CN108459307B - Clutter-based MIMO radar transmit-receive array amplitude-phase error correction method - Google Patents

Clutter-based MIMO radar transmit-receive array amplitude-phase error correction method Download PDF

Info

Publication number
CN108459307B
CN108459307B CN201810112602.4A CN201810112602A CN108459307B CN 108459307 B CN108459307 B CN 108459307B CN 201810112602 A CN201810112602 A CN 201810112602A CN 108459307 B CN108459307 B CN 108459307B
Authority
CN
China
Prior art keywords
array
receiving
vector
transmitting
transmit
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201810112602.4A
Other languages
Chinese (zh)
Other versions
CN108459307A (en
Inventor
纠博
高雨婷
刘源
刘宏伟
周生华
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Xidian University
Original Assignee
Xidian University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Xidian University filed Critical Xidian University
Priority to CN201810112602.4A priority Critical patent/CN108459307B/en
Publication of CN108459307A publication Critical patent/CN108459307A/en
Application granted granted Critical
Publication of CN108459307B publication Critical patent/CN108459307B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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
    • 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
    • G01S7/4004—Means for monitoring or calibrating of parts of a radar system

Landscapes

  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

The invention discloses a clutter-based MIMO radar transmit-receive array amplitude-phase error correction method, which mainly solves the problem that radar detection performance is reduced due to inconsistent array element amplitudes and phases. The implementation process comprises the following steps: constructing a receiving, transmitting and receiving combined guide vector of a radar and a receiving guide vector and a receiving and receiving combined guide vector of a radar receiving subarray; respectively calculating projection matrixes of receiving and transmitting joint guide vectors of the radar and the radar receiving subarrays; respectively constructing transmitting and receiving array error compensation coefficient cost functions by using the projection matrix and the echo data and solving the optimal solution of each cost function; and correcting the transmitting and receiving array guide vectors by using the transmitting and receiving array amplitude-phase error matrix to realize radar transmitting and receiving array amplitude-phase error correction. The method does not need to estimate the number of information source targets, can effectively estimate the amplitude-phase error of the MIMO radar receiving and transmitting array only by a single echo sample, has small calculated amount and low complexity, and is suitable for the error correction real-time processing of the MIMO radar receiving and transmitting array.

Description

Clutter-based MIMO radar transmit-receive array amplitude-phase error correction method
Technical Field
The invention belongs to the technical field of radars, mainly relates to space spectrum estimation and digital beam forming, and particularly relates to a clutter-based MIMO radar transmit-receive array amplitude-phase error correction method which can be used for amplitude-phase error correction of an MIMO radar transmitting array and a receiving array.
Background
The MIMO radar has attracted wide attention in recent years as a radar of a new system, and has the biggest characteristic that echoes of a plurality of receiving antennas are subjected to separation decoupling and coherent synthesis by radiating different signals through a plurality of transmitting antennas. Because the MIMO radar has the advantage of waveform diversity, the MIMO radar has better performance in the aspects of target angle estimation, detection tracking, clutter suppression and the like compared with the traditional phased array radar. However, in practical engineering applications, the amplitude-phase channel consistency of the array is difficult to guarantee, which will cause the above performance of the MIMO radar to be seriously deteriorated and even to be invalid. Therefore, the method has important practical significance for correcting the amplitude and phase errors of the array, and is a problem to be solved urgently in practical application.
The existing radar array amplitude and phase error correction methods are mainly divided into two main categories, namely active correction and self-correction (passive correction).
Active correction is to estimate the array amplitude and phase error parameters by introducing a plurality of auxiliary information sources with known directions and then correct the array by using the obtained error parameters. The current active correction method for amplitude and phase errors mainly comprises the following steps: based on the idea of maximum likelihood estimation: the method solves the extreme value of a likelihood function by utilizing the direction information of a correction source, and estimates the array error through multi-dimensional search, but the calculated amount of the method is large; the method also utilizes a time-sharing information source and combines the properties of a subspace algorithm to obtain an actual array guide vector, and the method requires that at each moment, only one correction source with accurately known position exists in the space, and extracts the actual array prevalence by carrying out feature decomposition on the covariance of array data, thereby estimating the array error. There is also a method of correcting array errors using more than three correction sources, which can estimate multiple types of array errors simultaneously. However, all active correction methods require setting a correction source whose position is precisely known, and the accuracy of correcting the position of the source cannot be guaranteed in many cases.
