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CN110609273A - Error Compensation Method for Wideband MIMO Imaging Radar Array Based on Multiple Specific Targets - Google Patents

Error Compensation Method for Wideband MIMO Imaging Radar Array Based on Multiple Specific Targets Download PDF

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CN110609273A
CN110609273A CN201910735487.0A CN201910735487A CN110609273A CN 110609273 A CN110609273 A CN 110609273A CN 201910735487 A CN201910735487 A CN 201910735487A CN 110609273 A CN110609273 A CN 110609273A
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array element
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CN110609273B (en
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曾涛
田卫明
胡程
王晶阳
龙腾
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Beijing University of Technology
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S13/00Systems 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
    • G01S13/02Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S13/00Systems 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
    • G01S13/88Radar or analogous systems specially adapted for specific applications
    • G01S13/89Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S7/00Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/40Means for monitoring or calibrating
    • G01S7/4052Means for monitoring or calibrating by simulation of echoes
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S7/00Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41Details 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
    • G01S7/418Theoretical aspects
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S13/00Systems 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
    • G01S13/02Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S2013/0236Special technical features
    • G01S2013/0245Radar with phased array antenna

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

Abstract

本发明公开了基于多特显点目标的宽带MIMO成像雷达阵列误差补偿方法,能够实现宽带MIMO成像雷达系统的良好聚焦,从而获得良好的成像性能。在MIMO成像雷达的远场区域设置特显点目标,获取含有阵列误差的MIMO成像雷达系统回波与阵列误差的一阶近似表达式。根据各通道目标距离向脉压结果峰值延时信息,利用最小二乘法估计特显点目标的位置。利用特显点目标距离向脉压结果峰值相位间的差分相位建立阵元位置误差的超定线性方程组,估计阵元位置误差。利用单个特显点目标的距离向脉压结果峰值幅度及相位信息估计通道幅相、延时误差,并对MIMO成像雷达通道相位误差进行补偿。

The invention discloses a wideband MIMO imaging radar array error compensation method based on multi-point targets, which can realize good focusing of the wideband MIMO imaging radar system, thereby obtaining good imaging performance. A special point target is set in the far field area of MIMO imaging radar, and the first-order approximate expression of the MIMO imaging radar system echo and array error including array error is obtained. According to the peak delay information of the target range pulse pressure results in each channel, the least square method is used to estimate the position of the prominent point target. The overdetermined linear equations of the array element position error are established by using the difference phase between the peak phases of the pulse pressure results in the range direction of the characteristic point, and the array element position error is estimated. The channel amplitude, phase and delay errors are estimated by using the peak amplitude and phase information of the range pulse pressure results of a single prominent point target, and the channel phase error of MIMO imaging radar is compensated.

Description

基于多特显点目标的宽带MIMO成像雷达阵列误差补偿方法Error Compensation Method for Wideband MIMO Imaging Radar Array Based on Multiple Specific Targets

技术领域technical field

本发明涉及MIMO雷达技术领域,具体涉及基于多特显点目标的宽带 MIMO成像雷达阵列误差补偿方法。The invention relates to the technical field of MIMO radars, in particular to a method for compensating errors of wideband MIMO imaging radar arrays based on multi-spot targets.

背景技术Background technique

MIMO雷达是近年来新兴的一种雷达体制。MIMO雷达系统将MIMO通信 领域的波形分集理论引入到了雷达领域,通过多个发射阵元发射相互正交的信 号波形,多个接收阵元同时对多路信号进行接收并依据信号的正交性对不同发 射通道的信号进行分选,从而得到远多于实际阵元个数的独立观测通道数。由 于波形分集技术大大提高了系统的观测自由度,因此MIMO雷达的总体性能相 较于传统的单通道雷达以及相控阵雷达具有很大优势。MIMO radar is a new radar system emerging in recent years. The MIMO radar system introduces the waveform diversity theory in the MIMO communication field into the radar field. Multiple transmitting array elements transmit mutually orthogonal signal waveforms, and multiple receiving array elements receive multiple signals at the same time and compare them according to the orthogonality of the signals. The signals of different transmission channels are sorted, so that the number of independent observation channels is much more than the actual number of array elements. Because the waveform diversity technology greatly improves the degree of freedom of system observation, the overall performance of MIMO radar has great advantages compared with traditional single-channel radar and phased array radar.

一般而言,对于MIMO雷达系统的各种分析方法及定位、成像算法均认为 MIMO雷达各个通道的幅相、延时特性完全一致,并且实际阵元位置与设计位 置完全相同。然而,实际系统由于各个观测通道的传输链路不同,各个通道的 幅相、延时特性必然存在差异;同时受器件加工精度所限,实际的阵元位置必 然与理想位置有所偏差。如果不对实际MIMO雷达系统中的上述阵列误差进行 补偿,雷达的整体性能将会严重恶化,难以达到设计的性能指标。Generally speaking, for various analysis methods and positioning and imaging algorithms of MIMO radar systems, it is believed that the amplitude, phase and delay characteristics of each channel of MIMO radar are completely consistent, and the actual array element position is exactly the same as the design position. However, due to the different transmission links of each observation channel in the actual system, there must be differences in the amplitude, phase and delay characteristics of each channel; at the same time, due to the limitation of device processing accuracy, the actual array element position must deviate from the ideal position. If the above-mentioned array error in the actual MIMO radar system is not compensated, the overall performance of the radar will be seriously deteriorated, and it is difficult to achieve the designed performance index.

对于宽带MIMO成像雷达而言,阵列中存在的通道间幅相误差会导致方位 向旁瓣抬升,甚至出现无法聚焦的情况;通道间延时误差会使得成像补偿所用 的距离徙动与实际值不符,从而使得距离向和方位向旁瓣均有抬升;阵元位置 误差则会导致阵列的空间采样不均匀,从而使得方位向成像结果中存在高栅瓣, 严重影响成像质量。For wideband MIMO imaging radars, the amplitude and phase errors between channels in the array will cause the azimuth side lobe to rise, and even the situation that it cannot be focused; the delay error between channels will make the distance migration used for imaging compensation inconsistent with the actual value , so that both the range and azimuth side lobes are lifted; the array element position error will lead to uneven spatial sampling of the array, resulting in high grating lobes in the azimuth imaging results, which seriously affects the imaging quality.

然而,现有的MIMO雷达阵列误差补偿方法主要针对窄带系统的目标定位 应用开展研究,关于阵列误差对成像性能的影响分析较少,同时并未考虑对宽 带成像雷达影响严重的延时误差,传统的阵列误差估计方法对于宽带MIMO成 像雷达系统的效果并不理想。However, the existing MIMO radar array error compensation methods are mainly researched on the target positioning application of narrowband systems, and there are few analyzes on the impact of array errors on imaging performance. The array error estimation method is not ideal for wideband MIMO imaging radar systems.

因此,为了使宽带MIMO成像雷达获得较好的成像性能,有必要针对系统 中存在的阵列误差研发新的阵列设计方法。Therefore, in order to obtain better imaging performance of wideband MIMO imaging radar, it is necessary to develop a new array design method for the array error existing in the system.

发明内容Contents of the invention

有鉴于此,本发明提供了基于多特显点目标的宽带MIMO成像雷达阵列误 差补偿方法,能够实现宽带MIMO成像雷达系统的良好聚焦,从而获得良好的 成像性能。In view of this, the present invention provides a wideband MIMO imaging radar array error compensation method based on multi-point targets, which can achieve good focusing of the wideband MIMO imaging radar system, thereby obtaining good imaging performance.

