CN111025294A - InSAR phase unwrapping method based on mean square volume Kalman filter - Google Patents

InSAR phase unwrapping method based on mean square volume Kalman filter Download PDF

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CN111025294A
CN111025294A CN201911273535.5A CN201911273535A CN111025294A CN 111025294 A CN111025294 A CN 111025294A CN 201911273535 A CN201911273535 A CN 201911273535A CN 111025294 A CN111025294 A CN 111025294A
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unwrapping
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insar
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CN111025294B (en
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罗晓梅
李洪涛
朱圣棋
董志龙
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Lattice Power Jiangxi Corp
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Abstract

The invention provides an InSAR phase unwrapping method based on a mean square cubature Kalman filter, which comprises the following steps: step 1, obtaining an interference phase diagram, and establishing a corresponding InSAR complex phase model; step 2, estimating a phase gradient in the interference phase diagram according to the winding phase of each pixel in the interference phase diagram; step 3, establishing a phase unwrapping system model of the interference phase diagram; and 4, constructing an optimized tracking path model based on the phase unwrapping system model, and unwrapping the phase of the interference phase diagram by adopting a mean square cubature Kalman filter algorithm to obtain an unwrapping result of the interference phase diagram. The invention adopts QR operation to decompose an error covariance matrix and a least square method to decompose Kalman gain. Therefore, under the constraint of semi-normality and symmetry of the error covariance matrix, the SCKFPU algorithm can freely select parameters without destroying the two basic characteristics, and the continuity of the whole phase unwrapping process is ensured.

Description

InSAR phase unwrapping method based on mean square volume Kalman filter
Technical Field
The invention belongs to the technical field of radars, and particularly relates to an InSAR phase unwrapping method based on a mean square volume Kalman filter.
Background
Phase unwrapping of interferometric synthetic aperture radar (InSAR) is a fundamental problem in the field of radar data processing, involving fields including radar, remote sensing, image and signal processing.
Existing studies indicate that conventional InSAR phase unwrapping methods, for example: the Branch-cut algorithm and the Least-squares algorithm can realize the relative effective and accurate unwrapping result. At present, InSAR phase unwrapping algorithms based on nonlinear tracking filters, for example: an extended Kalman filter unwrapping (EKFPU) algorithm, an unscented Kalman filter unwrapping (UKFPU) algorithm and a volumetric Kalman filter unwrapping (CKFPU) algorithm can effectively improve the InSAR phase unwrapping effect.
EKFPU is the simplest unwrapping algorithm based on a nonlinear tracking filter. When the InSAR phase diagram is simple and has high reliability, the EKFPU algorithm works well. Compared with the EKFPU algorithm, the UKFPU algorithm has better unwrapping effect. However, when the InSAR phase diagram has low reliability, such as a complex interferometric phase diagram, the unwrapping effect of both the EKFPU and the UKFPU algorithms is not ideal. Because the spherical volume rule and the radial rule are used for optimizing the signal points and the weight, the capacity of nonlinear estimation of a high-dimensional state is greatly improved by a volume Kalman filter (CKF) algorithm. Therefore, CKFPU is a well-behaved non-linear unwrapping algorithm.
When applying any of the aforementioned non-linear filtering methods to unwrap an InSAR phase map, it is important that the error covariance matrix remains symmetric and positive at each step of the update. However, due to the introduction of finite word length errors and the use of Cholesy operations to decompose the error covariance matrix, CKF often loses both of the basic properties of the error covariance matrix. Thus, the CKFPU algorithm is forced to stop running, and the whole unwinding process is interrupted.
Disclosure of Invention
In order to solve the above problems, the present invention aims to provide an InSAR phase unwrapping method based on a mean square volumetric kalman filter (SCKF). According to the method, the least square method is used for processing the Kalman gain and QR operation is adopted for decomposing the error covariance matrix, so that the mean square volume Kalman filter can well keep the symmetry and the normality of the error covariance matrix. In this way, the mean square cubature Kalman filter based unwrapping (SCKFPU) algorithm can set parameters arbitrarily, and better unwrapping performance is obtained. Meanwhile, the optimal tracking path model is designed, and the optimal phase unwrapping path is selected based on the optimal tracking path model, so that the whole phase unwrapping is carried out from a region with high quality of the phase diagram to a region with low quality, and a better unwrapping effect can be obtained.
In order to achieve the above object, the present invention adopts the following technical solutions.
