CN110609273B - Broadband MIMO imaging radar array error compensation method based on multiple special display point targets - Google Patents

Abstract

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

Description

Array Error Compensation Method for Wideband MIMO Imaging Radar Based on Multi-characteristic Targets

technical field

The present invention relates to the technical field of MIMO radar, in particular to a wideband MIMO imaging radar array error compensation method based on multi-feature salient targets.

Background technique

MIMO radar is an emerging radar system in recent years. The MIMO radar system introduces the waveform diversity theory in the field of MIMO communication into the radar field. Multiple transmitting array elements transmit mutually orthogonal signal waveforms. The signals of different transmission channels are sorted, so as to obtain the number of independent observation channels far more than the actual number of array elements. Because the waveform diversity technology greatly improves the observation freedom of the system, the overall performance of MIMO radar has great advantages compared with traditional single-channel radar and phased array radar.

Generally speaking, for various analysis methods, positioning and imaging algorithms of MIMO radar systems, it is considered that the amplitude, phase and delay characteristics of each channel of MIMO radar are completely consistent, and the actual array element positions are exactly the same as the design positions. However, in the actual system, due to the different transmission links of each observation channel, the amplitude, phase and delay characteristics of each channel must be different; at the same time, limited by the processing accuracy of the device, the actual position of the array element must deviate from the ideal position. If the above-mentioned array errors in the actual MIMO radar system are not compensated, the overall performance of the radar will be seriously deteriorated, and it is difficult to achieve the designed performance index.

For wideband MIMO imaging radars, the amplitude and phase errors between channels in the array will cause sidelobes to rise in the azimuth direction, and even fail to focus; the delay errors between channels will cause the range migration used for imaging compensation to be inconsistent with the actual value. , so that both the range and azimuth side lobes are raised; 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.

However, the existing MIMO radar array error compensation methods are mainly researched on the target positioning application of narrowband systems. There is little analysis on the impact of array errors on imaging performance, and the delay error, which has a serious impact on broadband imaging radars, is not considered. Traditional The effect of the array error estimation method for wideband MIMO imaging radar system is not ideal.

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

SUMMARY OF THE INVENTION

In view of this, the present invention provides a wideband MIMO imaging radar array error compensation method based on multi-feature prominent targets, which can achieve good focusing of the wideband MIMO imaging radar system, thereby obtaining good imaging performance.

An error compensation method for a wideband MIMO imaging radar array based on multi-feature salient targets includes the following steps:

Step 1: Set a characteristic point target in the far-field area of the MIMO imaging radar, and obtain the first-order approximate expression of the echo and the array error of the MIMO imaging radar system containing the array error.

In step 2, the position of the characteristic point target is estimated by the least squares method according to the delay information of the target distance to the peak value of the pulse pressure result of each channel.

In step 3, an overdetermined linear equation system of the position error of the array element is established by using the differential phase between the peak phases of the pulse pressure results in the distance to the target of the characteristic prominent point, and the position error of the array element is estimated.

Step 4: Use the peak amplitude and phase information of the range-direction pulse pressure result of a single characteristic point target to estimate the channel amplitude, phase and delay errors, and compensate the MIMO imaging radar array errors.

Further, in step 1, the first-order approximate expression of the echo and array error of the MIMO imaging radar system containing the array error is obtained, and the specific process is as follows:

和

记c为光速，A_T,m、φ_T,m和Δτ_T,m分别为第m个发射阵元幅度误差、相位误差和延时误差，A_R,n、φ_R,n和Δτ_R,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，

和

分别表示目标位置P_Tar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ΔR_T,m＝c·Δτ_T,m，第n个接收阵元的延时误差造成的距离误差为ΔR_R,n＝c·Δτ_R,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 and receiving antennas are respectively

and

Let c be 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} is the amplitude error, phase error and delay error of the nth receiving array element respectively; s(t) is the transmitted signal,

and

Respectively 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 ΔRT _,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 and receiving antennas of the radar system, respectively, The subscripts m and n represent the numbers of the transmitting array element and the receiving array element, respectively;

