CN104181531B - A kind of three-dimensional relevance imaging method based on phased-array radar - Google Patents

A kind of three-dimensional relevance imaging method based on phased-array radar Download PDF

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CN104181531B
CN104181531B CN201410416039.1A CN201410416039A CN104181531B CN 104181531 B CN104181531 B CN 104181531B CN 201410416039 A CN201410416039 A CN 201410416039A CN 104181531 B CN104181531 B CN 104181531B
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CN104181531A (en
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李亚超
许然
邢孟道
黄平平
全英汇
章浩波
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    • G—PHYSICS
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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
    • 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
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    • 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
    • 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
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    • 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
    • G01S13/904—SAR modes
    • G01S13/9064—Inverse SAR [ISAR]
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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
    • 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
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Abstract

本发明公开了一种基于相控阵雷达的三维关联成像方法，涉及雷达成像领域，其步骤为：步骤1，划分相控阵雷达天线阵面，相控阵雷达发射机发射线性调频信号，并接收目标散射点的回波信号，设定目标散射点的相移值；步骤2，将距离脉压后的基频回波信号按距离单元划分；步骤3，构建目标散射点的散射系数向量的目标函数；并且在稀疏约束条件下求解目标函数，得到第u个距离单元内的目标散射点的散射系数向量估计值；步骤4，先由第u个距离单元内的目标散射点的散射系数向量估计值形成二维图像，再由所有距离单元的二维图像按照距离单元的顺序排列得到三维图像。本发明实现了对目标的高分辨三维成像。

The invention discloses a three-dimensional correlation imaging method based on a phased array radar, which relates to the field of radar imaging. The steps are as follows: step 1, dividing the phased array radar antenna array, the phased array radar transmitter transmits a chirp signal, and Receive the echo signal of the target scattering point, and set the phase shift value of the target scattering point; step 2, divide the fundamental frequency echo signal after the distance pulse pressure into distance units; step 3, construct the scattering coefficient vector of the target scattering point objective function; and solve the objective function under the sparse constraint condition to obtain the estimated value of the scattering coefficient vector of the target scattering point in the uth distance unit; step 4, firstly by the scattering coefficient vector of the target scattering point in the uth distance unit The estimated values form a two-dimensional image, and then the three-dimensional image is obtained by arranging the two-dimensional images of all the distance units in the order of the distance units. The invention realizes the high-resolution three-dimensional imaging of the target.

Description

一种基于相控阵雷达的三维关联成像方法A 3D correlative imaging method based on phased array radar

技术领域technical field

本发明属于雷达成像技术领域，尤其涉及一种基于相控阵雷达的三维关联成像方法。The invention belongs to the technical field of radar imaging, in particular to a three-dimensional correlation imaging method based on phased array radar.

背景技术Background technique

微波雷达具有全天候、全天时、远距离和大范围观察等特性，可以对目标场景进行高分辨率成像，获取探测信息，在民用和军用领域均发挥着关键的作用。作为主要的二维微波成像方法，上世纪50年代迅速发展起来合成孔径雷达(SAR)成像和逆合成孔径雷达(ISAR)成像是利用载体平台与目标间的相对运动在空间形成合成的阵列流形，能够获取目标在距离-多普勒平面内的散射分布信息，即二维雷达图像，但图像存在几何失真并缺失了一维信息，对目标特性的测量造成很大的障碍。因此，高分辨三维成像是雷达成像领域的一个重要研究方向。Microwave radar has the characteristics of all-weather, all-time, long-distance and large-scale observation. It can perform high-resolution imaging of target scenes and obtain detection information. It plays a key role in both civilian and military fields. As the main two-dimensional microwave imaging methods, synthetic aperture radar (SAR) imaging and inverse synthetic aperture radar (ISAR) imaging were rapidly developed in the 1950s, which use the relative motion between the carrier platform and the target to form a synthetic array manifold in space. , can obtain the scattering distribution information of the target in the range-Doppler plane, that is, the two-dimensional radar image, but the image has geometric distortion and lacks one-dimensional information, which causes great obstacles to the measurement of the target characteristics. Therefore, high-resolution 3D imaging is an important research direction in the field of radar imaging.

大的天线孔径是实现高分辨微波雷达成像的直接途径。按照大孔径的实现方式，三维微波成像主要分为两类，一类是基于合成阵列，另一类是基于实孔径三维成像。前者利用单天线或线性阵列的扫描形成二维合成孔径，获得跨距离平面的二维分辨能力，再结合距离向脉冲压缩技术获得全三维目标分布图像，这类方法需要平台的运动，应用场合有限，数据获取实时性较差，而且信号处理难度较高；而后者依赖阵列天线形成的窄波束在空间进行扫描得到三维图像，其分辨率取决于波束宽度，即天线的真实的物理孔径大小，要获得高分辨率图像，需要增大阵列孔径，令系统复杂度和成本都急剧增加，所以在大多数应用场合中，由于天线体积和成本的限制，该方法分辨率不高。Large antenna aperture is a direct way to realize high-resolution microwave radar imaging. According to the realization of large aperture, 3D microwave imaging is mainly divided into two categories, one is based on synthetic array, and the other is based on real aperture 3D imaging. The former uses single-antenna or linear array scanning to form a two-dimensional synthetic aperture to obtain two-dimensional resolution capabilities across the distance plane, and then combines range-to-pulse compression technology to obtain a full three-dimensional target distribution image. This type of method requires platform movement and has limited applications. , the real-time data acquisition is poor, and the signal processing is difficult; while the latter relies on the narrow beam formed by the array antenna to scan in space to obtain a three-dimensional image, and its resolution depends on the beam width, that is, the real physical aperture size of the antenna. Obtaining high-resolution images requires increasing the aperture of the array, which increases the complexity and cost of the system dramatically. Therefore, in most applications, the resolution of this method is not high due to the limitations of antenna volume and cost.

发明内容Contents of the invention

本发明的目的在于克服上述已有技术的不足，提出一种基于相控阵雷达的三维关联成像方法，通过下面的仿真可以看出该成像方法能够突破常规实孔径阵列雷达三维成像的方位分辨力的限制，从而实现距离向、方位向和俯仰向高分辨三维成像。The purpose of the present invention is to overcome the deficiencies of the above-mentioned prior art, and propose a three-dimensional correlation imaging method based on phased array radar. It can be seen that the imaging method can break through the azimuth resolution of conventional real-aperture array radar three-dimensional imaging through the following simulation , so as to achieve high-resolution three-dimensional imaging in the range, azimuth and elevation directions.

为达到上述目的，本发明采用以下技术方案予以实现。In order to achieve the above object, the present invention adopts the following technical solutions to achieve.

一种基于相控阵雷达的三维关联成像方法，其特征在于，包括以下步骤：A three-dimensional correlation imaging method based on phased array radar, is characterized in that, comprises the following steps:

步骤1，将相控阵雷达天线阵面划分为M×N个子阵，每个子阵有K×L个阵元，总共有M×N×K×L个阵元，阵元按矩形均匀分布，相控阵雷达发射机在第q个脉冲下将线性调频信号s0q发射到成像场景中，并接收第q个脉冲下的含P个目标散射点的回波信号，将排列在相控阵雷达阵面的第m行n列的子阵中的第k行l列的阵元在第q个脉冲下的第p个目标散射点处的相移值设定为q＝1,2,...,Q,Q脉冲总个数,m＝1,2,3,...,M，M为天线阵面行数，n＝1,2,3,...,N，N为天线阵面列数，l＝1,2,3,...,L，L为子阵的列数，k＝1,2,3,...,K，K为子阵的行数；Step 1. Divide the phased array radar antenna array into M×N sub-arrays, each sub-array has K×L array elements, and there are a total of M×N×K×L array elements, and the array elements are uniformly distributed in a rectangle. The phased array radar transmitter transmits the chirp signal s0 q into the imaging scene under the qth pulse, and receives the echo signals containing P target scattering points under the qth pulse, which will be arranged in the phased array radar The phase shift value of the element at the p-th target scattering point under the q-th pulse of the array element in the k-th row and l-column of the sub-array in the m-th row and n-column of the array is set as q=1,2,...,Q, the total number of Q pulses, m=1,2,3,...,M, M is the number of antenna front lines, n=1,2,3,... ., N, N is the number of antenna array columns, l=1,2,3,...,L, L is the number of sub-array columns, k=1,2,3,...,K, K is the number of rows of the subarray;

