CN104977570B - Improve the sparse SAR moving target detection methods of binary channels based on kernel adjustment - Google Patents

Improve the sparse SAR moving target detection methods of binary channels based on kernel adjustment Download PDF

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CN104977570B
CN104977570B CN201510232444.2A CN201510232444A CN104977570B CN 104977570 B CN104977570 B CN 104977570B CN 201510232444 A CN201510232444 A CN 201510232444A CN 104977570 B CN104977570 B CN 104977570B
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CN104977570A (en
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朱圣棋
王震
廖桂生
张骏杰
宋萌萌
曾操
霍恩来
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Xidian University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • 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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/28—Details of pulse systems
    • G01S7/285—Receivers
    • G01S7/292—Extracting wanted echo-signals
    • G01S7/2923—Extracting wanted echo-signals based on data belonging to a number of consecutive radar periods
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • 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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/06—Systems determining position data of a target
    • G01S13/08—Systems for measuring distance only
    • G01S13/10—Systems for measuring distance only using transmission of interrupted, pulse modulated waves
    • G01S13/26—Systems for measuring distance only using transmission of interrupted, pulse modulated waves wherein the transmitted pulses use a frequency- or phase-modulated carrier wave
    • G01S13/28—Systems for measuring distance only using transmission of interrupted, pulse modulated waves wherein the transmitted pulses use a frequency- or phase-modulated carrier wave with time compression of received pulses
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • 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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9004—SAR image acquisition techniques
    • G01S13/9017—SAR image acquisition techniques with time domain processing of the SAR signals in azimuth
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • 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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9021—SAR image post-processing techniques
    • G01S13/9029—SAR image post-processing techniques specially adapted for moving target detection within a single SAR image or within multiple SAR images taken at the same time
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • 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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/28—Details of pulse systems
    • G01S7/285—Receivers
    • G01S7/292—Extracting wanted echo-signals
    • G01S7/2923—Extracting wanted echo-signals based on data belonging to a number of consecutive radar periods
    • G01S7/2928—Random or non-synchronous interference pulse cancellers

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  • Radar, Positioning & Navigation (AREA)
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Abstract

The sparse SAR moving target detection methods of binary channels based on kernel adjustment are improved the invention discloses a kind of, are comprised the following steps：First, the sparse SAR echo datas of the positive side view of binary channels, i.e. the echo data s of passage one are obtained1With the echo data s of passage two2；The observing matrix A of the passage one and observing matrix B of passage two is built respectively, and tectonic transition matrix T and binary channels joint observation matrix Φ, obtains restructuring matrix respectivelyWith echo transformation matrix R；Then, according to the echo data s of passage one1, the echo data s of passage two2With echo transformation matrix R, conversion obtains binary channels joint echo data s；Finally, by restructuring matrixThe sparse restructing algorithm based on kernel adjustment is improved with binary channels joint echo data s, the positional information of moving-target is obtained, realizes quick, the high-precision detection of SAR moving-targets sparse to binary channels.

Description

Improved two-channel sparse SAR moving target detection method based on null space adjustment
Technical Field
The invention belongs to the technical field of Synthetic Aperture Radar (SAR) moving target detection, and particularly relates to an improved two-channel sparse SAR moving target detection method based on zero-space adjustment, which is suitable for practical engineering application.
Background
The compressed sensing technology can effectively relieve the pressure of data storage and transmission, and is widely applied to the fields of optics, computers and image processing. The compressed sensing technology is also used in the field of Synthetic Aperture Radar (SAR) moving target detection and is used for solving the problems of high sampling rate and large data volume in SAR moving target detection. The theory of compressed sensing states that: as long as the signal is compressible or sparse in a certain transform domain, the transformed high-dimensional signal can be projected onto a low-dimensional space by using an observation matrix unrelated to the transform basis, and then the original signal can be reconstructed with high probability from a small number of projections by solving an optimization problem, so that the signal sampling rate depends greatly on the sparsity of the signal itself and the restricted isometry of the observation matrix, rather than the nyquist sampling theorem.
The compressed sensing technique mainly involves three problems: how to find a certain orthogonal base on which the signal is sparse; how to design an observation matrix and ensure the limiting equidistance of the observation matrix; how to select a sparse reconstruction algorithm to ensure that the reconstruction precision and the reconstruction speed can meet the requirements. The solving efficiency and the solving precision of the sparse reconstruction algorithm become important factors influencing the application of the compressive sensing technology. Sparse reconstruction algorithms can be divided into three major categories: convex relaxation-like algorithms, greedy iteration-like algorithms, and combination-like algorithms. The convex relaxation algorithm solves and finds the approximation of signals by converting a non-convex problem into a convex problem, the signals are reconstructed by solving the L1 norm, the whole observation matrix generally needs to be searched point by point, the method has the advantage of global optimization, but the calculation complexity is extremely high, so the accuracy is high but the speed is low; greedy iteration type algorithm approaches the original signal step by selecting a local optimal solution in each iteration, so that the speed is high and the precision is low, wherein the Orthogonal Matching Pursuit (OMP) algorithm is the most common algorithm; the combination algorithm requires the sampling of the signal to support the rapid reconstruction through the grouping test, and although the performance is good, the requirement on the self characteristics of the signal is high, and the combination algorithm is not universal.
