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

Broadband MIMO imaging radar array error compensation method based on multiple special display point targets Download PDF

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CN110609273B
CN110609273B CN201910735487.0A CN201910735487A CN110609273B CN 110609273 B CN110609273 B CN 110609273B CN 201910735487 A CN201910735487 A CN 201910735487A CN 110609273 B CN110609273 B CN 110609273B
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CN110609273A (en
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曾涛
田卫明
胡程
王晶阳
龙腾
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Beijing Institute of Technology BIT
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/40—Means for monitoring or calibrating
    • G01S7/4052—Means for monitoring or calibrating by simulation of echoes
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/418—Theoretical aspects
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S2013/0236—Special technical features
    • G01S2013/0245—Radar with phased array antenna

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Abstract

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.

Description

Broadband MIMO imaging radar array error compensation method based on multiple special display point targets
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, mutually orthogonal signal waveforms are transmitted through a plurality of transmitting array elements, 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 is necessarily deviated from the ideal position 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 broadband imaging radar are not considered, and the traditional array error estimation method is not ideal for the effect of the broadband 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 an error compensation method for a wideband MIMO imaging radar array based on a multi-feature 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 multiple-special-display-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 an echo and an 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.
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 respectively
Figure GDA0002252753100000031
And
Figure GDA0002252753100000032
notation 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,
Figure GDA00022527531000000311
and
Figure GDA00022527531000000312
respectively 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)：
Figure GDA0002252753100000033
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 respectively
Figure GDA0002252753100000034
And
Figure GDA0002252753100000035
Figure GDA0002252753100000036
is the actual position coordinate measurement of the mth transmitting array element,
Figure GDA0002252753100000037
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
Figure GDA0002252753100000038
Figure GDA0002252753100000039
Distance measurement value from (rho, theta) point to m-th transmitting array element;
Figure GDA00022527531000000310
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)：
Figure GDA0002252753100000041
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:
bistatic range measurements for the (m, n) th channel are
Figure GDA0002252753100000042
Figure GDA0002252753100000043
Wherein epsilonN,m,nIs an observation error;
Figure GDA0002252753100000044
the ideal distance value from the (rho, theta) point to the mth transmitting array element;
Figure GDA0002252753100000045
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
Figure GDA0002252753100000046
Figure GDA0002252753100000047
Is an estimate of ρ;
Figure GDA0002252753100000048
is an estimate of sin θ;
with co-linear and co-centric transmit-receive arrays in MIMO imaging radars, i.e.
Figure GDA0002252753100000051
The formula (6) is simplified into the formula (7)
Figure GDA0002252753100000052
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 target distance of the special display point and the peak phase of the pulse pressure result, 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
Figure GDA0002252753100000053
And
Figure GDA0002252753100000054
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)
Figure GDA0002252753100000055
The phase of the imaging reference function constructed according to the position of the ideal array element is phiref(m,n；ρ,θ)：
Figure GDA0002252753100000056
The residual phase obtained by compensating the measured phase with the reference phase is
Figure GDA0002252753100000061
Wherein k (m, n, θ) is the integer ambiguity;
Figure GDA0002252753100000062
ρ1,θ1is the position of the first special display point; rho2,θ2Is the position of the second special display point;
note the book
Figure GDA0002252753100000065
The solid matrix is a matrix of a plurality of pixels,
Figure GDA0002252753100000066
Figure GDA0002252753100000067
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,
Figure GDA0002252753100000068
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
Figure GDA0002252753100000063
At theta1≠θ2≠θ3And theta1-θ2≠θ2-θ3When there is
Figure GDA0002252753100000064
Considering the constraint equation (18):
Figure GDA0002252753100000071
wherein 1 isMIs a full 1 vector, 0MThe vector is a vector of all 0 s,
Figure GDA0002252753100000073
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
Figure GDA0002252753100000072
Wherein the content of the first and second substances,
Figure GDA0002252753100000074
i.e. the array element bits obtained by final estimationThe position of the error is determined,
Figure GDA0002252753100000075
Moore-Penrose inverse, I, of the representation matrix2M+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(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, and is represented by [ ln A1,1,ln A1,2,...,ln AM,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
Figure GDA0002252753100000081
Figure GDA0002252753100000083
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
Figure GDA0002252753100000082
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,n-φm,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 phicomAnd (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 and compensation of the position errors of the array elements by utilizing a constrained least square method in combination with the linear relation of the differential phase and the position errors of the array elements, and then carries out estimation and compensation on the amplitude and phase errors and the delay errors of the channel in combination with the one-dimensional peak point characteristic of a single specially displayed point target, thereby realizing good focusing of the 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 an echo and an array error of the MIMO imaging radar system containing 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 respectively
Figure GDA0002252753100000091
And
Figure GDA0002252753100000092
notation 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,
Figure GDA0002252753100000093
and
Figure GDA0002252753100000094
