CN115545100A - GB-InSAR atmospheric phase compensation method based on LSTM - Google Patents
GB-InSAR atmospheric phase compensation method based on LSTM Download PDFInfo
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Abstract
The invention relates to the technical field of atmospheric phase compensation, and discloses a GB-InSAR atmospheric phase compensation method based on LSTM. The method comprises the steps of firstly calculating correlation coefficients and phase average values of PS points, constructing evaluation factors, selecting the evaluation factors to input the LSTM to obtain time sequence phase change characteristics of the PS points, constructing a classification model, classifying all the PS points by using a K-means method, selecting the class with the minimum standard deviation as a stable point verification model to obtain reliability, and obtaining a proper classification model. And then classifying all the PS points by using a classification model to select stable PS points. And finally, lowess interpolation fitting is carried out according to the stable PS points, and the atmospheric phase of the PS points is compensated. The method can be suitable for scenes with more complex weather environments.
Description
Technical Field
The invention relates to the technical field of atmospheric phase compensation, in particular to a GB-InSAR atmospheric phase compensation method based on LSTM.
Background
The propagation coefficient of electromagnetic waves can be influenced by atmospheric conditions, and when the atmospheric conditions change, the electromagnetic wave coefficient can change, so that the electromagnetic wave coefficient is different at different moments, deformation obtained by GB-InSAR through twice differential interference calculation contains meteorological disturbance errors, and in order to more accurately obtain the deformation, atmospheric phase compensation needs to be carried out on pixel points in an interference phase diagram.
In the GB-InSAR measurement, there are two common methods of atmospheric phase compensation in use today, the first being to calculate the atmospheric phase from an atmospheric refractive index model using meteorological data. The second method is to establish an atmospheric parameter model based on the PS point, in the case of good weather conditions, the atmosphere can be considered to have homogeneity in space, and based on the homogeneity of the atmosphere, a linear model which changes with the slope distance is established to carry out atmospheric phase estimation on the PS point. Both of these methods, however, have drawbacks. In an actual monitoring scene, meteorological conditions change with time all the time, the atmosphere is different in quality in time and space, particularly, under a complex weather condition, the atmosphere changes more complexly in space, and a large error is caused by estimating the atmospheric phase by adopting a multi-parameter model, so that a compensation method for the space-time atmospheric phase is required to be researched.
Disclosure of Invention
The invention aims to provide an LSTM-based GB-InSAR atmospheric phase compensation method to solve the problem that in the existing method, under the condition of facing complex weather, the estimation error of the atmospheric phase is large.
In order to achieve the above object, the basic scheme of the invention is as follows: the GB-InSAR atmospheric phase compensation method based on the LSTM comprises the following steps,
the method comprises the following steps: calculating the correlation coefficient and the phase average value of the PS point, constructing an evaluation factor,
step two: selecting evaluation factors and inputting LSTM to obtain the time sequence phase change characteristics of PS points, constructing a classification model,
step three: classifying all PS points by using a K-means method, selecting the class with the minimum standard deviation as a stable point to verify the reliability of the model, obtaining a proper classification model,
step four: classifying all the PS points by using a classification model to select stable PS points,
step five: and carrying out Lowess interpolation fitting according to the stable PS point to compensate the atmospheric phase of the PS point.
The principle and the beneficial effects of the invention are as follows: the method is provided by considering the correlation of the acquired atmospheric phase on the time sequence, so that the method is suitable for the scene with a complex weather environment.
Furthermore, the LSTM is a long and short time sequence network, the long and short time sequence network is additionally provided with a forgetting gate and a self-circulation connection point on the basis of an output gate and an input gate of the recurrent neural network, in the training process of the long and short time sequence network, a tanh function is used as a core function, and a Simgomm function is used as an activation function.
Has the beneficial effects that: the long and short time sequence network can record or delete information through the forgetting gate to realize the forgetting and memorizing functions, and mainly realizes the forgetting and memorizing functions through the input gate and the output gate, the input gate can select to forget the information, and the output gate determines the output value of the memory storage grid and whether the output value is used as a neuron for inputting the next period.