步骤2，对第q个脉冲下的含P个目标散射点的回波信号进行去载频fc，得到第q个脉冲下的含P个目标散射点的基频回波信号s1q，对基频回波信号s1q进行距离脉压，得到距离脉压后的基频回波信号s2q；再从距离脉压后的基频回波信号s2q中得到第u个距离单元内的含P个目标散射点的回波信号u＝1,2,3...,U，U表示每个脉冲下的距离单元的总个数；Step 2, decarrier frequency f c is performed on the echo signal containing P target scattering points under the qth pulse, and the fundamental frequency echo signal s1 q containing P target scattering points under the qth pulse is obtained. The fundamental frequency echo signal s1 q is subjected to distance pulse pressure to obtain the fundamental frequency echo signal s2 q after the distance pulse pressure; then the content of the uth distance unit is obtained from the fundamental frequency echo signal s2 q after the distance pulse pressure Echo signals of P target scattering points u=1,2,3...,U, U represents the total number of distance units under each pulse;

步骤3，利用相控阵雷达阵面的第m行n列的子阵中的第k行l列的阵元在第q个脉冲下的每个目标散射点处的相移值得到Q个脉冲下的P个目标散射点的天线辐射方向性增益矩阵F，F维数Q×P；再利用天线辐射方向性增益矩阵F构建Q个脉冲下的第u个距离单元内的含P个目标散射点的回波信号su；再利用天线辐射方向性增益矩阵F和Q个脉冲下的第u个距离单元内的含P个目标散射点的回波信号su构建第u个距离单元内的P个目标散射点的散射系数向量σu的目标函数；并且在稀疏约束条件下求解目标函数得到第u个距离单元内的P个目标散射点的散射系数向量估计值 Step 3, using the phase shift value of the array element in the kth row and l column of the subarray of the mth row and nth column of the phased array radar array at each target scattering point under the qth pulse to obtain Q pulses The antenna radiation directional gain matrix F of the P target scattering points below, the dimension of F is Q×P; and then use the antenna radiation directional gain matrix F to construct the scattering points containing P targets in the u-th distance unit under Q pulses The echo signal s u of point ; and then use the antenna radiation directivity gain matrix F and the echo signal s u containing P target scattering points in the uth range unit under the Q pulse to construct the uth distance unit The objective function of the scattering coefficient vector σ u of the P target scattering points; and the objective function is solved under the sparse constraint condition to obtain the estimated value of the scattering coefficient vector of the P target scattering points in the u-th distance unit

步骤4，先由第u个距离单元内的P个目标散射点的散射系数向量估计值形成二维图像Zu，再由U个距离单元的二维图像Z1,Z2,...Zu...,ZU按照距离单元的顺序排列起来得到三维图像Z＝[Z1,Z2,...Zu...,ZU]。Step 4, first estimate the value of the scattering coefficient vector from the P target scattering points in the u-th distance unit Form a two-dimensional image Z u , and then arrange the two-dimensional images Z 1 , Z 2 ,...Z u ...,Z U of U distance units in the order of distance units to obtain a three-dimensional image Z=[Z 1 , Z 2 ,...Z u ...,Z U ].

上述技术方案的特点和进一步改进在于：The characteristics and further improvement of the above-mentioned technical scheme are:

(1)步骤1包括以下子步骤：(1) Step 1 includes the following sub-steps:

1a)将相控阵雷达天线阵面划分为M×N个子阵，每个子阵有K×L个阵元，总共有M×N×K×L个阵元，阵元按矩形均匀分，相控阵雷达发射机将第q个脉冲下的线性调频信号发射到成像场景中，并接收第q个脉冲下的含P个目标散射点的回波信号，式中是距离向快时间，为距离向窗函数，r是距离向调频率，fc是雷达发射信号的载频，tq＝qTr是第q个脉冲的慢时间，Tr是脉冲重复周期，q＝1,2,...,Q表示脉冲序号，Q表示雷达发射的总的脉冲个数；1a) Divide the phased array radar antenna array into M×N sub-arrays, each sub-array has K×L array elements, there are a total of M×N×K×L array elements, the array elements are evenly divided into rectangles, phase The control array radar transmitter converts the chirp signal under the qth pulse Transmit into the imaging scene, and receive the echo signal containing P target scattering points under the qth pulse, where is the distance-fast time, is the range window function, r is the range modulation frequency, f c is the carrier frequency of the radar transmitting signal, t q =qT r is the slow time of the qth pulse, T r is the pulse repetition period, q=1,2, ..., Q represents the pulse sequence number, Q represents the total number of pulses emitted by the radar;

1b)将排列在相控阵雷达阵面的第m行n列的子阵中的第k行l列的阵元在第q个脉冲下的第p个目标散射点处的相移值设定为：1b) The phase shift value of the array elements in the k-th row and l-column in the sub-array of the m-th row and n-column of the phased array radar array at the p-th target scattering point under the q-th pulse set as:

其中：in:

Δφx＝γdxsinθpcosβp (2)Δφ x = γd x sinθ p cosβ p (2)

Δφy＝γdysinβp (3)Δφ y = γd y sin β p (3)

式中Δφx为相邻阵元在X方向上的空间相位差，Δφy为相邻阵元在Y方向上的空间相位差；dx是X方向上的阵元间距，dy是Y方向上的阵元间距，X方向为雷达天线阵面的水平方向，Y方向为雷达天线阵面的垂直方向，k是阵元在子阵内X方向上的编号，k＝1,2,3...,K，l是阵元在子阵内Y方向上的编号，l＝1,2,3...,L，m是该阵元所在的子阵在X方向上的编号，m＝1,2,3...,M，n是该阵元所在的子阵在Y方向上的编号，n＝1,2,3...,N，p＝1,2,3...,P，P表示场景中目标散射点的总个数，θp表示第p个目标散射点的方位角，βp表示第p个目标散射点的俯仰角，γ＝2π/λ是自由空间波数，λ是雷达工作波长，Δφm,n(tq)是子阵间额外叠加的随机相移，且每次脉冲时间内都不变，而脉冲间都是随机变化的，即Δφm,n(tq)是独立同分布的随机过程函数且Δφm,n(tq)∈[-π,π]。In the formula, Δφ x is the spatial phase difference of adjacent array elements in the X direction, Δφ y is the spatial phase difference of adjacent array elements in the Y direction; d x is the array element spacing in the X direction, d y is the Y direction The array element spacing above, the X direction is the horizontal direction of the radar antenna front, the Y direction is the vertical direction of the radar antenna front, k is the number of the array elements in the X direction in the sub-array, k=1,2,3. .., K, l is the number of the array element in the Y direction of the sub-array, l=1,2,3...,L, m is the number of the sub-array where the array element is located in the X direction, m= 1,2,3...,M, n is the number in the Y direction of the sub-array where the array element is located, n=1,2,3...,N, p=1,2,3... , P, P represents the total number of target scattering points in the scene, θ p represents the azimuth angle of the p-th target scattering point, β p represents the pitch angle of the p-th target scattering point, γ=2π/λ is the free space wave number , λ is the working wavelength of the radar, Δφ m,n (t q ) is the additional superimposed random phase shift between the sub-arrays, and it remains unchanged in each pulse time, while the pulses are randomly changed, that is, Δφ m,n (t q ) is an independent and identically distributed stochastic process function and Δφ m,n (t q )∈[-π,π].