The InSAR phase unwrapping method based on the mean square cubature Kalman filter comprises the following steps:
step 1, obtaining an interference phase diagram, and establishing a corresponding InSAR complex phase model;
step 2, according to the winding phase of each pixel in the interference phase diagram, estimating a horizontal winding phase gradient between adjacent pixels along the X direction in the interference phase diagram and a vertical winding phase gradient between adjacent pixels along the Y direction in the interference phase diagram;
(2.1) extracting the central pixel as (g, h) and the size as B in the interference phase diagramn×BmThe image block is set to only contain single row and column frequencies, and the row and column frequencies are roughly estimated by adopting maximum likelihood estimation to obtain rough estimation values of the row and column frequencies
Figure BDA0002314900640000021
(2.2) use of CZT transform to roughly estimate the frequency
Figure BDA0002314900640000022
Carrying out fine estimation to obtain a corresponding fine estimation value;
(2.3) calculation of size Bn×BmFine estimation of InSAR image block frequency
Figure BDA0002314900640000031
Cramer-Loran (CLRB);
(2.4) since the local InSAR image block contains a single row and column frequency, the frequency of the local InSAR image block is the center pixel (g)H) frequency; fine frequency estimation using the image block
Figure BDA0002314900640000032
The Clarmet-Roche respectively carries out phase gradient estimation on any pixel (X, Y) on the image block along the X direction and the Y direction;
(2.5) frequency fine estimation Using the image Block
Figure BDA0002314900640000033
The Clarmer-Roche estimates the phase variance of any pixel (X, Y) on the image block along the X direction and the Y direction respectively;
and (3) dividing the interference phase diagram into a plurality of image blocks, and performing phase gradient estimation and phase variance estimation of the steps (2.1) - (2.5) on each image block so as to complete phase gradient estimation and phase variance estimation of the whole interference phase diagram.
Step 3, establishing a phase unwrapping system model of the interference phase diagram: and (3) enabling the phase unwrapping system model of the interference phase diagram to be equivalent to a maneuvering target tracking model comprising a state equation and a measurement equation.
And 4, constructing an optimized tracking path model, namely an optimal unwrapping path model, based on the phase unwrapping system model, and unwrapping the phase of the interference phase diagram by adopting a mean square cubature Kalman filter algorithm to obtain an unwrapping result of the interference phase diagram.
(4.1) constructing an optimized tracking path model:
Figure BDA0002314900640000034
wherein q (m, n) is the mass of the pixel (m, n); der (m, n) denotes the pixel (m, n) phase derivative variance; coh (m, n) represents a coherence coefficient of the pixel (m, n); r is a weight adjustment parameter;
(4.2) initializing the optimized tracking path model, i.e. selecting the starting pixel of unwrapping { x }0,y0Instruction of
Figure BDA0002314900640000035
Four neighbors of the starting pixelAdding pixels which are not unwound in the domain into a waiting set;
(4.3) calculating the quality of each pixel in the waiting set according to the optimized tracking path model, and selecting the pixel with the minimum quality as the current pixel to be unwound;
(4.4) adopting a mean square volume Kalman filter algorithm to perform unwrapping on the current pixel to be unwrapped to obtain an unwrapping result of the current pixel;
(4.5) updating the waiting set: moving out the current unwrapped pixels from the waiting set, and adding the pixels which are not unwrapped in the four neighborhoods of the pixels into the waiting set to form an updated waiting set;
and (4.6) judging whether the updated waiting set has pixels, if so, turning to (4.3), otherwise, ending the unwrapping process to obtain an unwrapping result of the whole interference phase diagram.
Compared with the conventional InSAR phase unwrapping technology based on the nonlinear tracking filter, the method has the beneficial effects that:
(1) the invention adopts QR operation to decompose an error covariance matrix and a least square method to decompose Kalman gain. Therefore, under the constraint of semi-normality and symmetry of the error covariance matrix, the SCKFPU algorithm can freely select parameters without destroying the two basic characteristics, and the continuity of the whole phase unwrapping process is ensured.
(2) The invention designs a path tracking function. By minimizing this function, the SCKFPU algorithm works along the optimal unwrapping path. Therefore, the entire phase unwrapping is performed from the region of high quality phase map to the region of low quality phase map, and a better unwrapping effect can be obtained.
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The invention is described in further detail below with reference to the figures and specific embodiments.
FIG. 1 is a flow chart of an implementation of the present invention;
fig. 2 is a graph of the unwrapping results obtained by different unwrapping methods for the Longs Peak data set according to the embodiment of the present invention, where (a) is a true interferometric phase map, (b) is an unwrapped image corresponding to an EKFPU, and (c) is a difference image corresponding to the EKFPU; (d) the interference phase image is a real interference phase image, (e) an unwrapping image corresponding to the UKFPU is adopted, and (f) a difference image corresponding to the UKFPU is adopted; (g) the phase image is a real interference phase image, (h) is an unwrapped image corresponding to CKFPU, (i) is a difference image corresponding to CKFPU; (j) the interference phase image is a real interference phase image, (k) is an unwrapping image corresponding to the SCKFPU adopting the invention, and (l) is a difference image corresponding to the SCKFPU adopting the invention;
