阅读说明：本技术 基于多特显点目标的宽带mimo成像雷达阵列误差补偿方法 (Broadband MIMO imaging radar array error compensation method based on multiple special display point targets ) 是由 曾涛 田卫明 胡程 王晶阳 龙腾 于 2019-08-09 设计创作，主要内容包括：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 broadband MIMO imaging radar array error compensation method based on a multi-special-display-point target, which can realize good focusing of a broadband MIMO imaging radar system so as to obtain good imaging performance. And setting an ultra-display point target in a far-field area of the MIMO imaging radar, and acquiring a first-order approximate expression of the echo and the array error of the MIMO imaging radar system containing the array error. And estimating the position of the special display point target by using a least square method according to the peak value delay information of the pulse pressure result from the target distance of each channel. And 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 phase, and estimating the array element position error. And estimating channel amplitude-phase and delay errors by using the distance of a single special display point target to the pulse pressure result peak amplitude and phase information, and compensating the phase errors of the MIMO imaging radar channel.)

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, A_T,m、φ_T,mAnd Δ τ_T,mRespectively the amplitude error, phase error and delay error of the mth transmitting array element, A_R,n、φ_R,nAnd Δ τ_R,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 P_TarThe 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 R_T,m＝c·Δτ_T,mThe distance error caused by the delay error of the nth receiving array element is Delta R_R,n＝c·Δτ_R,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 processing_m(t,m,n；P_Tar)：

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 s_m(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 epsilon_N,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;

x_T,m,y_T,mis the ideal value, x, of the actual position coordinate of the mth transmitting array element_R,n,y_R,nThe ideal value of the actual position coordinate of the nth receiving array element is obtained;

ε_sys,m,nis a delay error;

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)

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 x_T,m,Δy_T,mThe position error of the mth transmitting array element is obtained; Δ x_R,n,Δy_R,nThe position error of the nth receiving array element is obtained;

consider the phase term in equation (3) as phi_m(m,n；ρ,θ)

The phase of the imaging reference function constructed according to the position of the ideal array element is phi_ref(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;

ρ₁,θ₁is the position of the first special display point; rho₂,θ₂Is 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＝H₁₂Δp_TR (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＝H₂₃Δp_TR；ΔΦ₂₃＝H₂₃Δp_TR；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 theta₁-θ₂≠θ₂-θ₃When there is

Considering the constraint equation (18):

wherein 1 is_MIs a full 1 vector, 0_MThe vector is a vector of all 0 s,the constraints (18) are then rewritten in matrix form:

[e₁ e₂]^TΔp_TR＝L·Δp_TR＝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 the content of the first and second substances,namely the position error of the array element obtained by final estimation,Moore-Penrose inverse, I, of the representation matrix_2M+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(A_T,m)+ln(A_R,n)＝ln(A_m,n) (21)

Wherein A is_m,nThe peak amplitude of the actually measured single-feature display point target is obtained; will [ lnA ]_T,1,...,lnA_T,M,lnA_R,1,...,lnA_R,N]Is marked as X, will be [ lnA ]_1,1,lnA_1,2,...,lnA_M,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 A_T,1＝A_R,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:

φ_com(m,n)＝θ_m,n-φ_m,n (26)

wherein phi is_com(m, n) is a phase for compensation, theta_m,nIs an ideal peak phase, phi, calculated from the target position of the particular display point_m,nActual measurement peak phases of the special display point targets in all channels are obtained;

using A_com(m, n) and phi_com(m, n) compensating for the MIMO imaging radar array error.

Technical Field

The invention relates to the technical field of MIMO radars, in particular to a broadband MIMO imaging radar array error compensation method based on a plurality of special display point targets.

Background

MIMO radar is a radar system emerging in recent years. The MIMO radar system introduces a waveform diversity theory in the MIMO communication field into the radar field, a plurality of transmitting array elements transmit mutually orthogonal signal waveforms, a plurality of receiving array elements simultaneously receive multiple paths of signals and sort the signals of different transmitting channels according to the orthogonality of the signals, and therefore the number of independent observation channels far more than the number of actual array elements is obtained. Because the wave form diversity technology greatly improves the observation freedom degree of the system, the overall performance of the MIMO radar has great advantages compared with the traditional single-channel radar and phased array radar.