The self-correcting algorithm of the radar array is based on echo data, simultaneously estimates target parameters and array information, can be calibrated for many times and updated in real time, and is more suitable for an actual radar system. In general, array error self-correction algorithms are iterated cyclically through multiple parameters such that a cost function is minimized to achieve an estimate of the error parameters. The current self-correcting algorithm mainly comprises the following steps: weiss and Friedlander propose an array error correction algorithm using a likelihood function as a cost function, but this algorithm is not suitable for large error estimation because it requires a first-order taylor expansion of the array stream. In order to solve the problem of low convergence speed of a cost function of a self-correcting algorithm, a fast-convergence array error correction method is proposed, and the method solves the problem of maximum likelihood estimation by using an SAGE algorithm. In addition, Paulraj, Kailath and the like propose an array error correction method for realizing rapid convergence by using a special structure of data, the method uses a signal covariance matrix Toeplitz amplitude-phase error correction method, but the method is only suitable for arrays with special structures such as uniform linear arrays and the like, and the practical application scene is limited.
The existing self-correcting method is mostly based on a passive receiving array, the number of targets which are accurately known is often needed, the signal-to-noise ratio of target echoes has a large influence on estimation precision, a multi-dimensional joint iteration is needed in the solving process, the calculated amount is large, and the real-time processing is not facilitated. In addition, when the array is an equidistant uniform linear array, because the number of unknown quantities is 1 more than the known equation number and decoupling can not be effectively separated, the possibility of non-uniqueness exists in array error estimation.
Disclosure of Invention
The invention aims to provide a clutter-based MIMO radar receiving and transmitting array amplitude-phase error correction method which does not need to know the accurate target number and can simultaneously correct the receiving and transmitting array amplitude-phase error so as to overcome the adverse effect on the radar detection performance caused by the inconsistency of the array element amplitude-phase.
The invention relates to a clutter-based MIMO radar transmit-receive array amplitude-phase error correction method, which is characterized by comprising the following steps of:
(1) construction of receive steering vectors a using radar parametersr(theta) and a transmit steering vector at(θ): number of elements N of radar transmitting arraytAnd the number of receiving array elements Nr，NtIs the total number of transmitting array elements, NrFor receiving the total number of array elements, the spacing d between array elementstAnd the spacing d of receiving array elementsrThe radar operating wavelength lambda, the reception guide vector a being constructed using these radar parametersr(theta) and a transmit steering vector at(θ), θ is the direction angle of arrival;
(2) constructing a receiving and transmitting joint guide vector: based on received steering vector ar(theta) and a transmitterVector at(theta) construction of transmit-receive joint steering vectors
Figure BDA0001569694400000021
Figure BDA0001569694400000022
Represents the Kronecker product;
(3) calculating a projection matrix of the receiving and transmitting joint guide vector: by joint steering vectors a in both transmit and receivev(theta) calculating a projection matrix P⊥Make the projection matrix P⊥Joint steering vector a with transmit-receivevThe product of (theta) is 0, and P is satisfied⊥av(θ)＝0；
(4) And constructing a receiving guide vector of the receiving sub-array: according to the number p of the array elements of the calibrated receiving arrayrConstructing a receiving guide vector b (theta) of the receiving subarray, wherein the receiving subarray is an array formed by calibrated array elements (the guide vector has no amplitude-phase error) in the receiving array;
(5) constructing a receiving and transmitting joint guide vector of a receiving subarray: constructing a by using a receiving guide vector b (theta) of a receiving sub-array and a transmitting guide vector of the receiving arrayt(theta) Transmit-receive Joint steering vector for constructing receive subarrays
Figure BDA0001569694400000031
(6) Calculating a projection matrix of the receiving subarray receiving and transmitting combined guide vector: transmit-receive joint steering vector a with receive subarrayssub(theta) computing the projection matrix of the receiving subarray
Figure BDA0001569694400000032
Projection matrix of reception subarrays
Figure BDA0001569694400000033
Transmit-receive joint steering vector a with receive subarrayssubThe product of (theta) is 0
Figure BDA0001569694400000034
(7) Extracting receiving arraysEcho data and echo data of the receiving subarrays: performing pulse compression and matching separation on radar echo data Y, selecting echo data of a distance unit with stronger clutter energy in the radar echo data Y as echo data x of a receiving array, and extracting the echo data x of the receiving subarray from the echo data x of the receiving arraysub；
(8) Constructing a cost function of the error compensation coefficient of the transmitting array: echo data x using receiving subarrayssubAnd a projection matrix of the receiving sub-array
Figure BDA0001569694400000035
And estimating the error compensation coefficient of the transmitting array, wherein the cost function of the error compensation coefficient of the transmitting array is expressed as:
Figure BDA0001569694400000036
Figure BDA0001569694400000037
wherein q isTThe elements of the error compensation coefficient vector of the transmitting array respectively correspond to the reciprocal of the amplitude-phase error of the transmitting array element, wherein Γ (-) is a function for converting the vector into a diagonal matrix,
Figure BDA0001569694400000039
