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CN106569196B - A ground-based radar multi-target detection method based on compressed sensing - Google Patents

A ground-based radar multi-target detection method based on compressed sensing Download PDF

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CN106569196B
CN106569196B CN201610984778.XA CN201610984778A CN106569196B CN 106569196 B CN106569196 B CN 106569196B CN 201610984778 A CN201610984778 A CN 201610984778A CN 106569196 B CN106569196 B CN 106569196B
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CN106569196A (en
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张家庆
袁小琦
谢仁宏
芮义斌
郭山红
李鹏
王芮
朱唯唯
陈倩
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Nanjing University of Science and Technology
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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
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section

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  • Computer Networks & Wireless Communication (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
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  • Radar Systems Or Details Thereof (AREA)

Abstract

The invention discloses a kind of compressed sensing based ground radar multi-target detection methods, comprising: the rarefaction representation for completing echo-signal designs sparse transformation matrix；It selects random gaussian matrix as observing matrix, target echo signal is projected respectively using each row vector in observing matrix, obtains the partial information of signal, dimensionality reduction observation is carried out to echo-signal；Using the rarefaction representation of target echo signal as optimized variable, establishes convex Optimized model and solve, obtain the globally optimal solution of rarefaction representation signal；According to the rarefaction representation form of the building method of sparse matrix and echo-signal, the time delay and Doppler frequency of target are obtained.The present invention can correctly detect multiple targets in the case where unknown object number compared with conventional orthogonal matching method.