(2)步骤2包括以下子步骤：(2) Step 2 includes the following sub-steps:

2a)雷达对第q个脉冲下的含P个目标散射点的回波信号进行去载频fc，得到第q个脉冲下的P个目标散射点的基频回波信号s1q，即：2a) The radar removes the carrier frequency f c from the echo signals containing P target scattering points under the qth pulse, and obtains the fundamental frequency echo signals s1 q of P target scattering points under the qth pulse, namely:

sthe s 11 qq == ΣΣ pp == 11 PP σσ pp Ff qq pp aa rr (( tt ^^ -- 22 RR pp cc )) expexp [[ jπrjπr (( tt ^^ -- 22 RR pp cc )) 22 ]] expexp (( -- jj 44 ππ λλ RR pp )) -- -- -- (( 44 ))

式中Rp是雷达到第p个目标散射点的距离，σp是第p个目标散射点的散射系数，c是光速，表示第q个脉冲下的第p个目标散射点处的天线辐射方向性增益，表示第p个目标散射点相对雷达的延时；where R p is the distance from the radar to the p-th target scattering point, σ p is the scattering coefficient of the p-th target scattering point, c is the speed of light, Indicates the antenna radiation directivity gain at the pth target scattering point under the qth pulse, Indicates the delay of the pth target scattering point relative to the radar;

2b)用匹配滤波函数对第q个脉冲下的P个目标散射点的基频回波信号s1q进行距离脉压，得到距离脉压后的基频回波信号s2q：2b) Use the matched filter function Perform distance pulse pressure on the fundamental frequency echo signals s1 q of P target scattering points under the qth pulse to obtain the fundamental frequency echo signal s2 q after the distance pulse pressure:

sthe s 22 qq == IFFTIFFT {{ FFTFFT [[ sthe s 11 qq ]] FFTFFT [[ sthe s rr ]] }} == ΣΣ pp == 11 PP σσ pp Ff qq pp sinsin cc [[ ΔΔ ff rr (( tt ^^ -- 22 RR pp cc )) ]] expexp (( -- jj 44 ππ λλ RR pp )) -- -- -- (( 55 ))

式中Δfr为雷达发射线性调频信号的频带的带宽；where Δf r is the bandwidth of the frequency band where the radar transmits the chirp signal;

2c)将距离脉压后的基频回波信号s2q简化后得到第q个脉冲下的含P个目标散射点的回波信号将简化后的回波信号划分为U个距离单元，则在第q个脉冲下第u个距离单元内的P个目标散射点的回波信号表示为：2c) Simplify the fundamental frequency echo signal s2 q after the distance pulse pressure to obtain the echo signal containing P target scattering points under the qth pulse Divide the simplified echo signal into U range units, then the echo signals of P target scattering points in the uth range unit under the qth pulse Expressed as:

sthe s qq uu == ΣΣ pp == 11 PP σσ pp uu Ff qq pp -- -- -- (( 66 ))

式中表示第u个距离单元内的第p个目标散射点的散射系数，其中u＝1,2,3...,U，U表示每个脉冲下的距离单元的总个数。In the formula Indicates the scattering coefficient of the p-th target scattering point in the u-th range unit, where u=1, 2, 3..., U, and U indicates the total number of range units under each pulse.

(3)步骤3包括以下子步骤：(3) Step 3 includes the following sub-steps:

3a)将相控阵雷达阵面第m行n列的子阵中的第k行l列的阵元在第q个脉冲下的第p个目标散射点处的相移值的表达式代入天线辐射方向性增益函数，从而得到在第q个脉冲下的第p个目标散射点的天线辐射方向性增益 3a) The phase shift value of the array element in the k-th row and l-column in the sub-array of the m-th row and n-column of the phased array radar array at the p-th target scattering point under the q-th pulse The expression of is substituted into the antenna radiation directivity gain function, so as to obtain the antenna radiation directivity gain of the pth target scattering point under the qth pulse

式中dx是X方向上的阵元间距，dy是Y方向上的阵元间距，X方向为雷达天线阵面的水平方向，Y方向为雷达天线阵面的垂直方向，p＝1,2,3...,P，P表示场景中目标散射点的总个数，θp表示第p个目标散射点的方位角，βp表示第p个目标散射点的俯仰角，k是阵元在子阵内X方向上的编号，k＝1,2,3...,K，γ＝2π/λ是自由空间波数，λ是雷达工作波长，l是阵元在子阵内Y方向上的编号，l＝1,2,3...,L，m是该阵元所在的子阵在X方向上的编号，m＝1,2,3...,M，n是该阵元所在的子阵在Y方向上的编号，n＝1,2,3...,N，Δφm,n(tq)是子阵间额外叠加的随机相移，且每次脉冲时间内都不变，而脉冲间都是随机变化的，即Δφm,n(tq)是独立同分布的随机过程函数且Δφm,n(tq)∈[-π,π]；In the formula, d x is the array element spacing in the X direction, d y is the array element spacing in the Y direction, the X direction is the horizontal direction of the radar antenna front, and the Y direction is the vertical direction of the radar antenna front, p=1, 2,3...,P, P represents the total number of target scattering points in the scene, θ p represents the azimuth angle of the p-th target scattering point, β p represents the elevation angle of the p-th target scattering point, k is the array The number of the element in the X direction in the subarray, k=1,2,3...,K, γ=2π/λ is the free space wave number, λ is the radar operating wavelength, l is the Y direction of the array element in the subarray The number on the top, l=1,2,3...,L, m is the number of the sub-array in the X direction where the array element is located, m=1,2,3...,M, n is the number of the array The number of the sub-array where the element is located in the Y direction, n=1,2,3...,N, Δφ m,n (t q ) is the additional superimposed random phase shift between sub-arrays, and each pulse time are all unchanged, while the pulses are randomly changed, that is, Δφ m,n (t q ) is an independent and identically distributed random process function and Δφ m,n (t q )∈[-π,π];

进而得到Q个脉冲下的P个目标散射点的天线辐射方向性增益矩阵F，即：Then the antenna radiation directivity gain matrix F of P target scattering points under Q pulses is obtained, namely:

将Q个脉冲下第u个距离单元内的P个目标散射点的回波向量su表示为：su＝Fσu；其中表示Q个脉冲下第u个距离单元内的P个目标散射点的回波向量，表示第u个距离单元内的P个目标散射点的散射系数向量；Express the echo vector s u of P target scattering points in the u-th distance unit under Q pulses as: s u =Fσ u ; where Indicates the echo vectors of P target scattering points in the u-th range unit under Q pulses, Represent the scattering coefficient vector of the P target scattering points in the uth distance unit;

3b)利用Q个脉冲下的第u个距离单元内的P个目标散射点的回波向量su和Q个脉冲下的P个目标散射点的天线辐射方向性增益矩阵F来构造第u个距离单元内的P个目标散射点的散射系数向量σu的目标函数J(σu)：3b) Utilize the echo vector u of the P target scattering points in the u-th distance unit under the Q pulses and the antenna radiation directivity gain matrix F of the P target scattering points under the Q pulses to construct the u-th The objective function J(σ u ) of the scattering coefficient vector σ u of the P target scattering points in the distance unit:

JJ (( σσ uu )) == || || sthe s uu -- Ff σσ uu || || 22 22 ++ μμ || || σσ uu || || 11 -- -- -- (( 99 ))

式中||·||2是L2范数运算符，||·||1是L1范数运算符，μ是正则化参数；where ||·|| 2 is the L 2 norm operator, ||·|| 1 is the L 1 norm operator, μ is the regularization parameter;

3c)构造第u个距离单元内的P个目标散射点的散射系数向量σu的目标函数J(σu)在稀疏约束条件μ||σu||1下的方程为：3c) The equation of constructing the objective function J(σ u ) of the scattering coefficient vector σ u of the P target scattering points in the u-th distance unit under the sparse constraint condition μ||σ u || 1 is:

minmin || || sthe s uu -- Ff σσ uu || || 22 22 ++ μμ || || σσ uu || || 11 sthe s .. tt .. μμ || || σσ uu || || 11 -- -- -- (( 1010 ))

求在稀疏约束条件μ||σu||1下的方程得到第u个距离单元内的P个目标散射点的散射系数向量估计值为：Find the equation under the sparse constraint condition μ||σ u || 1 to obtain the estimated value of the scattering coefficient vector of the P target scattering points in the uth distance unit for:

σσ ^^ uu == argarg minmin J J (( σσ uu )) == [[ σσ ^^ 11 uu ,, σσ ^^ 22 uu ,, .. .. .. σσ ^^ pp uu .. .. .. ,, σσ ^^ PP uu ]] TT -- -- -- (( 1111 ))

式中argmin是最小化运算符，表示第u个距离单元内的P个目标散射点的散射系数向量的估计值，表示第u个距离单元内的第p个目标散射点的散射系数的估计值。where argmin is the minimization operator, Represents the estimated value of the scattering coefficient vector of P target scattering points in the u-th distance unit, Indicates the estimated value of the scattering coefficient of the p-th target scattering point within the u-th range cell.