Generally speaking, for various analysis methods, positioning and imaging algorithms of the MIMO radar system, the amplitude-phase and delay characteristics of each channel of the MIMO radar are considered to be completely consistent, and the actual array element position is completely the same as the design position. However, in an actual system, because transmission links of the observation channels are different, amplitude-phase and delay characteristics of the channels are different; meanwhile, the actual array element position deviates from the ideal position necessarily due to the limitation of the processing precision of the device. If the array error in the actual MIMO radar system is not compensated, the overall performance of the radar will be seriously deteriorated, and the designed performance index is difficult to achieve.

For a broadband MIMO imaging radar, the azimuth sidelobe is raised due to inter-channel amplitude-phase errors in an array, and even the condition that focusing cannot be performed occurs; the inter-channel delay error can cause the range migration used by imaging compensation to be inconsistent with an actual value, so that the range side lobe and the azimuth side lobe are raised; array element position errors can cause uneven spatial sampling of the array, so that high grating lobes exist in the azimuth imaging result, and imaging quality is seriously affected.

However, the existing MIMO radar array error compensation method mainly develops research for target positioning application of a narrow-band system, analysis on influence of array errors on imaging performance is less, delay errors seriously influencing a wide-band imaging radar are not considered, and the traditional array error estimation method is not ideal in effect on the wide-band MIMO imaging radar system.

Therefore, in order to obtain better imaging performance of the broadband MIMO imaging radar, it is necessary to develop a new array design method for array errors existing in the system.

Disclosure of Invention

In view of this, the invention provides a method for compensating for errors of a wideband MIMO imaging radar array based on a multi-bit point target, which can achieve good focusing of a wideband MIMO imaging radar system, thereby obtaining good imaging performance.

The broadband MIMO imaging radar array error compensation method based on the multi-feature point target comprises the following steps:

step one, setting a special display point target in a far-field area of the MIMO imaging radar, and obtaining a first-order approximate expression of the echo of the MIMO imaging radar system containing the array error and the array error.

And step two, estimating the position of the 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.

And step three, 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 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.

Further, in the first step, a first-order approximate expression of the echo and the array error of the MIMO imaging radar system containing the array error is obtained, and the specific process is as follows:

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, A_T,m、φ_T,mAnd Δ τ_T,mRespectively the m-th transmitting array element amplitude error, phase error and delay error, A_R,n、φ_R,nAnd Δ τ_R,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 P_TarThe distance between the target and 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 R_T,m＝c·Δτ_T,mThe distance error caused by the delay error of the nth receiving array element is Delta R_R,n＝c·Δτ_R,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 processing_m(t,m,n；P_Tar)：

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, and fitting all the transmitting arraysThe emitting array element is used as a y axis, and the side where the target is located is in 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 respectivelyAndis the actual position coordinate measurement of the mth transmitting array element,the actual position coordinate measurement value of the nth receiving array element is the target polar coordinate (rho, theta) under the coordinate system, and under the far-field condition

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 s_m(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.

Further, step two, estimating the position of the special display point target by using a least square method according to the peak value delay information of the pulse pressure result of the distance of each channel target, specifically:

bistyl of the (m, n) th channelThe ground distance measurement value is

Wherein epsilon_N,m,nIs an observation error;the ideal distance value from the (rho, theta) point to the mth transmitting array element;

the ideal distance value from the (rho, theta) point to the nth receiving array element;

x_T,m,y_T,mis the ideal value, x, of the actual position coordinate of the mth transmitting array element_R,n,y_R,nThe ideal value of the actual position coordinate of the nth receiving array element is obtained;

ε_sys,m,nis a delay error;

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)

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.

Further, an over-determined linear equation set of the array element position error is established by using the differential phase between the specific display point target distance and the pulse pressure result peak value phase, and the array element position error is estimated, which specifically comprises the following steps:

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 x_T,m,Δy_T,mThe position error of the mth transmitting array element is obtained; Δ x_R,n,Δy_R,nThe position error of the nth receiving array element is obtained;

consider the phase term in equation (3) as phi_m(m,n；ρ,θ)

The phase of the imaging reference function constructed according to the position of the ideal array element is phi_ref(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;

ρ₁,θ₁is the position of the first special display point; rho₂,θ₂Is 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＝H₁₂Δp_TR (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＝H₂₃Δp_TR；ΔΦ₂₃＝H₂₃Δp_TR；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 theta₁-θ₂≠θ₂-θ₃When there is

Considering the constraint equation (18):

wherein 1 is_MIs a full 1 vector, 0_MThe vector is a vector of all 0 s,the constraints (18) are then rewritten in matrix form:

[e₁e₂]^TΔp_TR＝L·Δp_TR＝0 (19)

will [ e ]₁e₂]^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 the content of the first and second substances,namely the position error of the array element obtained by final estimation,Moore-Penrose inverse, I, of the representation matrix_2M+2NIs an identity matrix of order 2M + 2N.