At present, SAR moving target detection usually adopts an automatic direction changing Algorithm (ADM) in a convex relaxation algorithm to carry out sparse reconstruction, the algorithm carries out optimization solution on an L1 norm of a sparse signal to reconstruct and obtain a target signal, the reconstruction precision can meet the requirement of SAR moving target detection, but the SAR moving target detection has the defects of slow solution speed, extremely high calculation complexity and difficulty in realizing moving target detection and imaging at high speed because the SAR moving target detection needs to search a whole observation matrix point by point.
Researchers also propose sparse reconstruction algorithms based on null space regularization (NST), which mainly have the following framework: estimating the target signal of the iteration according to a certain criterion to obtain the current output; performing orthogonal projection operation on the difference value between the current output and the target signal of the iteration to the null space of the observation matrix to obtain the projection of the target signal of the iteration; adding the projection of the target signal of the iteration and the target signal of the iteration to obtain a target signal of the next iteration; as the number of iterations increases, the output will approach the target vector more and more. The algorithm utilizes the zero-space information of the observation matrix, enhances the precision and the speed of sparse reconstruction, but requires the sparsity of a target vector to be known, so the algorithm cannot be applied to the field of Synthetic Aperture Radar (SAR) moving target detection.
Disclosure of Invention
Based on the defects of the prior art, the invention aims to provide an improved two-channel sparse SAR moving target detection method based on zero-space adjustment, which utilizes the correlation between two-channel SAR echo data to weaken clutter (static targets), enhances the sparsity of moving targets, improves a sparse reconstruction algorithm based on zero-space adjustment, and realizes the rapid and high-precision detection of the two-channel sparse SAR moving targets under the condition that the sparsity of target vectors is unknown.
The technical idea for realizing the invention is as follows: acquiring two-channel sparse SAR echo data; constructing a transformation matrix and a dual-channel joint observation matrix according to the correlation between the dual-channel SAR echo data; and improving a sparse reconstruction algorithm based on null space adjustment, realizing self-adaptive estimation of the sparsity of the target vector, and obtaining the position information of the moving target.
In order to achieve the technical purpose, the invention is realized by adopting the following technical scheme.
An improved two-channel sparse SAR moving target detection method based on null space adjustment is characterized by comprising the following steps:
step 1, acquiring double-channel front side view sparse SAR echo data, namely channel echo data s1Sum channel two-echo data s2；
Step 2, respectively constructing a channel-I observation matrix A and a channel-II observation matrix B, respectively constructing a transformation matrix T and a two-channel joint observation matrix phi to obtain a reconstruction matrixAnd an echo transformation matrix R;
step 3, according to the channel echo data s1Channel two echo data s2And an echo transformation matrix R, transforming to obtain two-channel joint echo data s, and reconstructing the matrixAnd two channels are combinedAnd improving a sparse reconstruction algorithm based on null space adjustment by the wave data s to obtain the position information of the moving target.
