristics of time sequence earth surface deformation, assuming that the time sequence types comprise linear deformation, periodic deformation, mining area deformation (Logsitic function) and jump displacement, and respectively simulating to generate corresponding interference phases; (3) and taking the difference value of the SRTMDEM and the TanDEM-XDEM of the real area as a terrain residual error, adding atmospheric noise with the maximum variation value of 1.0rad, simultaneously adding a random noise error with the standard deviation of 0.1rad, converting the random noise error into an interference phase, and adding the three components into a deformation interference graph.
In fig. 2, the deformation of the mine area is simulated by using Logistic function:
in the formula, d (t) is the accumulated subsidence value of the earth surface at the moment t; d0 is the maximum sedimentation value; and a and b are shape parameters of the Logistic function respectively. Let d0= -0.8m, change the deformed shape by a and b. A and b of Line1, line2, line3 and Line4 are 1200,0.02 respectively; 2400,0.02;1200,0.03;2400,0.03.
In fig. 4, each column represents a different model approach: respectively a traditional SBAS method linear model, a traditional SBAS method function group model and a hypothesis testing adaptive model; each row represents a different type of deformation: respectively linear deformation, periodic deformation, mine area deformation and jump displacement;
in fig. 5, each column represents a different model approach: respectively a traditional SBAS method linear model, a traditional SBAS method function group model and a hypothesis testing adaptive model; each row represents a different type of deformation: respectively linear deformation, periodic deformation, mining area deformation and jump displacement.
In order to compare the advantages of the method, the traditional SBAS linear model method and the traditional SBAS function group model method are respectively utilized to solve terrain residual errors and time sequence deformation of the simulation data. As shown in fig. 4 and 5: the solving results of the three methods of linear deformation are the same, and the three models can be well fitted to simple linear deformation; for complex deformation (periodic deformation and mining area deformation), the self-adaptive model based on hypothesis testing exerts the advantages of the model, and the calculated terrain residual value and the time sequence deformation are more accurate. Particularly, for the jump displacement, although the deformation model cannot accurately fit the deformation in the jump period, the result of the method is obviously improved compared with the traditional method, because the grouping fitting strategy adopted by the method improves the overall fitting precision.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (5)
1. A time sequence InSAR method based on hypothesis test and self-adaptive deformation model is characterized by comprising the following steps:
step 1, acquiring a time sequence SAR image of a research area, and carrying out registration, differential interference and unwrapping on the SAR image to obtain an InSAR interference pair data set meeting a set space-time baseline threshold;
step 2, converting the multi-main image interference pattern into a single main image time sequence phase to obtain observation data of hypothesis test;
step 3, constructing a time-related cubic function and periodic function combination as an original deformation model, redefining variables and writing the variables into a multivariate linear model;
step 4, performing hypothesis testing on the multivariate linear model parameters according to the observation data to obtain a deformation model, establishing an observation equation based on the deformation model and performing parameter calculation to obtain terrain residual errors and deformation model parameters;
and 5, extracting terrain residual errors and deformation obtained by the hypothesis test model from the observed values, removing atmosphere by performing space-time filtering on the residual phase of the observed values, and adding the filtered residual deformation and the deformation obtained by the hypothesis test model to obtain final time sequence deformation.
2. The hypothesis testing and adaptive deformation model-based time-series InSAR method according to claim 1, wherein the step 2 comprises:
the single master image timing phase is:
in order to enable the function groups to better fit the real deformation, time sequence phases are divided into J groups according to the time sequence to carry out hypothesis testing and deformation model parameter and terrain residual solution, and meanwhile, two adjacent groups are required to be provided with overlapped observed values, so that the two groups of deformation model parameters are mutually constrained.
3. The hypothesis testing and adaptive deformation model-based time-series InSAR method according to claim 2, wherein the step 3 comprises:
taking the combination of a cubic function and a periodic function as an original deformation model;
wherein k is j Is a constant term, v j Is the average velocity, a j Is the average acceleration, Δ a j Is the average acceleration rate, s j Is the coefficient of a sine function, c j Is a cosine function coefficient; t =365 days;
for the time-series deformation in the jth packet,
j =1, 2.. For the time corresponding to each observation value in the jth group, J is the number of observation value groups, n j The number of observed values in the jth group is;
let b1= t, b2= t 2 ,b 3 ＝t 3 ,
The original deformation model can be written as:
wherein k is j ,v j ,a j ,Δa j ,s j ,c j Is the model parameter to be solved.