基于多特显点目标的宽带MIMO成像雷达阵列误差补偿方法,包括如下步 骤:The method for compensating errors of wideband MIMO imaging radar arrays based on multi-point targets comprises the following steps:

步骤一、在MIMO成像雷达的远场区域设置特显点目标,获取含有阵列误 差的MIMO成像雷达系统回波与阵列误差的一阶近似表达式。Step 1. Set a special point target in the far field area of the MIMO imaging radar, and obtain the first-order approximate expression of the echo and array error of the MIMO imaging radar system including array error.

步骤二,根据各通道目标距离向脉压结果峰值延时信息,利用最小二乘法 估计特显点目标的位置。Step 2: According to the peak delay information of the target range pulse pressure results in each channel, the least square method is used to estimate the position of the prominent point target.

步骤三,利用特显点目标距离向脉压结果峰值相位间的差分相位建立阵元 位置误差的超定线性方程组,估计阵元位置误差。Step 3: Using the differential phase between the peak phases of the pulse pressure results in the distance direction of the target at the special point, the overdetermined linear equations of the array element position error are established to estimate the array element position error.

步骤四,利用单个特显点目标的距离向脉压结果峰值幅度及相位信息估计 通道幅相、延时误差,并对MIMO成像雷达阵列误差进行补偿。Step 4, using the range pulse pressure peak amplitude and phase information of a single prominent point target to estimate the channel amplitude, phase, and delay errors, and compensate the MIMO imaging radar array error.

进一步地,步骤一中,获取含有阵列误差的MIMO成像雷达系统回波与阵 列误差的一阶近似表达式,具体过程为:Further, in step 1, the first-order approximate expression of the echo and array error of the MIMO imaging radar system containing array error is obtained, and the specific process is:

对于含有阵列误差的MIMO成像雷达系统,其发射阵元数量为M,接收阵 元数量为N,其发射天线和接收天线的空间位置向量分别为记c为光速,AT,m、φT,m和ΔτT,m分别为第m个发射阵元幅度误 差、相位误差和延时误差,AR,n、φR,n和ΔτR,n分别为第n个接收阵元的幅度误差、 相位误差和延时误差;s(t)为发射信号,分别表示目标位置PTar处的目 标到第m个发射阵元和第n个接收阵元的距离,并记第m个发射阵元的延时误 差造成的距离误差为ΔRT,m=c·ΔτT,m,第n个接收阵元的延时误差造成的距离误差 为ΔRR,n=c·ΔτR,n;其中,下标T和R分别表示雷达系统的发射天线和接收天线, 下标m和n分别表示发射阵元和接收阵元的编号;For a MIMO imaging radar system with array errors, the number of transmitting array elements is M, the number of receiving array elements is N, and the spatial position vectors of the transmitting antenna and receiving antenna are respectively and Denote c as the speed of light, A T,m , φ T,m and Δτ T,m are the amplitude error, phase error and delay error of the mth transmitting element respectively, A R,n , φ R,n and Δτ R, n are the amplitude error, phase error and delay error of the nth receiving array element respectively; s(t) is the transmitting signal, and represent the distances from the target at the target position P Tar to the mth transmitting array element and the nth receiving array element, and record the distance error caused by the delay error of the mth transmitting array element as ΔR T,m = c· Δτ T,m , the distance error caused by the delay error of the nth receiving array element is ΔR R,n = c·Δτ R,n ; where, the subscripts T and R represent the transmitting antenna and receiving antenna of the radar system respectively, The subscripts m and n represent the numbers of the transmitting array element and the receiving array element respectively;

该雷达系统接收到的MN路回波数据经过脉冲压缩处理后为sm(t,m,n;PTar):The MN channel echo data received by the radar system is s m (t,m,n; P Tar ) after pulse compression processing:

式(1)给出了距离脉压处理后的一维回波信号;假设收发阵列均为线阵, 且所有阵元均与目标共面,在该平面建立二维直角坐标系;选取发射阵列的几 何中心作为目标原点,拟合所有发射阵元作为y轴,目标所在一侧为x轴正方 向;此时,该含误差的MIMO阵列各发射阵元和接收阵元的实际位置分别为 为第m个发射阵元的实际 位置坐标测量值,为第n个接收阵元的实际位置坐标测量值,在上述坐 标系下,假设目标极坐标为(ρ,θ),在远场条件下,有Equation (1) gives the one-dimensional echo signal after distance pulse pressure processing; assuming that the transceiver arrays are all linear arrays, and all array elements are in the same plane as the target, a two-dimensional Cartesian coordinate system is established on this plane; select the transmitting array The geometric center of the target is taken as the origin of the target, and all the transmitting elements are fitted as the y-axis, and the side where the target is located is the positive direction of the x-axis; at this time, the actual positions of the transmitting and receiving elements of the MIMO array with errors are respectively and is the measured value of the actual position coordinates of the mth transmitting array element, is the measured value of the actual position coordinates of the nth receiving array element. In the above coordinate system, assuming that the polar coordinates of the target are (ρ, θ), under far-field conditions, we have

为(ρ,θ)点到第m个发射阵元的距离测量值; is the measured distance from point (ρ, θ) to the mth transmitting array element;

为(ρ,θ)点到第n个接收阵元的距离测量值; is the distance measurement value from point (ρ, θ) to the nth receiving array element;

一维脉压后回波信号为sm(t,m,n;ρ,θ):The echo signal after one-dimensional pulse pressure is s m (t,m,n; ρ,θ):

B为发射信号的带宽,公式(3)即为含有阵列误差的MIMO成像雷达系统 回波与阵列误差的一阶近似表达式。B is the bandwidth of the transmitted signal, and formula (3) is the first-order approximate expression of the echo and array error of the MIMO imaging radar system with array error.

进一步地,步骤二,根据各通道目标距离向脉压结果峰值延时信息,利用 最小二乘法估计特显点目标的位置,具体为:Further, in step 2, according to the peak delay information of the target distance to pulse pressure results in each channel, the least square method is used to estimate the position of the prominent point target, specifically:

第(m,n)个通道的双基地距离测量值为 The bistatic distance measurement for the (m, n)th channel is

其中εN,m,n为观测误差;为(ρ,θ)点到第m个发射阵元的距离理想值;Where ε N,m,n is the observation error; is the ideal value of the distance from point (ρ, θ) to the mth transmitting array element;

为(ρ,θ)点到第n个接收阵元的距离理想值; is the ideal value of the distance from point (ρ, θ) to the nth receiving array element;

xT,m,yT,m为第m个发射阵元的实际位置坐标理想值,xR,n,yR,n为第n个接收阵 元的实际位置坐标理想值;x T, m , y T, m are the ideal values of the actual position coordinates of the mth transmitting array element, x R, n , y R, n are the ideal values of the actual position coordinates of the nth receiving array element;

εsys,m,n为延时误差;ε sys,m,n is the delay error;

εsys,m,n=ΔRT,m+ΔRR,n-(ΔxT,m+ΔxR,n)sinθ-(ΔyT,m+ΔyR,n)cosθ (5)ε sys, m, n = ΔR T, m + ΔR R, n - (Δx T, m + Δx R, n ) sinθ - (Δy T, m + Δy R, n ) cosθ (5)

利用MN个通道的观测建立超定方程组得到目标位置的最小二乘估计Using the observations of MN channels to establish an overdetermined equation system to obtain the least squares estimation of the target position

是ρ的估计值;是sinθ的估计值; is the estimated value of ρ; is the estimated value of sinθ;

MIMO成像雷达中收发阵列共线且共中心,即In the MIMO imaging radar, the transmitting and receiving arrays are collinear and co-centered, that is,

利用式(7)将式(6)化简为Use formula (7) to simplify formula (6) to

利用式(8)求解得到特显点目标的位置的最小二乘估计。Using equation (8) to solve the least squares estimation of the position of the prominent point target.