representative dimension is pr×prIdentity matrix of hT＝[1,0,…,0]TWith a representation dimension of NtX 1 column vector, NtFor transmitting array element number [ ·]TThe transpose is represented by,
Figure BDA0001569694400000038
represents the square of the Frobenius norm of the vector;
(9) obtaining a transmit array error compensation coefficient vector qT: obtaining a closed-form solution of the cost function by using a Lagrange multiplier method according to the cost function of the error compensation coefficient of the transmitting array, namely a vector q of the error compensation coefficient of the transmitting arrayT；
(10) Constructing a cost function of the error compensation coefficients of the receiving array: compensating coefficient vector q using transmit array errorsTEcho data x of a receiving array and a projection matrix P⊥And realizing the estimation of the error compensation coefficient of the receiving array, wherein the cost function of the error compensation coefficient of the receiving array is expressed as:
Figure BDA0001569694400000041
Figure BDA0001569694400000042
wherein q isRFor receiving array error compensation coefficient vector, its elements respectively correspond to reciprocal of amplitude-phase error of receiving array element, Γ (-) is function for converting vector into diagonal matrix, hR＝[1,0,…,0]TRepresents NrX 1 column vector, NrIn order to receive the number of array elements,
Figure BDA0001569694400000043
represents the square of the Frobenius norm of the vector;
(11) obtaining a receiving array error compensation coefficient vector qR: obtaining a closed-form solution of the cost function by using a Lagrange multiplier method according to the cost function of the error compensation coefficient of the receiving array, namely receiving the error compensation coefficient vector q of the receiving arrayR；
(12) Compensating coefficient vector q using transmit array errorsTAnd receiving the array error compensation coefficient vector qRObtaining a transmitting amplitude-phase error matrix GTAnd a received amplitude-phase error matrix GRRespectively as follows: gT＝[Γ(qT)]-1And GR＝[Γ(qR)]-1；
(13) Using transmitted amplitude-phase error matrix GTAnd a received amplitude-phase error matrix GRSeparately modifying transmit array steering vectors
Figure BDA0001569694400000044
And receiving array steering vectors
Figure BDA0001569694400000045
Comprises the following steps:
Figure BDA0001569694400000046
and
Figure BDA0001569694400000047
and amplitude and phase error correction of the radar receiving and transmitting array is realized.
The method provided by the invention can effectively estimate the amplitude-phase error of the MIMO radar receiving and transmitting array only by a single echo sample without estimating the number of the information source targets, has small calculated amount and low complexity, and is suitable for real-time processing.
The invention has the following advantages:
1) the invention realizes the correction of the amplitude-phase error of the receiving and transmitting array by using the echo signal of the clutter scattering point, and compared with the traditional array amplitude-phase error correction method, the invention does not need to estimate the number of the information source targets, and the number of the scatterers has no influence on the algorithm performance because of the ubiquitous clutter scattering point.
2) The method utilizes the projection matrix to construct the cost function, can realize the estimation of the error compensation coefficient of the receiving array and the error compensation coefficient of the transmitting array only by a single echo sample, has low complexity and small calculated amount compared with the traditional array amplitude-phase error correction method, and is suitable for real-time processing.
Drawings
FIG. 1 is a main flow chart of the experiment of the present invention;
FIG. 2 shows the estimation result of the amplitude-phase error of the transmitting array;
FIG. 3 is a diagram of the received array magnitude-phase error estimation;
fig. 4 is a relation between the root mean square of the amplitude-phase error of the transmit-receive array and the noise-to-noise ratio.
Detailed Description
The invention is described in detail below with reference to the attached drawing figures:
example 1
Amplitude errors and phase errors of the array are inevitable errors in the array signal processing, and when the amplitude and phase errors exist, mismatch of the array is caused, so that the spatial spectrum estimation and digital beam forming performance are reduced. In order to solve the above problems, the present invention provides a method for correcting an amplitude-phase error of a transmit-receive array of a MIMO radar based on clutter, which is shown in fig. 1 and includes the following steps:
firstly, the MIMO radar is assumed to be a transmitting and receiving separated equidistant linear array, and the distance between a transmitting array and a receiving array is assumed to be short and far less than the distance between an array antenna and a target and a clutter scene. The number of transmitting array elements of the MIMO radar is assumed to be NtThe number of receiving array elements is NrThe wavelength of the transmitted signal is lambda, the transmitting array and the receiving array are uniform linear arrays and are arranged in a transceiving mode, and the distance d between the transmitting array elements of the radartAnd the spacing d of receiving array elementsrAssuming that the spacing between the transmitting array elements is equal to the spacing between the receiving array elements by d, i.e. dt＝drAssuming that the radar reception echo data is Y, θ is the direction arrival angle.
(1) Obtaining a guide vector based on the radar array parameter information: when the radar array amplitude phase has errors, the guide vector contains array amplitude phase error information, and the receiving guide vector a of the radar is obtained through calculationr(theta) and emission guide at(θ) vector:
Figure BDA0001569694400000051
Figure BDA0001569694400000052
wherein j is an imaginary unit [ ·]TIndicating transposition.