Description

A kind of compressed sensing based ground radar multi-target detection method
Technical field
The invention belongs to radar signal processing field, especially a kind of compressed sensing based ground radar multi-target detection Method.
Background technique
Often it is mingled with the bigger environment clutter of intensity, useful signal in ground radar target detection, in echo-signal It floods wherein.The measure for carrying out clutter recognition has very much, can distinguish on antenna, transmitter, receiver and signal processor Corresponding technological means is taken to carry out clutter reduction.Wherein, clutter suppression method relevant to signal processing specifically includes that moving-target Show (Moving Target Indication, MTI) technology, moving-target detection (Moving Target Detection, MTD) technology, pulse Doppler (Pulse Doppler, PD) technology etc..In the 1950s, Emerson et al. propose it is dynamic Target shows the concept of (Moving Target Indication, MTI), and carries out clutter recognition with this.The MTI of early stage is filtered Device realizes that effect is poor by way of analog circuit and delay line.With the development of electronic technology and Radar Signal Processing, The various mti filters haveing excellent performance occur in succession, adaptive MTI (Adaptive MTI, AMTI) filter[38]It can basis The difference of clutter centre frequency is automatic to change filter notch position, and clutter recognition performance is further improved.But pass through After MTI clutter cancellation, still comprising residual clutter ingredient in signal.When noise intensity is very big, clutter residue can still interfere mesh Target correctly detects, and false-alarm probability is caused to rise.To have fixed false-alarm probability, constant false alarm when guaranteeing target detection (Constant False Alarm Rate, CFAR) detection[39]Technology is come into being, and CFAR detection is generally divided into unit perseverance False-alarm and time domain constant false alarm.In order to reduce influence of the clutter remnants to target detection, clutter amplitude in the time domain steady is utilized Property, time integral is carried out on azran unit, obtains the amplitude Estimation of clutter remnants, is obtained on the basis of remaining by clutter Thresholding is used for the output of target, thus reduces the false-alarm probability of target detection, here it is clutter map (Clutter Map, CM) inspections Survey technology[40-41].In the 1970s, Massachusetts Institute Technology's Lincoln laboratory proposes that moving-target detects (Moving Target Detection, MTD) method progress clutter recognition[42].Then again occur the MTD filter of various different structures with And adaptive M TD (Adaptive MTD, AMTD) filter.
Compressive sensing theory (Compressed Sensing, CS) can make full use of echo measurement signal sparsity or Compressibility realizes sampling and reconstruct to signal using the sampling rate far below twice of signal frequency, how breaches tradition The limitation of Qwest's sampling thheorem.By the way that compressive sensing theory to be introduced into Radar Signal Processing, echo can be substantially reduced The sample rate and data processing of signal.
But it there is no a kind of method that compressive sensing theory is applied to ground radar multi-target detection in the prior art.
Summary of the invention
The purpose of the present invention is to provide a kind of compressed sensing based ground radar multi-target detection methods.This method will Compressive sensing theory uses ground radar target detection, using the redundancy of data, only acquires a small amount of sample reduction original number According to.Restructing algorithm uses convex optimized algorithm, is able to achieve while the detection to multiple targets.
The technical solution for realizing the aim of the invention is as follows: a kind of compressed sensing based ground radar multi-target detection side Method, comprising:
Step 1 carries out rarefaction representation to echo-signal, is specifically carried out using sparse transformation matrix to echo-signal sparse It indicates；
Step 2 selects random gaussian matrix as observing matrix, using each row vector in observing matrix respectively to mesh Mark echo-signal is projected, and the partial information of signal is obtained, and carries out dimensionality reduction observation to echo-signal；
Step 3, using the rarefaction representation of target echo signal as optimized variable, establish convex Optimized model and solve, reconstruct dilute Dredge the globally optimal solution for indicating signal；
Step 4 is obtained by the globally optimal solution of the rarefaction representation signal in the sparse matrix and step 3 that construct in step 1 The time delay and Doppler shift of each target.