The echo data of the MN channel received by the radar system is s _m (t,m,n; P _Tar ) after pulse compression processing:

和

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 range pulse pressure processing; assuming that the transceiver arrays are all linear arrays, and all array elements are coplanar with the target, a two-dimensional rectangular coordinate system is established on this plane; select the transmitting array The geometric center of the MIMO array is used as the origin of the target, all the transmitting array 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 array elements of the MIMO array with errors are

and

is the actual position coordinate measurement value of the mth transmitting array element,

is the actual position coordinate measurement value of the nth receiving array element. In the above coordinate system, assuming that the target polar coordinates are (ρ, θ), under the far-field condition, there are

为(ρ,θ)点到第m个发射阵元的距离测量值；

is the measured value of the distance from the 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 measured value of the distance from the point (ρ, θ) to the nth receiving array element;

The echo signal after one-dimensional pulse pressure is s _m (t, m, n; ρ, θ):

B is the bandwidth of the transmitted signal, and formula (3) is the first-order approximate expression of the echo and the array error of the MIMO imaging radar system containing the array error.

Further, in step 2, according to the delay information of each channel target distance to the pulse pressure result peak value, the least squares method is used to estimate the position of the characteristic point target, specifically:

The bistatic distance measurement for the (m, n)th channel is

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 the 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 the point (ρ, θ) to the nth receiving array element;

x _T,m , y _T,m is the ideal value of the actual position coordinate of the mth transmitting array element, x _R,n , y _R,n is the ideal value of the actual position coordinate of the nth receiving array element;

ε _sys,m,n is the 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 squares estimation of target position by establishing overdetermined equations using observations of MN channels

是ρ的估计值；

是sinθ的估计值；

is the estimated value of ρ;

is the estimated value of sinθ;

In the MIMO imaging radar, the transceiver arrays are collinear and co-centered, that is,

Using Equation (7), Equation (6) can be simplified as

Use equation (8) to solve to obtain the least squares estimation of the position of the distinctive point target.

Further, an overdetermined linear equation system of the position error of the array element is established by using the differential phase between the peak phases of the pulse pressure results from the distance to the characteristic point target, and the position error of the array element is estimated, specifically:

The transceiver arrays in the MIMO imaging radar are collinear, and the positions of the corresponding error-free array elements are located at {(0,y _T,m )|m=1,2,...,M} and {(0,y respectively) _R,n )|n=1,2,...,N}, then the position errors of the transmitting and receiving array elements to be estimated are respectively

and

where 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;

Consider the phase term in equation (3) as φ _m (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):

The residual phase obtained by compensating the measured phase with the reference phase is

k(m,n,θ) in the formula is the ambiguity of the whole week;

ρ ₁ , θ ₁ is the position of the first characteristic point; ρ ₂ , θ ₂ is the position of the second characteristic point;

实矩阵，

可将所有方程列成方程组形式：remember

real matrix,

All equations can be formulated as a system of equations:

ΔΦ ₁₂ =H ₁₂ Δp _TR (15)

为待估计的阵元位置误差；Among them, ΔΦ ₁₂ is the differential phase matrix between the first characteristic point and the second characteristic point, H ₁₂ is the coefficient matrix between the first characteristic point and the second characteristic point,

is the position error of the array element to be estimated;

The rank of the coefficient matrix H ₁₂ is M+N-1, and a set of observation equations is added, that is, ΔΦ ₂₃ is added, ΔΦ ₂₃ =H ₂₃ Δp _TR ; ΔΦ ₂₃ =H ₂₃ Δp _TR ; ΔΦ ₂₃ is the second characteristic point and the differential phase matrix between the third characteristic point, H ₂₃ is the coefficient matrix between the second characteristic point and the third characteristic point;