Further, the training process of the long and short time sequence network consists of the following parts,
the first part is a forgetting gate which determines the recording or forgetting of information, and the formula is as follows,
in the formula, f t Indicates the output of the forgetting gate, and when it is 1, indicates that the current information is to be input to the next epoch, and when it is 0, the information is to be deleted, at [0,1]The size between indicates the next time the letter will be recordedHow much, W f Represents a weight, b f Representing bias, sigma an activation function, h t-1 Indicating information recorded during the last time period, x t An input indicative of the time period is entered,
the second part is that after the forgetting gate is judged, the input gate judges whether the input of the period is recorded or not, the formula is expressed as follows,
wherein i t Representing the output of the input gate, W i Weight matrix of representation, b i A bias term is represented in the form of,
value, W, representing the state of the new cell C Weight representing the current input cell state, b C A bias representing the state of the cell currently being input,
the third part is updating, and the long and short time sequence network is updated according to the output of the activation function and the information recorded in the previous time period, the formula is expressed as follows,
the fourth part is that the long and short time sequence network carries out input and output, when in output, the long and short time sequence network judges the output, whether the output result is output or not is determined according to the current unit state, which mainly depends on an activation function and a tanh function, the formula is expressed as follows,
h t ＝o t *tanh(C t ) (17)
wherein o is t Representing the output of the output gate, W 0 Representing a weight matrix, b 0 Represents a bias term, h t Indicating the output result.
Has the advantages that: the Simmgomm function can perform numerical value normalization on input samples, and the input value is converted into [0,1], so that the sample difference caused by overlarge factor value deviation between samples can be reduced, and great help is provided for training, however, the Simmgmod function has defects, and is easy to have the problems of slow convergence and gradient disappearance, and the formula is as follows:
the tanh has an advantage over the Simgmod function, and avoids the defect of the Simgmod, so that the tanh is often used as a core function of a long-short time sequence network.
Furthermore, the PS points are divided into two types, namely stable PS points and unstable PS points, and each PS point is described by two observation variables, namely a phase average value and a complex correlation coefficient.
Further, the phase mean value is calculated as the phase mean value of the kth PS point
Is shown as
Wherein
Representing the phase value of the PS dot k after the i-th image interferes with the first image and is unwrapped.
Further, the complex correlation coefficient is calculated by solving the correlation coefficient for each PS point and all PS points complex phase and averaging to obtain the average correlation coefficient
And the formula is as follows,
wherein, the first and the second end of the pipe are connected with each other,
represents the information of the PS point k in the ith image, and W represents the information of all PS points.
Furthermore, because the dimension and the value range of the phase average value and the complex correlation coefficient are different, the normalization processing for eliminating the dimension needs to be carried out, the formula is as follows,
then adding the two elements to obtain the evaluation factor
And selecting x% before and after the evaluation standard to train by using LSTM, and then classifying the rest PS points, wherein the front x% is a stable point, and the back x% is an unstable point.
Further, in order to verify a classification model constructed by LSTM, the K-means method is selected to cluster all PS points, then the classification model is verified by calculating the standard deviation of all the clustering categories and selecting the category with the minimum standard deviation as the category of the stable point, wherein the principle of the K-means algorithm is to divide a given sample set into clusters according to the distance, the K-means algorithm can set the center points of the families, the points close to each other in the adjacent distance are divided into the same category according to the distance, and the sample set x is supposed to be divided into K clusters (C) 1 ,C 1 ,...,C k ) The sum of squared errors E between clusters is expressed as:
where, | | · |, denotes a norm of order 2, i.e., the norm of the vector, μ i Is a cluster C i The mean values of (a) are adjacent,the formula is expressed as:
where | · | represents a norm of order 1, i.e., the number of cluster midpoints,
clustering all PS points, wherein the clustering category is k, calculating the standard deviation of each cluster, and the calculation formula is as follows:
wherein the content of the first and second substances,
indicating the phase value of the ith point in the kth cluster,
representing the phase mean of the kth cluster.
Has the beneficial effects that: and classifying the PS in the cluster with the minimum phase standard deviation as a stable PS point, testing the accuracy of a classification model obtained by x% before and after the evaluation standard, selecting the current model to classify all the PS points when the model meets the expected standard, selecting the stable PS point, and finally compensating the atmospheric phase by using the stable PS, wherein the compensation method adopts local weighted regression fitting.
Furthermore, lowess is a local weighted regression, the local weighted regression belongs to a nonparametric statistical learning method, and a global model can be fitted through local simplification and simple local model assumption in local weighted learning.
