CN112824927A - Sky wave over-the-horizon radar ionospheric phase pollution correction method based on sparse filtering - Google Patents

Sky wave over-the-horizon radar ionospheric phase pollution correction method based on sparse filtering Download PDF

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CN112824927A
CN112824927A CN201911138468.6A CN201911138468A CN112824927A CN 112824927 A CN112824927 A CN 112824927A CN 201911138468 A CN201911138468 A CN 201911138468A CN 112824927 A CN112824927 A CN 112824927A
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于文启
陈建文
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Air Force Early Warning Academy
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    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract

The invention discloses a sky wave over-the-horizon radar ionosphere phase pollution correction method based on sparse filtering, which is used for overcoming the problem that the phase correction precision of the conventional method is reduced under the condition of Bragg peak overlapping and improving the detection performance of a sky wave over-the-horizon radar on a slow ship target. The method comprises the steps of segmenting an original echo vector into a short-time sequence vector set by utilizing sliding window segmentation; eliminating zero elements in the short-time sequence vector set, establishing a sparse representation model by using the sparsity of the short-time sequence vector in a Doppler domain, and solving a sparse coefficient vector; and (3) filtering out the sea clutter strong Bragg component of each short-time sequence vector, combining an inverse sliding window operation to obtain a broadened strong Bragg peak signal of the original echo, and correcting the original echo data by using the data. The invention can completely extract the broadened strong Bragg component under the condition that the original echo Bragg peaks are overlapped, and obviously improves the ionosphere phase pollution correction effect.

Description

Sky wave over-the-horizon radar ionospheric phase pollution correction method based on sparse filtering
Technical Field
The invention belongs to the technical field of radars, and particularly provides a sky wave over-the-horizon radar ionosphere phase pollution correction method based on sparse filtering.
Background
The sky wave beyond visual range radar (OTHR) works in a high-frequency band of 3-30 MHz, the detection of beyond visual range targets is realized by utilizing the reflection effect of an ionization layer on electromagnetic waves, and the device belongs to remote strategic early warning equipment. The propagation channel ionosphere is considered as part of a sky-wave over-the-horizon radar system, and its time-varying, non-stationary nature gives the OTHR a phase perturbation of several meters. The phase disturbance of the ionized layer is obviously nonlinear under the condition of long coherent accumulation, thereby causing the Doppler spectrum peak of the sea/ground clutter to be widened and split and covering the adjacent slow ship targets. Therefore, the correction of ionospheric phase contamination is very important for improving the OTHR slow ship target detection performance.
The existing ionospheric phase pollution correction methods are mainly divided into two types: 1) phase estimation methods based on filtered out spread-out Bragg components, such as maximum entropy spectroscopy (Bourdillon a., Gauthier f., part j.use of large entropy spectral analysis to improve shield detection by over-the-same-the-horizontal radar [ J ]. Radio Science, 1987, 22 (2): 313-: 29-36), and polynomial phase modeling (Lu k., Wang j., Liu x.z.a piece wise parameter based on a polymeric phase model to complex ionic phase registration [ C ]. IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003: 405-; the method extracts a broadened strong Bragg component from an original radar echo in advance by a three-step method of FFT-Doppler band-pass filtering-IFFT, and estimates ionospheric phase pollution by using the component; 2) phase estimation methods based on raw echoes, such as MUSIC-type method (Anderson s.j., Abramovich y.i.a. uniform approach to detection, classification, and correlation of azimuthal deviation in HF sky wave systems [ J ]. Radio Science, 1998, 33 (4): 1055-: 455-462), and improved time-frequency distribution (Hou c.y., Xia t., Bao q.time-frequency method to reduce communication by means of iterative process, frequency surface frequency from HF skywave radars [ J ]. IET Radar, Sonar and Navigation, 2014, 8 (7): 742-748); the method directly carries out phase estimation on the original echo of the radar and carries out phase compensation by utilizing the estimated pollution phase.