(4)步骤4包括以下子步骤：(4) Step 4 includes the following sub-steps:

4a)建立以目标散射点的方位角度为横坐标、以目标散射点的俯仰角度为纵坐标的坐标系，在坐标系中，选择放置第u个距离单元内的第p个目标散射点的散射系数估计值的点，该点的横坐标等于第p个目标散射点的方位角度θp，该点的纵坐标等于第p个目标散射点的俯仰角度βp；进而得到第u个距离单元内的P个目标散射点的散射系数估计值形成的二维图像Zu；4a) Establish a coordinate system with the azimuth angle of the target scatter point as the abscissa and the pitch angle of the target scatter point as the ordinate. In the coordinate system, select the scattering point of the p-th target scatter point in the u-th distance unit. coefficient estimates , the abscissa of this point is equal to the azimuth angle θ p of the p-th target scattering point, and the ordinate of this point is equal to the pitch angle β p of the p-th target scattering point; and then P in the u-th distance unit is obtained Scatter coefficient estimates for target scatter points The formed two-dimensional image Z u ;

4b)令u从1至U进行遍历，重复步骤2、步骤3和步骤4a)，得到U个距离单元的二维图像Z1,Z2,...Zu...,ZU，将U个距离单元的二维图像Z1,Z2,...Zu...,ZU按照距离单元的顺序排列起来，最终得到场景的三维图像Z＝[Z1,Z2,...Zu...,ZU]。4b) Let u traverse from 1 to U, repeat step 2, step 3 and step 4a), to obtain two-dimensional images Z 1 , Z 2 ,...Z u ...,Z U of U distance units, and set The two-dimensional images Z 1 , Z 2 ,...Z u ...,Z U of U distance units are arranged in the order of the distance units, and finally the three-dimensional image of the scene Z=[Z 1 ,Z 2 ,.. .Zu ..., Zu ].

与现有技术相比，本发明具有突出的实质性特点和显著的进步。本发明与现有方法相比，具有以下优点：Compared with the prior art, the present invention has outstanding substantive features and remarkable progress. Compared with existing methods, the present invention has the following advantages:

1、本发明采用二维相控阵雷达，但与常规的扫描三维成像方法相比，通过对相控阵阵元进行反馈相移值并在空间形成时空随机辐射场，利用辐射分布方向图与散射回波的关联稀疏优化处理对目标散射信息进行提取，能够突破实孔径阵列理论分辨率的极限，实现距离向、方位向和俯仰向高分辨三维成像，并且只需要比场景单元数更少的采样；1. The present invention adopts a two-dimensional phased array radar, but compared with the conventional scanning three-dimensional imaging method, by feeding back the phase shift value to the phased array element and forming a space-time random radiation field in space, the radiation distribution pattern and the The associated sparse optimization processing of scattered echoes extracts the scattering information of the target, which can break through the limit of the theoretical resolution of the real aperture array and realize high-resolution three-dimensional imaging in the range direction, azimuth direction and elevation direction, and only requires fewer than the number of scene units. sampling;

2、本发明利用宽带的线性调频信号的脉冲压缩技术，获得距离向的高分辨率，结合关联处理技术可以实现三维成像，比现有的层析技术实时性更强；2. The present invention utilizes the pulse compression technology of the broadband chirp signal to obtain high resolution in the range direction, combined with the correlation processing technology to realize three-dimensional imaging, which is more real-time than the existing tomography technology;

3、本发明不依赖雷达载体和目标的相对运动而形成的合成孔径，可以根据应用需求灵活地调整波束指向角和照射范围，实现多视角下的三维成像，因而应用场合更广，既适用于运动平台，也适用于静止平台，并且数据采集和信号处理难度都较低。3. The invention does not rely on the synthetic aperture formed by the relative movement of the radar carrier and the target, and can flexibly adjust the beam pointing angle and irradiation range according to the application requirements, and realize three-dimensional imaging under multiple viewing angles, so the application occasions are wider, and it is suitable for both The motion platform is also suitable for the stationary platform, and the difficulty of data acquisition and signal processing is relatively low.

附图说明Description of drawings

图1是本发明的方案流程图；Fig. 1 is a scheme flowchart of the present invention;

图2是本发明建立的雷达工作坐标系图；在图中取场景平面中的场景中心点为坐标零点O，X轴是场景平面的水平方向，Y轴是场景平面的垂直方向，雷达法线方向作为Z轴；Fig. 2 is the radar working coordinate system diagram that the present invention establishes; Get the scene center point in the scene plane as coordinate zero point O in the figure, X-axis is the horizontal direction of scene plane, Y-axis is the vertical direction of scene plane, radar normal direction as the Z axis;

图3是本发明采用的天线阵元排布示意图；在图中取左下角的第一个阵元为坐标零点O，X方向为雷达天线阵面的水平方向，Y方向为雷达天线阵面的垂直方向，垂直于雷达天线阵面的法线方向作为Z方向；Fig. 3 is the antenna array element layout schematic diagram that the present invention adopts; Get the first array element of lower left corner in the figure and be coordinate zero point O, X direction is the horizontal direction of radar antenna front, and Y direction is the direction of radar antenna front Vertical direction, the normal direction perpendicular to the radar antenna front is taken as the Z direction;

图4是本发明仿真点目标分布图；图中X轴是雷达相对目标的方位向，Y轴是雷达相对目标的俯仰向，Z轴是雷达相对目标的距离向；Fig. 4 is the simulation point target distribution diagram of the present invention; Among the figure, the X-axis is the azimuth direction of the radar relative to the target, the Y-axis is the pitch direction of the radar relative to the target, and the Z-axis is the distance direction of the radar relative to the target;

图5是本发明产生的二维天线辐射方向性增益图；图中横坐标表示方位角度，纵坐标表示俯仰角度；Fig. 5 is the two-dimensional antenna radiation directivity gain diagram that the present invention produces; Among the figure, the abscissa represents the azimuth angle, and the ordinate represents the pitch angle;

图6是本发明625次回波的三维关联成像结果图；图中X轴是雷达相对目标的方位向，Y轴是雷达相对目标的俯仰向，Z轴是雷达相对目标的距离向；Fig. 6 is the three-dimensional correlative imaging result diagram of 625 echoes of the present invention; among the figure, the X-axis is the azimuth direction of the radar relative to the target, the Y-axis is the pitch direction of the radar relative to the target, and the Z-axis is the distance direction of the radar relative to the target;

图7是本发明80次回波的三维关联成像结果图。图中X轴是雷达相对目标的方位向，Y轴是雷达相对目标的俯仰向，Z轴是雷达相对目标的距离向。Fig. 7 is a three-dimensional correlative imaging result diagram of 80 echoes in the present invention. In the figure, the X axis is the azimuth direction of the radar relative to the target, the Y axis is the pitch direction of the radar relative to the target, and the Z axis is the distance direction of the radar relative to the target.

具体实施方式detailed description

参照本发明如图1所示的方案流程图，说明本发明的一种基于相控阵雷达的三维关联成像方法。具体实施步骤如下：Referring to the scheme flow chart of the present invention shown in FIG. 1 , a three-dimensional correlation imaging method based on phased array radar of the present invention is described. The specific implementation steps are as follows:

步骤1，将相控阵雷达天线阵面划分为M×N个子阵，每个子阵有K×L个阵元，总共有M×N×K×L个阵元，阵元按矩形均匀分布，相控阵雷达发射机在第q个脉冲下将线性调频信号s0q发射到成像场景中，并接收第q个脉冲下的含P个目标散射点的回波信号，将排列在相控阵雷达阵面的第m行n列的子阵中的第k行l列的阵元在第q个脉冲下的第p个目标散射点处的相移值设定为 Step 1. Divide the phased array radar antenna array into M×N sub-arrays, each sub-array has K×L array elements, and there are a total of M×N×K×L array elements, and the array elements are uniformly distributed in a rectangle. The phased array radar transmitter transmits the chirp signal s0 q into the imaging scene under the qth pulse, and receives the echo signals containing P target scattering points under the qth pulse, which will be arranged in the phased array radar The phase shift value of the element at the p-th target scattering point under the q-th pulse of the array element in the k-th row and l-column of the sub-array in the m-th row and n-column of the array is set as

1a)如图中3所示，将相控阵雷达天线阵面划分为M×N个子阵，每个子阵有K×L个阵元，总共有M×N×K×L个阵元，阵元按矩形均匀分。相控阵雷达发射机将第q个脉冲下的线性调频信号发射到成像场景中，并接收第q个脉冲下的含P个目标散射点的回波信号，式中是距离向快时间，为距离向窗函数，r是距离向调频率，fc是雷达发射信号的载频，tq＝qTr是第q个脉冲的慢时间，Tr是脉冲重复周期，q＝1,2,...,Q表示脉冲序号，Q表示雷达发射的总的脉冲个数。1a) As shown in Figure 3, the phased array radar antenna is divided into M×N sub-arrays, each sub-array has K×L array elements, and there are a total of M×N×K×L array elements. Elements are evenly divided into rectangles. The phased array radar transmitter converts the chirp signal under the qth pulse Transmit into the imaging scene, and receive the echo signal containing P target scattering points under the qth pulse, where is the distance-fast time, is the range window function, r is the range modulation frequency, f c is the carrier frequency of the radar transmitting signal, t q =qT r is the slow time of the qth pulse, T r is the pulse repetition period, q=1,2, ..., Q represents the pulse sequence number, and Q represents the total number of pulses emitted by the radar.