Has the advantages that: in practical application, the distribution of data often cannot provide enough distribution, different weights are given to training samples by local weighted learning according to the distance between a prediction point and a direct point of the training samples, the weight of the training sample closer to the point to be predicted is larger, and conversely, the weight of the training sample farther from the point to be predicted is smaller, so that the local weighted learning can learn local information of the data differently.
Further, for stable PS points, the window is first captured, the captured distance is selected as the set of points with the minimum distance to the specified point, the expression is as follows,
according to the set window d span Selecting a point set with the minimum distance from the designated point in the wide mouth range, wherein the expression is as follows,
each point from a given point has its own weight, which is:
these points are used to make a locally weighted regression with a loss function of:
and constructing a fitting curved surface f (x, y) by using local weighted regression, wherein the obtained f (x, y) is the estimated atmospheric interference phase value.
Drawings
Fig. 1 is a schematic diagram of a conventional LSTM model of an LSTM-based GB-InSAR atmospheric phase compensation method in an embodiment of the present invention.
Fig. 2 is a field picture and a radar picture of the LSTM-based GB-InSAR atmospheric phase compensation method according to the embodiment of the present invention.
Fig. 3 is a radar image and a differential interference phase diagram of the LSTM-based GB-InSAR atmospheric phase compensation method in the embodiment of the present invention.
FIG. 4 is a selection distribution diagram of an LSTM-based GB-InSAR atmospheric phase compensation method in an embodiment of the present invention.
FIG. 5 is a phase change curve when 3% is selected for the LSTM-based GB-InSAR atmospheric phase compensation method in the embodiment of the present invention.
FIG. 6 is a diagram of results of different evaluation factor percentage selections of the LSTM-based GB-InSAR atmospheric phase compensation method in the embodiment of the present invention.
FIG. 7 is a point clustering result and minimum standard deviation category diagram of the LSTM-based GB-InSAR atmospheric phase compensation method in the embodiment of the present invention.
FIG. 8 is a diagram illustrating the classification results of the LSTM-based GB-InSAR atmospheric phase compensation method according to the embodiment of the present invention.
Fig. 9 is a comparison graph of the LSTM-based atmospheric compensation result of the LSTM-based GB-InSAR atmospheric phase compensation method in the embodiment of the present invention with the atmospheric compensation of the conventional method.
Fig. 10 is a flowchart of an LSTM-based GB-InSAR atmospheric phase compensation method in an embodiment of the present invention.
Detailed Description
The following is further detailed by way of specific embodiments:
the embodiment is substantially as shown in figures 1 and 10 of the accompanying drawings: the GB-InSAR atmospheric phase compensation method based on the LSTM comprises the following steps,
the method comprises the following steps: calculating the correlation coefficient and the phase average value of the PS point, constructing an evaluation factor,
the phase average value is calculated as the phase average value of the kth PS point
Is shown as
Wherein
Representing the phase value of the PS point k after the ith image and the first image are subjected to interference unwrapping, and calculating the complex correlation coefficient by solving the correlation coefficient for the complex phase of each PS point and all the PS points and averaging to obtain the average
And the formula is as follows,
wherein the content of the first and second substances,
represents the information of the PS point k in the ith image, and W represents the information of all the PS points
Because the dimension and the value range of the phase average value and the complex correlation coefficient are different, the normalization processing for eliminating the dimension needs to be carried out firstly, the formula is as follows,
then adding the two elements to obtain the evaluation factor
Step two: selecting evaluation factors, inputting the evaluation factors into the LSTM to obtain the time sequence phase change characteristics of the PS points, constructing a classification model,
selecting x% before and after evaluation standard, training with LSTM, classifying the rest PS points, wherein the front x% is stable point, the back x% is unstable point, the LSTM training process comprises the following parts,
the first part is a forgetting gate which determines the recording or forgetting of information, and the formula is as follows,
in the formula (f) t Indicates the output of the forgetting gate, and when it is 1, indicates that the current information is to be input to the next epoch, and when it is 0, the information is to be deleted, at [0,1]The size between indicates how much information, W, will be recorded at the next time f Represents a weight, b f To representOffset, σ denotes the activation function, h t-1 Indicating information recorded during the last time period, x t An input indicative of the time period is entered,
the second part is that after the forgetting gate judges, the input gate judges whether the input of the period is recorded, the formula is expressed as follows,
wherein i t Representing the output of the input gate, W i Weight matrix of representation, b i A bias term is represented as a function of,
value, W, representing the state of the new cell C Weight representing the current input unit state, b C A bias representing the state of the cell currently being input,
the third part is updating, and the long and short time sequence network is updated according to the output of the activation function and the information recorded in the previous time period, the formula is expressed as follows,
the fourth part is that the long and short time sequence network carries out input and output, when in output, the long and short time sequence network judges the output, whether the output result is output or not is determined according to the current unit state, which mainly depends on an activation function and a tanh function, the formula is expressed as follows,
h t ＝o t *tanh(C t ) (17)
wherein o is t Representing the output of the output gate, W 0 Representing a weight matrix, b 0 Represents a bias term, h t Indicating the output result.