进一步地,利用特显点目标距离向脉压结果峰值相位间的差分相位建立阵 元位置误差的超定线性方程组,估计阵元位置误差,具体为:Further, using the differential phase between the peak phases of the pulse pressure results in the range direction of the special point to establish the overdetermined linear equations of the array element position error, and estimate the array element position error, specifically:

MIMO成像雷达中收发阵列共线,其中对应的无误差阵列各阵元的位置分 别位于{(0,yT,m)|m=1,2,...,M}和{(0,yR,n)|n=1,2,...,N},则待估计的收发阵列阵元位置 误差分别为In the MIMO imaging radar, the transceiver array is collinear, and the positions of the corresponding error-free array elements are respectively located in {(0,y T,m )|m=1,2,...,M} and {(0,y R,n )|n=1,2,...,N}, then the position errors of the transceiver array elements to be estimated are respectively

and

其中ΔxT,m,ΔyT,m为第m个发射阵列阵元位置误差;ΔxR,n,ΔyR,n为第n个接收阵列阵元位置误差;Among them, Δx T,m , Δy T,m is the position error of the mth transmitting array element; Δx R,n , Δy R,n is the position error of the nth receiving array element;

考虑式(3)中的相位项为φm(m,n;ρ,θ)Consider the phase term in equation (3) as φ m (m,n; ρ,θ)

根据理想阵元位置构造的成像参考函数的相位为φref(m,n;ρ,θ):The phase of the imaging reference function constructed according to the ideal array element position is φ ref (m,n; ρ,θ):

利用参考相位补偿实测相位得到的残差相位为The residual phase obtained by compensating the measured phase with the reference phase is

式中的k(m,n,θ)为整周模糊度;where k(m,n,θ) is the integer ambiguity;

ρ11为第一特显点位置;ρ22为第二特显点位置;ρ 1 , θ 1 is the position of the first prominent point; ρ 2 , θ 2 is the position of the second prominent point;

实矩阵, 可将所有方程列成方程组形式:remember real matrix, All equations can be listed in the form of a system of equations:

ΔΦ12=H12ΔpTR (15)ΔΦ 12 = H 12 Δp TR (15)

其中,ΔΦ12为第一特显点和第二特显点之间的差分相位矩阵,H12为第一特 显点和第二特显点之间系数矩阵,为待估计的阵元 位置误差;Among them, ΔΦ 12 is the difference phase matrix between the first prominent point and the second prominent point, H 12 is the coefficient matrix between the first prominent point and the second prominent point, is the position error of the array element to be estimated;

系数矩阵H12的秩为M+N-1,再添加一组观测方程组,即增加ΔΦ23, ΔΦ23=H23ΔpTR;ΔΦ23=H23ΔpTR;ΔΦ23为第二特显点和第三特显点之间的差分相 位矩阵,H23为第二特显点和第三特显点之间系数矩阵;The rank of the coefficient matrix H 12 is M+N-1, and then add a group of observation equations, that is, increase ΔΦ 23 , ΔΦ 23 =H 23 Δp TR ; ΔΦ 23 =H 23 Δp TR ; ΔΦ 23 is the second characteristic point and the difference phase matrix between the third characteristic point, H 23 is the coefficient matrix between the second characteristic point and the third characteristic point;

获得方程组为get the equation set as

在θ1≠θ2≠θ3且θ12≠θ23时,有When θ 1 ≠θ 2 ≠θ 3 and θ 12 ≠θ 23 , we have

考虑约束条件式(18):Consider the constraint condition (18):

其中1M为全1向量,0M为全0向量,则 上述约束条件(18)改写成矩阵形式:Among them, 1 M is a vector of all 1s, and 0 M is a vector of all 0s, Then the above constraint (18) is rewritten into a matrix form:

[e1e2]TΔpTR=L·ΔpTR=0 (19)[e 1 e 2 ] T Δp TR =L · Δp TR =0 (19)

将[e1e2]T记为L,则在约束条件(10)下,阵元位置误差的估计问题转化成 约束最小二乘问题,其闭式解为Denote [e 1 e 2 ] T as L, then under the constraint condition (10), the estimation problem of the array element position error is transformed into a constrained least squares problem, and its closed-form solution is

其中,即为最终估计获得的阵元位置误差,表示矩阵的 Moore-Penrose逆,I2M+2N为2M+2N阶单位矩阵。in, is the array element position error obtained by the final estimation, Represents the Moore-Penrose inverse of the matrix, and I 2M+2N is the identity matrix of order 2M+2N.

进一步地,步骤四,利用单个特显点目标的距离向脉压结果峰值幅度及相 位信息估计通道幅相误差、延时误差,并对述MIMO成像雷达阵列误差进行补 偿,具体为:Further, in step 4, use the peak amplitude and phase information of the range pulse pressure results of a single prominent point target to estimate the channel amplitude and phase error and delay error, and compensate the MIMO imaging radar array error, specifically:

各通道的峰值幅度可以拆解为The peak amplitude of each channel can be disassembled as

ln(AT,m)+ln(AR,n)=ln(Am,n) (21)ln(A T,m )+ln(A R,n )=ln(A m,n ) (21)

其中,Am,n为实测单特显点目标的峰值幅度;将[lnAT,1,...,lnAT,M,lnAR,1,...,lnAR,N] 记为X,将[lnA1,1,lnA1,2,...,lnAM,N]记为Y,即得到通道幅度误差的矩阵形式:Among them, A m,n is the peak amplitude of the measured single specific point target; record [lnA T,1 ,...,lnA T,M ,lnA R,1 ,...,lnA R,N ] as X , record [lnA 1,1 ,lnA 1,2 ,...,lnA M,N ] as Y, that is, the matrix form of the channel amplitude error is obtained:

Y=HX (22)Y=HX (22)

其中,H为公式(21)中的系数矩阵;添加约束条件AT,1=AR,1,写成矩阵形 式为Among them, H is the coefficient matrix in the formula (21); adding the constraint condition A T,1 = AR,1 , written in matrix form as

L1X=0 (23)L 1 X=0 (23)

其中,L1=[1,0,...,0,-1,0,...,0];于是得到通道幅度误差的最小二乘估计Among them, L 1 =[1,0,...,0,-1,0,...,0]; then the least squares estimation of the channel amplitude error is obtained

为X的估计值,则对于理想特显点目标而言,各个通道的峰值相位相同, 因此补偿用的幅度值应为 is the estimated value of X, then for an ideal prominent point target, the peak phases of each channel are the same, so the amplitude value used for compensation should be

延时误差远小于分辨率,忽略延时误差对峰值位置的影响,仅消除峰值相 位的影响,此处将延时引入的相位误差与通道相位误差统一校正,将特显点目 标在各个通道的峰值相位补偿成理想相位,即:The delay error is much smaller than the resolution, and the influence of the delay error on the peak position is ignored, and only the influence of the peak phase is eliminated. Here, the phase error introduced by the delay and the channel phase error are uniformly corrected, and the special point is targeted at each channel. The peak phase is compensated to the ideal phase, namely:

φcom(m,n)=θm,nm,n (26)φ com (m,n)=θ m,nm,n (26)

其中,φcom(m,n)为补偿用的相位,θm,n为根据特显点目标位置计算出来的理 想峰值相位,φm,n为特显点目标在各个通道的实测峰值相位;Among them, φ com (m, n) is the phase used for compensation, θ m, n is the ideal peak phase calculated according to the position of the special point target, and φ m, n is the measured peak phase of the special point target in each channel;

利用Acom(m,n)以及φcom(m,n)对上述MIMO成像雷达阵列误差进行补偿。A com (m,n) and φ com (m,n) are used to compensate the above MIMO imaging radar array error.