Among the above methods, the first method can achieve a high-precision phase compensation effect through single correction, but excessively depends on the extracted spread Bragg component, so that the phase pollution correction effect of the method is sharply reduced when an ideal strong Bragg component cannot be extracted through a three-step method of FFT-doppler bandpass filtering-IFFT. Compared with the first method, the second method has the advantage that strong Bragg components do not need to be extracted in advance, and can realize coarse correction of phase pollution under the condition of serious echo Doppler spectrum broadening so as to initially sharpen a spectral peak, but the phase estimation precision of the method is poor. In sky wave radar echoes where actual phase contamination occurs, severe phase contamination can cause the echo Bragg peaks to overlap, in which case both of the above methods make it difficult to achieve ideal phase contamination correction. In order to solve the problem, a more effective filtering technique needs to be adopted to completely extract the broadened Bragg component from the echo with overlapped spectral peaks so as to assist in realizing a high-precision phase correction effect.
Disclosure of Invention
The invention aims to solve the problem that the phase correction precision of the existing method is reduced under the condition of overlapping echo Bragg peaks, improve the ionosphere phase correction effect and improve the detection performance of sky-wave over-the-horizon radar on slow ship targets.
In order to achieve the purpose, the invention provides a sky wave over-the-horizon radar ionospheric phase pollution correction method based on sparse filtering, which comprises the following steps:
(1) the radar receiving data of a single range unit form an original echo vector:
x＝[x(1)，x(2)，...，x(N)]T (1)
wherein N is the number of radar transmission pulses in a coherent processing time;
(2) sending x into a sliding window segmentation module to obtain a short-time sequence vector set
Figure BSA0000194905120000021
yi＝Hix，i＝1，2，...，N (2)
Wherein, yiThe ith N × 1-dimensional short-time sequence vector after the sliding window segmentation is represented, which includes zero elementsAnd also includes non-zero elements formed by multiplying the original echo vector data by the sliding window amplitude; hiDenotes yiA corresponding nxn dimensional sliding window partition matrix;
(3) structure N2X1 dimensional vector
Figure BSA0000194905120000022
And (3) removing zero elements in y:
z＝Fy (3)
wherein z is Mx 1(M < N)2) A dimension vector representing residual data with zero elements in y removed; f represents M × N2The wiki-divided matrix is from N2×N2Extracting M rows in the dimensional unit matrix according to rows, wherein the number of the extracted rows corresponds to non-zero elements in y;
(4) according to the sparsity of the short-time sequence in the Doppler domain, z sparsity is expressed as:
z＝FTs (4)
wherein, T ═ ifft (I), I represents N2×N2Dimension unit matrix, IFFT (-) represents inverse fourier transform;
Figure BSA0000194905120000023
is N2X 1-dimensional vector; siDenotes yiThe corresponding N multiplied by 1 dimensional sparse coefficient vector comprises the distribution conditions of sea/ground clutter, targets and noise of the short-time sequence in the complete Doppler frequency spectrum; s is reduced from z by solving the following convex problem:
Figure BSA0000194905120000024
wherein | · | purple sweetPRepresents a calculation of lPNorm, P ═ 1, 2; min (-) represents the minimum value, epsilon represents the radar noise base;
(5) according to the formula (6) and the formula (7), the position set of the sea clutter strong Bragg component of each short-time sequence in s is calculated
Figure BSA0000194905120000025
The extracted components are allEither positive or both negative Bragg components:
Figure BSA0000194905120000026
qi＝ji+(i-1)×N，i＝1，2，...，N (7)
wherein, l is the search radius, and max (·) represents the maximum value;
(6) calculating a filtering vector h:
Figure BSA0000194905120000027
(7) strong Bragg component with N x1 dimensional broadening obtained by inverse sliding window operation
Figure BSA0000194905120000028
Figure BSA0000194905120000029
H has the function of filtering out the strong Bragg component of the sea clutter of each short-time sequence in z, and the process utilizes the distribution information of the sea/ground clutter, targets and noise of each short-time sequence in a sparse coefficient vector s, so that the method is called sparse filtering; g represents an N × M dimensional inverse sliding window matrix:
Figure BSA0000194905120000031
g (i, j) is the ith row and j column elements of G, and the G has the function of converting the filtered sea clutter intensity Bragg component of each short-time sequence into the spread Bragg component of the original echo; z (j) is the jth element of z; x (i) is the ith element of x; h isjZ (j) the sliding window amplitude introduced during sliding window segmentation; alpha is alphaiThe number of non-zero elements in the ith row of G;
(7) from
Figure BSA0000194905120000034
And (3) pollution phase extraction:
Figure BSA0000194905120000032
where angle (·) denotes taking the phase, N ═ 1, 2]T，β＝±2πfBTsCorresponding to positive and negative Bragg peaks, T, respectivelysIn the form of a pulse repetition period,
Figure BSA0000194905120000033
g is the acceleration of gravity, f0Is the radar carrier frequency, c is the speed of light;
(8) phase correction of x with γ:
x1(n)＝x(n)·e-jγ(n)，n＝1，2，...，N (12)
wherein x is1Representing an Nx 1-dimensional echo vector after phase correction of x; x is the number of1(n) represents x1The nth element of (1); x (n) represents the nth element of x.