Step three: classifying all PS points by using a K-means method, selecting the class with the minimum standard deviation as a stable point to verify the reliability of the model, obtaining a proper classification model,
in order to verify a classification model constructed by LSTM, the K-means method is selected to cluster all PS points, then the classification model is verified by calculating the standard deviation of all the clustering classes and selecting the class with the minimum standard deviation as the class of a stable point, wherein the principle of the K-means algorithm is to divide a given sample set into clusters according to the distance, the K-means algorithm can set the center point of the cluster, the points close to each other in the adjacent distance are divided into the same class according to the distance, and the sample set x is supposed to be divided into K clusters (C) 1 ,C 1 ,...,C k ) The sum of squared errors E between clusters is expressed as:
where, | | · |, denotes a norm of order 2, i.e., the norm of the vector, μ i Is a cluster C i Is adjacent, can be expressed as:
where, |, represents a norm of order 1, i.e., the number of cluster midpoints.
Step four: classifying all the PS points by using a classification model to select stable PS points,
clustering all PS points, wherein the clustering category is k, calculating the standard deviation of each cluster, and the calculation formula can be expressed as follows:
wherein the content of the first and second substances,
indicating the phase value of the ith point in the kth cluster,
represents the mean of the phases of the k-th cluster,
and classifying the PS in the cluster with the minimum phase standard deviation as a stable PS point, testing the accuracy of a classification model obtained by x% before and after the evaluation standard, and selecting the current model to classify all the PS points when the model meets the expected standard to select the stable PS point.
Step five: lowess interpolation fitting is carried out according to the stable PS points to compensate the atmospheric phase of the PS points, wherein Lowess is local weighted regression which belongs to a nonparametric statistical learning method, the local weighted learning can fit a global model by local simplification and simple local model assumption, then for the stable PS points, firstly, a screenshot window is selected, the intercepted distance is a set of points with the minimum distance to the specified point, and the expression is as follows,
according to the set window d span Selecting a point set with the minimum distance from the appointed point in the wide mouth range, wherein the expression is as follows,
each point from a given point has its own weight, which is:
these points are used to make a locally weighted regression with a loss function of:
and (3) constructing a fitting curved surface f (x, y) by using local weighted regression, wherein the obtained f (x, y) is the estimated atmospheric interference phase value.
Experimental information:
as shown in fig. 2 (a), a photograph of a landslide scene is shown. The landslide is located in the Zhongtai group of the village of six shafts in the land county of Wulong district, 29 DEG 28 'to north latitude 53' to east longitude 107 DEG 55 'to 43'. About 25 kilometers away from Wulong city area, 319 national roads are directly connected with Wulong city area, and the traffic is more convenient. The exposed slope body has stable scattering effect in the radar image due to the dense vegetation growing on the slope body. A slope radar detection radar developed by Beijing Physician Lei Ke works in a wave band, the measurement period is 0.3m multiplied by 4.0m, and the spatial resolution (at 1 km) is adopted. The photograph of the system is shown in FIG. (b).
As shown in fig. 3, 30 radar images, which were continuously acquired at 11/7/28/2020, were now analyzed, and the average acquisition time of the images was two minutes. The diagram (a) shows the radar image of the area, and the amplitude of the pixel points in the diagram is subjected to dB processing. And (2) carrying out differential interference by taking the 1 st image as a main image and the last image as an auxiliary image to obtain an interference phase image (b), wherein the phases of a plurality of pixel points in the image (b) slowly change along with the skew distance and the azimuth angle, namely the interference phase presents stronger space variation, the region shown by a red circle is a deformation region, and the interference phase is obviously different from other regions.