有益效果:Beneficial effect:

本发明所提供的基于多特显点目标的宽带MIMO成像雷达阵列误差补偿方 法,利用多个特显点目标回波的峰值相位差分处理消除通道相位误差及相位整 周模糊度的影响,然后结合差分相位与阵元位置误差的线性关系利用约束最小 二乘法实现阵元位置误差的估计补偿,之后结合单特显点目标的一维峰值点特 性对通道幅相、延时误差进行估计补偿,从而实现宽带MIMO成像雷达系统的 良好聚焦。The error compensation method for broadband MIMO imaging radar arrays based on multi-point targets provided by the present invention uses the peak phase difference processing of the echoes of multiple points targets to eliminate the influence of channel phase error and phase ambiguity, and then combines The linear relationship between the differential phase and the position error of the array element is estimated and compensated by the constrained least squares method, and then the channel amplitude, phase and delay error are estimated and compensated in combination with the one-dimensional peak point characteristics of the single-point target, so that Achieving good focus for wideband MIMO imaging radar systems.

附图说明Description of drawings

图1为本发明所提供的基于多特显点目标的宽带MIMO成像雷达阵列误差 补偿方法流程图;Fig. 1 is the flow chart of the wideband MIMO imaging radar array error compensation method based on multi-specific point targets provided by the present invention;

图2为含阵列误差的MIMO阵列二维空间坐标系的示意图;Fig. 2 is a schematic diagram of a MIMO array two-dimensional spatial coordinate system with array errors;

图3为阵元位置误差补偿前三个转发器的距离向和方位向成像结果;图3 (a)(b)(c)分别针对(685.6m,-26.36°)的目标、(740.4m,0.468°)的目标 以及(796.3m,17.63°)的目标的方位向BP成像结果以及距离向BP成像结果;Figure 3 shows the range and azimuth imaging results of the three transponders before the array element position error compensation; Figure 3 (a)(b)(c) is respectively for the target at (685.6m, -26.36°), (740.4m, 0.468°) target and (796.3m, 17.63°) target’s azimuth BP imaging results and range BP imaging results;

图4为阵元位置误差补偿后三个转发器的距离向和方位向成像结果;图4 (a)(b)(c)分别针对(685.6m,-26.36°)的目标、(740.4m,0.468°)的目标 以及(796.3m,17.63°)的目标的方位向BP成像结果以及距离向BP成像结果。Figure 4 shows the range and azimuth imaging results of the three transponders after sensor position error compensation; Figure 4 (a)(b)(c) is respectively for the target at (685.6m, -26.36°), (740.4m, 0.468°) target and (796.3m, 17.63°) target’s azimuth BP imaging results and range BP imaging results.

具体实施方式Detailed ways

下面结合附图并举实施例,对本发明进行详细描述。The present invention will be described in detail below with reference to the accompanying drawings and examples.

如图1所示,本发明提供了基于多特显点目标的宽带MIMO成像雷达阵列 误差补偿方法,包括如下步骤:As shown in Figure 1, the present invention provides the error compensation method based on the broadband MIMO imaging radar array of multi-specific point target, comprises the steps:

步骤一、在MIMO成像雷达的远场区域设置特显点目标,获取含有阵列误 差的MIMO成像雷达系统回波与阵列误差的一阶近似表达式。Step 1. Set a special point target in the far field area of the MIMO imaging radar, and obtain the first-order approximate expression of the echo and array error of the MIMO imaging radar system including array error.

具体过程为:The specific process is:

对于含有阵列误差的MIMO成像雷达系统,其发射阵元数量为M,接收阵 元数量为N,其发射天线和接收天线的空间位置向量分别为记c为光速,AT,m、φT,m和ΔτT,m分别为第m个发射阵元幅度误 差、相位误差和延时误差,AR,n、φR,n和ΔτR,n分别为第n个接收阵元的幅度误差、 相位误差和延时误差;s(t)为发射信号,分别表示目标位置PTar处的目 标到第m个发射阵元和第n个接收阵元的距离,并记第m个发射阵元的延时误 差造成的距离误差为ΔRT,m=c·ΔτT,m,第n个接收阵元的延时误差造成的距离误差 为ΔRR,n=c·ΔτR,n;其中,下标T和R分别表示雷达系统的发射天线和接收天线, 下标m和n分别表示发射阵元和接收阵元的编号;For a MIMO imaging radar system with array errors, the number of transmitting array elements is M, the number of receiving array elements is N, and the spatial position vectors of the transmitting antenna and receiving antenna are respectively and Denote c as the speed of light, A T,m , φ T,m and Δτ T,m are the amplitude error, phase error and delay error of the mth transmitting element respectively, A R,n , φ R,n and Δτ R, n are the amplitude error, phase error and delay error of the nth receiving array element respectively; s(t) is the transmitting signal, and represent the distances from the target at the target position P Tar to the mth transmitting array element and the nth receiving array element, and record the distance error caused by the delay error of the mth transmitting array element as ΔR T,m = c· Δτ T,m , the distance error caused by the delay error of the nth receiving array element is ΔR R,n = c·Δτ R,n ; where, the subscripts T and R represent the transmitting antenna and receiving antenna of the radar system respectively, The subscripts m and n represent the numbers of the transmitting array element and the receiving array element respectively;

该雷达系统接收到的MN路回波数据经过脉冲压缩处理后为sm(t,m,n;PTar):The MN channel echo data received by the radar system is s m (t,m,n; P Tar ) after pulse compression processing:

式(1)给出了距离脉压处理后的一维回波信号;假设收发阵列均为线阵, 且所有阵元均与目标共面,在该平面建立二维直角坐标系;选取发射阵列的几 何中心作为目标原点,拟合所有发射阵元作为y轴,目标所在一侧为x轴正方 向;此时,该含误差的MIMO阵列各发射阵元和接收阵元的实际位置分别为 为第m个发射阵元的实际 位置坐标测量值,为第n个接收阵元的实际位置坐标测量值,在上述坐 标系下,假设目标极坐标为(ρ,θ),在远场条件下,有Equation (1) gives the one-dimensional echo signal after distance pulse pressure processing; assuming that the transceiver arrays are all linear arrays, and all array elements are in the same plane as the target, a two-dimensional Cartesian coordinate system is established on this plane; select the transmitting array The geometric center of the target is taken as the origin of the target, and all the transmitting elements are fitted as the y-axis, and the side where the target is located is the positive direction of the x-axis; at this time, the actual positions of the transmitting and receiving elements of the MIMO array with errors are respectively and is the measured value of the actual position coordinates of the mth transmitting array element, is the measured value of the actual position coordinates of the nth receiving array element. In the above coordinate system, assuming that the polar coordinates of the target are (ρ, θ), under far-field conditions, we have

为(ρ,θ)点到第m个发射阵元的距离测量值; is the measured distance from point (ρ, θ) to the mth transmitting array element;

为(ρ,θ)点到第n个接收阵元的距离测量值; is the distance measurement value from point (ρ, θ) to the nth receiving array element;

一维脉压后回波信号为sm(t,m,n;ρ,θ):The echo signal after one-dimensional pulse pressure is s m (t,m,n; ρ,θ):

B为发射信号的带宽,公式(3)即为含有阵列误差的MIMO成像雷达系统 回波与阵列误差的一阶近似表达式。B is the bandwidth of the transmitted signal, and formula (3) is the first-order approximate expression of the echo and array error of the MIMO imaging radar system with array error.