Get the equation system as

When θ ₁ ≠θ ₂ ≠θ ₃ and θ ₁ -θ ₂ ≠θ ₂ -θ ₃ , we have

Consider the constraint equation (18):

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) can be rewritten into matrix form:

[e ₁ e ₂ ] ^T Δp _TR =L·Δp _TR =0 (19)

Denote [e ₁ e ₂ ] ^T as L, then under the constraint condition (10), the estimation problem of the position error of the array element is transformed into a constrained least squares problem, and its closed-form solution is

即为最终估计获得的阵元位置误差，

表示矩阵的 Moore-Penrose逆，I_2M+2N为2M+2N阶单位矩阵。in,

is the position error of the array element obtained by the final estimation,

Representing the Moore-Penrose inverse of the matrix, I _2M+2N is an identity matrix of order 2M+2N.

Further, in step 4, the peak amplitude and phase information of the range-to-pulse pressure result of a single characteristic point target are used to estimate the channel amplitude-phase error and delay error, and the MIMO imaging radar array error is compensated, specifically:

The peak amplitude of each channel can be decomposed as

ln(A _T,m )+ln(A _R,n )=ln(A _m,n ) (21)

Among them, A _m,n is the peak amplitude of the measured single-point target; denote [lnA _T,1 ,...,lnA _T,M ,lnA _R,1 ,...,lnA _R,N ] as X , denote [ln A _1,1 ,ln A _1,2 ,...,ln A _M,N ] as Y, that is, the matrix form of channel amplitude error is obtained:

Y=HX (22)

Among them, H is the coefficient matrix in formula (21); adding the constraint A _T,1 =A _R,1 , it is written in the matrix form as

L ₁ X = 0 (23)

where L ₁ =[1,0,...,0,-1,0,...,0]; then the least squares estimate of the channel magnitude 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 the ideal characteristic point target, the peak phase of each channel is the same, so the amplitude value for compensation should be

The delay error is much smaller than the resolution, the influence of the delay error on the peak position is ignored, and only the influence of the peak phase is eliminated. The peak phase is compensated to the ideal phase, namely:

φ _com (m,n)＝θ _m,n -φ _m,n (26)

Among them, φ _com (m,n) is the phase used for compensation, θ _m,n is the ideal peak phase calculated according to the target position of the characteristic point, φ _m,n is the measured peak phase of the characteristic point target in each channel;

The above-mentioned MIMO imaging radar array errors are compensated by using A _com (m,n) and φ _com (m,n).

Beneficial effects:

The broadband MIMO imaging radar array error compensation method based on the multi-characteristic point targets provided by the invention utilizes the peak phase differential processing of the echoes of the multiple characteristic point targets to eliminate the influence of the channel phase error and the phase integer ambiguity, and then combines The linear relationship between the differential phase and the position error of the array element uses the constrained least squares method to realize the estimation and compensation of the position error of the array element, and then combines the one-dimensional peak point characteristics of the single-characterized point target to estimate and compensate the channel amplitude, phase and delay errors, so that Achieving good focusing for wideband MIMO imaging radar systems.

Description of drawings

FIG. 1 is a flowchart of a method for compensating wideband MIMO imaging radar array errors based on multi-characteristic point targets provided by the present invention;

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

Figure 3 shows the range and azimuth imaging results of the first three transponders before the array element position error compensation; 0.468°) target and (796.3m, 17.63°) target azimuth BP imaging results and range BP imaging results;

Figure 4 shows the range and azimuth imaging results of the three transponders after the array element position error compensation; 0.468°) target and (796.3m, 17.63°) target azimuth BP imaging results and range BP imaging results.

Detailed ways

The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

As shown in FIG. 1 , the present invention provides a wideband MIMO imaging radar array error compensation method based on multi-characteristic point targets, including the following steps:

Step 1: Set a characteristic point target in the far-field area of the MIMO imaging radar, and obtain the first-order approximate expression of the echo and the array error of the MIMO imaging radar system containing the array error.