In the step (2), the sliding window segmentation module may adopt a sliding window mode and a window value type in a time-frequency analysis method, pre-establish an offline sliding window segmentation matrix database, and directly call the database according to requirements during work.
In the step (4), a convex optimization toolkit can be used for solving the convex problem.
In the step (5), the search radius is determined according to different ionospheric phase pollution degrees, and when the echo Bragg peaks are overlapped due to serious phase pollution, the value of l is 15.
Due to the adoption of the technical scheme, the invention has the beneficial effects that: under the condition that echo Bragg peaks are overlapped, a broadened strong Bragg component can be completely extracted, the ionosphere phase estimation and correction accuracy can be improved by utilizing the component, and the detection performance of OTHR on a slow ship target is improved.
Drawings
FIG. 1 is a flow chart of the operation of the correction method for ionospheric phase pollution of sky-wave over-the-horizon radar based on sparse filtering.
Fig. 2 is a working schematic diagram of the sliding window segmentation module of the present invention.
Fig. 3 is an echo doppler spectrogram of a 450 th range unit in the embodiment of the present invention, specifically a comparison chart before and after ionospheric phase contamination.
Fig. 4 is a doppler spectrogram of the spread Bragg component extracted based on the sparse filtering in the embodiment of the present invention.
Fig. 5 is a doppler spectrogram after phase contamination correction in an embodiment of the present invention, where fig. (a) is an output doppler spectrogram of an HRR method, fig. (b) is an output doppler spectrogram of a PWVD (pseudo Wigner-Ville distribution) method, and fig. (c) is an output doppler spectrogram based on a sparse filtering method.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
The sky wave over-the-horizon radar carries out conventional beam forming and pulse compression on received echoes, and in a coherent processing time, the nth slow-time echo data of a certain distance unit is represented by x (n) after being polluted by ionosphere phase. And x (n) comprises sea/ground clutter, slow ship targets and noise, wherein the Bragg peak energy of the sea clutter is strongest. Due to ionosphere phase pollution, the echo Doppler spectrum is seriously widened, strong clutter has Bragg peak overlapping and spectrum peak splitting, and an adjacent slow ship target is covered. The ionospheric phase pollution correction method based on sparse filtering is described below, and fig. 1 shows a work flow diagram of the proposed method, which specifically includes the following steps:
(1) the radar receiving data of a single range unit form an original echo vector:
x＝[x(1)，x(2)，...，x(N)]T (13)
wherein, N is the number of radar transmission pulses in a coherent processing time, and in the embodiment, N is 512;
(2) receiving the inspiration of a time-frequency analysis method, establishing a sliding window segmentation module, and the working principle is shown in figure 2; the sliding window segmentation module can adopt different sliding window modes and window value typesAn off-line sliding window segmentation matrix database is established in advance and is directly called according to requirements during work; in the embodiment, a sliding window mode which is the same as the short-time Fourier transform in an MATLAB time-frequency tool box is adopted, and a rectangular window with 32 data points is adopted; sending x into a sliding window segmentation module to obtain a short-time sequence vector set
Figure BSA0000194905120000041
yi＝Hix，i＝1，2，...，N (14)