1b)将排列在相控阵雷达阵面的第m行n列的子阵中的第k行l列的阵元在第q个脉冲下的第p个目标散射点处的相移值设定为：1b) The phase shift value of the array elements in the k-th row and l-column in the sub-array of the m-th row and n-column of the phased array radar array at the p-th target scattering point under the q-th pulse set as:

其中：in:

Δφx＝γdxsinθpcosβp (2)Δφ x = γd x sinθ p cosβ p (2)

Δφy＝γdysinβp (3)Δφ y = γd y sin β p (3)

式中Δφx为相邻阵元在X方向上的空间相位差，Δφy为相邻阵元在Y方向上的空间相位差；dx是X方向上的阵元间距，dy是Y方向上的阵元间距。X方向为雷达天线阵面的水平方向，Y方向为雷达天线阵面的垂直方向。p＝1,2,3...,P，P表示场景中目标散射点的总个数。θp表示第p个目标散射点的方位角，βp表示第p个目标散射点的俯仰角，k是阵元在子阵内X方向上的编号，k＝1,2,3...,K，γ＝2π/λ是自由空间波数，λ是雷达工作波长，l是阵元在子阵内Y方向上的编号，l＝1,2,3...,L。m是该阵元所在的子阵在X方向上的编号，m＝1,2,3...,M，n是该阵元所在的子阵在Y方向上的编号，n＝1,2,3...,N，Δφm,n(tq)是子阵间额外叠加的随机相移，且每次脉冲时间内都不变，而脉冲间都是随机变化的，即Δφm,n(tq)是独立同分布的随机过程函数且Δφm,n(tq)∈[-π,π]。In the formula, Δφ x is the spatial phase difference of adjacent array elements in the X direction, Δφ y is the spatial phase difference of adjacent array elements in the Y direction; d x is the array element spacing in the X direction, d y is the Y direction The element spacing on . The X direction is the horizontal direction of the radar antenna front, and the Y direction is the vertical direction of the radar antenna front. p=1, 2, 3..., P, where P represents the total number of target scattering points in the scene. θ p represents the azimuth angle of the p-th target scattering point, β p represents the elevation angle of the p-th target scattering point, k is the number of the array element in the X direction in the sub-array, k=1,2,3... , K, γ=2π/λ is the free space wave number, λ is the radar operating wavelength, l is the number of the array element in the Y direction in the sub-array, l=1,2,3...,L. m is the number of the sub-array where the array element is located in the X direction, m=1,2,3...,M, n is the number of the sub-array where the array element is located in the Y direction, n=1,2 ,3...,N, Δφ m,n (t q ) is the additional superimposed random phase shift between sub-arrays, and it remains unchanged in each pulse time, while the pulses are all randomly changed, that is, Δφ m, n (t q ) is an independent and identically distributed stochastic process function and Δφ m,n (t q )∈[-π,π].

相控阵雷达发射机将线性调频信号发射到成像场景中，取场景平面中的场景中心点为坐标零点O，并以雷达法线方向作为Z轴，在场景平面内建立XOY轴，建立的雷达工作坐标系如图2所示，以场景平面内的点a为例，a点投影到X轴为b点，则相控阵雷达和b点的连线与Z轴的夹角就是方位角θ，相控阵雷达和a点的连线、与相控阵雷达和b点的连线的夹角就是俯仰角β。The phased array radar transmitter transmits the chirp signal into the imaging scene, takes the center point of the scene in the scene plane as the coordinate zero point O, and takes the normal direction of the radar as the Z axis, establishes the XOY axis in the scene plane, and the established radar The working coordinate system is shown in Figure 2. Taking point a in the scene plane as an example, point a is projected onto the X axis as point b, then the angle between the phased array radar and point b and the Z axis is the azimuth θ , the angle between the line connecting the phased array radar and point a, and the line connecting the phased array radar and point b is the pitch angle β.

步骤2，对第q个脉冲下的含P个目标散射点的回波信号进行去载频fc，得到第q个脉冲下的P个目标散射点的基频回波信号s1q，对基频回波信号s1q进行距离脉压，得到距离脉压后的基频回波信号s2q；再从距离脉压后的基频回波信号s2q中得到第u个距离单元内的含P个目标散射点的回波信号 Step 2, decarrier frequency f c is performed on the echo signals containing P target scattering points under the qth pulse, and the fundamental frequency echo signals s1 q of P target scattering points under the qth pulse are obtained. Frequency echo signal s1 q is subjected to distance pulse pressure to obtain the fundamental frequency echo signal s2 q after the distance pulse pressure; then from the fundamental frequency echo signal s2 q after the distance pulse pressure to obtain the u-th distance unit containing P The echo signal of target scattering point

2a)雷达对第q个脉冲下的含P个目标散射点的回波信号进行去载频fc，得到第q个脉冲下的P个目标散射点的基频回波信号s1q，即：2a) The radar removes the carrier frequency f c from the echo signals containing P target scattering points under the qth pulse, and obtains the fundamental frequency echo signals s1 q of P target scattering points under the qth pulse, namely:

sthe s 11 qq == ΣΣ pp == 11 PP σσ pp Ff qq pp aa rr (( tt ^^ -- 22 RR pp cc )) expexp [[ jπrjπr (( tt ^^ -- 22 RR pp cc )) 22 ]] expexp (( -- jj 44 ππ λλ RR pp )) -- -- -- (( 44 ))

式中Rp是雷达到第p个目标散射点的距离，σp是第p个目标散射点的散射系数，c是光速，表示第q个脉冲下的第p个目标散射点处的天线辐射方向性增益，表示第p个目标散射点相对雷达的延时。where R p is the distance from the radar to the p-th target scattering point, σ p is the scattering coefficient of the p-th target scattering point, c is the speed of light, Indicates the antenna radiation directivity gain at the pth target scattering point under the qth pulse, Indicates the delay of the pth target scatter point relative to the radar.

2b)用匹配滤波函数对第q个脉冲下的P个目标散射点的基频回波信号s1q进行距离脉压，得到距离脉压后的基频回波信号s2q。2b) Use the matched filter function Perform distance pulse pressure on the fundamental frequency echo signals s1 q of P target scattering points under the qth pulse to obtain the fundamental frequency echo signal s2 q after distance pulse pressure.

sthe s 22 qq == IFFTIFFT {{ FFTFFT [[ sthe s 11 qq ]] FFTFFT [[ sthe s rr ]] }} == ΣΣ pp == 11 PP σσ pp Ff qq pp sinsin cc [[ ΔΔ ff rr (( tt ^^ -- 22 RR pp cc )) ]] expexp (( -- jj 44 ππ λλ RR pp )) -- -- -- (( 55 ))

式中Δfr为雷达发射线性调频信号的频带的带宽。In the formula, Δfr is the bandwidth of the frequency band where the radar transmits the chirp signal.

由于距离脉压后的第q个脉冲下的含P个目标散射点的基频回波信号s2q中的幅度项是距离向的点散布函数，只与雷达系统的信号带宽Δfr有关，且对固定的散射点都是常数；而相位项对固定的散射点而言也是常数项。这对三维关联成像没有影响，故可以将这两项忽略。Due to the amplitude term in the fundamental frequency echo signal s2 q containing P target scattering points under the qth pulse after the distance pulse pressure is the point spread function in the distance direction, which is only related to the signal bandwidth Δf r of the radar system, and is constant for fixed scattering points; while the phase term It is also a constant term for fixed scatter points. This has no effect on 3D correlative imaging, so these two items can be ignored.