步骤二,根据各通道目标距离向脉压结果峰值延时信息,利用最小二乘法 估计特显点目标的位置。具体为:Step 2: According to the peak delay information of the target range pulse pressure results in each channel, the least square method is used to estimate the position of the prominent point target. Specifically:

第(m,n)个通道的双基地距离测量值为 The bistatic distance measurement for the (m, n)th channel is

其中εN,m,n为观测误差;为(ρ,θ)点到第m个发射阵元的距离理想值;Where ε N,m,n is the observation error; is the ideal value of the distance from point (ρ, θ) to the mth transmitting array element;

为(ρ,θ)点到第n个接收阵元的距离理想值; is the ideal value of the distance from point (ρ, θ) to the nth receiving array element;

xT,m,yT,m为第m个发射阵元的实际位置坐标理想值,xR,n,yR,n为第n个接收阵 元的实际位置坐标理想值;x T, m , y T, m are the ideal values of the actual position coordinates of the mth transmitting array element, x R, n , y R, n are the ideal values of the actual position coordinates of the nth receiving array element;

εsys,m,n为延时误差;ε sys,m,n is the delay error;

εsys,m,n=ΔRT,m+ΔRR,n-(ΔxT,mxR,n)sinθ-(ΔyT,m+ΔyR,n)cosθ (5)ε sys, m, n = ΔR T,m +ΔR R,n -(Δx T,mxR,n )sinθ-(Δy T,m +Δy R,n )cosθ (5)

利用MN个通道的观测建立超定方程组得到目标位置的最小二乘估计Using the observations of MN channels to establish an overdetermined equation system to obtain the least squares estimation of the target position

是ρ的估计值;是sinθ的估计值; is the estimated value of ρ; is the estimated value of sinθ;

MIMO成像雷达中收发阵列共线且共中心,即In the MIMO imaging radar, the transmitting and receiving arrays are collinear and co-centered, that is,

利用式(7)将式(6)化简为Use formula (7) to simplify formula (6) to

利用式(8)求解得到特显点目标的位置的最小二乘估计。Using equation (8) to solve the least squares estimation of the position of the prominent point target.

步骤三,利用特显点目标距离向脉压结果峰值相位间的差分相位建立阵元 位置误差的超定线性方程组,估计阵元位置误差。Step 3: Using the differential phase between the peak phases of the pulse pressure results in the distance direction of the target at the special point, the overdetermined linear equations of the array element position error are established to estimate the array element position error.

具体为:Specifically:

MIMO成像雷达中收发阵列共线,其中对应的无误差阵列各阵元的位置分 别位于{(0,yT,m)|m=1,2,...,M}和{(0,yR,n)|n=1,2,...,N},则待估计的收发阵列阵元位置 误差分别为In the MIMO imaging radar, the transmitting and receiving arrays are collinear, and the positions of the corresponding error-free array elements are respectively located in {(0, y T, m )|m=1,2,...,M} and {(0, y R, n )|n=1,2,...,N}, then the position errors of the transceiver array elements to be estimated are respectively

and

其中ΔxT,m,ΔyT,m为第m个发射阵列阵元位置误差;ΔxR,n,ΔyR,n为第n个接收阵列阵元位置误差;Among them, Δx T,m , Δy T,m is the position error of the mth transmitting array element; Δx R,n , Δy R,n is the position error of the nth receiving array element;

考虑式(3)中的相位项为φm(m,n;ρ,θ)Consider the phase term in equation (3) as φ m (m,n; ρ,θ)

根据理想阵元位置构造的成像参考函数的相位为φref(m,n;ρ,θ):The phase of the imaging reference function constructed according to the ideal array element position is φ ref (m,n; ρ,θ):

利用参考相位补偿实测相位得到的残差相位为The residual phase obtained by compensating the measured phase with the reference phase is

式中的k(m,n,θ)为整周模糊度;where k(m,n,θ) is the integer ambiguity;

ρ11为第一特显点位置;ρ22为第二特显点位置;ρ 1 , θ 1 is the position of the first prominent point; ρ 2 , θ 2 is the position of the second prominent point;

实矩阵, 可将所有方程列成方程组形式:remember real matrix, All equations can be listed in the form of a system of equations:

ΔΦ12=H12ΔpTR (15)ΔΦ 12 = H 12 Δp TR (15)

其中,ΔΦ12为第一特显点和第二特显点之间的差分相位矩阵,H12为第一特 显点和第二特显点之间系数矩阵,为待估计的阵元 位置误差;Among them, ΔΦ 12 is the difference phase matrix between the first prominent point and the second prominent point, H 12 is the coefficient matrix between the first prominent point and the second prominent point, is the position error of the array element to be estimated;

系数矩阵H12的秩为M+N-1,再添加一组观测方程组,即增加ΔΦ23, ΔΦ23=H23ΔpTR;ΔΦ23=H23ΔpTR;ΔΦ23为第二特显点和第三特显点之间的差分相 位矩阵,H23为第二特显点和第三特显点之间系数矩阵;The rank of the coefficient matrix H 12 is M+N-1, and then add a group of observation equations, that is, increase ΔΦ 23 , ΔΦ 23 =H 23 Δp TR ; ΔΦ 23 =H 23 Δp TR ; ΔΦ 23 is the second characteristic point and the difference phase matrix between the third characteristic point, H 23 is the coefficient matrix between the second characteristic point and the third characteristic point;

获得方程组为get the equation set as

在θ1≠θ2≠θ3且θ12≠θ23时,有When θ 1 ≠θ 2 ≠θ 3 and θ 12 ≠θ 23 , we have

考虑约束条件式(18):Consider the constraint condition (18):

其中1M为全1向量,0M为全0向量,则 上述约束条件(18)改写成矩阵形式:Among them, 1 M is a vector of all 1s, and 0 M is a vector of all 0s, Then the above constraint (18) is rewritten into a matrix form:

[e1e2]TΔpTR=L·ΔpTR=0 (19)[e 1 e 2 ] T Δp TR =L · Δp TR =0 (19)

将[e1e2]T记为L,则在约束条件(10)下,阵元位置误差的估计问题转化成 约束最小二乘问题,其闭式解为Denote [e 1 e 2 ] T as L, then under the constraint condition (10), the estimation problem of the array element position error is transformed into a constrained least squares problem, and its closed-form solution is

其中,即为最终估计获得的阵元位置误差,表示矩阵的 Moore-Penrose逆,I2M+2N为2M+2N阶单位矩阵。in, is the array element position error obtained by the final estimation, Represents the Moore-Penrose inverse of the matrix, and I 2M+2N is the identity matrix of order 2M+2N.

步骤四,利用单个特显点目标的距离向脉压结果峰值幅度及相位信息估计 通道幅相、延时误差,并对MIMO成像雷达阵列误差进行补偿。Step 4, using the range pulse pressure peak amplitude and phase information of a single prominent point target to estimate the channel amplitude, phase, and delay errors, and compensate the MIMO imaging radar array error.