The specific process is:

和

记c为光速，A_T,m、φ_T,m和Δτ_T,m分别为第m个发射阵元幅度误差、相位误差和延时误差，A_R,n、φ_R,n和Δτ_R,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，

和

分别表示目标位置P_Tar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ΔR_T,m＝c·Δτ_T,m，第n个接收阵元的延时误差造成的距离误差为ΔR_R,n＝c·Δτ_R,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 and receiving antennas are respectively

and

Let c be 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} is the amplitude error, phase error and delay error of the nth receiving array element respectively; s(t) is the transmitted signal,

and

Respectively 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 ΔRT _,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 and receiving antennas of the radar system, respectively, The subscripts m and n represent the numbers of the transmitting array element and the receiving array element, respectively;

The echo data of the MN channel received by the radar system is s _m (t,m,n; P _Tar ) after pulse compression processing:

和

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 range pulse pressure processing; assuming that the transceiver arrays are all linear arrays, and all array elements are coplanar with the target, a two-dimensional rectangular coordinate system is established on this plane; select the transmitting array The geometric center of the MIMO array is used as the origin of the target, all the transmitting array 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 array elements of the MIMO array with errors are

and

is the actual position coordinate measurement value of the mth transmitting array element,

is the actual position coordinate measurement value of the nth receiving array element. In the above coordinate system, assuming that the target polar coordinates are (ρ, θ), under the far-field condition, there are

为(ρ,θ)点到第m个发射阵元的距离测量值；

is the measured value of the distance from the 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 measured value of the distance from the point (ρ, θ) to the nth receiving array element;

The echo signal after one-dimensional pulse pressure is s _m (t, m, n; ρ, θ):

B is the bandwidth of the transmitted signal, and formula (3) is the first-order approximate expression of the echo and the array error of the MIMO imaging radar system containing the array error.

In step 2, the position of the characteristic point target is estimated by the least squares method according to the delay information of the target distance to the peak value of the pulse pressure result of each channel. Specifically:

The bistatic distance measurement for the (m, n)th channel is

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 the 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 the point (ρ, θ) to the nth receiving array element;

x _T,m , y _T,m is the ideal value of the actual position coordinate of the mth transmitting array element, x _R,n , y _R,n is the ideal value of the actual position coordinate of the nth receiving array element;

ε _sys,m,n is the 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 squares estimation of target position by establishing overdetermined equations using observations of MN channels

是ρ的估计值；

是sinθ的估计值；

is the estimated value of ρ;

is the estimated value of sinθ;

In the MIMO imaging radar, the transceiver arrays are collinear and co-centered, that is,

Using Equation (7), Equation (6) can be simplified as

Use equation (8) to solve to obtain the least squares estimation of the position of the distinctive point target.

In step 3, an overdetermined linear equation system of the position error of the array element is established by using the differential phase between the peak phases of the pulse pressure results in the distance to the target of the characteristic prominent point, and the position error of the array element is estimated.

Specifically:

The transceiver arrays in the MIMO imaging radar are collinear, and the positions of the corresponding error-free array elements are located at {(0,y _T,m )|m=1,2,...,M} and {(0,y respectively) _R,n )|n=1,2,...,N}, then the position errors of the transmitting and receiving array elements to be estimated are respectively

and

where 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;

Consider the phase term in equation (3) as φ _m (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):

The residual phase obtained by compensating the measured phase with the reference phase is

k(m,n,θ) in the formula is the ambiguity of the whole week;

ρ ₁ , θ ₁ is the position of the first characteristic point; ρ ₂ , θ ₂ is the position of the second characteristic point;

实矩阵，

可将所有方程列成方程组形式：remember

real matrix,

All equations can be formulated as a system of equations:

ΔΦ ₁₂ =H ₁₂ Δp _TR (15)