2c)将距离脉压后的基频回波信号s2q简化后得到第q个脉冲下的P个目标散射点的回波信号将简化后的回波信号划分为U个距离单元，则在第q个脉冲下第u个距离单元内的含P个目标散射点的回波信号表示为：2c) Simplify the fundamental frequency echo signal s2 q after the distance pulse pressure to obtain the echo signal of P target scattering points under the qth pulse Divide the simplified echo signal into U range units, then the echo signal containing P target scattering points in the uth range unit under the qth pulse Expressed as:

sthe s qq uu == ΣΣ pp == 11 PP σσ pp uu Ff qq pp -- -- -- (( 66 ))

式中表示第u个距离单元内的第p个目标散射点的散射系数。其中u＝1,2,3...,U，U表示划分的距离单元的总个数。In the formula Indicates the scattering coefficient of the pth target scattering point within the uth range unit. Where u=1, 2, 3..., U, where U represents the total number of divided distance units.

步骤3，利用相控阵雷达阵面的第m行n列的子阵中的第k行l列的阵元在第q个脉冲下的每个目标散射点处的相移值得到Q个脉冲下的P个目标散射点的天线辐射方向性增益矩阵F；再利用天线辐射方向性增益矩阵F构建Q个脉冲下的第u个距离单元内的含P个目标散射点的回波信号su；再利用天线辐射方向性增益矩阵F和Q个脉冲下的第u个距离单元内的含P个目标散射点的回波信号su构建第u个距离单元内的P个目标散射点的散射系数向量σu的目标函数；并且在稀疏约束条件下求解目标函数得到第u个距离单元内的P个目标散射点的散射系数向量估计值 Step 3, using the phase shift value of the array element in the kth row and l column of the subarray of the mth row and nth column of the phased array radar array at each target scattering point under the qth pulse to obtain Q pulses The antenna radiation directional gain matrix F of the P target scattering points below; then use the antenna radiation directional gain matrix F to construct the echo signal s u containing P target scattering points in the u-th distance unit under Q pulses ; Utilize the antenna radiation directivity gain matrix F and the echo signal s u containing P target scattering points in the uth range unit under Q pulses to construct the scattering of P target scattering points in the uth range unit The objective function of the coefficient vector σ u ; and solve the objective function under the sparse constraints to obtain the estimated value of the scattering coefficient vector of the P target scattering points in the u-th distance unit

3a)将相控阵雷达阵面第m行n列的子阵中的第k行l列的阵元在第q个脉冲下的第p个目标散射点处的相移值的表达式代入天线辐射方向性增益函数，从而得到在第q个脉冲下的第p个目标散射点的天线辐射方向性增益 3a) The phase shift value of the array element in the k-th row and l-column in the sub-array of the m-th row and n-column of the phased array radar array at the p-th target scattering point under the q-th pulse The expression of is substituted into the antenna radiation directivity gain function, so as to obtain the antenna radiation directivity gain of the pth target scattering point under the qth pulse

进而得到Q个脉冲下的P个目标散射点的天线辐射方向性增益矩阵F，即：Then the antenna radiation directivity gain matrix F of P target scattering points under Q pulses is obtained, namely:

将Q个脉冲下第u个距离单元内的P个目标散射点的回波向量su表示为：su＝Fσu。其中表示Q个脉冲下第u个距离单元内的P个目标散射点的回波向量，表示第u个距离单元内的P个目标散射点的散射系数向量。The echo vector s u of P target scattering points in the u-th range unit under Q pulses is expressed as: s u =Fσ u . in Indicates the echo vectors of P target scattering points in the u-th range unit under Q pulses, Indicates the scattering coefficient vector of P target scattering points in the uth range cell.

3b)利用Q个脉冲下的第u个距离单元内的P个目标散射点的回波向量su和Q个脉冲下的P个目标散射点的天线辐射方向性增益矩阵F来构造第u个距离单元内的P个目标散射点的散射系数向量σu的目标函数J(σu)：3b) Utilize the echo vector u of the P target scattering points in the u-th distance unit under the Q pulses and the antenna radiation directivity gain matrix F of the P target scattering points under the Q pulses to construct the u-th The objective function J(σ u ) of the scattering coefficient vector σ u of the P target scattering points in the distance unit:

JJ (( σσ uu )) == || || sthe s uu -- Ff σσ uu || || 22 22 ++ μμ || || σσ uu || || 11 -- -- -- (( 99 ))

式中||·||2是L2范数运算符，||·||1是L1范数运算符，μ是正则化参数；where ||·|| 2 is the L 2 norm operator, ||·|| 1 is the L 1 norm operator, μ is the regularization parameter;

在现有技术中，对Q个脉冲下的第u个距离单元内的P个目标散射点的回波向量su进行一阶线性关联处理，即解方程su＝Fσu得到第u个距离单元内的P个目标散射点的散射系数向量σu，我们希望得到σu的唯一解，但由于阵元的个数有限，所得到的Q个脉冲下的P个目标散射点的天线辐射方向性增益矩阵F无法达到完全随机，即方程的系数矩阵F非满秩，所以方程的解不唯一，故在本发明中采用了三维场景的稀疏特性，在求解过程中加入稀疏约束条件μ||σu||1来求第u个距离单元内的P个目标散射点的散射系数向量σu的稀疏解，即可得到σu的唯一解。In the prior art, first-order linear correlation processing is performed on the echo vectors u of P target scattering points in the u-th distance unit under Q pulses, that is, the u-th distance is obtained by solving the equation s u =Fσ u The scattering coefficient vector σ u of the P target scattering points in the unit, we hope to obtain the unique solution of σ u , but due to the limited number of array elements, the obtained antenna radiation direction of the P target scattering points under Q pulses The linear gain matrix F cannot be completely random, that is, the coefficient matrix F of the equation is not full rank, so the solution of the equation is not unique, so the sparse characteristic of the three-dimensional scene is used in the present invention, and the sparse constraint condition μ|| is added in the solution process σ u || 1 to find the sparse solution of the scattering coefficient vector σ u of the P target scattering points in the uth distance unit, and then the unique solution of σ u can be obtained.

3c)构造第u个距离单元内的P个目标散射点的散射系数向量σu的目标函数J(σu)在稀疏约束条件μ||σu||1下的方程为：3c) The equation of constructing the objective function J(σ u ) of the scattering coefficient vector σ u of the P target scattering points in the u-th distance unit under the sparse constraint condition μ||σ u || 1 is:

minmin || || sthe s uu -- Ff σσ uu || || 22 22 ++ μμ || || σσ uu || || 11 sthe s .. tt .. μμ || || σσ uu || || 11 -- -- -- (( 1010 ))

求解式(10)即可得到第u个距离单元内的P个目标散射点的散射系数向量估计值为：Solve formula (10) to get the estimated value of scattering coefficient vector of P target scattering points in the uth distance unit for:

σσ ^^ uu == argarg minmin J J (( σσ uu )) == [[ σσ ^^ 11 uu ,, σσ ^^ 22 uu ,, .. .. .. σσ ^^ pp uu .. .. .. ,, σσ ^^ PP uu ]] TT -- -- -- (( 1111 ))

式中argmin是最小化运算符，表示第u个距离单元内的P个目标散射点的散射系数向量的估计值。表示第u个距离单元内的第p个目标散射点的散射系数的估计值。where argmin is the minimization operator, Indicates the estimated value of the scattering coefficient vector of P target scattering points in the uth range cell. Indicates the estimated value of the scattering coefficient of the p-th target scattering point within the u-th range cell.

本发明中实现3c)的过程可以利用匹配追踪算法。匹配追踪算法的具体步骤可参考J.A.Tropp和A.C.Gilbert在2007年12月发表的IEEE论文“Signal recovery from randommeasurements via orthogonal matching pursuit”。The process of realizing 3c) in the present invention can utilize the matching pursuit algorithm. For the specific steps of the matching pursuit algorithm, please refer to the IEEE paper "Signal recovery from random measurements via orthogonal matching pursuit" published by J.A.Tropp and A.C.Gilbert in December 2007.

步骤4，先由第u个距离单元内的P个目标散射点的散射系数向量估计值形成二维图像Zu，再由U个距离单元的二维图像Z1,Z2,...Zu...,ZU按照距离单元的顺序排列起来得到三维图像Z＝[Z1,Z2,...Zu...,ZU]。Step 4, first estimate the value of the scattering coefficient vector from the P target scattering points in the u-th distance unit Form a two-dimensional image Z u , and then arrange the two-dimensional images Z 1 , Z 2 ,...Z u ...,Z U of U distance units in the order of distance units to obtain a three-dimensional image Z=[Z 1 , Z 2 ,...Z u ...,Z U ].