4. The hypothesis testing and adaptive deformation model-based time-series InSAR method according to claim 3, wherein the step 4 comprises:
the hypothesis testing is performed in two steps:
step 41, checking whether the model is valid;
42, on the premise that the model is effective, checking the significance of each parameter, then gradually eliminating non-significant parameters, and adaptively selecting a deformation model; if the individual point model is invalid, all parameters are used;
the model test assumes: h 0 :X＝[0,0,0,0,0] T ；
Wherein the content of the first and second substances,
p 0 j is the number of elements, p, in the unknown parameter vector X 0 j The initial values of (1) are 5,j =1,2,. And J is the grouping number of the observed values;
if it accepts H 0 Linear regression was considered not significant; otherwise, the linear regression is considered to be obvious, and the model is effective;
when H is present 0 When it is established, have
The rejection region is F > F α (p 0 j ,n j -p 0 j -1) when the model is valid;
wherein the content of the first and second substances,
for the ith observation of the jth group,
solved for the model
The values of the fit are determined,
is the average of the j-th group of observations, n j Is the number of observations in group j, p 0 j Is the number of elements in the unknown parameter vector X, alpha is the significance level and the value is 0.99;
parameter testing hypothesis:
if it accepts H 0 Then consider the u-th parameter in X
The effect is not significant, and the parameters should be
Removing the model; if it refuses H 0 Then, it represents the u-th parameter in X
The influence is significant, and the influence should be kept;
when H is present 0 When it is established, there are
The rejection region is
The parameter is significant, and the parameter is reserved;
wherein the content of the first and second substances,
is an estimate of the jth parameter of the jth group, Q = ((B) j ) T B j ) -1 ，
p j The number of parameters of the deformation model after hypothesis testing is set; q. q.s uu The u +1 th row and the u +1 th column element of Q,
for the ith observation of the jth group,
is composed of
Fitting value of n j Is the number of observations in group j, p 0 j Is the number of elements in the unknown parameter vector X, alpha is the significance level and the value is 0.99;
according to the method, the deformation model suitable for the observed value can be obtained by removing the insignificant parameters
Wherein the content of the first and second substances,
p j the number of parameters of the deformation model after hypothesis testing is shown.
5. The hypothesis testing and adaptive deformation model-based time series InSAR method according to claim 4, wherein the step 4 further comprises:
the observation equations are divided into two types, wherein the first type is an observation equation of internal data of J groups of observation values, and the second type is an observation equation of an overlapping part of two adjacent groups of observation values;
the first type of observation equation considers that the terrain residual phase in the time sequence phase has less contribution than the deformation quantity, and takes the phase difference value of the adjacent time as the observation value of the part to improve the occupation ratio of the terrain residual phase and improve the parameter resolving precision; meanwhile, assuming that the atmospheric delay error and the phase loss noise error in the InSAR observed value are random noise, the random noise exists
Wherein the content of the first and second substances,
for the jth group of adjacent time instant phase difference vectors,
for the distortion value vector for the jth group of adjacent time instants,
a phase contribution vector of the interference pair to the terrain residual error for the jth group of virtual adjacent moments;
and substituting the terrain residual error model and the deformation model after hypothesis testing into:
wherein the content of the first and second substances,
represents the phase observation of the j-th group, n j Representing the number of observed values;
to assume the coefficients of the deformation model parameters at the ith time in the jth group after the test,
for corresponding deformation model parameters, p j The number of the parameters;
is the vertical baseline of the ith moment image in the jth group relative to the initial reference moment image; i =1,2.., n j J =1, 2.. Said, J is the number of groups, dz is the terrain residual value to be solved, λ, r, θ respectively represent the wavelength of the transmitted signal, the slope distance between the sensor and the ground point and the incident angle of the sensor, and the observation equations of the type have in common
A plurality of;
in the second type of observation equation, two adjacent groups of observation values have overlapping moments, and the observation values of the part are equal under the condition of two adjacent groups of deformation model parameters, so that the following results are obtained:
wherein r is 1, 2.., J-1, l r The number of the r-th overlapped part observation values is 5; j is the number of observation value groups, and the observation equations are shared
A plurality of;
integrating the two types of observed values into the same matrix, the observation equation is as follows:
solving by using a least square method to obtain a parameter [ X ] of deformation and terrain residual error to be solved 1 ,X 2 ...,X J ,dz] T 。
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