Compared with prior art, the present invention having the advantage that 1) compressive sensing theory is applied to ground thunder by the present invention The target detection reached, to be far below the rate collecting sample of nyquist sampling rate, reduces acquisition compared with conventional target detection The memory space and calculation amount of signal；2) present invention uses convex optimized algorithm to the reconstruct of target echo signal, with it is traditional just It hands over matching algorithm to compare, can detect multiple targets simultaneously in the uncertain situation of target numbers, and between each target It influences each other smaller, therefore the present invention is more adaptable；3) present invention in sparse transformation matrix construction, be will test region draw It is divided into delay-Doppler domain grid, the target echo in each grid is fixed, do not need to do matched filtering etc. to echo-signal Reason, directly can obtain the time delay and Doppler shift of target echo signal by reconstruction result, reduce calculation amount, improve measurement Precision.
Present invention is further described in detail with reference to the accompanying drawing.
Detailed description of the invention
Fig. 1 is the method for the present invention flow chart.
Fig. 2 is time shift-Doppler's grid dividing figure in the present invention.
Fig. 3 is echo-signal rarefaction representation result figure obtained in the embodiment of the present invention.
Fig. 4 is the theoretical echo-signal and reconstruct echo-signal comparison result figure of the embodiment of the present invention.
Specific embodiment
In conjunction with Fig. 1, a kind of compressed sensing based ground radar multi-target detection method of the invention, including following step It is rapid:
Step 1 carries out rarefaction representation to echo-signal, is specifically carried out using sparse transformation matrix to echo-signal sparse It indicates；Specifically:
Step 1-1, the echo-signal x of M echo signal, formula used are determined are as follows:
In formula, τmAnd υmThe time shift and Doppler shift of respectively m-th target,For time of m-th of target Wave signal；
Step 1-2, delay-Doppler domain is divided into Nw=Nτ×NυA grid, temporal resolution are Δ τ, Doppler point Resolution is Δ υ, so that it is determined that sparse transformation matrix, completes rarefaction representation of the target echo signal on sparse transformation matrix, institute With formula are as follows:
In formula,For the corresponding target echo signal of target (i, j), time shift at this time is τi=(i-1) × Δ τ, Doppler shift is υj=(j-1) × Δ υ；
Step 1-3, the coefficient representation of target echo signal, formula used are determined are as follows:
X=Psi*xp
In formula, xpIt is the N after the rarefaction representation by echo-signalw× 1 dimension matrix, and
Then xpIn only M nonzero value and M < < Nw- M, so xpIt is sparse.
Step 2 selects random gaussian matrix as observing matrix, using each row vector in observing matrix respectively to mesh Mark echo-signal is projected, and the partial information of signal is obtained, and carries out dimensionality reduction observation to echo-signal；Select random gaussian matrix As observing matrix Phi, formula used are as follows:
Phi=sqrt (1/Mwid) * randn (Mwid, Nwid)
In formula, Nwid indicates the length of target echo signal sampling, and Mwid indicates the number of observation；To echo-signal into The observation of row dimensionality reduction, formula used are y=Phi*x, and y is observation, if the Mwid chosen meets Mwid >=c × M × lg (Nwid/ M), then original signal can be reconstructed from observation y with high probability, otherwise cannot reconstructs original signal, wherein c is constant.
Step 3, using the rarefaction representation of target echo signal as optimized variable, establish convex Optimized model and solve, reconstruct dilute Dredge the globally optimal solution for indicating signal；The convex Optimized model are as follows:
min imize||xp||1
Subject to y=Phi*Psi*xp。
Step 4 is obtained by the globally optimal solution of the rarefaction representation signal in the sparse matrix and step 3 that construct in step 1 The time delay and Doppler shift of each target.Specifically: according to the globally optimal solution x of sparse matrix Psi and rarefaction representation signalpIn The position that absolute value is not zero obtains the time shift and Doppler shift of each target.
Compressive sensing theory is applied to the target detection of ground radar by the present invention, compared with conventional target detection, with remote Lower than the rate collecting sample of nyquist sampling rate, the memory space and calculation amount of acquisition signal are reduced.
It is described in more detail below.
In conjunction with Fig. 1, a kind of compressed sensing based ground radar multi-target detection method, comprising the following steps:
Step 1 carries out rarefaction representation to echo-signal, is specifically carried out using sparse transformation matrix to echo-signal sparse It indicates；In conjunction with Fig. 1 and 2, which determines the echo-signal x of M echo signal, formula used first are as follows:
In formula, τmAnd υmThe time shift and Doppler shift of respectively m-th target,For time of m-th of target Wave signal is that Nwid × 1 ties up matrix.
It is N that region, which be will test, by time delay-Doppler domain grid dividingw=Nτ×NυA grid, the interior point target of grid (i, j) Corresponding time shift is τi=(i-1) × Δ τ, Doppler shift υj=(j-1) × Δ υ, echo-signal areLater, Sparse transformation matrix Psi, formula used can be obtained are as follows:
Determine the coefficient representation of target echo signal, formula used are as follows:
X=Psi*xp
In formula, xpIt is the N after the rarefaction representation by echo-signalw× 1 dimension matrix, and
From the above equation, we can see that xpIn only M nonzero value and M < < Nw- M, so xpIt is sparse, and xpDilution is M.
Step 2 selects random gaussian matrix as observing matrix, using each row vector in observing matrix respectively to mesh Mark echo-signal is projected, and the partial information of signal is obtained, and carries out dimensionality reduction observation to echo-signal；In conjunction with Fig. 1, the step is true Determining observation matrix Phi is that Mwid × Nwid ties up random gaussian matrix, formula used are as follows:
Phi=sqrt (1/Mwid) * randn (Mwid, Nwid)
In formula, Nwid is the length of target echo signal sampling, and Mwid indicates the number of observation.Echo-signal is carried out Dimensionality reduction observation, formula used are as follows:
Y=Phi*x
In formula, y is observation, and dimension is the matrix of Mwid × 1.According to compressive sensing theory, if the Mwid chosen meets Mwid >=c × M × lg (Nwid/M) (c is constant) then can accurately reconstruct original signal from observed value y with high probability.
Step 3, using the rarefaction representation of target echo signal as optimized variable, establish convex Optimized model and solve, reconstruct dilute Dredge the globally optimal solution for indicating signal；The step is established convex Optimized model and is solved, and the globally optimal solution of convex Optimized model is obtained. Obtain rarefaction representation signal xp0 norm (number of non-zero value) it is minimum, but 0 norm optimization's problem is difficult to solve, true Prove, solve 1 norm can also approach with effect as above, so with xp1 norm be optimized variable, establish convex optimization Model:
min imize||xp||1
Subject to y=Phi*Psi*xp
Obtain xpGlobally optimal solution, can be obtained according to delay-Doppler domain grid multiple target time delay and Doppler frequency Partially.
Step 4 is obtained by the globally optimal solution of the rarefaction representation signal in the sparse matrix and step 3 that construct in step 1 The time delay and Doppler shift of each target.
Further detailed description is done to the present invention below with reference to embodiment.
Embodiment
The present invention is verified using following parameter:
Whole system composition such as Fig. 1, system are ground radar target detection, and detecting distance is 10km~12km, detection speed Degree is 0~60m/s.Distance resolution is 40m, velocity resolution 1m/s, Nτ=40, Nυ=40.Three targets, distance are set For [10100,11000,11600], speed is [10,20,30].
The echo-signal x of multiple target is obtained according to step 1 first, sparse transformation matrix Psi is designed, so that x is sparse It is sparse under transformation matrix Psi.According to step 2, chooses Mwid=500 and determine 500 × 1067 dimension random gaussian matrixes, obtain 500 observations of the target echo signal that length is 1067.According to step 3 with xp1 norm be optimized variable, establish convex Optimized model:
min imize||xp||1
Subject to y=Phi*Psi*xp
Obtain the x that length is 2400pIt is non-zero in the 130th, 1220,1,950 three point value, corresponding delay-Doppler domain grid On (3,11), (21,21), (33,31), the position and speeds of corresponding three targets is respectively [10100m, 10m/s], [11000m, 20m/s], [11600m, 30m/s], object detection results are correct.
Fig. 3 is sparse signal representation form x in examplepOutput as a result, Fig. 4 be original object echo-signal with reconstruct Target echo signal comparison diagram.What three targets can will be apparent that as seen from the figure detected, and the multiple target reconstructed is returned Wave signal results are correct.
From the foregoing, it will be observed that ground radar multi-target detection method provided by the invention is obtained with the network analysis of delay-Doppler domain To sparse transformation matrix, the time delay and Doppler shift of target echo signal can be directly obtained based on convex optimal reconfiguration algorithm, Without carrying out the normal radars signal processings such as pulse compression, Sidelobe Suppression, moving-target detection to echo-signal, can effectively drop Low calculation amount reduces leakage error, improves measurement accuracy.The reconstruct of echo signal uses convex optimization method, with conventional orthogonal It is compared with method, can correctly detect multiple targets in the case where unknown object number.