Further, step four, estimating channel amplitude-phase error and delay error by using the distance of a single special display point target to the pulse pressure result peak amplitude and phase information, and compensating the MIMO imaging radar array error, specifically:

the peak amplitude of each channel can be decomposed into

ln(A_T,m)+ln(A_R,n)＝ln(A_m,n) (21)

Wherein A is_m,nThe peak amplitude of the actually measured single-feature display point target is obtained; will [ lnA ]_T,1,...,lnA_T,M,lnA_R,1,...,lnA_R,N]Is marked as X, will be [ lnA ]_1,1,lnA_1,2,...,lnA_M,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 A_T,1＝A_R,1Written in the form of a matrix of

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, the influence of the peak position is only eliminated, the phase error introduced by delay and the channel phase error are corrected in a unified mode, the peak phase of the special display point target in each channel is compensated into an ideal phase, namely:

φ_com(m,n)＝θ_m,n-φ_m,n (26)

wherein phi is_com(m, n) is a phase for compensation, theta_m,nTo calculate an ideal peak phase, phi, from the target position of the distinctive point_m,nActual measurement peak phases of the special display point targets in all channels are obtained;

using A_com(m, n) and phi_comAnd (m, n) compensating the MIMO imaging radar array error.

Has the advantages that:

the broadband MIMO imaging radar array error compensation method based on the multiple specially displayed point targets eliminates the influence of channel phase errors and phase integer ambiguity by utilizing peak phase difference processing of echoes of the multiple specially displayed point targets, then realizes estimation compensation of the position errors of the array elements by utilizing constraint minimum two-multiplication by combining the linear relation of the difference phase and the position errors of the array elements, and then carries out estimation compensation on the amplitude phase and delay errors of the channel by combining one-dimensional peak point characteristics of a single specially displayed point target, thereby realizing good focusing of a broadband MIMO imaging radar system.

Drawings

FIG. 1 is a flowchart of a method for compensating an error of a broadband MIMO imaging radar array based on a multi-bit-display target according to the present invention;

FIG. 2 is a schematic diagram of a two-dimensional spatial coordinate system of a MIMO array with array errors;

FIG. 3 shows the distance and azimuth imaging results of the first three transponders for array element position error compensation; fig. 3 (a) (b) (c) azimuthal BP imaging results and range BP imaging results for targets of (685.6m, -26.36 °), (740.4m, 0.468 °), and (796.3m, 17.63 °), respectively;

FIG. 4 shows the distance and azimuth imaging results of three transponders after array element position error compensation; fig. 4(a) (b) (c) azimuth-to-BP imaging results and distance-to-BP imaging results for targets of (685.6m, -26.36 °), (740.4m, 0.468 °), and (796.3m, 17.63 °), respectively.

Detailed Description

The invention is described in detail below by way of example with reference to the accompanying drawings.

As shown in FIG. 1, the invention provides a method for compensating errors of a broadband MIMO imaging radar array based on a multi-bit target, which comprises the following steps:

step one, setting a special display point target in a far-field area of the MIMO imaging radar, and obtaining a first-order approximate expression of the echo of the MIMO imaging radar system containing the array error and the array error.

The specific process is as follows:

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, A_T,m、φ_T,mAnd Δ τ_T,mRespectively the m-th transmitting array element amplitude error, phase error and delay error, A_R,n、φ_R,nAnd Δ τ_R,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 P_TarThe distance between the target and 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 R_T,m＝c·Δτ_T,mThe distance error caused by the delay error of the nth receiving array element is Delta R_R,n＝c·Δτ_R,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 received by the radar systemThe road echo data is s after pulse compression processing_m(t,m,n；P_Tar)：

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 respectivelyAndis the actual position coordinate measurement of the mth transmitting array element,the actual position coordinate measurement value of the nth receiving array element is the target polar coordinate (rho, theta) under the coordinate system, and under the far-field condition

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 s_m(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.