Wherein, yiRepresenting the ith Nx 1-dimensional short-time sequence vector after the sliding window segmentation, wherein the ith Nx 1-dimensional short-time sequence vector comprises zero elements and non-zero elements formed by multiplying original echo vector data by the amplitude of the sliding window; hiDenotes yiA corresponding nxn dimensional sliding window partition matrix;
(3) structure N2X1 dimensional vector
Figure BSA0000194905120000042
And (3) removing zero elements in y:
z＝Fy (15)
wherein z is Mx 1(M < N)2) A dimension vector representing residual data with zero elements in y removed; f represents M × N2The wiki-divided matrix is from N2×N2Extracting M rows in the dimensional unit matrix according to rows, wherein the number of the extracted rows corresponds to non-zero elements in y;
(4) according to the sparsity of the short-time sequence in the Doppler domain, z sparsity is expressed as:
z＝FTs (16)
wherein, T ═ ifft (I), I represents N2×N2Dimension unit matrix, IFFT (-) represents inverse fourier transform;
Figure BSA0000194905120000043
is N2X 1-dimensional vector; siDenotes yiThe corresponding N multiplied by 1 dimensional sparse coefficient vector comprises the distribution conditions of sea/ground clutter, targets and noise of the short-time sequence in the complete Doppler frequency spectrum; by solving the following convex problem, s is derived from zReduction:
Figure BSA0000194905120000044
wherein | · | purple sweetPRepresents a calculation of lPNorm, P ═ 1, 2; min (-) represents the minimum value, epsilon represents the radar noise base; in the embodiment, equation (5) is solved by adopting a convex optimization toolkit, wherein epsilon is 0.1;
(5) according to the formula (6) and the formula (7), the position set of the sea clutter strong Bragg component of each short-time sequence in s is calculated
Figure BSA0000194905120000045
The extracted components are both positive Bragg components or both negative Bragg components:
Figure BSA0000194905120000046
qi＝ji+(i-1)×N，i＝1，2，...，N (19)
wherein, l is the search radius, and max (·) represents the maximum value; example i 15;
(6) calculating a filtering vector h:
Figure BSA0000194905120000047
(7) strong Bragg component with N x1 dimensional broadening obtained by inverse sliding window operation
Figure BSA0000194905120000048
Figure BSA0000194905120000051
H has the function of filtering out the strong Bragg component of the sea clutter of each short-time sequence in z, and the process utilizes the distribution information of the sea/ground clutter, targets and noise of each short-time sequence in a sparse coefficient vector s, so that the method is called sparse filtering; g represents an N × M dimensional inverse sliding window matrix:
Figure BSA0000194905120000052
g (i, j) is the ith row and j column elements of G, and the G has the function of converting the filtered sea clutter intensity Bragg component of each short-time sequence into the spread Bragg component of the original echo; z (j) is the jth element of z; x (i) is the ith element of x; h isjZ (j) the sliding window amplitude introduced during sliding window segmentation; alpha is alphaiThe number of non-zero elements in the ith row of G;
(7) from
Figure BSA0000194905120000053
And (3) pollution phase extraction:
Figure BSA0000194905120000054
where angle (·) denotes taking the phase, N ═ 1, 2]T，β＝±2πfBTsCorresponding to positive and negative Bragg peaks, T, respectivelysIn the form of a pulse repetition period,
Figure BSA0000194905120000055
g is the acceleration of gravity, f0Is the radar carrier frequency, c is the speed of light;
(8) phase correction of x with γ:
x1(n)＝x(n)·e-jγ(n)，n＝1，2，...，N (24)
wherein x is1Representing an Nx 1-dimensional echo vector after phase correction of x; x is the number of1(n) represents x1The nth element of (1); x (n) represents the nth element of x.