The invention is characterized by further improvement:
(1) the specific substeps of the step 2 are as follows:
2.1 according to the slope distance historical relationship of the sparse sampling target echo, respectively constructing a first channel observation matrix A and a second channel observation matrix B
Where M is the number of sparsely sampled points, N is the number of azimuthally distinguishable points in the total synthetic aperture time, a (t)m-i Δ t) andrespectively representing clutter with Doppler being zero corresponding to ith column vector in channel-one observation matrix and ith column vector in channel-two observation matrix as
a(tm-iΔt)＝wa(t-iΔt)exp(jπk0(tm-iΔt)2)
Wherein i isToInteger of (m), t is the fast time in distance, tmIs azimuthally slow time, k0In order to adjust the frequency for the doppler,Δ t is the sparse sampling time interval, corresponding to the in-azimuth resolution, Δ t may be equal to or slightly less than the reciprocal of the doppler bandwidth, which is the product of the doppler tuning frequency and the total synthetic aperture time, wa(t-i Δ t) represents the azimuthal window function of the chirp signal with (t-i Δ t) as a parameter, v is the carrier platform velocity, d is the two-channel spacing, λ is the carrier wavelength, RBThe shortest slant distance between the target and the radar, and j is an imaginary number unit;
2.2 constructing a transformation matrix T of
Wherein O represents an all-zero matrix, IN×NRepresenting an NxN dimensional unit array, d being a two-channel spacing, λ being a carrier wavelength, RBThe shortest slant distance between the target and the radar;
according to the channel-I observation matrix A and the channel-II observation matrix B, a two-channel joint observation matrix phi is constructed
2.3 solving the conjugate transpose matrix phi of the constructed double-channel joint observation matrix phiHAnd then to the conjugate transpose matrix phiHPerforming orthogonal triangular (QR) decomposition, i.e. phiHQR, a reconstruction matrix is obtainedAnd the echo transformation matrix R is
R＝Q-1ΦH
(2) The specific substeps of the step 3 are as follows:
3.1 from channel echo data s1Channel two echo data s2And an echo transformation matrix R, and obtaining the dual-channel joint echo data s by transforming according to the following formula
Wherein, the symbol represents the left division operation of the matrix;
3.2 reconstruction from matricesand the two channels are combined with the echo data s, the initial parameters required by iteration are calculated, and alpha is definedk,lrepresenting the sparse vector of the k-th cycle with a sparsity of l, α0As an initial value of the sparse vector, letSetting l as sparsity of dual-channel joint echo data s, making initial value of l zero, and making initial value of normalized estimation error gammaex 0＝1；
3.3 improving the sparse reconstruction algorithm based on null-space adjustment as follows:
increasing the outer loop sparsity l by 1, setting the inner loop times k to be 0, and performing outer loop iteration and inner loop iteration;
3.3.1 outer loop iteration formula is
wherein alpha isk,lrepresenting the sparse vector of the kth cycle when the sparsity is l, and determining alphak,lthe first I elements with the maximum modulus are obtained, and the elements are obtained at alphak,lThe position information in (1) constitutes an index set TkAnd index set TkComplement ofwill be alphak,lMiddle corresponding index set TkThe elements of (1) are reserved, and the other elements are zero to form a vectorwill be alphak,lSet of corresponding indexesThe elements of (1) are reserved, and the other elements are zero to form a vector
Wherein,representing a to-be-reconstructed matrixMiddle corresponding index set TkThe column vector of (1) is reserved, and other elements are zero Representing a to-be-reconstructed matrixSet of corresponding indexesThe column vector of (1) is reserved, and other elements are zero
3.3.2 calculating sparse vector alpha of the k +1 th inner loop estimation according to the following inner loop iteration formulak+1,l：
αk+1,l＝αk,l+P(uk,l-αk,l)
Wherein,representation-oriented reconstruction matrixIs subjected to orthogonal projection operation, uk,lRepresentation mergingAndvectors formed after, i.e. in vector uk,lMiddle corresponding index set TkPosition filling inThe elements in the same position in the index setPosition filling inElements in the same position;
3.3.3 calculating the normalized error between two inner loopsCompares it with the inner loop threshold th1If it satisfies γin≤th1If not, increasing k by 1 and continuing to perform inner loop iteration;
3.3.4 calculating the normalized estimation error at sparsity lCalculating the difference error gamma of two outer loopsex l-γex l-1Comparing the difference error with an extrinsic threshold th2If not, the magnitude of (c) isex l-γex l-1|≤th2continuing to carry out outer loop iteration, otherwise, terminating the program to obtain a sparse vector alphak,lLocation information characterizing the target.
The improved two-channel sparse SAR moving target detection method based on the zero space adjustment is suitable for two-channel sparse SAR moving target detection, a threshold iteration (HT) thought and a Feedback (FB) thought are introduced, a normalized error is designed to serve as a reference threshold, self-adaptive estimation of target vector sparsity is achieved, the iteration speed is accelerated, the speed of two-channel sparse SAR moving target detection is accelerated, the precision of the two-channel sparse SAR moving target detection is improved, and the noise suppression capability is enhanced.
Drawings
The invention is described in further detail below with reference to the following description of the drawings and the detailed description.
FIG. 1 is a schematic diagram of two-channel front-side view sparse SAR echo data sampling in the present invention;
FIG. 2 is a flow chart of an improved null-space adjustment based sparse reconstruction algorithm of the present invention;
FIG. 3a is a schematic diagram of the signal-to-noise ratio of the output of 100 detection experiments with different algorithms;
FIG. 3b is a schematic diagram of the results of a single test run with different algorithms;
FIG. 4 is a schematic diagram of average output signal-to-noise ratio (SNR) with input SNR for different algorithms;
FIG. 5 is a schematic diagram of the variation of the operation time of different algorithms with the length of a target vector;
FIG. 6a is a diagram showing the result of moving object detection of measured data according to the present invention;
FIG. 6b is a diagram showing the result of the ADM algorithm performing moving target detection on the measured data.