And step two, estimating the position of the 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. The method specifically comprises the following steps:

bistatic range measurements for the (m, n) th channel are

Wherein epsilon_N,m,nIs an observation error;the ideal distance value from the (rho, theta) point to the mth transmitting array element;

the ideal distance value from the (rho, theta) point to the nth receiving array element;

x_T,m,y_T,mis the ideal value, x, of the actual position coordinate of the mth transmitting array element_R,n,y_R,nThe ideal value of the actual position coordinate of the nth receiving array element is obtained;

ε_sys,m,nis a delay error;

ε_sys，m，n＝ΔR_T,m+ΔR_R，n-(Δx_T,m+Δ_xR，n)sinθ-(Δy_T,m+Δy_R,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.

And step three, 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 phase, and estimating the array element position error.

The method specifically comprises the following steps:

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 x_T,m,Δy_T,mThe position error of the mth transmitting array element is obtained; Δ x_R,n,Δy_R,nFor the nth receptionArray element position error;

consider the phase term in equation (3) as phi_m(m,n；ρ,θ)

The phase of the imaging reference function constructed according to the position of the ideal array element is phi_ref(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;

ρ₁,θ₁is the position of the first special display point; rho₂,θ₂Is 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＝H₁₂Δp_TR (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＝H₂₃Δp_TR；ΔΦ₂₃＝H₂₃Δp_TR；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 theta₁-θ₂≠θ₂-θ₃When there is

Considering the constraint equation (18):

wherein 1 is_MIs a full 1 vector, 0_MThe vector is a vector of all 0 s,the constraints (18) are then rewritten in matrix form:

[e₁e₂]^TΔp_TR＝L·Δp_TR＝0 (19)

will [ e ]₁e₂]^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 the content of the first and second substances,namely the position error of the array element obtained by final estimation,Moore-Penrose inverse, I, of the representation matrix_2M+2NIs an identity matrix of order 2M + 2N.

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.

The method specifically comprises the following steps:

the peak amplitude of each channel can be decomposed into

l_n(A_T,m)+ln(A_R,n)＝ln(A_m,n) (21)

Wherein A is_m,nThe peak amplitude of the actually measured single-feature display point target is obtained; will [ lnA ]_T,1,...,lnA_T,M,lnA_R,1,...,lnA_R,N]Is marked as X, will be [ lnA ]_1,1,lnA_1,2,...,lnA_M,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 A_T,1＝A_R,1Written in the form of a matrix of

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, eachThe peak phases of the channels are the same, so the amplitude value 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, the influence of the peak position is only eliminated, the phase error introduced by delay and the channel phase error are corrected in a unified mode, the peak phase of the special display point target in each channel is compensated into an ideal phase, namely:

φ_com(m,n)＝θ_m,n-φ_m,n (26)

wherein phi is_com(m, n) is a phase for compensation, theta_m,nTo calculate an ideal peak phase, phi, from the target position of the distinctive point_m,nActual measurement peak phases of the special display point targets in all channels are obtained;

using A_com(m, n) and phi_com(m, n) compensating the MIMO imaging radar array error.

In this embodiment, the indexes of the MIMO imaging radar and the special display target (repeater) are as follows:

carrier frequency: 16.2 GHz; pulse width of the transmitted signal: 2 ms; the working bandwidth is as follows: 400 MHz; the number of transmitting array elements is as follows: 16; the number of receiving array elements: 32, a first step of removing the first layer; transmitting array element spacing: 9.3 mm; receiving array element spacing: 74.4 mm; scene range: 500 m-900 m; the number of repeaters: 3

The array error estimation compensation is carried out on the measured data by adopting the broadband MIMO imaging radar array error compensation method based on the multi-special display point target disclosed by the invention. For a 16-transmitting 32-receiving centralized MIMO imaging radar array containing array errors as shown in FIG. 2, the spatial position vectors of the transmitting antenna and the receiving antenna are respectivelyAndnotation c as the speed of light, A_T,m、φ_T,mAnd Δ τ_T,mRespectively, the m-th transmitting array element amplitude error, phase error and delay error, A_R,n、φ_R,nAnd Δ τ_R,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 P_TarThe distance between the target and the m-th transmitting array element and the n-th receiving array element is recorded as delta R_T,m＝c·Δτ_T,m，ΔR_R,n＝c·Δτ_R,n. Subscripts T and R denote the transmitting and receiving antennas, respectively, and subscripts m and n denote the numbers of the transmitting and receiving elements, respectively.

The invention provides an array error compensation method of a broadband MIMO imaging radar based on a multi-bit point-of-display target, which comprises the following steps:

step one, obtaining a first-order approximate expression of an echo and an array error of the MIMO imaging radar system containing the array error: the echo amplitude, the phase characteristic and the like of the MIMO radar system containing the array error are closely related to the array error, and in order to obtain a simpler relational expression, a first-order approximate relational expression of the echo phase and the array error can be obtained by arranging an ultra-display point target in a far-field area, so that the high-precision estimation of the array error is realized by using a simpler mode.