FIG. 3 is a diagram of unwrapping results based on different path tracking models for a Longs Peak dataset in an embodiment of the present invention; the method comprises the following steps of (a) obtaining a true interference phase image, (b) obtaining a unwrapping image under an optimal path tracking model based on the method, and (c) obtaining a difference image under the optimal path tracking model based on the method; (d) the method comprises the following steps of (1) obtaining a true interference phase image, (e) obtaining a unwrapped image based on a traditional path tracking model, and (f) obtaining a difference image based on the traditional path tracking model;
FIG. 4 is a simple actual measurement ENVISAT-ASAR dataset image in an embodiment of the invention, wherein (a) is a true interference phase map and (b) is a corresponding coherence map;
FIG. 5 is a diagram of simulation results for a simple actual measurement ENVISAT-ASAR dataset according to an embodiment of the present invention; the method comprises the following steps of (a) adopting an unwrapping image corresponding to EKFPU, (b) adopting a difference image corresponding to EKFPU, (c) adopting an unwrapping image corresponding to UKFPU, (d) adopting a difference image corresponding to UKFPU, (e) adopting an unwrapping image corresponding to SCKFPU, and (f) adopting a difference image corresponding to SCKFPU;
FIG. 6 is a single-view complex image for 6ERS-1/ERS-2InSAR according to an embodiment of the present invention, in which (a) is a real interference phase map and (b) is a corresponding coherence map;
fig. 7 is a graph of the unwrapping result obtained by using different methods for 6ERS-1/ERS-2InSAR single-vision complex image pairs in the embodiment of the present invention, where (a) is an unwrapped image corresponding to EKFPU, (b) is a difference image corresponding to EKFPU, (c) is an unwrapped image corresponding to UKFPU, (d) is a difference image corresponding to UKFPU, (e) is an unwrapped image corresponding to CKFPU, (f) is a difference image corresponding to CKFPU, (g) is an unwrapped image corresponding to SCKFPU, and (h) is a difference image corresponding to SCKFPU;
fig. 8 is a graph of the unwrapping result based on different tracking paths for a 6ERS-1/ERS-2InSAR single-vision complex image pair according to an embodiment of the present invention, where (a) is an unwrapped image corresponding to SCKFPUop, (b) is a difference image corresponding to SCKFPUop, (c) is an unwrapped image corresponding to SCKFPUco, and (d) is a difference image corresponding to SCKFPUco.
Detailed Description
The embodiments and effects of the present invention will be described in further detail below with reference to the accompanying drawings.
Referring to fig. 1, the InSAR phase unwrapping method based on the mean square volumetric kalman filter of the present invention is implemented according to the following steps:
step 1, obtaining an interference phase diagram, and establishing a corresponding InSAR complex phase model;
(1.1) in the interference phase diagram, the winding phase of any pixel { x, y } is the interference mode 2 π mapping phase of the pixel { x, y }, therefore, the winding phase thereof
Figure BDA0002314900640000061
The expression of (a) is:
Figure BDA0002314900640000062
where φ (x, y) represents the true unambiguous phase of the pixel { x, y }; e.g. of the typeφ(x, y) represents the true phase error for pixel { x, y };
Figure BDA0002314900640000063
representing the wrapped phase error for pixel x, y.
Assuming that the size of the interference phase diagram is M × N, the expression of the interference phase diagram expressed by polar coordinates is:
Figure BDA0002314900640000071
wherein the content of the first and second substances,
Figure BDA0002314900640000072
{ x, y } represents the spatial position coordinates of the pixel;
Figure BDA0002314900640000073
representing the amplitude of the pixel x, y.
(1.2) reaction of the compound of the above formula
Figure BDA0002314900640000074
Taylor expansion is performed at {0,0} and first order approximation:
Figure BDA0002314900640000075
(1.3) then the expression for the interference phase map can be written as:
Figure BDA0002314900640000076
wherein the content of the first and second substances,
Figure BDA0002314900640000077
representing additive noise.
(1.4) setting local InSAR image block to contain single sine frequency set
Figure BDA0002314900640000078
Figure BDA0002314900640000079
And
Figure BDA00023149006400000710
respectively representing the row and column frequencies of the central pixel of the image block; let the position of the starting pixel of the unwrapped image be { x }0,y0And order
Figure BDA00023149006400000711
Figure BDA00023149006400000712
Represents InSAR phase diagram { x }0,y0The winding phase at.Let the true unambiguous phase phi (x, y) at pixel { x, y } be expressed as:
Figure BDA00023149006400000713
wherein the content of the first and second substances,
Figure BDA00023149006400000714
is gradient operator expressed as
Figure BDA00023149006400000715
Unit vectors respectively representing the directions of X and Y axes;
(1.5) setting the noisy interferogram to be non-undersampled, then
Figure BDA00023149006400000716
Wherein f isxAnd fyThe statistical average frequency in the row and column directions of the local unwrapped image is shown.
(1.6) then the true unambiguous phase φ (x, y) at pixel { x, y } can be approximated as:
φ(x,y)≈2πfxx+2πfyy.
(1.7) substituting the approximate expression of phi (x, y) in the above formula into the expression (1.3) of the interference phase diagram and carrying out normalization processing to obtain the final expression of the interference phase diagram:
Figure BDA0002314900640000081
the above formula is a complex phase model of the interference phase diagram.
Step 2, according to the winding phase of each pixel in the interference phase diagram, estimating a horizontal winding phase gradient between adjacent pixels along the X direction in the interference phase diagram and a vertical winding phase gradient between adjacent pixels along the Y direction in the interference phase diagram;
(2.1) extracting the central pixel as (g, h) and the size as B in the interference phase diagramn×BmImage of (2)Setting the image block to contain only single row and column frequency, and adopting maximum likelihood estimation to carry out rough estimation on the row and column frequency respectively to obtain rough estimation values of the row and column frequency
Figure BDA0002314900640000082
The expression is as follows:
Figure BDA0002314900640000083
k-(Bn-1)/2≤x≤k+(Bn-1)/2,
k-(Bm-1)/2≤y≤k+(Bm-1)/2.