4a)建立以目标散射点的方位角度为横坐标、以目标散射点的俯仰角度为纵坐标的坐标系，在坐标系中，选择放置第u个距离单元内的第p个目标散射点的散射系数估计值的点，该点的横坐标等于第p个目标散射点的方位角度θp，该点的纵坐标等于第p个目标散射点的俯仰角度βp；进而得到第u个距离单元内的P个目标散射点的散射系数估计值形成的二维图像Zu；4a) Establish a coordinate system with the azimuth angle of the target scatter point as the abscissa and the pitch angle of the target scatter point as the ordinate. In the coordinate system, select the scattering point of the p-th target scatter point in the u-th distance unit. coefficient estimates , the abscissa of this point is equal to the azimuth angle θ p of the p-th target scattering point, and the ordinate of this point is equal to the pitch angle β p of the p-th target scattering point; and then P in the u-th distance unit is obtained Scatter coefficient estimates for target scatter points The formed two-dimensional image Z u ;

4b)令u从1至U进行遍历，重复步骤2、步骤3和步骤4a)，得到U个距离单元的二维图像Z1,Z2,...Zu...,ZU，将U个距离单元的二维图像Z1,Z2,...Zu...,ZU按照距离单元的顺序排列起来，最终得到场景的三维图像Z＝[Z1,Z2,...Zu...,ZU]。4b) Let u traverse from 1 to U, repeat step 2, step 3 and step 4a), to obtain two-dimensional images Z 1 , Z 2 ,...Z u ...,Z U of U distance units, and set The two-dimensional images Z 1 , Z 2 ,...Z u ...,Z U of U distance units are arranged in the order of the distance units, and finally the three-dimensional image of the scene Z=[Z 1 ,Z 2 ,.. .Zu ..., Zu ].

下面结合仿真实验对本发明的效果做进一步说明。The effects of the present invention will be further described below in combination with simulation experiments.

1.仿真条件1. Simulation conditions

本仿真采用图2所示的几何模型进行仿真验证，令坐标原点为场景平面中的场景中心点，雷达相位中心在距场景中心点1Km处，即R＝1000m；目标散射点的分布如图4所示，成像区域被划分为25*25*25(距离*方位*俯仰)的矩形网格。假设二维平面相控阵雷达阵元按矩形均匀分布，共有阵元40*40＝1600个，在X方向上的阵元间距dx＝0.004m，在Y方向上的阵元间距dy＝0.004m。则天线方位向孔径Dx＝0.004*40＝0.16m，天线俯仰向孔径Dy＝0.004*40＝0.16m；雷达发射信号的载频fc＝35GHz，带宽B＝100MHz，采样频率Fs＝200MHz。This simulation uses the geometric model shown in Figure 2 for simulation verification. The origin of the coordinates is the center point of the scene in the scene plane, and the radar phase center is 1Km away from the center point of the scene, that is, R=1000m; the distribution of target scattering points is shown in Figure 4 As shown in , the imaging area is divided into a rectangular grid of 25*25*25 (distance*azimuth*pitch). Assuming that the elements of the two-dimensional planar phased array radar are uniformly distributed in a rectangle, there are a total of 40*40=1600 elements, the element spacing in the X direction d x =0.004m, and the element spacing d y in the Y direction = 0.004m. Then the antenna azimuth aperture D x = 0.004*40 = 0.16m, the antenna pitch aperture D y = 0.004*40 = 0.16m; the carrier frequency f c of the radar transmitting signal = 35GHz, the bandwidth B = 100MHz, and the sampling frequency F s = 200MHz.

2.仿真内容与结果2. Simulation content and results

令相控阵雷达天线阵面按照常规扫描模式进行反馈相移值，则会在空间形成窄波束辐射方向图，波束的宽度决定常规扫描三维成像的分辨率；将相控阵雷达天线阵面划分为5*5个子阵，每个子阵由8*8个阵元组成，按照本发明所述进行反馈相移值，形成的二维天线辐射方向性增益图如图5所示，可以看出二维天线辐射方向性增益图代表的波前平面辐射场强度呈现出随机涨落的形式，使得同一波前平面上的不同散射点受到的辐射信号的幅相具有独立随机的编码形式，因而具备空间可区分特性。Let the phased array radar antenna face feed back the phase shift value according to the conventional scanning mode, and a narrow beam radiation pattern will be formed in space. The width of the beam determines the resolution of the conventional scanning three-dimensional imaging; the phased array radar antenna face is divided into It is 5*5 sub-arrays, and each sub-array is composed of 8*8 array elements. According to the present invention, the phase shift value is fed back, and the two-dimensional antenna radiation directivity gain diagram formed is shown in Figure 5. It can be seen that two The radiation field strength of the wavefront plane represented by the three-dimensional antenna radiation directional gain diagram presents a form of random fluctuation, which makes the amplitude and phase of the radiation signal received by different scattering points on the same wavefront plane have an independent random encoding form, so it has the space distinguishable features.

现有技术的实孔径三维成像的理论分辨率由带宽和天线孔径决定，按照给出的数字仿真参数，距离向分辨率ρr＝C/2B＝1.5m，距离向可以分辨点目标；但是方位向分辨率ρa＝λR/Dx＝53.57m，俯仰向分辨率ρp＝λR/Dy＝53.57m；方位向和俯仰向分辨率大大超出了点目标10m的空间间隔，使得在中心参考距离面上的散射点无法分辨。The theoretical resolution of the real-aperture 3D imaging in the prior art is determined by the bandwidth and the antenna aperture. According to the given digital simulation parameters, the resolution in the range direction ρ r =C/2B=1.5m, and the point target can be resolved in the range direction; but the azimuth Resolution ρ a = λR/D x = 53.57m in pitch direction, resolution in pitch direction ρ p = λR/D y = 53.57m; the resolution in azimuth and pitch direction greatly exceeds the 10m spatial interval of point targets, so that in the center reference Scattered points on the distance surface cannot be resolved.

采用本发明提出的基于相控阵雷达的三维关联成像方法，结合稀疏优化算法，得到目标散射点的仿真图，如图6所示是利用625次脉冲对场景的散射点进行三维成像验证，距离向分辨率ρr＝C/2B＝1.5m，方位向分辨率ρa＝Dx/2＝0.08m；俯仰向分辨率ρp＝Dy/2＝0.08m；不仅散射点被有效地分辨出，而且获得了雷达照射场景的散射点的高分辨三维图像，验证了本发明的高分辨三维成像效果，且散射点位置估计准确，旁瓣较低，而用现有技术的常规实孔径成像方法无法区出散射点；如图7所示给出了只利用80次脉冲的三维关联成像结果，可以看出本发明在采样的脉冲次数不足的情况下，依旧可以得到较好的成像结果，可以大大降低数据采集存储和信号实时处理的要求。具有很强的工程应用价值。The three-dimensional correlation imaging method based on phased array radar proposed by the present invention is combined with the sparse optimization algorithm to obtain the simulation map of the target scattering points. As shown in Figure 6, 625 pulses are used to perform three-dimensional imaging verification on the scattering points of the scene. resolution in direction ρ r =C/2B=1.5m, resolution in azimuth direction ρ a =D x /2=0.08m; resolution in elevation direction ρ p =D y /2=0.08m; not only the scattering points are effectively resolved In addition, a high-resolution three-dimensional image of the scattering point of the radar irradiation scene is obtained, which verifies the high-resolution three-dimensional imaging effect of the present invention, and the estimation of the scattering point position is accurate, and the side lobe is low, while the conventional real-aperture imaging of the prior art The method cannot distinguish the scattering points; as shown in Figure 7, the three-dimensional correlation imaging results using only 80 pulses are given, and it can be seen that the present invention can still obtain better imaging results when the number of pulses sampled is insufficient. It can greatly reduce the requirements for data acquisition and storage and real-time signal processing. It has strong engineering application value.