And 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 of the target as the positive direction of the x axis. At this time, the actual positions of each transmitting array element and each receiving array element of the MIMO array containing errors are respectivelyAndin the above coordinate system, the target pole is assumedThe coordinate is (rho, theta), and under the far field condition, the echo signal after one-dimensional pulse pressure is

Estimating the position of the special display point target: since the subsequent estimation of the array error requires the use of the position information of the outlier target, the position of the outlier target needs to be obtained first. Generally, phase information is mainly utilized for positioning a target by an imaging radar, but the imaging position has obvious distortion due to phase errors in the system of the invention and cannot be utilized, so that the target position is considered to be roughly positioned according to the echo peak position information of each channel.

Least squares estimation of three transponder positions can be obtained by establishing over-determined equations using 512 channel observations

The spatial positions of the transponders can be determined to be (685.6m, -26.36 °), (740.4m, 0.468 °), and (796.3m, 17.63 °), respectively.

Thirdly, estimating the position error of the array element by using the differential phase between the specially displayed point targets: formula (3) shows that the peak phase of the special display point target is affected by the channel phase, the delay error and the array element position error, the influence is eliminated by utilizing the target peak phase difference processing considering that the channel error does not change along with the target, and the linear relation between the differential peak value phase and the array element position error is obtained, so that the array element position error is estimated firstly.

Eliminating the influence of array element phase error and whole cycle ambiguity by using phase difference processing between the repeater 1 and the repeater 2

Similarly, the differential phase can be obtained by performing the phase difference processing between the transponder 2 and the transponder 3

Therefore, the estimation result of the array element position error can be obtained according to the following formula

Estimating channel amplitude and phase and delay errors to realize good focusing: after the position error of the array element is compensated, the estimation compensation of the channel error can be realized by comparing the actually measured echo peak characteristic of the single special display point target with the ideal echo peak characteristic.

The amplitude phase error and the delay error can be solved by using least square estimation of a single bit. The least squares estimate of the channel amplitude error can be written as

For an ideal saliency target, the peak phase of each channel should be the same, so the amplitude value for compensation should be the same

Since the delay error is generally small relative to the resolution, the influence of the delay error on the peak position can be ignored, and the influence of the delay error on the peak phase can be eliminated. Then, the phase error introduced by the time delay and the channel phase error are corrected uniformly, and the peak value phase of the special display point target in each channel is compensated to be an ideal phase, namely

φ_com(m,n)＝θ_m,n-φ_m,n(34)

Wherein phi is_com(m, n) is a phase for compensation, theta_m,nTo calculate an ideal peak phase, phi, from the target position of the distinctive point_m,nActual measurement of point-specific targets in each channelThe peak phase.

The imaging results of the three transponders before and after compensating the array element position error are shown in fig. 3 and 4, respectively. Fig. 3 (a) (b) (c) azimuth-to-BP imaging results and distance-to-BP imaging results for targets of (685.6m, -26.36 °), (740.4m, 0.468 °), and (796.3m, 17.63 °), respectively. Fig. 4(a) (b) (c) azimuth-to-BP imaging results and distance-to-BP imaging results for targets of (685.6m, -26.36 °), (740.4m, 0.468 °), and (796.3m, 17.63 °), respectively. The azimuth peak sidelobe ratios before the array element position error compensation are-11.2917 dB, -13.2915dB and-11.7017 dB respectively, and the azimuth peak sidelobe ratios after the compensation are-12.9174 dB, -13.1375dB and-13.6108 dB respectively. By comparing the imaging quality before and after the position error compensation of the array element, when one repeater is selected as a calibration reference point, the imaging quality of the point is good, but the imaging quality of the other two points is obviously unsatisfactory, and the maximum difference between the peak side lobe ratio level and the ideal value reaches about 2 dB; when the three point targets are used for calibration, an estimated value of the position error of the array element can be obtained, after the position error of the array element is compensated, the imaging quality of the three point targets reaches an ideal level, and the difference between the peak value side lobe ratio level and the theoretical value is less than 0.4 dB.

Through the actual measurement data processing of the embodiment, the invention can realize good estimation of array errors by utilizing a plurality of special salient point targets, and the imaging quality compensated based on the method is obviously better than that based on a single special salient point target compensation method.

The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.