具体为:Specifically:

各通道的峰值幅度可以拆解为The peak amplitude of each channel can be disassembled as

ln(AT,m)+ln(AR,n)=ln(Am,n) (21)l n (A T,m )+ln(A R,n )=ln(A m,n ) (21)

其中,Am,n为实测单特显点目标的峰值幅度;将[lnAT,1,...,lnAT,M,lnAR,1,...,lnAR,N] 记为X,将[lnA1,1,lnA1,2,...,lnAM,N]记为Y,即得到通道幅度误差的矩阵形式:Among them, A m,n is the peak amplitude of the measured single specific point target; record [lnA T,1 ,...,lnA T,M ,lnA R,1 ,...,lnA R,N ] as X , record [lnA 1,1 ,lnA 1,2 ,...,lnA M,N ] as Y, that is, the matrix form of the channel amplitude error is obtained:

Y=HX (22)Y=HX (22)

其中,H为公式(21)中的系数矩阵;添加约束条件AT,1=AR,1,写成矩阵形 式为Among them, H is the coefficient matrix in the formula (21); adding the constraint condition A T,1 = AR,1 , written in matrix form as

L1X=0 (23)L 1 X=0 (23)

其中,L1=[1,0,...,0,-1,0,...,0];于是得到通道幅度误差的最小二乘估计Among them, L 1 =[1,0,...,0,-1,0,...,0]; then the least squares estimation of the channel amplitude error is obtained

为X的估计值,则对于理想特显点目标而言,各个通道的峰值相位相同, 因此补偿用的幅度值应为 is the estimated value of X, then for an ideal prominent point target, the peak phases of each channel are the same, so the amplitude value used for compensation should be

延时误差远小于分辨率,忽略延时误差对峰值位置的影响,仅消除峰值相 位的影响,此处将延时引入的相位误差与通道相位误差统一校正,将特显点目 标在各个通道的峰值相位补偿成理想相位,即:The delay error is much smaller than the resolution, and the influence of the delay error on the peak position is ignored, and only the influence of the peak phase is eliminated. Here, the phase error introduced by the delay and the channel phase error are uniformly corrected, and the special point is targeted at each channel. The peak phase is compensated to the ideal phase, namely:

φcom(m,n)=θm,nm,n (26)φ com (m,n)=θ m,nm,n (26)

其中,φcom(m,n)为补偿用的相位,θm,n为根据特显点目标位置计算出来的理 想峰值相位,φm,n为特显点目标在各个通道的实测峰值相位;Among them, φ com (m, n) is the phase used for compensation, θ m, n is the ideal peak phase calculated according to the position of the special point target, and φ m, n is the measured peak phase of the special point target in each channel;

利用Acom(m,n)以及φcom(m,n)对述MIMO成像雷达阵列误差进行补偿。Use A com (m,n) and φ com (m,n) to compensate the MIMO imaging radar array error.

下面给出本实施例中,MIMO成像雷达及特显点目标(转发器)的指标如 下:Provide below in the present embodiment, the index of MIMO imaging radar and special point target (transponder) is as follows:

载波频率:16.2GHz;发射信号脉宽:2ms;工作带宽:400MHz;发射阵元 个数:16;接收阵元个数:32;发射阵元间距:9.3mm;接收阵元间距:74.4mm; 场景范围:500m~900m;转发器个数:3Carrier frequency: 16.2GHz; pulse width of transmitting signal: 2ms; working bandwidth: 400MHz; number of transmitting array elements: 16; number of receiving array elements: 32; spacing of transmitting array elements: 9.3mm; spacing of receiving array elements: 74.4mm; Scene range: 500m ~ 900m; Number of transponders: 3

采用本发明所公开的基于多特显点目标的宽带MIMO成像雷达阵列误差补 偿方法对实测数据进行阵列误差估计补偿。对于如图2所示的16发32收的含 有阵列误差的集中式MIMO成像雷达阵列,其发射天线和接收天线的空间位置 向量分别为记c为光速,AT,m、φT,m和ΔτT,m分 别为第m个发射阵元幅度误差、相位误差和延时误差,AR,n、φR,n和ΔτR,n分别为 第n个接收阵元的幅度误差、相位误差和延时误差;s(t)为发射信号,分别表示PTar处的目标到第m个发射阵元和第n个接收阵元的距离,并记 ΔRT,m=c·ΔτT,m,ΔRR,n=c·ΔτR,n。其中,下标T和R分别表示发射和接收天线,下标 m和n分别表示发射阵元和接收阵元的编号。The method for compensating the array error of the broadband MIMO imaging radar based on the multi-distinct point target disclosed by the present invention is used to estimate and compensate the array error for the measured data. For the centralized MIMO imaging radar array with 16 transmissions and 32 receptions as shown in Figure 2, the spatial position vectors of the transmitting antenna and the receiving antenna are respectively and Denote c as the speed of light, A T,m , φ T,m and Δτ T,m are the amplitude error, phase error and delay error of the mth transmitting element respectively, A R,n , φ R,n and Δτ R, n are the amplitude error, phase error and delay error of the nth receiving array element respectively; s(t) is the transmitting signal, and Denote the distances from the target at P Tar to the mth transmitting element and the nth receiving element, and record ΔR T,m =c·Δτ T,m , ΔR R,n =c·Δτ R,n . Wherein, the subscripts T and R represent the transmitting and receiving antennas respectively, and the subscripts m and n represent the serial numbers of the transmitting array element and the receiving array element respectively.

本发明给出的一种基于多特显点目标的宽带MIMO成像雷达的阵列误差补 偿方法,包括如下步骤:A kind of array error compensation method based on the wide-band MIMO imaging radar of multi-significant point target that the present invention provides, comprises the following steps:

步骤一,得到含有阵列误差的MIMO成像雷达系统回波与阵列误差的一阶 近似表达式:含有阵列误差的MIMO雷达系统的回波幅度、相位特性等均与阵 列误差有密切联系,为了获得较为简单的关系式,可以通过在远场区域设置特 显点目标得到回波相位与阵列误差的一阶近似关系表达式,从而利用较为简单 的方式实现阵列误差的高精度估计。Step 1. Obtain the first-order approximate expressions of the echo and array error of the MIMO imaging radar system with array error: the echo amplitude and phase characteristics of the MIMO radar system with array error are closely related to the array error. In order to obtain a comparative The simple relational expression can obtain the first-order approximate relational expression between the echo phase and the array error by setting a special point target in the far-field area, so as to realize the high-precision estimation of the array error in a relatively simple way.

选取发射阵列的几何中心作为目标原点,拟合所有发射阵元作为y轴,目 标所在一侧为x轴正方向。此时,该含误差的MIMO阵列各发射阵元和接收阵 元的实际位置分别为在上述坐标 系下,假设目标极坐标为(ρ,θ),在远场条件下,一维脉压后回波信号应为Select the geometric center of the transmitting array as the target origin, fit all transmitting array elements as the y-axis, and the side where the target is located is the positive direction of the x-axis. At this time, the actual positions of each transmitting element and receiving element of the error-containing MIMO array are respectively and In the above coordinate system, assuming that the polar coordinates of the target are (ρ, θ), under far-field conditions, the echo signal after one-dimensional pulse pressure should be

步骤二,估计特显点目标的位置:由于后续估计阵列误差需要利用到特显 点目标的位置信息,因此需要先得出特显点目标的位置。一般来见,成像雷达 对目标的定位主要利用相位信息,但是由于本发明系统中存在的相位误差导致 成像位置存在明显的畸变,不能加以利用,因此考虑根据各通道回波峰值位置 信息对目标位置进行粗定位。Step 2: Estimating the position of the prominent point target: Since the subsequent estimation of the array error needs to use the position information of the prominent point target, it is necessary to obtain the position of the prominent point target first. Generally speaking, imaging radar mainly utilizes phase information for target positioning, but due to the phase error in the system of the present invention, there is obvious distortion in the imaging position, which cannot be used. Perform coarse positioning.