(2) Constructing a receiving and transmitting joint guide vector: based on received steering vector ar(theta) and a transmit steering vector at(theta) construction of transmit-receive joint steering vectors
Figure BDA0001569694400000053
The transmit-receive joint steering vector is equal to the Kronecker product of the receive steering vector and the transmit steering vector:
Figure BDA0001569694400000054
transmit-receive joint steering vector a in the present inventionvThe number of independent centers of (theta) is Nt+Nr-1, its dimension being less than Nt*NrThe transmit and receive joint steering vectors are not row full rank.
(3) Calculating a projection matrix of the receiving and transmitting joint guide vector: by joint steering vectors a in both transmit and receivev(theta) calculating a projection matrix P⊥Make the projection matrix P⊥Joint steering vector a with transmit-receivevThe product of (theta) is 0, and P is satisfied⊥av(θ)＝0。
The projection matrix in the invention is constructed according to the following method: traversing all direction angles of possible occurrence of the echo of the receiving array, and constructing an echo joint steering vector space, namely av(θ), there must be some non-zero space orthogonal to the echo joint steering vector. Specifically, a can be obtained firstly by adopting a Schmidt orthogonalization methodvThe orthogonal basis of (θ), and then a projection matrix is obtained.
(4) And constructing a receiving guide vector of the receiving sub-array: according to the number p of the array elements of the calibrated receiving arrayrAnd constructing a receiving guide vector b (theta) of the receiving subarray, wherein the receiving subarray is an array formed by calibrated array elements (the guide vector has no amplitude-phase error) in the receiving array.
(5) Constructing a receiving and transmitting joint guide vector of a receiving subarray: constructing a by using a receiving guide vector b (theta) of a receiving sub-array and a transmitting guide vector of the receiving arrayt(theta) Transmit-receive Joint steering vector for constructing receive subarrays
Figure BDA0001569694400000061
To ensure the stability of the radar system, the operation needs to be increasedAnd additional measuring equipment is added, so that the actual working performance of the array element is monitored in real time. For large scale arrays, monitoring of each array element is clearly impractical, but efficient measurements for a small number of array elements are feasible. Therefore, the invention has low requirement on the radar array and wide application scene. The invention is provided with prThe array elements are calibrated, and the array element spacing of the calibration array is consistent with that of the transmitting array.
(6) Calculating a projection matrix of the receiving subarray receiving and transmitting combined guide vector: transmit-receive joint steering vector a with receive subarrayssub(theta) computing the projection matrix of the receiving subarray
Figure BDA0001569694400000062
Projection matrix of reception subarrays
Figure BDA0001569694400000063
Transmit-receive joint steering vector a with receive subarrayssubThe product of (theta) is 0
Figure BDA0001569694400000064
The projection matrix in the invention is constructed according to the following method: traversing all direction angles which may appear in the echo of the receiving subarray, and constructing a joint steering vector space of the echo of the receiving subarray, namely asub(θ), there must be some non-zero space orthogonal to the echo joint steering vector. Specifically, a can be obtained firstly by adopting a Schmidt orthogonalization methodsubThe orthogonal basis of (θ), and then a projection matrix is obtained.
(7) Extracting echo data of a receiving array and echo data of a receiving sub-array: performing pulse compression and matching separation on radar echo data Y, selecting echo data of a distance unit with stronger clutter energy in the radar echo data Y as echo data x of a receiving array, and extracting the echo data x of the receiving subarray from the echo data x of the receiving arraysub。
The invention utilizes the clutter in the radar echo to correct the amplitude and phase errors of the receiving and transmitting array, and the clutter scattering points generally exist, so the invention can correct the amplitude and phase errors of the radar receiving and transmitting array without estimating the number of information source targets, which is the main technical advantage of the invention.
(8) Constructing a cost function of the error compensation coefficient of the transmitting array: echo data x using the receiving subarrays in step (7)subAnd the projection matrix of the receiving subarray in step (6)
Figure BDA0001569694400000071
And estimating the error compensation coefficient of the transmitting array, wherein the cost function of the error compensation coefficient of the transmitting array is expressed as:
Figure BDA0001569694400000072
Figure BDA0001569694400000073
wherein q isTThe transmitting array error compensation coefficient vector has elements corresponding to the reciprocal of the transmitting array element error, wherein the gamma (-) is a function for converting the vector into a diagonal matrix,
Figure BDA0001569694400000075
representative dimension is pr×prThe unit matrix of (a) is,
hT＝[1,0,…,0]Trepresents NtX 1 column vector, NtFor transmitting array element number [ ·]TThe transpose is represented by,
Figure BDA0001569694400000074
representing the square of the Frobenius norm of the vector.
In the invention, a cost function of the error compensation coefficient of the transmitting array is established by taking the minimum output power of the echo projection of the receiving subarray as a criterion, and the construction method of the specific cost function is as follows: echo data x using receiving subarrayssubAnd compensating the transmitting array error to minimize the clutter projection output power of the receiving subarray.