Claims (4)

1. a three-dimensional relevance imaging method based on phased-array radar, it is characterised in that comprise the following steps:
Step 1, is divided into M × N number of submatrix by Phased Array Radar Antenna front, and each submatrix has K × L array element, a total of M × N × K × L array element, and array element is distributed by rectangular uniform, phased-array radar transmitter under q-th pulse by linear FM signal s0qIt is transmitted in image scene, and receiving the echo-signal containing P target scattering point under q-th pulse, the phase-shift value at the array element of the row k l row in the submatrix arrange the m row n being arranged in phased-array radar front pth target scattering point under q-th pulse is set asQ=1,2 ..., the total number of Q, Q pulse, m=1,2,3 ..., M, M are antenna array line number, n=1,2,3 ..., N, N are antenna array columns, l=1,2,3 ..., L, L are the columns of submatrix, k=1,2,3 ..., K, K are the line number of submatrix；
Step 2,
2a) echo-signal containing P target scattering point under q-th pulse is removed carrier frequency f by radarc, obtain fundamental frequency echo-signal s1 of P target scattering point under q-th pulseq, it may be assumed that
R in formulapIt is the radar distance that arrives pth target scattering point, σpBeing the scattering coefficient of pth target scattering point, c is the light velocity,Represent the Antenna gain pattern gain at pth the target scattering point under q-th pulse,Represent the time delay relative to radar of pth the target scattering point；
2b) use matched filtering functionFundamental frequency echo-signal s1 to P target scattering point under q-th pulseqCarry out distance pulse pressure, obtain fundamental frequency echo-signal s2 after distance pulse pressureq:
Δ f in formularBandwidth for the frequency band of radar emission linear FM signal；
2c) by fundamental frequency echo-signal s2 after distance pulse pressureqThe echo-signal containing P target scattering point under q-th pulse is obtained after simplificationEcho-signal after simplifying is divided into U distance unit, the then echo-signal of P target scattering point in the u distance unit under q-th pulseIt is expressed as:
In formulaRepresenting the scattering coefficient of the u pth target scattering point in unit, wherein u=1,2,3..., U, U represent total number of the distance unit under each pulse；
Step 3, the phase-shift value at the array element of the row of row k l in the submatrix that the m row n of phased-array radar front the arranges each target scattering point under q-th pulse is utilized to obtain Antenna gain pattern gain matrix F, the F dimension Q × P of P target scattering point under Q pulse；Recycling Antenna gain pattern gain matrix F builds echo-signal s containing P target scattering point in the u distance unit under Q pulseu；Echo-signal s containing P target scattering point in the u distance unit under recycling F and Q pulse of Antenna gain pattern gain matrixuBuild the scattering coefficient vector σ of the u P target scattering point in unituObject function；And under the conditions of sparse constraint, solve object function obtain the scattering coefficient vector estimated value of P target scattering point in the u distance unit
Step 4, first by the scattering coefficient vector estimated value of P target scattering point in the u distance unitForm two dimensional image Zu, then the two dimensional image Z by U distance unit1,Z2,...Zu...,ZULine up according to the order of distance unit and obtain 3-D view Z=[Z1,Z2,...Zu...,ZU]。
A kind of three-dimensional relevance imaging method based on phased-array radar the most according to claim 1, it is characterised in that step 1 includes following sub-step:
1a) Phased Array Radar Antenna front being divided into M × N number of submatrix, each submatrix has K × L array element, a total of M × N × K × L array element, and array element is divided by rectangular uniform, and phased-array radar transmitter is by the linear FM signal under q-th pulseIt is transmitted in image scene, and receives the echo-signal containing P target scattering point under q-th pulse, in formulaBe distance to the fast time,For distance to window function, r is that distance is to frequency modulation rate, fcIt is the carrier frequency of radar emission signal, tq=qTrIt is the slow time of q-th pulse, TrIt is the pulse repetition period, q=1,2 ..., Q represents pulse sequence number, and Q represents total pulse number of radar emission；
1b) the phase-shift value at the array element of the row k l row in the submatrix that the m row n being arranged in phased-array radar front is arranged pth target scattering point under q-th pulseIt is set as:
Wherein:
Δφx=γ dx sinθp cosβp (2)
Δφy=γ dy sinβp (3)
Δ φ in formulaxFor adjacent array element space quadrature in the X direction, Δ φyFor adjacent array element space quadrature in the Y direction；dxIt is the array element distance in X-direction, dyBeing the array element distance in Y-direction, X-direction is the horizontal direction of antenna arrays of radar, and Y-direction is the vertical direction of antenna arrays of radar, k is array element numbering in submatrix in X-direction, k=1,2,3..., K, l are array element numberings in submatrix in Y-direction, l=1,2,3..., L, m are the submatrix numberings in the X direction at this array element place, m=1,2,3..., M, n is the submatrix numbering in the Y direction at this array element place, n=1,2,3..., N, p=1,2,3..., P, P represents total number of target scattering point, θ in scenepRepresent the azimuth of pth target scattering point, βpRepresenting the angle of pitch of pth target scattering point, γ=2 π/λ is free space wave number, and λ is radar operation wavelength, Δ φm,n(tq) be the random phase shift of extra superposition between submatrix, and every time the most constant in the burst length, and interpulse be all change at random, i.e. Δ φm,n(tq) it is independent identically distributed a functional of a stochastic process and Δ φm,n(tq)∈[-π,π]。
A kind of three-dimensional relevance imaging method based on phased-array radar the most according to claim 2, it is characterised in that step 3 includes following sub-step:
3a) the phase-shift value at the array element of the row k l row in the submatrix that phased-array radar front m row n is arranged pth target scattering point under q-th pulseExpression formula substitute into Antenna gain pattern gain function, thus obtain the Antenna gain pattern gain of pth the target scattering point under q-th pulse
D in formulaxIt is the array element distance in X-direction, dyBeing the array element distance in Y-direction, X-direction is the horizontal direction of antenna arrays of radar, and Y-direction is the vertical direction of antenna arrays of radar, p=1, and 2,3..., P, P represent total number of target scattering point, θ in scenepRepresent the azimuth of pth target scattering point, βpRepresenting the angle of pitch of pth target scattering point, k is array element numbering in submatrix in X-direction, k=1,2,3..., K, γ=2 π/λ is free space wave number, and λ is radar operation wavelength, l is array element numbering in submatrix in Y-direction, l=1,2,3..., L, m are the submatrix numberings in the X direction at this array element place, m=1,2,3..., M, n are the submatrix numberings in the Y direction at this array element place, n=1,2,3..., N, Δ φm,n(tq) be the random phase shift of extra superposition between submatrix, and every time the most constant in the burst length, and interpulse be all change at random, i.e. Δ φm,n(tq) it is independent identically distributed a functional of a stochastic process and Δ φm,n(tq)∈[-π,π]；
And then obtain the Antenna gain pattern gain matrix F of P target scattering point under Q pulse, it may be assumed that
Echo vector s by P target scattering point in the u distance unit under Q pulseuIt is expressed as: su=F σu；WhereinThe echo vector of P the target scattering point represented under Q pulse in the u distance unit,Represent the scattering coefficient vector of the u P target scattering point in unit；
3b) utilize the echo vector s of P target scattering point under Q pulse the u distance unituWith the scattering coefficient vector σ that the Antenna gain pattern gain matrix F of P target scattering point under Q pulse constructs the u P target scattering point in unituObject function J (σu):
In formula | | | |2It is L2Norm operator, | | | |1It is L1Norm operator, μ is regularization parameter；
3c) construct the scattering coefficient vector σ of the u P target scattering point in unituObject function J (σu) in sparse constraint condition μ | | σu||1Under equation be:
Ask in sparse constraint condition μ | | σu||1Under equation obtain the scattering coefficient vector estimated value of P target scattering point in the u distance unitFor:
In formula, argmin is minimum operation symbol,Represent the estimated value of the scattering coefficient vector of the u P target scattering point in unit,Represent the estimated value of the scattering coefficient of the u pth target scattering point in unit.
A kind of three-dimensional relevance imaging method based on phased-array radar the most according to claim 1, it is characterised in that step 4 includes following sub-step:
4a) set up with the orientation angles of target scattering point as abscissa, coordinate system with the luffing angle of target scattering point as vertical coordinate, in a coordinate system, select to place the scattering coefficient estimated value of the u pth target scattering point in unitPoint, the abscissa of this point is equal to orientation angles θ of pth target scattering pointp, the vertical coordinate of this point is equal to the luffing angle β of pth target scattering pointp；And then obtain the scattering coefficient estimated value of the u P target scattering point in unitThe two dimensional image Z formedu；
4b) make u travel through from 1 to U, repeat step 2, step 3 and step 4a), obtain the two dimensional image Z of U distance unit1,Z2,...Zu...,ZU, by the two dimensional image Z of U distance unit1,Z2,...Zu...,ZULine up according to the order of distance unit, finally give the 3-D view Z=[Z of scene1,Z2,...Zu...,ZU]。
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