(2.2) use of CZT transform to roughly estimate the frequency
Figure BDA0002314900640000084
Carrying out fine estimation to obtain corresponding fine estimation value
Figure BDA0002314900640000085
According to separability of two-dimensional CZT transformation, firstly, one-dimensional CZT transformation is carried out on an image block according to a row direction, and then one-dimensional CZT transformation is carried out on a row transformation result according to a column direction, so that a frequency domain signal of the image block is obtained. The specific process is as follows:
first, the frequency is roughly estimated
Figure BDA0002314900640000091
Centering on a small frequency range selected in each of the row and column directions
Figure BDA0002314900640000092
And secondly, in a small frequency range, carrying out CZT conversion on the time domain data row by row along the X direction, and then carrying out CZT conversion column by column along the Y direction.
(2.2a) in the X direction: setting the sampling frequency fs1024Hz, the starting frequency of the refined frequency segment
Figure BDA0002314900640000093
Refining end point frequencies of frequency bins
Figure BDA0002314900640000094
m represents the number of refined frequency points, the span of the refined frequency band and the starting point of the refined frequency band are respectively expressed as:
Figure BDA0002314900640000095
Figure BDA0002314900640000096
then using CZT function of MATLAB signal processing tool box
Figure BDA0002314900640000097
In the range, the data is subjected to CZT conversion line by line according to the X direction to obtain line conversion data Y1。
(2.2b) in the Y direction: let by frequency fs1024Hz, the starting frequency of the refined frequency segment
Figure BDA0002314900640000098
Refining end point frequencies of frequency bins
Figure BDA0002314900640000099
m represents the number of refined frequency points, the span of the refined frequency band and the starting point of the refined frequency band are respectively expressed as:
Figure BDA00023149006400000910
Figure BDA00023149006400000911
then using CZT function of MATLAB signal processing tool box
Figure BDA00023149006400000912
Result Y of line-to-line transformation within range1Carrying out CZT conversion column by column according to Y direction to obtain frequency domain signal Y2。
(2.2c) adopting a maximum likelihood estimator to perform fine estimation on the row and column frequencies of the image block, wherein the expression is as follows:
Figure BDA0002314900640000101
(2.3) calculation of size Bn×BmFine estimation of InSAR image block frequency
Figure BDA0002314900640000102
The Clarmer-Loran (CLRB) of (1), which are respectively expressed as:
Figure BDA0002314900640000103
Figure BDA0002314900640000104
wherein γ is a local coherence coefficient of the InSAR image block, and the expression is as follows:
Figure BDA0002314900640000105
wherein the content of the first and second substances,
Figure BDA0002314900640000106
represents the average power of the local pixel; e (| v (x, y))2) Representing the average power of the local noise.
(2.4) since the local InSAR image block contains a single row and column frequency, the frequency of the local InSAR image block is the frequency of the central pixel (g, h); fine frequency estimation using the image block
Figure BDA0002314900640000107
The Claimei-Rou boundary estimates the phase gradient of any pixel (X, Y) on the image block along the X direction and the Y direction respectively, and the expressions are respectively:
(2.4a) the phase gradient in the X direction is estimated as:
Figure BDA0002314900640000108
(2.4b) the phase gradient in the Y direction is estimated as:
Figure BDA0002314900640000109
(2.5) frequency fine estimation Using the image Block
Figure BDA00023149006400001010
The Claimei-Roman boundary estimates the phase variance of any pixel (X, Y) on the image block along the X direction and the Y direction respectively, and the expressions are respectively:
(2.5a) phase variance estimation in the X direction:
Figure BDA0002314900640000111
(2.5b) phase variance estimation in Y direction:
Figure BDA0002314900640000112
and (3) dividing the interference phase diagram into a plurality of image blocks, and performing phase gradient estimation and phase variance estimation of the steps (2.1) - (2.5) on each image block so as to complete phase gradient estimation and phase variance estimation of the whole interference phase diagram.
And 3, establishing a phase unwrapping system model of the interference phase diagram.
And (3) enabling the phase unwrapping system model of the interference phase diagram to be equivalent to a maneuvering target tracking model comprising a state equation and a measurement equation. Writing the real phase phi (x, y) into a column vector phi (k), wherein the corresponding expressions of the state equation and the measurement equation are respectively:
(3.1) equation of state:
Figure BDA0002314900640000113
wherein the content of the first and second substances,
Figure BDA0002314900640000114
is the base state, representing the true unambiguous phase of pixel k;
Figure BDA0002314900640000115
a slope estimate representing the true unambiguous phase of pixel k;
Figure BDA0002314900640000116
the slope estimation error, namely the process noise, which represents the real unambiguous phase of the pixel k satisfies E [ w (k)]＝0，
Figure BDA0002314900640000117
QkRepresents the self-variance function of the process noise w (k),
Figure BDA0002314900640000118
representing the variance of the process noise.