(9) Obtaining transmit array error compensation coefficient vectorsqT: obtaining a closed-form solution of the cost function by using a Lagrange multiplier method according to the cost function of the error compensation coefficient of the transmitting array, namely a vector q of the error compensation coefficient of the transmitting arrayT。
There are many methods for calculating the cost function, such as newton method, penalty function method, lagrange multiplier method, etc. The invention obtains the closed-form solution of the cost function by using the Lagrange multiplier method, and the solution is simple and convenient. The invention can also adopt a penalty function method to obtain a closed-form solution of the cost function.
(10) Constructing a cost function of the error compensation coefficients of the receiving array: using the transmission compensation coefficient q in step (8)TThe echo data x of the receiving array extracted in the step (7) and the projection matrix P obtained in the step (3)⊥And realizing the estimation of the error compensation coefficient of the receiving array, wherein the cost function of the error compensation coefficient of the receiving array is expressed as:
Figure BDA0001569694400000081
Figure BDA0001569694400000082
wherein q isRFor receiving array error compensation coefficient vector, its elements respectively correspond to reciprocal of amplitude-phase error of receiving array element, Γ (-) is function for converting vector into diagonal matrix, hR＝[1,0,…,0]TRepresents NrX 1 column vector, NrIn order to receive the number of array elements,
Figure BDA0001569694400000083
representing the square of the Frobenius norm of the vector.
In the invention, a cost function of the error compensation coefficient of the receiving array is established by taking the minimum output power of the echo projection of the receiving array as a criterion, and the construction method of the specific cost function is as follows: echo data x using a receive arraysubAnd compensating the errors of the receiving array to minimize the projection output power of the echo of the receiving array.
(11) ObtainObtaining a receiving array error compensation coefficient vector qR: obtaining a closed-form solution of the cost function by using a Lagrange multiplier method according to the cost function of the error compensation coefficient of the receiving array, namely receiving the error compensation coefficient vector q of the receiving arrayR。
There are many methods for calculating the cost function, such as newton method, penalty function method, lagrange multiplier method, etc. The invention obtains the closed-form solution of the cost function by using the Lagrange multiplier method, and the solution is simple and convenient. The invention can also adopt a penalty function method to obtain a closed-form solution of the cost function.
(12) Utilizing the transmitting array error compensation coefficient vector q obtained in the step (9)TAnd the receiving array error compensation coefficient vector q obtained in the step (11)RObtaining a transmitting amplitude-phase error matrix GTAnd a received amplitude-phase error matrix GRRespectively as follows: gT＝[Γ(qT)]-1And GR＝[Γ(qR)]-1。
(13) Using transmitted amplitude-phase error matrix GTAnd a received amplitude-phase error matrix GRSeparately modifying transmit array steering vectors
Figure BDA0001569694400000084
And receiving array steering vectors
Figure BDA0001569694400000085
Comprises the following steps:
Figure BDA0001569694400000086
and
Figure BDA0001569694400000087
and amplitude and phase error correction of the radar receiving and transmitting array is realized.
The invention constructs a projection matrix by compensating amplitude-phase errors in a receiving array and a transmitting array by utilizing clutter data in echo data, and constructs a cost function by enabling the echo projection output power to be minimum. The traditional array amplitude and phase error method has high requirement on echo, can realize the estimation of the receiving array error compensation coefficient and the transmitting array error compensation coefficient only by a single echo sample, has low complexity and small calculated amount, and is suitable for real-time processing.
Example 2
The clutter MIMO radar transmit-receive array amplitude-phase error correction method is the same as that in the embodiment 1, and the projection matrix of the transmit-receive joint steering vector is calculated in the step (3), and is specifically calculated by the following formula:
(3a) the range of azimuth angle [ - π/2]Evenly dividing K parts by K > NtNrConstructing a transmit-receive joint steering matrix AV:
Figure BDA0001569694400000091
Where K is the number of azimuthal divisions, θi(i ═ 1, 2.., K) is the azimuth angle, NtIs the number of transmitting array elements, NrIs the number of receive array elements.
(3b) Calculating its projection matrix P⊥
Figure BDA0001569694400000092
Wherein the content of the first and second substances,
Figure BDA0001569694400000094
with a representation dimension of NtNr×NtNrIdentity matrix of AVIs a transmit-receive joint steering matrix [ ·]TRepresents a transposition [ ·]-1Indicating inversion.
In this example, the number of array elements of the transmitting array of the radar is 6, the number of array elements of the receiving array of the radar is 6, the azimuth angle interval is evenly divided into 150 parts, and a transmitting-receiving steering matrix A with the dimension of 36 multiplied by 150 is constructed by utilizing a transmitting-receiving joint steering vectorVThereby calculating a projection matrix P of the receiving and transmitting joint guide vector⊥Wherein, in the step (A),
Figure BDA0001569694400000095
an identity matrix of dimensions 36 x 36 is used.