Detailed Description
The invention discloses an improved two-channel sparse SAR moving target detection method based on zero space adjustment, which comprises the following steps:
step 1, acquiring double-channel front side view sparse SAR echo data, namely channel echo data s1Sum channel two-echo data s2。
Referring to fig. 1, a schematic diagram of sampling of dual-channel front-side view sparse SAR echo data in the present invention is shown. The invention is suitable for the double-channel front side view synthetic aperture radar. In FIG. 1, C1 represents channel one, C2 represents channel two, T (T)0) Indicating that the target is at t0Position of time, T (T)m) Indicating that the target is at tmAt the time, the pulse is randomly transmitted through a channel, the pulse is simultaneously received through the two channels, delta t is the sparse sampling time interval, and t is the time intervalmThe instantaneous slope distance between the time target and the first channel is R1(tm)，tmThe instantaneous slope distance between the target and the second channel is R2(tm)：
Wherein R isBIs the shortest slant distance between the target and the radar, v is the carrier platform speed, d is the two-channel interval, tmFor azimuthally slow time, vaAnd aaRespectively the azimuthal velocity and azimuthal acceleration of the target, vcAnd acRespectively range-wise velocity and range-wise acceleration of the target.
Randomly sampling in azimuth to obtain slow-time (azimuth) sparse dual-channel echo data, performing range walk correction and pulse compression on the dual-channel echo data in all azimuths to obtain range-compressed dual-channel echo data in all azimuths, and respectively representing the dual-channel echo data in the same range gate into vector form s1(t,tm) And s2(t,tm)：
Where t is the fast time in distance, tmFor azimuthal slow time, σ is the scattering coefficient of the target, G1And G2Gain, w, for channel one and channel two, respectivelyr(. and w)a(. DEG) is a window function of the chirp signal and a window function in the orientation of the chirp signal, respectively, gamma (. DEG.) is the transmit signal modulation frequency, lambda is the carrier wavelength, tau2The echo delay for channel one is the time delay of the echo,τ2is the echo delay of the second channel,c is the speed of light, R1(tm) Is tmInstantaneous slope distance, R, of time target and channel one2(tm) Is tmAnd the instantaneous slope distance between the target and the second channel at the moment.
Referring to fig. 2, the principle and flow of the present invention for improving the sparse reconstruction algorithm based on the null-space adjustment will be described in detail.
Step 2, respectively constructing a channel-I observation matrix A and a channel-II observation matrix B, respectively constructing a transformation matrix T and a two-channel joint observation matrix phi to obtain a reconstruction matrixAnd an echo transformation matrix R.
The specific substeps of step 2 are:
2.1 according to the slope distance historical relationship of the sparse sampling target echo, respectively constructing a first channel observation matrix A and a second channel observation matrix B
Where M is the number of sparsely sampled points, N is the number of azimuthally distinguishable points in the total synthetic aperture time, a (t)m-i Δ t) andrespectively representing clutter (static targets) with Doppler being zero corresponding to ith column vector in first channel observation matrix and ith column vector in second channel observation matrix
a(tm-iΔt)＝wa(t-iΔt)exp(jπk0(tm-iΔt)2)
Wherein i isToInteger of (m), t is the fast time in distance, tmIs azimuthally slow time, k0In order to adjust the frequency for the doppler,Δ t is the sparse sampling time interval, corresponding to the in-azimuth resolution, Δ t may be equal to or slightly less than the reciprocal of the doppler bandwidth, which is the product of the doppler tuning frequency and the total synthetic aperture time, wa(t-i Δ t) represents the azimuthal window function of the chirp signal with (t-i Δ t) as a parameter, v is the carrier platform velocity, d is the two-channel spacing, λ is the carrier wavelength, RBThe shortest slant distance between the target and the radar, and j is an imaginary number unit;
2.2 constructing a transformation matrix T of
Wherein O represents an all-zero matrix, IN×NRepresenting an NxN dimensional unit array, d being a two-channel spacing, λ being a carrier wavelength, RBThe shortest slant distance between the target and the radar;
according to the channel-I observation matrix A and the channel-II observation matrix B, a two-channel joint observation matrix phi is constructed
2.3 the conjugate of the constructed two-channel joint observation matrix phi is solvedTransposed matrix phiHAnd then to the conjugate transpose matrix phiHPerforming orthogonal triangular (QR) decomposition, i.e. phiHQR, a reconstruction matrix is obtainedAnd the echo transformation matrix R is
R＝Q-1ΦH
Step 2.3 is referred to herein as matrix decomposition, MA.