利用512个通道的观测建立超定方程组可得到三个转发器位置的最小二乘 估计Using the observations of 512 channels to establish an overdetermined equation system can obtain the least squares estimation of the positions of the three transponders

可以求得各个转发器的空间位置分别为(685.6m,-26.36°),(740.4m,0.468 °)和(796.3m,17.63°)。The spatial positions of each transponder can be obtained as (685.6m, -26.36°), (740.4m, 0.468°) and (796.3m, 17.63°).

步骤三,利用特显点目标间的差分相位估计阵元位置误差:公式(3)表明 特显点目标的峰值相位受通道相位、延时误差和阵元位置误差的共同影响,考 虑到通道误差不随目标变化,可以利用目标峰值相位差分处理消除该影响,得 到差分峰值相位与阵元位置误差的线性关系,从而首先估计出阵元位置误差。Step 3: Estimate the position error of the array element by using the differential phase between the prominent point targets: Equation (3) shows that the peak phase of the prominent point target is affected by the channel phase, delay error and array element position error. Considering the channel error It does not vary with the target, the target peak phase difference processing can be used to eliminate the influence, and the linear relationship between the differential peak phase and the position error of the array element is obtained, so that the position error of the array element can be estimated first.

利用转发器1和转发器2之间相位差分处理消除掉阵元相位误差及整周模 糊度的影响得到Using the phase difference processing between transponder 1 and transponder 2 to eliminate the influence of array element phase error and integer ambiguity, we get

同理,可以得到转发器2和转发器3之间相位差分处理得到差分相位In the same way, the phase difference processing between transponder 2 and transponder 3 can be obtained to obtain the differential phase

因此,根据下面的公式即可得到阵元位置误差的估计结果Therefore, the estimation result of the array element position error can be obtained according to the following formula

步骤四,估计通道幅相、延时误差,实现良好聚焦:补偿完阵元位置误差 之后,利用单特显点目标的实测回波峰值特性与理想回波峰值特性对比即可实 现通道误差的估计补偿。Step 4: Estimate channel amplitude, phase, and delay errors to achieve good focus: After compensating for the position error of the array element, the channel error can be estimated by comparing the measured echo peak characteristics with the ideal echo peak characteristics of the single-point display target compensate.

幅相误差和延时误差可以利用单特显点的最小二乘估计求解。通道幅度误 差的最小二乘估计可以写为Amplitude and phase errors and delay errors can be solved by using the least squares estimation of a single characteristic point. The least squares estimate of the channel magnitude error can be written as

对于理想特显点目标而言,各个通道的峰值相位应该相同,因此补偿用的 幅度值应为For an ideal point target, the peak phase of each channel should be the same, so the amplitude value used for compensation should be

由于延时误差一般相对于分辨率而言都很小,因此可以忽略其对峰值位置 的影响,只需将其对峰值相位的影响消除即可。接下来将延时引入的相位误差 与通道相位误差统一校正,将特显点目标在各个通道的峰值相位补偿成理想相 位,即Since the delay error is generally very small relative to the resolution, its influence on the peak position can be ignored, and its influence on the peak phase can only be eliminated. Next, the phase error introduced by the delay and the channel phase error are uniformly corrected, and the peak phase of the specific point target in each channel is compensated to an ideal phase, that is,

φcom(m,n)=θm,nm,n(34)φ com (m,n)=θ m,nm,n (34)

其中,φcom(m,n)为补偿用的相位,θm,n为根据特显点目标位置计算出来的理 想峰值相位,φm,n为特显点目标在各个通道的实测峰值相位。Among them, φ com (m,n) is the phase used for compensation, θ m,n is the ideal peak phase calculated according to the position of the special point target, and φ m,n is the measured peak phase of the special point target in each channel.

补偿阵元位置误差前后三个转发器的成像结果分别如图3和图4所示。图3 (a)(b)(c)分别针对(685.6m,-26.36°)的目标、(740.4m,0.468°)的目标 以及(796.3m,17.63°)的目标的方位向BP成像结果以及距离向BP成像结果。 图4(a)(b)(c)分别针对(685.6m,-26.36°)的目标、(740.4m,0.468°)的 目标以及(796.3m,17.63°)的目标的方位向BP成像结果以及距离向BP成像 结果。从中可以得到阵元位置误差补偿前的方位向峰值旁瓣比分别为 -11.2917dB、-13.2915dB和-11.7017dB,补偿后的方位向峰值旁瓣比分别为 -12.9174dB、-13.1375dB和-13.6108dB。通过对比阵元位置误差补偿前后的成像 质量可知,当选取其中一个转发器作为定标参考点时,该点的成像质量很好, 但是另外两点的成像质量明显不理想,峰值旁瓣比水平与理想值最大差距达到 约2dB;当利用三个点目标进行定标时,可以得到阵元位置误差的估计值,同时 补偿阵元位置误差之后,三个点目标的成像质量均达到了理想的水平,峰值旁 瓣比水平与理论值差距小于0.4dB。The imaging results of the three transponders before and after compensating the element position error are shown in Fig. 3 and Fig. 4 respectively. Figure 3 (a)(b)(c) the azimuth BP imaging results of (685.6m, -26.36°), (740.4m, 0.468°) and (796.3m, 17.63°) targets respectively and Rangewise BP imaging results. Figure 4(a)(b)(c) are the azimuth BP imaging results of (685.6m, -26.36°) target, (740.4m, 0.468°) target and (796.3m, 17.63°) target respectively and Rangewise BP imaging results. It can be obtained that the azimuth peak side lobe ratios before the element position error compensation are -11.2917dB, -13.2915dB and -11.7017dB respectively, and the azimuth peak side lobe ratios after compensation are -12.9174dB, -13.1375dB and - 13.6108dB. By comparing the imaging quality before and after the position error compensation of the array element, it can be seen that when one of the transponders is selected as the calibration reference point, the imaging quality of this point is very good, but the imaging quality of the other two points is obviously not ideal, and the peak side lobe ratio is horizontal. The maximum difference from the ideal value is about 2dB; when using three point targets for calibration, the estimated value of the array element position error can be obtained, and after compensating for the array element position error, the imaging quality of the three point targets has reached the ideal level, the difference between the peak sidelobe ratio level and the theoretical value is less than 0.4dB.

通过本实施例的实测数据处理,可以发现本发明可以利用多个特显点目标 实现阵列误差的良好估计,基于本方法补偿后的成像质量明显好于基于单特显 点目标补偿方法的成像质量。Through the actual measurement data processing in this embodiment, it can be found that the present invention can use multiple prominent point targets to achieve good estimation of array errors, and the imaging quality after compensation based on this method is obviously better than that based on the compensation method based on a single specific point target .