为待估计的阵元位置误差；Among them, ΔΦ ₁₂ is the differential phase matrix between the first characteristic point and the second characteristic point, H ₁₂ is the coefficient matrix between the first characteristic point and the second characteristic point,

is the position error of the array element to be estimated;

The rank of the coefficient matrix H ₁₂ is M+N-1, and a set of observation equations is added, that is, ΔΦ ₂₃ is added, ΔΦ ₂₃ =H ₂₃ Δp _TR ; ΔΦ ₂₃ =H ₂₃ Δp _TR ; ΔΦ ₂₃ is the second characteristic point and the differential phase matrix between the third characteristic point, H ₂₃ is the coefficient matrix between the second characteristic point and the third characteristic point;

Get the equation system as

When θ ₁ ≠θ ₂ ≠θ ₃ and θ ₁ -θ ₂ ≠θ ₂ -θ ₃ , we have

Consider the constraint equation (18):

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) can be rewritten into matrix form:

[e ₁ e ₂ ] ^T Δp _TR =L·Δp _TR =0 (19)

Denote [e ₁ e ₂ ] ^T as L, then under the constraint condition (10), the estimation problem of the position error of the array element is transformed into a constrained least squares problem, and its closed-form solution is

即为最终估计获得的阵元位置误差，

表示矩阵的 Moore-Penrose逆，I_2M+2N为2M+2N阶单位矩阵。in,

is the position error of the array element obtained by the final estimation,

Representing the Moore-Penrose inverse of the matrix, I _2M+2N is an identity matrix of order 2M+2N.

Step 4: Use the peak amplitude and phase information of the range-direction pulse pressure result of a single characteristic point target to estimate the channel amplitude, phase and delay errors, and compensate the MIMO imaging radar array errors.

Specifically:

The peak amplitude of each channel can be decomposed into ln(A _T,m )+ln(A _R,n )=ln(A _m,n ) (21)

Among them, A _m,n is the peak amplitude of the measured single-point target; denote [lnA _T,1 ,...,lnA _T,M ,lnA _R,1 ,...,lnA _R,N ] as X , denote [lnA _1,1 ,lnA _1,2 ,...,lnA _M,N ] as Y, that is, the matrix form of channel amplitude error is obtained:

Y=HX (22)

Among them, H is the coefficient matrix in formula (21); adding the constraint A _T,1 =A _R,1 , it is written in the matrix form as

L ₁ X = 0 (23)

where L ₁ =[1,0,...,0,-1,0,...,0]; then the least squares estimate of the channel magnitude 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 the ideal characteristic point target, the peak phase of each channel is the same, so the amplitude value for compensation should be

The delay error is much smaller than the resolution, the influence of the delay error on the peak position is ignored, and only the influence of the peak phase is eliminated. The peak phase is compensated to the ideal phase, namely:

φ _com (m,n)＝θ _m,n -φ _m,n (26)

Among them, φ _com (m,n) is the phase used for compensation, θ _m,n is the ideal peak phase calculated according to the target position of the characteristic point, φ _m,n is the measured peak phase of the characteristic point target in each channel;

The MIMO imaging radar array error is compensated by using A _com (m,n) and φ _com (m,n).

The following provides the indicators of the MIMO imaging radar and the characteristic point target (transponder) in this embodiment as follows:

Carrier frequency: 16.2GHz; Transmitting signal pulse width: 2ms; Working bandwidth: 400MHz; Number of transmitting array elements: 16; Number of receiving array elements: 32; Scene range: 500m ~ 900m; number of repeaters: 3

和

记c为光速，A_T,m、φ_T,m和Δτ_T,m分别为第m个发射阵元幅度误差、相位误差和延时误差，A_R,n、φ_R,n和Δτ_R,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，