The graph of each pixel point calculated by using the amplitude dispersion method shows the result obtained by selecting the PS point by using the amplitude dispersion method. At this time, the set amplitude dispersion threshold is 0.25, and the amplitude threshold is-25 dB. The selected PS points total 18171, as shown in fig. 4.
The experimental results are as follows:
obtaining a classification model:
for 18171 high-quality pixel points selected in the previous subsection, firstly obtaining the interference phases of the pixel points in 29 differential interference phase images, averaging the correlation coefficient of each high-quality pixel point and all other high-quality pixel points, obtaining the correlation coefficient corresponding to each high-quality pixel point, then calculating the phase average value of each high-quality pixel point in 29 differential interference phase images, and finally normalizing the correlation coefficient and the phase average value to be used as a reference element to construct an evaluation factor.
Selecting different percentages before and after as a high-quality set and a low-quality set respectively, and displaying the difference by using a time-series interference phase diagram, as shown in the following fig. 5 (a) and (b), wherein fig. 5 (a) represents a phase change curve of the front 3% point, and (b) represents a phase change curve of the rear 3%, when 3% before and after an evaluation factor is selected, the selected PS points of the high-quality set are obviously different in 29 differential interference phase diagrams, the fluctuation of the front 3% of the evaluation factor in the 29 differential interference phase diagrams is obvious, the highest difference reaches 3rad, the lowest difference is-4 rad, the fluctuation of the rear 3% in the 29 differential interference phase diagrams is smooth, and the phase fluctuation does not exceed 2rad.
And (3) utilizing time sequence phase characteristics of the evaluation factors before and after the LSTM is obtained in 29 differential interference phase diagrams to construct a classification model, and then classifying all PS points to select stable PS points and unstable PS points. The following table 1 shows the number of stable points and unstable points selected according to different evaluation factor percentages, and it can be seen from the table that as the percentages before and after the selected evaluation factor increase, the number of the selected stable points decreases, and in the process of interpolation fitting, enough stable points are needed for interpolation fitting, so that when the evaluation factor percentage is selected, too many percentages cannot be selected, so as to avoid that the number of the classified stable points is too small, which is not favorable for later-stage interpolation fitting to compensate the atmospheric phase. In order to avoid different classification results caused by constructing a classification model each time, the same percentage evaluation factor is selected for classifying by using the LSTM constructed classification model for multiple times, and when the frequency of a PS point appearing in a stable point in the multiple classification results exceeds 90%, the PS point is listed as a stable PS point.
TABLE 1 number of stable points and unstable points selected based on different evaluation factor percentages
After stable points and unstable points are selected, differential interference is carried out between the last radar image and the first radar image to display stable PS points and unstable PS points, the display results are shown in the following graphs, classification models are built for input LSTM in 1%, 2% and 3% before and after evaluation factor selection in fig. 6 (a), (c) and (e), obtained unstable PS point distribution graphs are obtained, the obtained stable PS point distribution graphs are shown in fig. 6 (b), (d) and (f), and it can be seen from the graphs that when 1% before and after the evaluation factor selection is selected, relatively more stable points are obtained, and atmospheric phase compensation through later-stage interpolation fitting is facilitated.
In order to verify the accuracy of the model, K-means was selected to cluster all PS points, and the clustering result is shown in fig. 7 (a). Calculating all the class standard deviations, selecting the class with the smallest standard deviation, and taking the class as a stable point class as a result as shown in fig. 7 (b), putting the class into classification models constructed by different evaluation factor percentages, and verifying the accuracy of the classification models. The obtained accuracy is shown in the following table, and in order to prevent errors, the accuracy is an average value obtained after multiple classifications. As can be seen from the table, when the selection rate is from 1% to 2% before and after the evaluation factor, the accuracy rate jumps, so that the model is more reliable when the selection rate is 1% before and after the evaluation factor.