(3.2) measurement equation:
Figure BDA0002314900640000119
wherein the content of the first and second substances,
Figure BDA00023149006400001110
a normalized observation vector representing pixel k;
Figure BDA00023149006400001111
a normalized observed noise vector representing pixel k, satisfying E [ v (k)]＝0，
Figure BDA0002314900640000123
diag (. cndot.) denotes a diagonalization operation, v1(k) And v2(k) Respectively representing the real part and the imaginary part of the pixel k normalized complex measurement error; h [. C]Representing an observation function.
And 4, constructing an optimized tracking path model, namely an optimal unwrapping path model, based on the phase unwrapping system model, and unwrapping the phase of the interference phase diagram by adopting a mean square cubature Kalman filter algorithm.
(4.1) constructing an optimized tracking path model:
Figure BDA0002314900640000121
wherein q (m, n) is the mass of the pixel (m, n); der (m, n) denotes the pixel (m, n) phase derivative variance; coh (m, n) represents a coherence coefficient of the pixel (m, n); r is a weight value adjusting parameter and reflects the action of coh (m, n) on q (m, n), the larger the r value is, the smaller the action of the coherence coefficient coh (m, n) on q (m, n) is, otherwise, the larger the action is, the larger the r value is, the receiving range of r is more than or equal to 1.1 and less than or equal to 2.2;
(4.2) initializing the optimized tracking path model, i.e. selecting the starting pixel of unwrapping { x }0,y0Instruction of
Figure BDA0002314900640000122
Adding pixels which are not unwound in four neighborhoods of the starting pixel into a waiting set;
(4.3) calculating the quality of each pixel in the waiting set according to the optimized tracking path model, and selecting the pixel with the minimum quality as the current pixel to be unwound;
(4.4) adopting a mean square volume Kalman filter algorithm to perform unwrapping on the current pixel to be unwrapped to obtain an unwrapping result of the current pixel;
(4.5) updating the waiting set: moving out the current unwrapped pixels from the waiting set, and adding the pixels which are not unwrapped in the four neighborhoods of the pixels into the waiting set to form an updated waiting set;
and (4.6) judging whether the updated waiting set has pixels, if so, turning to (4.3), otherwise, ending the unwrapping process to obtain an unwrapping result of the whole interference phase diagram.
The method comprises the following steps that a mean square cubature Kalman filter algorithm is adopted to perform unwrapping on a current pixel to be unwrapped, and the unwrapping is based on a single pixel and comprises two parts, namely time updating and measurement value updating;
firstly, explaining the symbolic meaning in the mean square cubature Kalman filter algorithm:
a) general trigonometric algorithm: s ═ tria (a), where P ═ AA ' ═ SS ', () ' is a conjugated transposed symbol; p is some semi-positive definite matrix; a is a matrix obtained by Cholesky decomposition; and S is a matrix obtained by orthogonal triangle (QR) decomposition.
b)
Figure BDA0002314900640000131
And
Figure BDA0002314900640000132
respectively, process noise in InSAR phase unwrapping system model
Figure BDA0002314900640000133
And measuring the noise vector
Figure BDA0002314900640000134
Of the self-variance function
Figure BDA0002314900640000135
Sum and auto-variance matrix
Figure BDA0002314900640000136
Root mean square (rms).
The specific process comprises the following steps:
and (3) time updating: state and measurement prediction:
(1) calculating volume points
Figure BDA0002314900640000137
i＝1,2,…,m,
Figure BDA0002314900640000138
Wherein the content of the first and second substances,
Figure BDA0002314900640000139
representing the unwrapping phase error function at the time k-1;n x1 denotes the number of pixels unwrapped at one time; m is 2nx2 denotes the number of volume points; volume point
Figure BDA00023149006400001310
Satisfy the requirement of
Figure BDA00023149006400001311
Belong to the following set of points:
uk-1＝{1,-1}；
(2) calculating propagation volume points
Figure BDA00023149006400001312
i＝1,2,…,m,
Figure BDA00023149006400001313
Wherein the content of the first and second substances,
Figure BDA00023149006400001314
representing the calculated volume points.
(3) Estimating a predicted state
Figure BDA00023149006400001315
Figure BDA0002314900640000141
Wherein K represents the number of pixels in the neighborhood of the pixel to be unwrapped;
Figure BDA0002314900640000142
representing the calculated propagation volume points;
Figure BDA0002314900640000143
representing the phase gradient estimation of pixels in the neighborhood of the pixels to be unwound at the moment of k-1; SNRj,k-1Representing the signal-to-noise ratio of pixels in the neighborhood of the pixel to be unwound; UPj,k-1An identifier indicating whether or not to unwind, which is defined as:
Figure BDA0002314900640000144
(4) root mean square of the estimated prediction error auto-covariance function
Figure BDA0002314900640000145
Figure BDA0002314900640000146
Wherein the content of the first and second substances,
Figure BDA0002314900640000147
is Qj,k-1Root mean square of
Figure BDA0002314900640000148
Representing phase variance estimation in the neighborhood of the pixel to be unwound at the moment of k-1;
Figure BDA0002314900640000149
represents a weighted, centered state prediction matrix:
Figure BDA00023149006400001410
wherein the content of the first and second substances,
Figure BDA00023149006400001411
representing the calculated propagation volume points;
Figure BDA00023149006400001412
representing the estimated prediction state.