和

分别表示P_Tar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ΔR_T,m＝c·Δτ_T,m，ΔR_R,n＝c·Δτ_R,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 array error compensation method of the wideband MIMO imaging radar based on the multi-feature salient target disclosed in the present invention is used to estimate and compensate the array error for the measured data. For the centralized MIMO imaging radar array with array errors with 16 transmitters and 32 receivers as shown in Figure 2, the spatial position vectors of the transmitting antenna and the receiving antenna are respectively

and

Let c be 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} is the amplitude error, phase error and delay error of the nth receiving array element respectively; s(t) is the transmitted signal,

and

Respectively represent the distances from the target at P _Tar to the mth transmitting array element and the nth receiving array element, and denote ΔRT _,m =c·Δτ _T,m , ΔR _R,n =c·Δτ _R,n . Among them, the subscripts T and R represent the transmitting and receiving antennas, respectively, and the subscripts m and n represent the numbers of the transmitting array element and the receiving array element, respectively.

An array error compensation method for a wideband MIMO imaging radar based on a multi-feature salient target provided by the present invention includes the following steps:

Step 1: Obtain the first-order approximate expression 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. With a simple relational expression, the first-order approximate relational expression between the echo phase and the array error can be obtained by setting the characteristic point target in the far-field region, so that the high-precision estimation of the array error can be achieved in a relatively simple way.

和

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 the 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 the transmitting and receiving elements of the MIMO array with errors are

and

In the above coordinate system, assuming that the target polar coordinates are (ρ, θ), under the far-field condition, the echo signal after the one-dimensional pulse pressure should be

Step 2, estimating the position of the distinctive point target: since the subsequent estimation of the array error needs to use the position information of the characteristic point target, the position of the characteristic point target needs to be obtained first. Generally speaking, the positioning of the target by the imaging radar mainly uses the phase information. However, due to the phase error in the system of the present invention, the imaging position has obvious distortion and cannot be used. Therefore, it is considered to determine the target position according to the echo peak position information of each channel. Perform rough positioning.

Least-squares estimates of the three transponder positions are obtained by establishing an overdetermined system of equations using observations from 512 channels

The spatial positions of each transponder can be obtained as (685.6m, -26.36°), (740.4m, 0.468°) and (796.3m, 17.63°).

Step 3: Estimate the position error of the array element by using the differential phase between the characteristic point targets: formula (3) shows that the peak phase of the characteristic point target is jointly affected by the channel phase, delay error and array element position error, considering the channel error If it does not change with the target, the effect can be eliminated by using the target peak phase differential processing, and the linear relationship between the differential peak phase and the position error of the array element can be obtained, so that the position error of the array element can be estimated first.

Using the phase difference processing between transponder 1 and transponder 2 to eliminate the influence of the phase error of the array element and the ambiguity of the whole cycle,

In the same way, the phase difference processing between the repeater 2 and the repeater 3 can be obtained to obtain the differential phase

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

Step 4: Estimate the channel amplitude, phase, and delay errors to achieve good focusing: After compensating for the position error of the array element, the channel error can be estimated by comparing the measured echo peak characteristics of the single-point obvious target with the ideal echo peak characteristics. compensate.

The amplitude and phase errors and delay errors can be solved by the least squares estimation of the single characteristic point. The least squares estimate of the channel magnitude error can be written as

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

Since the delay error is generally small relative to the resolution, its influence on the peak position can be ignored, and only its influence on the peak phase can be eliminated. Next, the phase error introduced by the delay and the channel phase error are corrected uniformly, and the peak phase of the characteristic point target in each channel is compensated to the ideal phase, that is,

φ _com (m,n)=θ _m,n -φ _m,n (34)

Among them, φ _com (m,n) is the phase used for compensation, θ _m,n is the ideal peak phase calculated according to the target position of the characteristic point, and φ _m,n is the measured peak phase of the characteristic point target in each channel.