Step 3, according to the channel echo data s1Channel two echo data s2And an echo transformation matrix R, transforming to obtain two-channel joint echo data s, and reconstructing the matrixAnd improving a sparse reconstruction algorithm based on null space adjustment by combining the two channels with the echo data s to obtain the position information of the moving target.
The specific substeps of step 3 are:
3.1 from channel echo data s1Channel two echo data s2And an echo transformation matrix R, and obtaining the dual-channel joint echo data s by transformation according to the following formula:
wherein, the symbol represents the matrix left division operation.
3.2 reconstruction from matricesand the two channels are combined with the echo data s, the initial parameters required by iteration are calculated, and alpha is definedk,lrepresenting the sparse vector of the k-th cycle with a sparsity of l, α0As an initial value of the sparse vector, letSetting l as sparsity of dual-channel joint echo data s, making initial value of l zero, and making initial value of normalized estimation error gamma for smooth execution of iterationex 0＝1。
3.3 improving the sparse reconstruction algorithm based on null-space adjustment as follows:
and increasing the outer loop sparsity l by 1, setting the inner loop frequency k to be 0, and performing outer loop iteration and inner loop iteration.
3.3.1 on the basis of the concept of zero space adjustment (NST), introducing a threshold iteration (HT) concept and a Feedback (FB) concept to obtain the following outer loop iteration formula:
wherein alpha isk,lrepresenting the sparse vector of the kth cycle when the sparsity is l, and determining alphak,lthe first I elements with the maximum modulus are obtained, and the elements are obtained at alphak,lThe position information in (1) constitutes an index set TkAnd index set TkComplement ofwill be alphak,lMiddle corresponding index set TkThe elements of (1) are reserved, and the other elements are zero to form a vectorwill be alphak,lSet of corresponding indexesThe elements of (1) are reserved, and the other elements are zero to form a vector
for example, for the sparse vector α of the k-th cycle with sparsity of 2k,2，αk,2＝[a1a2a3a4…anan+1…]TIs provided with a3≥an≥an-1Not less than …, then index set Tk(iii) complementary set {3, n }, ofTo obtain
Wherein,representing a to-be-reconstructed matrixMiddle corresponding index set TkThe column vector of (1) is reserved, and other elements are zero Representing a to-be-reconstructed matrixSet of corresponding indexesThe column vector of (1) is reserved, and other elements are zero
3.3.2 calculating sparse vector alpha of the k +1 th inner loop estimation according to the following inner loop iteration formulak+1,l：
αk+1,l＝αk,l+P(uk,l-αk,l)
Wherein,representation-oriented reconstruction matrixIs subjected to orthogonal projection operation, uk,lRepresentation mergingAndvectors formed after, i.e. in vector uk,lMiddle corresponding index set TkPosition filling inThe elements in the same position in the index setPosition filling inElements of the same position.
3.3.3 calculating the normalized error between two inner loopsCompares it with the inner loop threshold th1If it satisfies γin≤th1And if not, increasing k by 1 and continuing the inner loop iteration.
3.3.4Calculating the normalized estimation error when the sparsity is lCalculating the difference error gamma of two outer loopsex l-γex l-1Comparing the difference error with an extrinsic threshold th2If not, the magnitude of (c) isex l-γex l-1|≤th2continuing to carry out outer loop iteration, otherwise, terminating the program to obtain a sparse vector alphak,lCharacterizing location information of the target;
in the step 3, matrix decomposition and echo transformation are carried out, so that the speed and the precision of reconstruction solving are improved; by setting an inner loop threshold th1In practical application, the absolute magnitude of noise is not required to be known, so that the parameter selection of the algorithm is facilitated; by comparing the difference error gamma of two outer loops when the sparsity is lex l-γex l-1| and extrinsic cycle threshold th2The value of l can be judged whether the l is the sparsity of the target vector, and the self-adaptive estimation of the sparsity is realized; by improving the sparse reconstruction algorithm based on the null space adjustment, the fast and high-precision reconstruction of the two-channel sparse SAR echo data is realized.
The effects of the present invention can be further illustrated by the following simulation experiments and actual measurement data tests:
1) simulation parameters:
3 clutter scattering points with the backscattering coefficient amplitude of 1 and 1 moving target with the backscattering coefficient amplitude of 0.3 are arranged in the same range gate with the slant distance of 9000m, the radar carrier frequency is 1GHz, linear frequency modulation signals are transmitted, the bandwidth is 37.5MHz, the repetition frequency of transmitted pulses is 120Hz, the interval of two channels is 2m, and the speed of a carrier platform is 120 m/s.