And (3) updating the measured value: status update
(5) Calculating volume points
Figure BDA00023149006400001413
i＝1,2,…,m,
Figure BDA00023149006400001414
Wherein S isk|k-1The root mean square of the prediction error auto-covariance function at the k moment is represented;
Figure BDA00023149006400001415
representing a volume point;
Figure BDA00023149006400001416
representing the estimated prediction state;
(6) calculating propagation volume points
Figure BDA00023149006400001417
i＝1,2,…,m,
Figure BDA0002314900640000151
Wherein H [. C]Is an observation function;
Figure BDA0002314900640000152
belong to the following point sets
uk＝{1,-1}.
(7) Estimating a predicted measurement
Figure BDA0002314900640000153
Figure BDA0002314900640000154
Wherein the content of the first and second substances,
Figure BDA0002314900640000155
representing the calculated propagation volume points.
(8) Root mean square for estimating covariance matrix innovation
Figure BDA0002314900640000156
Szz,k|k-1＝Tria([Zk|k-1,SR,k]),
Wherein the content of the first and second substances,
Figure BDA0002314900640000157
is that
Figure BDA0002314900640000158
Root mean square of (1), satisfies Rk＝SR,kS'R,kThe value of the auto-covariance matrix is equal to the auto-covariance matrix of the observation noise of the to-be-unwrapped pixel at the moment k;
Figure BDA0002314900640000159
the weighted, centered observation prediction matrix is represented:
Figure BDA00023149006400001510
wherein the content of the first and second substances,
Figure BDA00023149006400001511
representing the calculated propagation volume points;
Figure BDA00023149006400001512
representing the estimated predictive measurements.
(9) Estimating a cross-covariance matrix
Figure BDA00023149006400001513
Pxz,k|k-1＝χk|k-1Z′k|-1；
Wherein the content of the first and second substances,
Figure BDA00023149006400001514
representing weighted, centered state re-prediction matrices
Figure BDA00023149006400001515
Wherein the content of the first and second substances,
Figure BDA00023149006400001516
representing a calculated volume point;
Figure BDA00023149006400001517
representing the estimated prediction state.
(10) Estimation of Kalman gain
Figure BDA00023149006400001518
Wk＝(Pxz,k|k-1/S'ZZ,k|k-1)/SZZ,k|k-1；
Wherein the content of the first and second substances,
Figure BDA0002314900640000161
representing an estimated cross-covariance matrix;
Figure BDA0002314900640000162
the root mean square of the estimated covariance matrix innovation.
(11) Estimating update states
Figure BDA0002314900640000163
Figure BDA0002314900640000164
Wherein the content of the first and second substances,
Figure BDA0002314900640000165
representing the estimated prediction state;
Figure BDA0002314900640000166
representing an estimated predicted measurement;
Figure BDA0002314900640000167
representing an observed value;
Figure BDA0002314900640000168
representing the estimated kalman gain.
(12) Estimating root mean square of corresponding error autocorrelation function matrix
Figure BDA0002314900640000169
Sk|k＝Tria([χk|k-1-WkZk|k-1,WkSR,k]')；
Wherein the content of the first and second substances,
Figure BDA00023149006400001610
representing a weighted, centered state re-prediction matrix;
Figure BDA00023149006400001611
representing weighted, centered observation prediction matrices and
Figure BDA00023149006400001612
representing the estimated kalman gain.
In the above process, for phase unwrapping, the state is updated
Figure BDA00023149006400001613
And corresponding to the unwrapping result of the current pixel k, the moment in the target tracking process corresponds to the pixel in the phase unwrapping process.
In the invention, the smaller the value of the quality estimation function q (m, n), the higher the InSAR phase diagram quality, and conversely, the worse the quality. Therefore, by minimizing the path tracking function q (m, n), an optimal unwrapping path is found, thereby ensuring that the InSAR phase unwrapping proceeds from a region of high phase map quality to a region of low phase map quality.
Simulation experiment
The correctness and effectiveness of the present invention are further illustrated by experiments below.
(1) Evaluation index
The simulation experiment adopts three technical indexes of residual number (residual number), Mean Square Error (MSE) based on a winding phase diagram and error Number (NELP) larger than pi to evaluate the quality of the unwrapping algorithm.
The number of residuals is defined as the number of nonzero sums of the winding gradients for a 2 x 2 region in the InSAR image. In general, a smaller number of residues means better unwinding performance.
Winding phase map MSE based definition
Figure BDA0002314900640000171
Where E represents the statistical mathematical expectation,
Figure BDA0002314900640000172
representing the InSAR phase without noise,
Figure BDA0002314900640000173
representing the winding phase generated based on the unwrapping phase, |, representing the modulo.
Generally, the smaller the MSE value, the better the InSAR phase unwrapping performance.
In addition, NELP definition
NELP:＝Ns-|I|,
Wherein, { phii,i＝1,…,NsDenotes the phase without noise,
Figure BDA0002314900640000174
indicating the unwrapping phase.
The smaller the NELP value, the better the phase discontinuity after unwrapping is maintained.
(2) Simulation parameters:
the three simulations were performed based on different data sets. The adjustment parameter of the optimal path tracking function is set to be 1.8.