The invention establishes the cost function of the receiving array guide vector compensation coefficient by taking the minimum receiving array echo projection output power as a criterion, obtains the receiving array guide vector compensation coefficient by solving the cost function, and realizes the amplitude-phase error correction of the receiving array. The method realizes the correction of the amplitude-phase error of the receiving array by constructing a cost function by using a projection matrix, and has novel thought and small calculated amount.
Example 3
The clutter MIMO radar transmitting and receiving array amplitude-phase error correction method is the same as that in the embodiment 1-2, and the projection matrix of the receiving subarray transmitting and receiving combined steering vector is calculated in the step (6), and is specifically calculated through the following formula:
(6a) the range of azimuth angle [ - π/2]Evenly dividing K parts by K > NtPrConstructing a transmit-receive joint steering matrix Asub：
Figure BDA0001569694400000093
Where K is the number of azimuthal divisions, θi(i ═ 1, 2.., K) is the azimuth angle, NtIs the number of transmitting array elements, prThe number of array elements calibrated for the receive array.
(6b) Calculating its projection matrix
Figure BDA0001569694400000101
Figure BDA0001569694400000102
Wherein the content of the first and second substances,
Figure BDA0001569694400000103
is dimension NtPr×NtPrThe identity matrix of [ ·]TRepresents a transposition [ ·]-1Indicating inversion.
In this example, the number of elements of the transmitting array of the radar is 10, the number of elements of the receiving subarray of the radar is 3, and the azimuth angle interval is uniformly divided400 parts, constructing a transmitting and receiving steering matrix A with the dimension of 30 multiplied by 400 by using a transmitting and receiving combined steering vectorsubThereby calculating the projection matrix of the receiving subarray receiving and transmitting joint guide vector
Figure BDA0001569694400000104
Wherein the content of the first and second substances,
Figure BDA0001569694400000105
an identity matrix of dimensions 30 x 30 is used.
The invention also establishes a cost function of the transmitting array guide vector compensation coefficient by taking the minimum receiving subarray echo projection output power as a criterion, obtains the transmitting array guide vector compensation coefficient by solving the cost function, and realizes the amplitude-phase error correction of the transmitting array.
According to the invention, the cost function of the transmitting array guide vector compensation coefficient and the cost function of the receiving array guide vector compensation coefficient are respectively constructed by the receiving array transmitting and receiving joint guide vector projection matrix and the receiving subarray transmitting and receiving joint guide vector projection matrix, so that amplitude-phase error correction can be simultaneously carried out on the transmitting and receiving arrays, and the real-time performance is good.
Example 4
The clutter MIMO radar based transmit-receive array amplitude-phase error correction method is the same as that in embodiments 1-3, and the extraction of the echo data of the receive array and the echo data of the receive sub-array in step (7) is specifically calculated by the following formula:
(7a) MIMO radar radiates orthogonal signal S, then thetaiThe directional echo Y can be expressed as
Figure BDA0001569694400000106
Wherein beta isiIs thetaiDirectional clutter scattering coefficient, gTAnd gRRepresenting the transmit and receive array amplitude-phase errors, respectively, Γ (·) is a function that converts the vector into a diagonal matrix, and N is the receiver noise.
(7b) Since the waveforms are orthogonal, then
Figure BDA0001569694400000107
Performing pulse compression on the echo Y by using a radiation waveform S, and vectorizing the obtained matrix to obtain echo data x of the receiving array:
Figure BDA0001569694400000111
where vec represents a function that converts the matrix into a column vector, and n is noise.
(7c) Selecting the echo x of the receiving subarray according to the echo data x of the receiving arraysubIs shown as
Figure BDA0001569694400000112
Wherein n issubIn order to be a noise, the noise is,
Figure BDA0001569694400000119
the expression dimension is Pr×PrThe identity matrix of (2).
The echo data of the receiving array is obtained by pulse compressing the echo data and vectorizing the obtained matrix, and the echo data of the receiving subarray is obtained by selecting the echo data. The invention constructs the cost function by utilizing the clutter data in the echo, has no requirement on the number of the information source targets because clutter scattering points generally exist, and has wide application range.
Example 5
The method for correcting the amplitude-phase error of the receiving and transmitting array based on the clutter MIMO radar is the same as the method in the embodiment 1 to 4, and the vector q of the error compensation coefficient of the transmitting array is obtained in the step (9)TSpecifically, the calculation is performed through the following steps:
(9a) simplifying the cost function:
due to the fact that
Figure BDA0001569694400000113
Wherein the content of the first and second substances,
Figure BDA0001569694400000114
represents prX 1 dimensional all 1 column vectors, the cost function can be simplified as:
Figure BDA0001569694400000115
Figure BDA0001569694400000116
wherein the content of the first and second substances,
Figure BDA0001569694400000117
[·]Hrepresenting a conjugate transpose.