respectively represent target positions PTarThe distance between the target and the m-th transmitting array element and the n-th receiving array element is recordedThe distance error caused by the delay error of the array element is 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)：
Figure GDA0002252753100000101
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 respectively
Figure GDA0002252753100000102
And
Figure GDA0002252753100000103
Figure GDA0002252753100000104
is the actual position coordinate measurement of the mth transmitting array element,
Figure GDA0002252753100000105
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
Figure GDA0002252753100000106
Figure GDA0002252753100000107
Distance measurement value from (rho, theta) point to m-th transmitting array element;
Figure GDA0002252753100000108
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)：
Figure GDA0002252753100000109
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
Figure GDA0002252753100000111
Figure GDA0002252753100000112
Wherein epsilonN,m,nIs an observation error;
Figure GDA0002252753100000116
the ideal distance value from the (rho, theta) point to the mth transmitting array element;
Figure GDA0002252753100000117
the ideal distance value from the (rho, theta) point to the nth receiving array element;
xT,m,yT,mis the m < th > oneIdeal value of actual position coordinate, x, of 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
Figure GDA0002252753100000113
Figure GDA0002252753100000118
Is an estimate of ρ;
Figure GDA0002252753100000119
is an estimate of sin θ;
with co-linear and co-centric transmit-receive arrays in MIMO imaging radars, i.e.
Figure GDA0002252753100000114
The formula (6) is simplified into the formula (7)
Figure GDA0002252753100000115
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:
transmit-receive arrays collinear in MIMO imaging radar with corresponding error-freeThe position of each array element of the array is respectively positioned at { (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
Figure GDA0002252753100000121
And
Figure GDA0002252753100000122
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)
Figure GDA0002252753100000123
The phase of the imaging reference function constructed according to the position of the ideal array element is phiref(m,n；ρ,θ)：
Figure GDA0002252753100000124
The residual phase obtained by compensating the measured phase with the reference phase is
Figure GDA0002252753100000125
Wherein k (m, n, θ) is the integer ambiguity;
Figure GDA0002252753100000126
ρ1,θ1is the position of the first special display point; rho2,θ2Is the position of the second special display point;
note the book
Figure GDA0002252753100000127
The solid matrix is a matrix of a plurality of pixels,
Figure GDA0002252753100000128
Figure GDA0002252753100000134
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,
Figure GDA0002252753100000135
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
Figure GDA0002252753100000131
At theta1≠θ2≠θ3And theta1-θ2≠θ2-θ3When there is
Figure GDA0002252753100000132
Considering the constraint equation (18):
Figure GDA0002252753100000133
wherein 1 isMIs a full 1 vector, 0MThe vector is a vector of all 0 s,
Figure GDA0002252753100000136
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
Figure GDA0002252753100000141
Wherein the content of the first and second substances,
Figure GDA0002252753100000142
namely the position error of the array element obtained by final estimation,
Figure GDA0002252753100000143
Moore-Penrose inverse, I, of the representation matrix2M+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 ln (A)T,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
Figure GDA0002252753100000145
Figure GDA0002252753100000146
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
Figure GDA0002252753100000147
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,n-φm,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) error correction for the MIMO imaging radar arrayAnd (4) line compensation.
In this embodiment, the indexes of the MIMO imaging radar and the special display point 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 with array errors as shown in FIG. 2, the spatial position vectors of the transmitting antenna and the receiving antenna are respectively
Figure GDA0002252753100000151
And
Figure GDA0002252753100000152
notation 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,
Figure GDA0002252753100000154
and
Figure GDA0002252753100000153
respectively represent PTarThe distance between the target and the m-th transmitting array element and the n-th receiving array element is recorded as delta RT,m＝c·ΔτT,m，ΔRR,n＝c·ΔτR,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-special display point 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 a special 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 where the target is located as the positive direction of the 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 respectively
Figure GDA0002252753100000161
And
Figure GDA0002252753100000162
in the above coordinate system, assuming the target polar coordinates are (ρ, θ), under the far field condition, the echo signal after one-dimensional pulse pressure should be (ρ, θ)
Figure GDA0002252753100000163
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
Figure GDA0002252753100000164
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: the 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, and the influence can be eliminated by utilizing the target peak phase difference processing in consideration of the fact that the channel error does not change along with the target, so that the linear relation between the differential peak phase and the array element position error is obtained, and the array element position error is estimated firstly.
Eliminating the influence of array element phase error and integer ambiguity by using phase difference processing between the repeater 1 and the repeater 2
Figure GDA0002252753100000171
Similarly, the differential phase can be obtained by performing the phase difference processing between the transponder 2 and the transponder 3
Figure GDA0002252753100000172
Therefore, the estimation result of the array element position error can be obtained according to the following formula
Figure GDA0002252753100000173
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
Figure GDA0002252753100000174
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
Figure GDA0002252753100000175
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 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 into an ideal phase, namely
φcom(m,n)＝θm,n-φm,n (34)
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,nAnd the actual measured peak phase of the specific point target in each channel is obtained.
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 display point targets, and the imaging quality compensated based on the method is obviously better than that based on a single special display 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.