(3) Simulation content:
the data for simulation 1 was derived from the Longs Peak dataset. This data is the simulation data synthesized by a high performance InSAR simulator, the data collection site is in Colorado, the size of the data is 151 x 457. Under the simulation parameters, an EKFPU algorithm, a UKFPU algorithm and an SCKFPU algorithm based on optimal path tracking are respectively adopted for phase unwrapping. The unwrapped image and the difference wrapped image are shown in fig. 2, and the residue number, MSE and NELP performance comparisons are shown in table 1.
TABLE 1 comparison of parameter Performance for different algorithms
Figure BDA0002314900640000181
Although the EKFPU and UKFPU algorithms are simple, the phase unwrapping problem is a highly nonlinear optimization problem. Thus, as can be seen from fig. 2, the unwrapping effect of these two algorithms is less than ideal for such more complex synthetic data sets. Furthermore, the unwrapping performance of the CKFPU algorithm is the worst due to the reduced feasible range of selection parameters. Compared with other algorithms, the SCKFPU algorithm has the least speckle noise in a small elliptical area and the best filtering and unwrapping performance. Similar conclusions can be drawn from the data in table 1, with the SCKFPU algorithm not only having the minimum MSE values, but also having the minimum number of residuals. In addition, the NELP value of the SCKFPU algorithm is minimum, which means that the SCKFPU algorithm of the invention can better maintain the continuity of the image.
In addition, the SCKFPU algorithm of the invention is respectively based on the designed optimal path tracking function and the optimal path tracking function der (m, n) [1-coh (m, n)]rThe data set is phase unwrapped. The corresponding SCKFPU methods are referred to as SCKFPU1 and SCKFPU2, respectively. The unwrapped image and the difference wrapped image are shown in fig. 3, and the residue number and MSE performance comparison is shown in table 2.
FIG. 3 and Table 2 show that the unwrapping performance based on the designed optimized tracking path is better than that based on the phase quality estimation function der (m, n) [1-coh (m, n) ]]rNot only has fewer number of residue, but also has smaller MSE and NELP.
TABLE 2 number of residuals and MSE for different treatment methods
Figure BDA0002314900640000191
Data for simulation 2 was derived from the C-band, 1 day apart, heavy-track (repeat-pass) ENVISAT-ASAR dataset. The data is actually measured data, the data acquisition place is Tianjin in China, and the size of the data is 891 multiplied by 891. Under the simulation parameters, an EKFPU algorithm, a UKFPU algorithm and an SCKFPU algorithm based on optimal path tracking are respectively adopted for phase unwrapping. The raw data and the corresponding coherence map are shown in fig. 4. The unwrapped image and the difference-wrapped image are shown in fig. 5, and the residue number comparison is shown in table 3.
TABLE 3 comparison of residuals for different algorithms
Figure BDA0002314900640000192
As can be seen from fig. 4(b), the coherence value of each pixel of the measured data is substantially high, so the data is simple.
As can be seen from fig. 5 and table 3, for this simple measured data set, the three types of unwrapping algorithms based on the nonlinear tracking filter can perform phase unwrapping and noise filtering simultaneously, and exhibit good unwrapping effect. The unwrapping performance of the SCKFPU algorithm is slightly superior to that of the EKFPU algorithm and the UKFPU algorithm, the best difference wrapped image is provided, the number of residual points is the least, and the advantage of the invention on the processing of complex data is more obvious.
The data set for simulation 3 was derived from a European space agency ERS-1/ERS-2InSAR single vision complex image pair. This is measured data, and the data collection site is the area near Greek Nazeppary (38 ° 18 '30 "to 38 ° 19' 30" for north latitude, 23 ° 01 '15 "to 23 ° 4' 24" for east longitude), and the size of the data is 249 × 199. Under the simulation parameters, an EKFPU algorithm, a UKFPU algorithm and an SCKFPU algorithm based on optimal path tracking are respectively adopted for phase unwrapping. The raw data and the corresponding coherence map are shown in fig. 6. The unwrapped image and the difference wrapped image are shown in fig. 7.
As can be seen from fig. 6(a), this measured data is heavily contaminated with noise. A similar conclusion can also be obtained from fig. 6 (b). Fig. 6(b) shows that the coherence value of each pixel of this data is substantially small, indicating that this data is heavily contaminated with noise. Therefore, it is very challenging to unwrap this data with a non-linear tracking filter algorithm.
The entire analysis is quite quantitative because there is no real phase surface. As can be seen from fig. 5, compared to EKFPU, UKFPU and CKFPU,the difference unwrapped image of the SCKFPU algorithm has less speckle noise. This means that the SCKFPU algorithm of the present invention can filter more noise and has better unwrapping effect. Consider that
Figure BDA0002314900640000201
Wherein the content of the first and second substances,
Figure BDA0002314900640000202
is the phase obtained by rewinding after the unwinding,
Figure BDA0002314900640000203
is the original noisy winding phase. Since ε is usually small, if the estimation error is small
Figure BDA0002314900640000204
At large values of the discontinuity areas, the corresponding non-linear filter smoothes the discontinuity areas excessively. As is apparent from fig. 6(a), discontinuity occurs in the measured data connecting the top of the mountain and the top of the true interference phase. Fig. 7(b), 7(d), 7(f) and 7(h) are difference wrap images using the EKFPU algorithm, the UKFPU algorithm, the CKFPU algorithm and the SCKFPU algorithm of the present invention, respectively. Comparing the values of the pixels (57,65) in the graphs, fig. 7(b), fig. 7(d) and fig. 7(f) are all large and fig. 7(h) is small. This means that EKFPU, UKFPU and CKFPU algorithms excessively smooth the discontinuous regions and cannot find the discontinuous regions well, whereas the SCKFPU algorithm of the present invention not only minimizes the structural errors but also minimizes the deviations.