Claims (4)

1.一种基于压缩感知的地面雷达多目标检测方法，其特征在于，包括以下步骤：1. a ground radar multi-target detection method based on compressed sensing, is characterized in that, comprises the following steps: 步骤1、对回波信号进行稀疏表示，具体是利用稀疏变换矩阵对回波信号进行稀疏表示,具体为：Step 1. Perform sparse representation on the echo signal, specifically using a sparse transformation matrix to sparsely represent the echo signal, specifically: 步骤1-1、确定M个目标信号的回波信号x，所用公式为：Step 1-1. Determine the echo signals x of the M target signals, and the formula used is: 式中，τm和υm分别为第m个目标的时移和多普勒频偏，为第m个目标的回波信号；where τ m and υ m are the time shift and Doppler frequency offset of the m-th target, respectively, is the echo signal of the mth target; 步骤1-2、将时延-多普勒域划分为Nw＝Nτ×Nυ个网格，时间分辨率为Δτ，多普勒分辨率为Δυ，从而确定稀疏变换矩阵，完成目标回波信号在稀疏变换矩阵上的稀疏表示，所用公式为：Step 1-2. Divide the delay-Doppler domain into N w =N τ ×N υ grids, the time resolution is Δτ, and the Doppler resolution is Δυ, so as to determine the sparse transformation matrix and complete the target return. The sparse representation of the wave signal on the sparse transformation matrix, the formula used is: 式中，Nwid表示目标回波信号采样的长度，为目标(i,j)对应的目标回波信号，此时时移为τi＝(i-1)×Δτ，多普勒频偏为υj＝(j-1)×Δυ；In the formula, Nwid represents the length of the target echo signal sampling, is the target echo signal corresponding to the target (i, j), at this time the time shift is τ i =(i-1)×Δτ, and the Doppler frequency offset is υ j =(j-1)×Δυ; 步骤1-3、确定目标回波信号的系数表示形式，所用公式为：Steps 1-3, determine the coefficient representation of the target echo signal, the formula used is: x＝Psi*xp x = Psi*xp 式中，xp是将回波信号的稀疏表示后的Nw×1维矩阵，且In the formula, x p is the N w ×1-dimensional matrix after the sparse representation of the echo signal, and 则xp中只有M个非零值且M＜＜Nw-M，所以xp是稀疏的；Then there are only M non-zero values in x p and M<<N w -M, so x p is sparse; 步骤2、选择随机高斯矩阵作为观测矩阵，利用观测矩阵中的每个行向量分别对目标回波信号进行投影，获取信号的部分信息，对回波信号进行降维观测；Step 2. Select a random Gaussian matrix as the observation matrix, and use each row vector in the observation matrix to project the target echo signal respectively, obtain part of the information of the signal, and perform dimension reduction observation on the echo signal; 步骤3、以目标回波信号的稀疏表示为优化变量，建立凸优化模型求解，重构出稀疏表示信号的全局最优解；Step 3, taking the sparse representation of the target echo signal as the optimization variable, establishing a convex optimization model to solve, and reconstructing the global optimal solution of the sparse representation signal; 步骤4、由步骤1中构建的稀疏矩阵和步骤3中的稀疏表示信号的全局最优解得到各目标的时延和多普勒频偏。Step 4: Obtain the time delay and Doppler frequency offset of each target from the global optimal solution of the sparse matrix constructed in step 1 and the sparse representation signal in step 3. 2.根据权利要求1所述的基于压缩感知的地面雷达多目标检测方法，其特征在于，步骤2中选择随机高斯矩阵作为观测矩阵Phi，所用公式为：2. the ground radar multi-target detection method based on compressed sensing according to claim 1, is characterized in that, in step 2, selects random Gaussian matrix as observation matrix Phi, and used formula is: Phi＝sqrt(1/Mwid)*randn(Mwid,Nwid)Phi=sqrt(1/Mwid)*randn(Mwid,Nwid) 式中，Nwid表示目标回波信号采样的长度，Mwid表示观测值的个数；对回波信号进行降维观测，所用公式为y＝Phi*x，y为观测值，若选取的Mwid满足Mwid≥c×M×lg(Nwid/M)，则能从观测值y以高概率重构出原始信号，否则不能重构原始信号，其中c为常数。In the formula, Nwid represents the sampling length of the target echo signal, and Mwid represents the number of observation values; for the dimensionality reduction observation of the echo signal, the formula used is y=Phi*x, y is the observation value, if the selected Mwid satisfies Mwid ≥c×M×lg(Nwid/M), the original signal can be reconstructed from the observed value y with high probability, otherwise the original signal cannot be reconstructed, where c is a constant. 3.根据权利要求1所述的基于压缩感知的地面雷达多目标检测方法，其特征在于，步骤3中所述凸优化模型为：3. the ground radar multi-target detection method based on compressed sensing according to claim 1, is characterized in that, the convex optimization model described in step 3 is: minimize||xp||1 minimize||x p || 1 subject to y＝Phi*Psi*xp。subject to y=Phi*Psi*x p . 4.根据权利要求1所述的基于压缩感知的地面雷达多目标检测方法，其特征在于，步骤4由步骤1中构建的稀疏矩阵和步骤3中的稀疏表示信号的全局最优解得到各目标的时延和多普勒频偏，具体是：根据稀疏矩阵Psi和稀疏表示信号的全局最优解xp中绝对值不为零的位置得到各个目标的时移和多普勒频偏。4. The ground radar multi-target detection method based on compressed sensing according to claim 1, wherein in step 4, each target is obtained by the global optimal solution of the sparse matrix constructed in step 1 and the sparse representation signal in step 3 The time delay and Doppler frequency offset of each target are obtained by obtaining the time delay and Doppler frequency offset of each target according to the sparse matrix Psi and the position where the absolute value is not zero in the global optimal solution x p of the sparse representation signal.
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