The imaging results of the three transponders before and after compensating for the position error of the array elements are shown in Figure 3 and Figure 4, respectively. Figure 3 (a)(b)(c) The azimuth BP imaging results for the (685.6m, -26.36°) target, (740.4m, 0.468°) target and (796.3m, 17.63°) target respectively and Distance to BP imaging results. Figure 4(a)(b)(c) The azimuth BP imaging results for the target of (685.6m, -26.36°), the target of (740.4m, 0.468°) and the target of (796.3m, 17.63°) and Distance to BP imaging results. It can be obtained that the azimuth peak-to-side lobe ratios before the compensation of the element position error are -11.2917dB, -13.2915dB and -11.7017dB respectively, and the azimuth-to-peak side lobe ratios after compensation are -12.9174dB, -13.1375dB and - 13.6108dB. By comparing the imaging quality before and after the compensation of the position error 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 unsatisfactory, and the peak sidelobe ratio level The maximum difference from the ideal value is about 2dB; when three point targets are used for calibration, the estimated value of the position error of the array element can be obtained, and after compensating the position error of the array element, 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.

Through the actual measurement data processing in this embodiment, it can be found that the present invention can utilize multiple distinctive point targets to achieve a good estimation of the array error, and the imaging quality after compensation based on this method is obviously better than that based on the compensation method based on a single distinctive point target .

In conclusion, the above are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims (1)

1. based on the wideband MIMO imaging radar array error compensation method of multi-feature prominent target, it is characterized in that, comprise the steps: Step 1: Set characteristic prominent point targets in the far-field area of the MIMO imaging radar, and obtain a first-order approximate expression of the MIMO imaging radar system echo and array error containing array errors. The specific process is as follows: 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 receiving and transmitting antennas are respectively

and

Let c be 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} is the amplitude error, phase error and delay error of the nth receiving array element respectively; s(t) is the transmitted signal,

and

Respectively 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 ΔRT _,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 the receiving antenna of the radar system, respectively Antenna, the subscripts m and n represent the numbers of the transmitting array element and the receiving array element respectively; The echo data of the MN channel received by the radar system is s _m (t,m,n; P _Tar ) after pulse compression processing:

Equation (1) gives the one-dimensional echo signal after range pulse pressure processing; assuming that the transceiver arrays are all linear arrays, and all array elements are coplanar with the target, a two-dimensional rectangular coordinate system is established on this plane; select the transmitting array The geometric center of the MIMO array is used as the origin of the target, all the transmitting array 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 array elements of the MIMO array with errors are

and

is the actual position coordinate measurement value of the mth transmitting array element,

is the actual position coordinate measurement value of the nth receiving array element. In the above coordinate system, assuming that the target polar coordinates are (ρ, θ), under the far-field condition, there are

is the measured value of the distance from the point (ρ, θ) to the mth transmitting array element;

is the measured value of the distance from the point (ρ, θ) to the nth receiving array element; The echo signal after one-dimensional pulse pressure is s _m (t, m, n; ρ, θ):

B is the bandwidth of the transmitted signal, and formula (3) is the first-order approximate expression of the MIMO imaging radar system echo and array error with array error; Step 2: According to the delay information of each channel target distance to the peak value of the pulse pressure result, use the least squares method to estimate the position of the characteristic point target, specifically: The bistatic distance measurement for the (m, n)th channel is

where ε _N,m,n is the observation error;

The ideal value of the distance from the point to the mth transmitting array element;

is the ideal value of the distance from the point (ρ, θ) to the nth receiving array element; x _T,m , y _T,m is the ideal value of the actual position coordinate of the mth transmitting array element, x _R,n , y _R,n is the ideal value of the actual position coordinate of the nth receiving array element; ε _sys,m,n is the 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 squares estimation of target position by establishing overdetermined equations using observations of MN channels

is the estimated value of ρ;

is the estimated value of sinθ; In the MIMO imaging radar, the transceiver arrays are collinear and co-centered, that is,