In addition, the SCKFPU algorithm is adopted to perform phase unwrapping on the data set based on the designed optimized path tracking model and the coherent value based on the pixel only respectively. The corresponding SCKFPU methods are referred to as SCKFPUop and SCKFPUco, respectively. The adjustment parameter of the optimal path tracking model is set to be 2.2. The unwrapped image and the difference wrapped image are shown in fig. 8.
From the simulation conclusion of FIG. 8, it can be seen that SCKFPUcoThe unwrapped image has a lot of speckle noise. Furthermore, SCKFPUopThe value of the pixel (93,124) in the difference wrap-around image is much smaller than the SCKFPUcoThe difference value wraps around the value of the image. This means SCKFPUopThe algorithm is able to preserve image discontinuities very well.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.

Claims (3)

1. The InSAR phase unwrapping method based on the mean square cubature Kalman filter is characterized in that: the method comprises the following steps:
step 1, obtaining an interference phase diagram, and establishing a corresponding InSAR complex phase model;
step 2, according to the winding phase of each pixel in the interference phase diagram, estimating a horizontal winding phase gradient between adjacent pixels along the X direction in the interference phase diagram and a vertical winding phase gradient between adjacent pixels along the Y direction in the interference phase diagram;
step 3, establishing a phase unwrapping system model of the interference phase diagram: the phase unwrapping system model of the interference phase diagram is equivalent to a maneuvering target tracking model which comprises a state equation and a measurement equation;
and 4, constructing an optimized tracking path model, namely an optimal unwrapping path model, based on the phase unwrapping system model, and unwrapping the phase of the interference phase diagram by adopting a mean square cubature Kalman filter algorithm to obtain an unwrapping result of the interference phase diagram.
2. The InSAR phase unwrapping method based on mean square volumetric Kalman filter according to claim 1, characterized in that: the step 2 comprises the following steps:
step 2.1, extracting a central pixel (g, h) with the size of B from the interference phase imagen×BmThe image block of (2) is set to contain only a single row and column frequency, and the row and column frequencies are roughly estimated by maximum likelihood estimationCalculating to obtain coarse estimated values of row and column frequencies
Figure FDA0002314900630000011
Step 2.2, coarse frequency estimation by CZT conversion
Figure FDA0002314900630000012
Carrying out fine estimation to obtain a corresponding fine estimation value;
step 2.3, calculate size Bn×BmFine estimation of InSAR image block frequency
Figure FDA0002314900630000013
Cramer-Loran (CLRB);
step 2.4, because the local InSAR image block contains single row and column frequency, the frequency of the local InSAR image block is the frequency of the central pixel (g, h); fine frequency estimation using the image block
Figure FDA0002314900630000014
The Clarmet-Roche respectively carries out phase gradient estimation on any pixel (X, Y) on the image block along the X direction and the Y direction;
step 2.5, adopting the frequency fine estimation of the image block
Figure FDA0002314900630000021
The Clarmer-Roche estimates the phase variance of any pixel (X, Y) on the image block along the X direction and the Y direction respectively;
and dividing the interference phase diagram into a plurality of image blocks, and performing phase gradient estimation and phase variance estimation of steps 2.1-2.5 on each image block so as to finish phase gradient estimation and phase variance estimation of the whole interference phase diagram.
3. The InSAR phase unwrapping method based on mean square volumetric Kalman filter according to claim 1, characterized in that: the step 4 comprises the following steps:
step 4.1, constructing an optimized tracking path model:
Figure FDA0002314900630000022
wherein q (m, n) is the mass of the pixel (m, n); der (m, n) denotes the pixel (m, n) phase derivative variance; coh (m, n) represents a coherence coefficient of the pixel (m, n); r is a weight adjustment parameter;
step 4.2, initialize the optimized tracking path model, i.e. select the starting pixel of unwrapping { x }0,y0Instruction of
Figure FDA0002314900630000023
Adding pixels which are not unwound in four neighborhoods of the starting pixel into a waiting set;
4.3, calculating the quality of each pixel in the waiting set according to the optimized tracking path model, and selecting the pixel with the minimum quality as the current pixel to be unwound;
4.4, adopting a mean square cubature Kalman filter algorithm to perform unwrapping on the current pixel to be unwrapped to obtain an unwrapping result of the current pixel;
and 4.5, updating the waiting set: moving out the current unwrapped pixels from the waiting set, and adding the pixels which are not unwrapped in the four neighborhoods of the pixels into the waiting set to form an updated waiting set;
and 4.6, judging whether the updated waiting set has pixels, if so, turning to the step 4.3, otherwise, ending the unwrapping process to obtain an unwrapping result of the whole interference phase diagram.
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