TABLE 1 Classification model accuracy under different evaluation factors
Atmospheric phase compensation:
as can be seen from the above, when 1% of the evaluation factors are selected, the classification result is more reliable than that when 2% of the evaluation factors are selected, and therefore, the classification model is required to be constructed before 1%, and when 2% of the evaluation factors are selected and 3%, fewer stable points are obtained compared with 1%, which is not favorable for the Lowess interpolation fitting to compensate the atmospheric phase. Here, after a classification model is constructed by inputting the time-series phase of 1% PS points before and after the evaluation factor is selected and the classification model is obtained, all remaining PS points are classified, and the classification results are shown in fig. 8 (a) and 8 (b), where fig. 8 (a) shows the unstable point classification result and fig. 8 (b) shows the stable point classification result.
And after stable PS points are obtained, performing atmospheric phase compensation on all the PS points by utilizing interpolation fitting, wherein the LOWESS method is selected as an interpolation fitting compensation method. After compensation, 29 differential interference phase maps are added, and the result is shown in fig. 9 (b). To verify the effectiveness of this method, the results were compared to conventional compensation methods. As can be seen from the figure, the phase diagram 9 (b) after compensating the atmospheric phase by the method used in this chapter is relative to the phase diagram 9 (a) after compensating by the conventional method, and most of the PS point phase is around 0 rad.
In order to more intuitively compare the difference of the compensated atmospheric phase under the conventional method and the LSTM-based method provided by the chapter, 3 PS points with the minimum amplitude deviation are selected from different slope distances to serve as reference points. As shown in fig. 9 (c) and 9 (d), fig. 9 (c) is a phase curve of the reference point under the compensation of the conventional method, and fig. (d) is a phase curve of the reference point under the compensation of the LSTM. As can be seen from fig. 9 (c), the phase curve of the reference point after compensation is more gradual based on the LSTM atmospheric phase compensation method, the highest phase is 0.2rad, whereas the phase of the compensation result in the conventional method in fig. 9 (c) is up to 1rad, and the phase of the reference point is accumulated with time, which is caused by the residual atmospheric phase. Therefore, the atmospheric phase compensation method in this chapter is improved in compensation result compared with the conventional compensation method.
The foregoing is merely an example of the present invention and common general knowledge in the art of specific structures and/or features of the invention has not been set forth herein in any way. It should be noted that, for those skilled in the art, without departing from the structure of the present invention, several changes and modifications can be made, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicability of the patent. The scope of the claims of the present application shall be determined by the contents of the claims, and the description of the embodiments and the like in the specification shall be used to explain the contents of the claims.
Claims (10)
1. The GB-InSAR atmospheric phase compensation method based on the LSTM is characterized by comprising the following steps: comprises the following steps of (a) carrying out,
the method comprises the following steps: calculating the correlation coefficient and the phase average value of the PS point, constructing an evaluation factor,
step two: selecting evaluation factors, inputting the evaluation factors into the LSTM to obtain the time sequence phase change characteristics of the PS points, constructing a classification model,
step three: classifying all PS points by using a K-means method, selecting the class with the minimum standard deviation as the reliability of a stable point verification model, obtaining a proper classification model,
step four: classifying all the PS points by using a classification model to select stable PS points,
step five: and carrying out Lowess interpolation fitting according to the stable PS point to compensate the atmospheric phase of the PS point.
2. The LSTM-based GB-InSAR atmospheric phase compensation method according to claim 1, characterized in that: the LSTM is a long and short time sequence network, a forgetting gate and a self-circulation connection point are added on the basis of an output gate and an input gate of a circulation neural network in the long and short time sequence network, in the training process of the long and short time sequence network, a tanh function is used as a core function, and a Simgommd function is used as an activation function.
3. The LSTM-based GB-InSAR atmospheric phase compensation method of claim 2, characterized in that: the training process of the long and short time sequence network consists of the following parts,
the first part is a forgetting gate which determines the recording or forgetting of information, and the formula is as follows,
in the formula (f) t Indicates the output of the forgetting gate, and when it is 1, indicates that the current information is to be input to the next epoch, and when it is 0, the information is to be deleted, at [0,1]The size between indicates how much information will be recorded next time, W f Represents a weight, b f Representing bias, sigma an activation function, h t-1 Indicating information recorded during the last time period, x t An input indicative of the time period is entered,
the second part is that after the forgetting gate is judged, the input gate judges whether the input of the period is recorded or not, the formula is expressed as follows,
wherein i t Representing the output of the input gate, W i Weight matrix of representation, b i A bias term is represented as a function of,
value, W, representing the state of the new cell C Weight representing the current input unit state, b C A bias representing the state of the cell currently being input,
the third part is updating, and the long and short time sequence network is updated according to the output of the activation function and the information recorded in the previous time period, the formula is expressed as follows,
the fourth part is that the long and short time sequence network carries out input and output, when in output, the long and short time sequence network judges the output, whether the output result is output or not is determined according to the current unit state, which mainly depends on an activation function and a tanh function, the formula is expressed as follows,
h t ＝o t *tanh(C t ) (17)
wherein o is t Representing the output of the output gate, W 0 Representing a weight matrix, b 0 Indicating the offsetItem, h t Indicating the output result.