Claims (1)

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, wherein the specific process comprises the following steps:
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 receiving antennas and transmitting antennas are respectively
Figure FDA0003162643810000011
And
Figure FDA0003162643810000012
notation 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)In order to transmit the signal(s),
Figure FDA0003162643810000013
and
Figure FDA0003162643810000014
respectively 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)：
Figure FDA0003162643810000015
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 respectively
Figure FDA0003162643810000016
And
Figure FDA0003162643810000017
Figure FDA0003162643810000018
is the actual position coordinate measurement of the mth transmitting array element,
Figure FDA0003162643810000021
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
Figure FDA0003162643810000022
Figure FDA0003162643810000023
Distance measurement value from (rho, theta) point to m-th transmitting array element;
Figure FDA0003162643810000024
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)：
Figure FDA0003162643810000025
B is the bandwidth of the transmitted signal, and formula (3) is a first-order approximate expression of the echo and 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, specifically:
bistatic range measurements for the (m, n) th channel are
Figure FDA0003162643810000026
Figure FDA0003162643810000027
Wherein epsilonN,m,nIs an observation error;
Figure FDA0003162643810000028
ideal distance value from the point to the m-th transmitting array element;
Figure FDA0003162643810000029
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
Figure FDA0003162643810000031
Figure FDA0003162643810000032
Is an estimate of ρ;
Figure FDA0003162643810000033
is an estimate of sin θ;
with co-linear and co-centric transmit-receive arrays in MIMO imaging radars, i.e.
Figure FDA0003162643810000034
The formula (6) is simplified into the formula (7)
Figure FDA0003162643810000035
Solving by using the formula (8) to obtain the least square estimation of the position of the special display point target;
establishing an over-determined linear equation set of the array element position error by using the differential phase between the specific display point target distance and the pulse pressure result peak value phase, and estimating the array element position error, wherein 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
Figure FDA0003162643810000036
And
Figure FDA0003162643810000037
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)
Figure FDA0003162643810000041
The phase of the imaging reference function constructed according to the position of the ideal array element is phiref(m,n；ρ,θ)：
Figure FDA0003162643810000042
The residual phase obtained by compensating the measured phase with the reference phase is
Figure FDA0003162643810000043
Wherein k (m, n, θ) is the integer ambiguity;
Figure FDA0003162643810000044
ρ1,θ1is the position of the first special display point; rho2,θ2Is the position of the second special display point;
note the book
Figure FDA0003162643810000045
The solid matrix is a matrix of a plurality of pixels,
Figure FDA0003162643810000046
Figure FDA0003162643810000047
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,
Figure FDA0003162643810000048
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 secondA differential phase matrix between the distinctive points and a third distinctive point, H23A coefficient matrix between the second special display point and the third special display point;
obtain the system of equations as
Figure FDA0003162643810000051
At theta1≠θ2≠θ3And theta1-θ2≠θ2-θ3When there is
Figure FDA0003162643810000052
Considering the constraint equation (18):
Figure FDA0003162643810000053
wherein 1 isMIs a full 1 vector, 0MThe vector is a vector of all 0 s,
Figure FDA0003162643810000054
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
Figure FDA0003162643810000055
Wherein the content of the first and second substances,
Figure FDA0003162643810000056
namely the position error of the array element obtained by final estimation,
Figure FDA0003162643810000057
Moore-Penrose inverse, I, of the representation matrix2M+2NIs a 2M +2N order identity matrix;
estimating channel amplitude phase and delay errors from 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
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
Figure FDA0003162643810000061
Figure FDA0003162643810000062
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
Figure FDA0003162643810000063
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,n-φm,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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