Examples
Based on the detailed technical scheme of the invention, the method is verified and implemented by adding pollution to measured data of the sky wave over-the-horizon radar, and the 4 th step is adoptedEcho data of 50 distance units, wherein the data comprises sea clutter, ground clutter and slow ship targets. The frequency of the transmitted signal is 14.4MHz, and the pulse repetition period Ts0.096s, the number of radar transmission pulses N is 512 in a coherent processing time, and a phase pollution function 5cos (0.1 pi nT) is addeds)·exp(0.02nTs)。
FIG. 3 is an echo Doppler spectrogram before and after ionospheric phase contamination, in which a solid line represents an echo Doppler spectrum without ionospheric phase contamination, a dotted line represents an echo Doppler spectrum with ionospheric phase contamination, ground clutter is near zero frequency, sea clutter Bragg peaks are respectively at + -0.387 Hz, and a cooperative slow ship target is located at-0.67 Hz. Fig. 3 shows that phase contamination causes sea/ground clutter to spread and that Bragg peaks overlap, flooding adjacent slow vessel targets, which results in reduced performance of the OTHR for slow vessel target detection. The positive Bragg component is stronger in fig. 3 and a high precision phase correction method requires that this component be filtered out beforehand. It is difficult to extract the complete positive Bragg component from the overlapping echoes of the Bragg peaks directly through a band-pass filter. Fig. 4 shows a doppler spectrogram of a broadened positive Bragg component extracted based on sparse filtering, and it can be seen that the broadened positive Bragg component can be completely extracted by the proposed method, and there are residual other components caused by rectangular sliding window leakage at clutter edges, but the residual components are at least 40dB smaller than the positive Bragg peak as a whole, and can be almost ignored. Fig. 5 shows echo doppler spectrograms processed by an HRR method, a PWVD method and an ionospheric phase pollution correction method based on sparse filtering, and the three methods can compress and broaden spectral peaks, improve the diffusion effect of doppler frequency to a certain extent, and inhibit the overlapping phenomenon of Bragg peaks. Because the HRR method requires strict frequency slow change, the PWVD method takes the strong Bragg component extracted by the FFT-Doppler band-pass filtering-IFFT three-step method as the parameter estimation premise, which is difficult to meet under the condition of Bragg peak overlapping caused by serious phase pollution, so that the HRR method and the PWVD method have the worst correction precision, the corrected echo still has obvious broadening, and a cooperative target cannot be detected. The Doppler spectrogram of the method is most obviously sharpened, and the slow targets near the clutter are clearly visible, which shows that the calibration signal extracted by the method is relatively good, so that the method has the advantage of high-precision phase estimation, and is beneficial to improving the OTHR slow ship target detection performance under the condition of Bragg overlapping caused by severe phase pollution.
Through the above example, the beneficial effects of the invention are verified, and compared with the existing ionospheric phase pollution correction method, under the condition that echo Bragg peaks are overlapped, the ionospheric phase pollution correction method based on sparse filtering provided by the invention can further improve the precision of ionospheric phase estimation and correction.
While the invention has been described with reference to specific embodiments, any feature disclosed in this specification may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise; all of the disclosed features, or all of the method or process steps, may be combined in any combination, except mutually exclusive features and/or steps.