4. The LSTM-based GB-InSAR atmospheric phase compensation method according to claim 3, characterized in that: the PS points are divided into two types, namely stable PS points and unstable PS points, and each PS point is described by two observation variables, namely a phase average value and a complex correlation coefficient.
5. The LSTM-based GB-InSAR atmospheric phase compensation method according to claim 4, characterized in that: the phase average value is calculated in the way of the phase average value of the kth PS point
Is shown as
Wherein
Representing the phase value of the PS dot k after interference and unwrapping of the ith image with the first image.
6. The LSTM-based GB-InSAR atmospheric phase compensation method of claim 5, characterized in that: the calculation mode of the complex correlation coefficient is that each PS point and all PS points complex phase are calculated to obtain the correlation coefficient and the correlation coefficient is averaged to obtain
And the formula is as follows,
wherein, the first and the second end of the pipe are connected with each other,
represents the information of the PS point k in the ith image, and W represents the information of all PS points.
7. The LSTM-based GB-InSAR atmospheric phase compensation method according to claim 6, characterized in that: because the dimensions and the value ranges of the phase average value and the complex correlation coefficient are different, the normalization processing for eliminating the dimensions needs to be carried out firstly, the formula is as follows,
then adding the two elements to obtain the evaluation factor
And selecting x% before and after the evaluation standard to train by using LSTM, and then classifying the rest PS points, wherein the front x% is a stable point, and the back x% is an unstable point.
8. The LSTM-based GB-InSAR atmospheric phase compensation method of claim 7, characterized in that: in order to verify a classification model constructed by LSTM, the K-means method is selected to cluster all PS points, then the classification model is verified by calculating the standard deviation of all the clustering classes and selecting the class with the minimum standard deviation as the class of a stable point, wherein the principle of the K-means algorithm is to divide a given sample set into clusters according to the distance, the K-means algorithm can set the center point of the cluster, the points close to each other in the adjacent distance are divided into the same class according to the distance, and the sample set x is supposed to be divided into K clusters (C) 1 ,C 1 ,...,C k ) The sum of squared errors E between clusters is expressed as:
wherein, | | · | | represents a norm of order 2, i.e., the modulus of the vector, μ i Is a cluster C i Is adjacent, the formula is:
where | · | represents a norm of order 1, i.e., the number of cluster midpoints,
clustering all PS points, wherein the clustering category is k, calculating the standard deviation of each cluster, and the calculation formula is as follows:
wherein the content of the first and second substances,
indicating the phase value of the ith point in the kth cluster,
representing the phase mean of the kth cluster.
9. The LSTM-based GB-InSAR atmospheric phase compensation method of claim 8, wherein: the Lowess is a local weighted regression, the local weighted regression belongs to a nonparametric statistical learning method, and a global model can be fitted through local simplification and simple local model assumption in local weighted learning.
10. The LSTM-based GB-InSAR atmospheric phase compensation method of claim 9, wherein: for the stable PS point, the window is first captured, the captured distance is selected as the set of points with the minimum distance to the specified point, the expression is as follows,
according to the set window d span Selecting the point set with the minimum distance from the specified point in the wide opening range, and expressing the minimum distance as follows,
each point from a given point has its own weight, which is:
these points are used to make a locally weighted regression with a loss function of:
and (3) constructing a fitting curved surface f (x, y) by using local weighted regression, wherein the obtained f (x, y) is the estimated atmospheric interference phase value.
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| CN116068511A (en) * | 2023-03-09 | 2023-05-05 | 成都理工大学 | Deep learning-based InSAR large-scale system error correction method |
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