2) Simulation experiment and result analysis
Simulation experiment 1 and result analysis: under the condition that the input signal-to-noise ratio is 0dB, echo data with the sparse sampling rate of 50% are respectively processed by the improved two-channel sparse SAR moving target detection method (MNST algorithm for short), the automatic direction changing algorithm ADM and the orthogonal matching pursuit algorithm OMP based on the null space adjustment. Referring to fig. 3a, a schematic diagram of the output signal-to-noise ratio for 100 detection experiments for different algorithms is shown. In fig. 3a, the abscissa is the number of trials and the ordinate is the output signal-to-noise-and-noise ratio of the algorithm in decibels (dB). Fig. 3b is a diagram showing the results of a single detection experiment performed by different algorithms. In fig. 3b, the abscissa is the number of azimuth gates, and the ordinate is the output signal amplitude.
As can be seen from FIG. 3a, the output signal-to-noise-and-noise ratio of the MNST algorithm is 2-4 dB higher than that of the ADM algorithm as a whole, and 4-6 dB higher than that of the OMP algorithm as a whole, so that the MNST algorithm is better in detection performance than the ADM algorithm and the OMP algorithm as a whole, and better in target detection effect. Referring to fig. 3b, the MNST algorithm of the present invention forms peaks at the target, while spurious peaks formed by reconstruction errors and noise around the target are much less than those formed by the ADM algorithm and the OMP algorithm, making it easier to detect the target.
Simulation experiment 2 and result analysis: the input signal-to-noise ratio is gradually increased from-20 dB to 10dB, 100 Monte Carlo experiments are carried out at each input signal-to-noise ratio value, and the average output signal-to-noise ratios detected by 100 Monte Carlo experiments of different algorithms are compared. Referring to fig. 4, the variation of the average output signal-to-noise ratio with the input signal-to-noise ratio in different algorithms is shown. In fig. 4, the ordinate is the average output signal-to-noise ratio in decibels (dB) for 100 monte carlo experiments, and the abscissa is the input signal-to-noise ratio in decibels (dB).
As can be seen from fig. 4, when the OMP algorithm is used to detect the target, the output target signal-to-noise ratio is low, and the detection effect is poor (not applicable in the field of actual sparse SAR moving target detection); when the input signal-to-noise ratio is larger than-13 dB, the ADM algorithm can well detect the target, and when the input signal-to-noise ratio is smaller than-13 dB, the target cannot be effectively detected by adopting the ADM algorithm; the MNST algorithm can effectively detect the target when the input signal-to-noise ratio is larger than-15 dB, and the algorithm has stronger inhibition capability on noise.
Simulation experiment 3 and result analysis: when the signal-to-noise ratio is input to be 0dB, the length of a target vector is changed (different numbers of sampling points are taken in the direction), and the average operation time of 100 tests of different algorithms is calculated. Referring to fig. 5, the operation time of different algorithms changes with the length of the target vector. In fig. 5, the abscissa represents the target vector length in units of points, and the ordinate represents the calculation time in units of seconds(s).
As can be seen from fig. 5, when the target vector length is small (the length is less than 300), the operation time difference of each algorithm is not large, that is, the operation speed difference is not large, as the target vector length is larger, the operation speed advantage of the MNST algorithm of the present invention gradually becomes larger, and when the target vector length is 700, the operation speed of the MNST algorithm of the present invention is already about 1 time faster than that of the ADM algorithm. In practice, the SAR data is often larger in scale, and the advantages are more obvious by using the algorithm.
3) Actual measurement data testing and result analysis
The MNST algorithm and the ADM algorithm of the invention are used for carrying out sparse sampling on the actually measured dual-channel SAR echo data, and the sparse sampling rate is 60%. FIG. 6a is a diagram illustrating the result of performing moving object detection on measured data according to the present invention. Referring to fig. 6b, a result diagram of moving target detection performed on the measured data by the ADM algorithm is shown. The circle in fig. 6a and 6b is the target.
As can be seen from fig. 6a and 6b, moving objects are observed in both methods, but false noise spots formed by recombination errors and noise in a scene by using the MNST algorithm of the present invention are fewer, the objects are clearer, and actually measured data of the same size are processed in the same processing environment, the MNST algorithm of the present invention only needs 305s, whereas the traditional algorithm needs 1559s, and the MNST algorithm of the present invention is greatly improved in operation speed compared with the traditional algorithm.