Claims (4)

1. The sky wave over-the-horizon radar ionospheric phase pollution correction method based on sparse filtering comprises the following steps:
(1) the radar receiving data of a single range unit form an original echo vector:
x＝[x(1)，x(2)，...，x(N)]T (1)
wherein N is the number of radar transmission pulses in a coherent processing time;
(2) sending x into a sliding window segmentation module to obtain a short-time sequence vector set
Figure FSA0000194905110000011
yi＝Hix，i＝1，2，...，N (2)
Wherein, yiRepresenting the ith Nx 1-dimensional short-time sequence vector after the sliding window segmentation, wherein the ith Nx 1-dimensional short-time sequence vector comprises zero elements and non-zero elements formed by multiplying original echo vector data by the amplitude of the sliding window; hiDenotes yiA corresponding nxn dimensional sliding window partition matrix;
(3) structure N2X1 dimensional vector
Figure FSA0000194905110000012
And (3) removing zero elements in y:
z＝Fy (3)
wherein z is Mx 1(M < N)2) A dimension vector representing residual data with zero elements in y removed; f represents M × N2The wiki-divided matrix is from N2×N2Extracting M rows in the dimensional unit matrix according to rows, wherein the number of the extracted rows corresponds to non-zero elements in y;
(4) according to the sparsity of the short-time sequence in the Doppler domain, z sparsity is expressed as:
z＝FTs (4)
wherein, T ═ ifft (I), I represents N2×N2Dimension unit matrix, IFFT (-) represents inverse fourier transform;
Figure FSA0000194905110000013
is N2X 1-dimensional vector; siDenotes yiThe corresponding N multiplied by 1 dimensional sparse coefficient vector comprises the distribution conditions of sea/ground clutter, targets and noise of the short-time sequence in the complete Doppler frequency spectrum; s is reduced from z by solving the following convex problem:
Figure FSA0000194905110000014
wherein | · | purple sweetPRepresents a calculation of lPNorm, P ═ 1, 2; min (-) represents the minimum value, epsilon represents the radar noise base;
(5) according to the formula (6) and the formula (7), the position set of the sea clutter strong Bragg component of each short-time sequence in s is calculated
Figure FSA0000194905110000015
The extracted components are both positive Bragg components or both negative Bragg components:
Figure FSA0000194905110000016
qi＝ji+(i-1)×N，i＝1，2，...，N (7)
wherein, l is the search radius, and max (·) represents the maximum value;
(6) calculating a filtering vector h:
Figure FSA0000194905110000017
(7) strong Bragg component with N x1 dimensional broadening obtained by inverse sliding window operation
Figure FSA0000194905110000018
Figure FSA0000194905110000019
H has the function of filtering out the strong Bragg component of the sea clutter of each short-time sequence in z, and the process utilizes the distribution information of the sea/ground clutter, targets and noise of each short-time sequence in a sparse coefficient vector s, so that the method is called sparse filtering; g represents an N × M dimensional inverse sliding window matrix:
Figure FSA0000194905110000021
g (i, j) is the ith row and j column elements of G, and the G has the function of converting the filtered sea clutter intensity Bragg component of each short-time sequence into the spread Bragg component of the original echo; z (j) is the jth element of z; x (i) is the ith element of x; h isjZ (j) the sliding window amplitude introduced during sliding window segmentation; alpha is alphaiThe number of non-zero elements in the ith row of G;
(7) from
Figure FSA0000194905110000024
And (3) pollution phase extraction:
Figure FSA0000194905110000022
where angle (·) denotes taking the phase, N ═ 1, 2]T，β＝±2πfBTsCorresponding to positive and negative Bragg peaks, T, respectivelysIn the form of a pulse repetition period,
Figure FSA0000194905110000023
g is the acceleration of gravity, f0Is the radar carrier frequency, c is the speed of light;
(8) phase correction of x with γ:
x1(n)＝x(n)·e-jγ(n)，n＝1，2，...，N (12)
wherein x is1Representing an Nx 1-dimensional echo vector after phase correction of x; x is the number of1(n) represents the nth element of x 1; x (n) represents the nth element of x.
2. The sparse filtering-based sky-wave over-the-horizon radar ionospheric phase pollution correction method according to claim 1, wherein: in the step (2), the sliding window segmentation module can adopt a sliding window mode and a window value type in a time-frequency analysis method, an offline sliding window segmentation matrix database is established in advance, and the sliding window segmentation matrix database is directly called according to requirements during work.
3. The sparse filtering-based sky-wave over-the-horizon radar ionospheric phase pollution correction method according to claim 1, wherein: in the step (4), a convex optimization toolkit can be used for solving the convex problem.
4. The sparse filtering-based sky-wave over-the-horizon radar ionospheric phase pollution correction method according to claim 1, wherein: in the step (5), the search radius is determined according to different ionospheric phase pollution degrees, and when echo Bragg peaks overlap due to severe phase pollution, the value l is 15.
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