(9b) By the Lagrange multiplier method, qTThere is a unique closed-form solution:
Figure BDA0001569694400000118
the method for calculating the cost function is multiple, and because the Lagrangian method is simple and convenient to calculate and is commonly used, the method adopts the Lagrangian multiplier method to calculate the closed solution of the cost function. The invention can also adopt methods such as Newton method, penalty function method, etc. to solve the solution of the cost function.
Example 6
The clutter MIMO radar-based receiving and transmitting array amplitude-phase error correction method is the same as that in the embodiment 1-5, and the receiving array error compensation coefficient vector q is obtained in the step (11)RSpecifically, the calculation is performed through the following steps:
(11a) the cost function is simplified.
Due to the fact that
Figure BDA0001569694400000121
The cost function can be simplified as follows:
Figure BDA0001569694400000122
Figure BDA0001569694400000123
wherein the content of the first and second substances,
Figure BDA0001569694400000124
[·]Hrepresenting a conjugate transpose.
(11b) By the Lagrange multiplier method, qRCan be expressed as:
Figure BDA0001569694400000125
the method for calculating the cost function is various, and because the Lagrange multiplier method is simple and convenient to calculate and is commonly used, the method adopts the Lagrange multiplier method to calculate the closed solution of the cost function. The invention can also adopt methods such as Newton method, penalty function method, etc. to solve the solution of the cost function.
A more detailed example is given below to further illustrate the invention:
example 7
The clutter MIMO radar based transmit-receive array amplitude-phase error correction method is the same as the embodiments 1-6, and referring to FIG. 1, the implementation steps of the invention are as follows:
the MIMO radar is assumed to be a transmitting and receiving separated equidistant linear array, and the distance between a transmitting array and a receiving array is assumed to be short and far smaller than the distance between an array antenna and a target and a clutter scene. The number of transmitting array elements of the MIMO radar is assumed to be NtThe number of receiving array elements is NrAssuming that the array element number of the calibrated receiving subarray is lambda of the wavelength of the transmitting signal, the transmitting array and the receiving array are uniform linear arrays and are arranged in a transmitting and receiving mode, and the radar transmitting array element spacing dtAnd the spacing d of receiving array elementsrAssuming that the spacing between the transmitting array elements is equal to the spacing between the receiving array elements by d, i.e. dt＝drLet d be the radar acceptance echo data Y.
Step 1: and constructing a receiving and transmitting joint guide vector.
(1a) Constructing a transmitting guide vector according to a transmitting array structure:
Figure BDA0001569694400000126
(1b) according to the receive array structure, a receive steering vector is constructed:
Figure BDA0001569694400000131
(1c) according to at(theta) and ar(θ), constructing a transmit-receive joint steering vector:
Figure BDA0001569694400000132
and obtaining a radar receiving guide vector and a radar transmitting guide vector based on the radar array parameter information, wherein when the radar array amplitude phase has errors, the guide vector contains array amplitude phase error information.
Step 2: and calculating a projection matrix of the receiving and transmitting joint guide vector.
The range of azimuth angle [ - π/2]Evenly dividing K parts by K > NtNrConstructing a transmit-receive joint steering matrix AV：
Figure BDA0001569694400000133
Calculating its projection matrix P⊥：
Figure BDA0001569694400000134
And step 3: and constructing a receiving and transmitting joint guide vector of the receiving subarray.
(3a) Constructing a transmitting guide vector according to a transmitting array structure:
Figure BDA0001569694400000135
(3b) and constructing a receiving guide vector according to the receiving subarray array structure:
Figure BDA0001569694400000136
wherein p isrThe number of the array elements of the receiving subarrays;
(3c) according to at(θ) and b (θ), constructing a corresponding transmit-receive joint steering vector:
Figure BDA0001569694400000137
and 4, step 4: and calculating a projection matrix of the receiving subarray receiving and transmitting combined guide vector.
The range of azimuth angle [ - π/2]Evenly dividing K parts by K > NtNrConstructing a transmit-receive joint steering matrix Asub：
Figure BDA0001569694400000138
Calculating its projection matrix
Figure BDA0001569694400000141
Figure BDA0001569694400000142
And 5: and extracting echo data of the receiving array and echo data of the receiving subarray by pulse compression and matching separation of the echo Y.
(5a) The MIMO radar radiates orthogonal signals S, and then a certain range unit echo Y can be expressed as:
Figure BDA0001569694400000143
wherein beta isiIs thetaiDirectional clutter scattering coefficient, gTAnd gRRespectively represent emission,Receiving array amplitude-phase errors, wherein gamma (-) is a function for converting vectors into diagonal matrixes, and N is receiver noise;
(5b) since the waveforms are orthogonal, then
Figure BDA0001569694400000144
Performing pulse compression by using a radiation waveform S, and vectorizing an obtained matrix:
Figure BDA0001569694400000145
where vec represents a function that converts the matrix into a column vector.