Claims (1)

1. An improved two-channel sparse SAR moving target detection method based on null space adjustment is characterized by comprising the following steps:
step 1, acquiring double-channel front side view sparse SAR echo data, namely channel echo data s1Sum channel two-echo data s2；
Step 2, respectively constructing a channel-I observation matrix A and a channel-II observation matrix B, respectively constructing a transformation matrix T and a two-channel joint observation matrix phi to obtain a reconstruction matrixAnd an echo transformation matrix R;
the specific substeps of the step 2 are as follows:
2.1 according to the slope distance historical relationship of the sparse sampling target echo, respectively constructing a first channel observation matrix A and a second channel observation matrix B
<mrow> <msub> <mi>A</mi> <mrow> <mi>M</mi> <mo>&amp;times;</mo> <mi>N</mi> </mrow> </msub> <mo>=</mo> <mo>&amp;lsqb;</mo> <mi>a</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>-</mo> <mo>(</mo> <mrow> <mn>1</mn> <mo>-</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> <mi>&amp;Delta;</mi> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>a</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>-</mo> <mo>(</mo> <mrow> <mn>2</mn> <mo>-</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> <mi>&amp;Delta;</mi> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <mo>...</mo> <mi>a</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>-</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> <mi>&amp;Delta;</mi> <mi>t</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow>
<mrow> <msub> <mi>B</mi> <mrow> <mi>M</mi> <mo>&amp;times;</mo> <mi>N</mi> </mrow> </msub> <mo>=</mo> <mo>&amp;lsqb;</mo> <mi>a</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>-</mo> <mo>(</mo> <mrow> <mn>1</mn> <mo>-</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> <mi>&amp;Delta;</mi> <mi>t</mi> <mo>-</mo> <mfrac> <mi>d</mi> <mrow> <mn>2</mn> <mi>v</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>,</mo> <mi>a</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>-</mo> <mo>(</mo> <mrow> <mn>1</mn> <mo>-</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> <mi>&amp;Delta;</mi> <mi>t</mi> <mo>-</mo> <mfrac> <mi>d</mi> <mrow> <mn>2</mn> <mi>v</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>,</mo> <mo>...</mo> <mi>a</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>-</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> <mi>&amp;Delta;</mi> <mi>t</mi> <mo>-</mo> <mfrac> <mi>d</mi> <mrow> <mn>2</mn> <mi>v</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow>
Where M is the number of sparsely sampled points, N is the number of azimuthally distinguishable points in the total synthetic aperture time, a (t)m-i Δ t) andrespectively representing clutter with Doppler being zero corresponding to ith column vector in channel-one observation matrix and ith column vector in channel-two observation matrix as
a(tm-iAt)＝wa(t-iΔt)exp(jπk0(tm-iΔt)2)
<mrow> <mi>a</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>-</mo> <mi>i</mi> <mi>&amp;Delta;</mi> <mi>t</mi> <mo>-</mo> <mfrac> <mi>d</mi> <mrow> <mn>2</mn> <mi>v</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>w</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>i</mi> <mi>&amp;Delta;</mi> <mi>t</mi> <mo>-</mo> <mfrac> <mi>d</mi> <mrow> <mn>2</mn> <mi>v</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mi>exp</mi> <mrow> <mo>(</mo> <msub> <mi>j&amp;pi;k</mi> <mn>0</mn> </msub> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>t</mi> <mi>m</mi> </msub> <mo>-</mo> <mi>i</mi> <mi>&amp;Delta;</mi> <mi>t</mi> <mo>-</mo> <mfrac> <mi>d</mi> <mrow> <mn>2</mn> <mi>v</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow>
Wherein i isToInteger of (m), t is the fast time in distance, tmIs azimuthally slow time, k0In order to adjust the frequency for the doppler,Δ t is the sparse sampling time interval, corresponding to the in-azimuth resolution, Δ t may be equal to or slightly less than the reciprocal of the doppler bandwidth, which is the product of the doppler tuning frequency and the total synthetic aperture time, wa(t-i Δ t) represents the azimuthal window function of the chirp signal with (t-i Δ t) as a parameter, v is the carrier platform velocity, d is the two-channel spacing, λ is the carrier wavelength, RBThe shortest slant distance between the target and the radar, and j is an imaginary number unit;
2.2 constructing a transformation matrix T of
<mrow> <mi>T</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>I</mi> <mrow> <mi>N</mi> <mo>&amp;times;</mo> <mi>N</mi> </mrow> </msub> </mtd> <mtd> <mrow> <mo>-</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msup> <mi>j&amp;pi;d</mi> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <msub> <mi>R</mi> <mi>B</mi> </msub> <mi>&amp;lambda;</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>I</mi> <mrow> <mi>N</mi> <mo>&amp;times;</mo> <mi>N</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>O</mi> </mtd> <mtd> <msub> <mi>I</mi> <mrow> <mi>N</mi> <mo>&amp;times;</mo> <mi>N</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>