Using Equation (7), Equation (6) can be simplified as

Use formula (8) to solve to obtain the least squares estimation of the position of the distinctive point target; Step 3, using the differential phase between the peak phases of the characteristic point target distance to the pulse pressure result to establish an overdetermined linear equation system for the position error of the array element, and to estimate the position error of the array element, specifically: The transceiver arrays in the MIMO imaging radar are collinear, and the positions of the corresponding error-free array elements are respectively located at {(0,y _T,m )|m=1,2,...,M} and {(0 ,y _R,n )|n=1,2,...,N}, the position errors of the transmitting and receiving array elements to be estimated are respectively

and

where 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; Consider the phase term in equation (3) as φ _m (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):

The residual phase obtained by compensating the measured phase with the reference phase is

k(m,n,θ) in the formula is the ambiguity of the whole week;

ρ ₁ , θ ₁ is the position of the first characteristic point; ρ ₂ , θ ₂ is the position of the second characteristic point; remember

real matrix,

All equations can be formulated as a system of equations: ΔΦ ₁₂ =H ₁₂ Δp _TR (15) Among them, ΔΦ ₁₂ is the differential phase matrix between the first characteristic point and the second characteristic point, H ₁₂ is the coefficient matrix between the first characteristic point and the second characteristic point,

is the position error of the array element to be estimated; The rank of the coefficient matrix H ₁₂ is M+N-1, and a set of observation equations is added, that is, ΔΦ ₂₃ is added, ΔΦ ₂₃ =H ₂₃ Δp _TR ; ΔΦ ₂₃ =H ₂₃ Δp _TR ; ΔΦ ₂₃ is the second characteristic point and the differential phase matrix between the third characteristic point, H ₂₃ is the coefficient matrix between the second characteristic point and the third characteristic point; Get the equation system as

When θ ₁ ≠θ ₂ ≠θ ₃ and θ ₁ -θ ₂ ≠θ ₂ -θ ₃ , we have

Consider the constraint equation (18):

Among them, 1 _M is a vector of all 1s, and 0 _M is a vector of all 0s.

Then the above constraint (18) can be rewritten into matrix form: [e ₁ e ₂ ] ^T Δp _TR =L·Δp _TR =0 (19) Denote [e ₁ e ₂ ] ^T as L, then under the constraint condition (10), the estimation problem of the position error of the array element is transformed into a constrained least squares problem, and its closed-form solution is

in,

is the position error of the array element obtained by the final estimation,

Represents the Moore-Penrose inverse of the matrix, I _2M+2N is the 2M+2N order identity matrix; Step 4, using the peak amplitude and phase information of the range-to-pulse pressure result of a single characteristic point target to estimate the channel amplitude, phase and delay errors, and to compensate the MIMO imaging radar array error; specifically: The peak amplitude of each channel can be decomposed as ln(A _T,m )+ln(A _R,n )=ln(A _m,n ) (21) Among them, A _m,n is the peak amplitude of the measured single-point target; denote [lnA _T,1 ,...,lnA _T,M ,lnA _R,1 ,...,lnA _R,N ] as X , denote [lnA _1,1 ,lnA _1,2 ,...,lnA _M,N ] as Y, that is, the matrix form of channel amplitude error is obtained: Y=HX (22) Among them, H is the coefficient matrix in formula (21); adding the constraint A _T,1 =A _R,1 , it is written in the matrix form as L ₁ X = 0 (23) where L ₁ =[1,0,...,0,-1,0,...,0]; then the least squares estimate of the channel magnitude error is obtained

is the estimated value of X, then for the ideal characteristic point target, the peak phase of each channel is the same, so the amplitude value for compensation should be

The delay error is much smaller than the resolution, the influence of the delay error on the peak position is ignored, and only the influence of the peak phase is eliminated. The peak phase is compensated to the ideal phase, namely: φ _com (m,n)＝θ _m,n -φ _m,n (26) Among them, φ _com (m,n) is the phase used for compensation, θ _m,n is the ideal peak phase calculated according to the target position of the characteristic point, φ _m,n is the measured peak phase of the characteristic point target in each channel; The MIMO imaging radar array errors are compensated using A _com (m,n) and φ _com (m,n).

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