综上,以上仅为本发明的较佳实施例而已,并非用于限定本发明的保护范 围。凡在本发明的精神和原则之内,所作的任何修改、等同替换、改进等,均 应包含在本发明的保护范围之内。To sum up, the above are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims (5)

1. The broadband MIMO imaging radar array error compensation method based on the multi-bit display target is characterized by comprising the following steps of:
step one, setting a special display point target in a far-field area of the MIMO imaging radar, and acquiring a first-order approximate expression of an echo and an array error of the MIMO imaging radar system containing the array error;
estimating the position of a special display point target by using a least square method according to the peak value delay information of the pulse pressure result of the target distance of each channel;
establishing an over-determined linear equation set of the array element position error by using the differential phase between the target distance of the special display point and the pulse pressure result peak value phase, and estimating the array element position error;
and step four, estimating channel amplitude-phase and delay errors from the pulse pressure result peak amplitude and phase information by using the distance of a single special display point target, and compensating the MIMO imaging radar array errors.
2. The method according to claim 1, wherein in the first step, a first-order approximate expression of the echo and the array error of the MIMO imaging radar system with the array error is obtained by:
for the MIMO imaging radar system containing array errors, the number of transmitting array elements is M, the number of receiving array elements is N, and the space position vectors of transmitting antennas and receiving antennas are respectivelyAndnotation c as the speed of light, AT,m、φT,mAnd Δ τT,mRespectively the amplitude error, phase error and delay error of the mth transmitting array element, AR,n、φR,nAnd Δ τR,nRespectively the amplitude error, the phase error and the delay error of the nth receiving array element; s (t) is a transmission signal,andrespectively represent target positions PTarThe distance from the target to the mth transmitting array element and the nth receiving array element, and the distance error caused by the delay error of the mth transmitting array element is recorded as delta RT,m=c·ΔτT,mThe distance error caused by the delay error of the nth receiving array element is Delta RR,n=c·ΔτR,n(ii) a Subscripts T and R respectively represent a transmitting antenna and a receiving antenna of the radar system, and subscripts m and n respectively represent the numbers of a transmitting array element and a receiving array element;
MN path echo data received by the radar system is s after pulse compression processingm(t,m,n;PTar):
The formula (1) gives a one-dimensional echo signal after distance pulse pressure processing; assuming that the receiving and transmitting arrays are linear arrays and all array elements are coplanar with a target, and establishing a two-dimensional rectangular coordinate system on the plane; selecting the geometric center of the transmitting array as a target origin, fitting all transmitting array elements as a y axis, and setting the side where the target is located as the positive direction of an x axis; in this case, the actual positions of each transmitting array element and each receiving array element of the MIMO array containing errors are respectivelyAnd is the actual position coordinate measurement of the mth transmitting array element,for the actual position coordinate measurement of the nth receiving array element, assuming the target polar coordinate is (rho, theta) in the above coordinate system, under the far field condition, there are
Distance measurement value from (rho, theta) point to m-th transmitting array element;
distance measurement value from (rho, theta) point to nth receiving array element;
one-dimensional pulse pressure back echo signal is sm(t,m,n;ρ,θ):
And B is the bandwidth of the transmitted signal, and formula (3) is a first-order approximate expression of the echo and the array error of the MIMO imaging radar system containing the array error.
3. The method as claimed in claim 2, wherein in the second step, the position of the particular display point target is estimated by using a least square method according to the peak delay information of the pulse pressure result from the distance of each channel target, specifically:
bistatic range measurements for the (m, n) th channel are
Wherein epsilonN,m,nIs an observation error;ideal distance value from the point to the m-th transmitting array element;
the ideal distance value from the (rho, theta) point to the nth receiving array element;
xT,m,yT,mis the ideal value, x, of the actual position coordinate of the mth transmitting array elementR,n,yR,nThe ideal value of the actual position coordinate of the nth receiving array element is obtained;
εsys,m,nis a delay error;
εsys,m,n=ΔRT,m+ΔRR,n-(ΔxT,m+ΔxR,n)sinθ-(ΔyT,m+ΔyR,n)cosθ (5)
least square estimation of target position by using observation of MN channels to establish over-determined equation set
Is an estimate of ρ;is an estimate of sin θ;
with co-linear and co-centric transmit-receive arrays in MIMO imaging radars, i.e.
The formula (6) is simplified into the formula (7)
And (5) solving by using the formula (8) to obtain the least square estimation of the position of the special display point target.
4. The method as claimed in claim 3, wherein the step of establishing an over-determined linear equation set of the array element position error from the specific apparent point target distance to the differential phase between the pulse pressure result peak phases estimates the array element position error by:
the receiving and transmitting arrays in the MIMO imaging radar are collinear, wherein the positions of array elements of the corresponding error-free arrays are respectively positioned in { (0, y)T,m) 1,2,. M } and { (0, y)R,n) If 1,2, as, N, the position errors of the transmit/receive array elements to be estimated are respectively 1,2
And
wherein Δ xT,m,ΔyT,mThe position error of the mth transmitting array element is obtained; Δ xR,n,ΔyR,nThe position error of the nth receiving array element is obtained;
consider the phase term in equation (3) as phim(m,n;ρ,θ)
The phase of the imaging reference function constructed according to the position of the ideal array element is phiref(m,n;ρ,θ):
The residual phase obtained by compensating the measured phase with the reference phase is
Wherein k (m, n, θ) is the integer ambiguity;
ρ11is the position of the first special display point; rho22Is the position of the second special display point;
note the bookThe solid matrix is a matrix of a plurality of pixels, all equations can be listed in the form of a set of equations:
ΔΦ12=H12ΔpTR (15)
wherein, Δ Φ12Is a differential phase matrix between a first and a second distinctive point, H12Is a coefficient matrix between the first and second distinctive points,the position error of the array element to be estimated is obtained;
coefficient matrix H12Is M + N-1, and then a group of observation equations is added, namely, delta phi is increased23,ΔΦ23=H23ΔpTR;ΔΦ23=H23ΔpTR;ΔΦ23Is a differential phase matrix between the second and third distinctive points, H23A coefficient matrix between the second special display point and the third special display point;
obtain the system of equations as
At theta1≠θ2≠θ3And theta12≠θ23When there is
Considering the constraint equation (18):
wherein 1 isMIs a full 1 vector, 0MThe vector is a vector of all 0 s,the constraints (18) are then rewritten in matrix form:
[e1 e2]TΔpTR=L·ΔpTR=0 (19)
will [ e ]1 e2]TAnd if the L is recorded, under the constraint condition (10), the estimation problem of the array element position error is converted into a constraint least square problem, and the closed form solution is
Wherein,namely the position error of the array element obtained by final estimation,Moore-Penrose inverse, I, of the representation matrix2M+2NIs an identity matrix of order 2M + 2N.
5. The method as claimed in claim 4, wherein the fourth step of estimating channel amplitude-phase error and delay error from the pulse pressure result peak amplitude and phase information by using the distance of a single distinctive point target, and compensating the MIMO imaging radar array error comprises:
the peak amplitude of each channel can be decomposed into
ln(AT,m)+ln(AR,n)=ln(Am,n) (21)
Wherein A ism,nThe peak amplitude of the actually measured single-feature display point target is obtained; will [ lnA ]T,1,...,lnAT,M,lnAR,1,...,lnAR,N]Is marked as X, will be [ lnA ]1,1,lnA1,2,...,lnAM,N]And recording as Y to obtain a matrix form of the channel amplitude error:
Y=HX (22)
wherein, H is a coefficient matrix in formula (21); add constraint AT,1=AR,1Written in matrix form as
L1X=0 (23)
Wherein L is1=[1,0,...,0,-1,0,...,0](ii) a A least squares estimate of the channel amplitude error is then obtained
Is an estimate of X, then for an ideal saliency target, the peak phases of the individual channels are the same, so the amplitude values for compensation should be
The delay error is far smaller than the resolution, the influence of the delay error on the peak position is ignored, only the influence of the peak phase is eliminated, the phase error introduced by delay and the channel phase error are corrected in a unified way, and the peak phase of the special display point target in each channel is compensated into an ideal phase, namely:
φcom(m,n)=θm,nm,n (26)
wherein phi iscom(m, n) is a phase for compensation, thetam,nIs an ideal peak phase, phi, calculated from the target position of the particular display pointm,nActual measurement peak phases of the special display point targets in all channels are obtained;
using Acom(m, n) and phicom(m, n) compensating for the MIMO imaging radar array error.
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