Wherein O represents an all-zero matrix, IN×NRepresenting an NxN dimensional unit array, d being a two-channel spacing, λ being a carrier wavelength, RBThe shortest slant distance between the target and the radar;
according to the channel-I observation matrix A and the channel-II observation matrix B, a two-channel joint observation matrix phi is constructed
<mrow> <mi>&amp;Phi;</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>A</mi> <mrow> <mi>M</mi> <mo>&amp;times;</mo> <mi>N</mi> </mrow> </msub> </mtd> <mtd> <mi>O</mi> </mtd> </mtr> <mtr> <mtd> <mi>O</mi> </mtd> <mtd> <msub> <mi>B</mi> <mrow> <mi>M</mi> <mo>&amp;times;</mo> <mi>N</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>&amp;CenterDot;</mo> <msup> <mi>T</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>;</mo> </mrow>
2.3 solving the conjugate transpose matrix phi of the constructed double-channel joint observation matrix phiHAnd then to the conjugate transpose matrix phiHPerforming orthogonal triangular QR decomposition, i.e. phiHQR, a reconstruction matrix is obtainedAnd the echo transformation matrix R is
R＝Q-1ΦH
Step 3, according to the channel echo data s1Channel two echo data s2And an echo transformation matrix R, transforming to obtain two-channel joint echo data s, and reconstructing the matrixImproving a sparse reconstruction algorithm based on null space adjustment by combining the two-channel combined echo data s to obtain the position information of the moving target;
wherein, the specific substeps of the step 3 are as follows:
3.1 from channel echo data s1Channel two echo data s2And an echo transformation matrix R, and obtaining the dual-channel joint echo data s by transformation according to the following formula:
<mrow> <mi>s</mi> <mo>=</mo> <msup> <mi>R</mi> <mi>H</mi> </msup> <mo>\</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>s</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>s</mi> <mn>2</mn> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>
wherein, the symbol represents the left division operation of the matrix;
3.2 reconstruction from matricesand the two channels are combined with the echo data s, the initial parameters required by iteration are calculated, and alpha is definedk，lSparse vector representing the k-th cycle with sparsity of l，α0，lAs an initial value of the sparse vector, let
Setting l as sparsity of dual-channel joint echo data s, making initial value of l zero, and making initial value of normalized estimation error gammaex 0＝1；
3.3 improving the sparse reconstruction algorithm based on null-space adjustment as follows:
increasing the outer loop sparsity l by 1, setting the inner loop times k to be 0, and performing outer loop iteration and inner loop iteration;
3.3.1 outer loop iteration formula is
<mrow> <msubsup> <mi>u</mi> <msubsup> <mi>T</mi> <mi>k</mi> <mi>C</mi> </msubsup> <mrow> <mi>k</mi> <mo>,</mo> <mi>l</mi> </mrow> </msubsup> <mo>=</mo> <mn>0</mn> </mrow>
wherein alpha isk，lrepresenting the sparse vector of the kth cycle when the sparsity is l, and determining alphak，lthe first I elements with the maximum modulus are obtained, and the elements are obtained at alphak，lThe position information in (1) constitutes an index set TkAnd index set TkComplement ofwill be alphak，lMiddle corresponding index set TkThe elements of (1) are reserved, and the other elements are zero to form a vectorwill be alphak，lSet of corresponding indexesThe elements of (1) are reserved, and the other elements are zero to form a vector
Wherein,representing a to-be-reconstructed matrixMiddle corresponding index set TkThe column vector of (1) is reserved, and other elements are zero Representing a to-be-reconstructed matrixSet of corresponding indexesThe column vector of (1) is reserved, and other elements are zero
3.3.2 calculating sparse vector alpha of the k +1 th inner loop estimation according to the following inner loop iteration formulak+1，l：
αk+1，l＝αk，l+P(uk，l-αk，l)
Wherein,representation-oriented reconstruction matrixIs subjected to orthogonal projection operation, uk，lRepresentation mergingAndvectors formed after, i.e. in vector uk，lMiddle corresponding index set TkPosition filling inThe elements in the same position in the index setPosition filling inElements in the same position;
3.3.3 calculating the normalized error between two inner loopsCompares it with the inner loop threshold th1If it satisfies γin≤th1If not, increasing k by 1 and continuing to perform inner loop iteration;
3.3.4 calculating the normalized estimation error at sparsity lCalculating the difference error gamma of two outer loopsex l-γex l-1Comparing the difference error with an extrinsic threshold th2If not, the magnitude of (c) isex l-γex l-1|≤th2Continuing to carry out outer loop iteration, otherwise, terminating the program to obtain the sparsevector alphak，lLocation information characterizing the target.
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