(5c) The echoes of the selected receiving subarrays are represented as x
Figure BDA0001569694400000146
Step 6: and establishing a cost function by taking the minimum receiving subarray echo projection output energy as a criterion to obtain the estimation of the error compensation coefficient of the transmitting array.
(6a) Echo data x using receiving subarrayssubBy compensating for transmit array errors and minimizing the echo projection output power, an estimate of the transmit array error compensation coefficients can be obtained. Its cost function can be expressed as:
Figure BDA0001569694400000147
Figure BDA0001569694400000148
wherein q isTIs an emission compensation coefficient vector, the elements of which respectively correspond to the reciprocal of the emission amplitude phase error of the array element, namely [ gamma (q) ]T)]-1＝Γ(gT). Γ (-) is a function that converts a vector into a diagonal matrix,
Figure BDA0001569694400000151
representative dimension is pr×prIdentity matrix of hT＝[1,0,…,0]TRepresents NtX 1 column vector, NtFor transmitting array element number [ ·]TThe transpose is represented by,
Figure BDA0001569694400000152
represents the square of the Frobenius norm of the vector;
(6b) the cost function is simplified.
Due to the fact that
Figure BDA0001569694400000153
Figure BDA0001569694400000154
Represents prX 1 dimensional all 1 column vector. The cost function can be simplified as follows:
Figure BDA0001569694400000155
Figure BDA00015696944000001514
wherein the content of the first and second substances,
Figure BDA0001569694400000156
[·]Hrepresenting a conjugate transpose. By the Lagrange multiplier method, qTThere is a unique closed-form solution:
Figure BDA0001569694400000157
and 7: and establishing a cost function by taking the minimum projection output energy of the received echo as a criterion to obtain the estimation of the error compensation coefficient of the receiving array.
(7a) By using the echo data x, an estimate of the receive array error compensation coefficient can be obtained by compensating for receive array errors and minimizing the echo projection output power. Its cost function can be expressed as
Figure BDA0001569694400000158
Figure BDA0001569694400000159
Wherein q isRThe elements of the received compensation coefficient vector are respectively corresponding to the reciprocal of the received amplitude-phase error of the array element. h isR＝[1,0,…,0]TRepresents NrX 1 column vector, NrIs the number of receiving array elements.
The cost function can obtain a closed-form solution by using a Lagrange multiplier method.
(7b) The cost function is simplified.
Due to the fact that
Figure BDA00015696944000001510
The cost function can be simplified to
Figure BDA00015696944000001511
Figure BDA00015696944000001512
Wherein the content of the first and second substances,
Figure BDA00015696944000001513
by the Lagrange multiplier method, qRCan be expressed as:
Figure BDA0001569694400000161
and 8: obtaining a transmitting amplitude-phase error matrix G according to the relation between the array error compensation coefficient and the array error matrixTAnd a received amplitude-phase error matrix GRRespectively as follows: gT＝[Γ(qT)]-1And GR＝[Γ(qR)]-1。
And step 9: the modified transmit steering vector and the receive steering vector are respectively:
Figure BDA0001569694400000162
and
Figure BDA0001569694400000163
and realizing the amplitude and phase error correction of the radar array.
The method realizes array amplitude and phase error correction by using the echo signals of clutter scattering points, constructs a cost function by using a projection matrix, can effectively estimate the amplitude and phase errors of the MIMO radar receiving and transmitting array only by a single echo sample without estimating the number of information source targets, corrects the amplitude and phase errors of the radar receiving and transmitting array, has small calculated amount and low complexity, and is suitable for real-time processing.
The technical effects of the invention are further illustrated by the following simulation experiments:
example 8
The method for correcting the amplitude-phase error of the receiving and transmitting array based on the clutter MIMO radar is the same as the embodiments 1 to 7,
simulation scenario
The MIMO radar system is assumed to be composed of uniform linear arrays of transmitting and receiving arrays, and the number of transmitting array elements is NtNumber of receiving array elements N as 8r8, the array elements are spaced one-half wavelength apart. The number of elements of the calibrated receiving subarray is prThe amplitude phase error of the other receiving array elements is [1.34e ] respectively as 3j48.04° 0.98ej11.06° 1.03e-j27.40° 0.8ej22.25° 0.67ej55.85°]，
The amplitude-phase error of the transmitting array is
[1 1.40ej34.90° 1.01ej46.94° 1.31e-j54.18° 0.96ej35.14° 1.49e-j49.86° 0.80e-j9.98°0.77e-j31.13°]，
And the direction clutter block K is 181.
Emulated content
Assuming that the noise-to-noise ratio is 30dB, estimating the amplitude-phase error of the MIMO radar transmitting array by adopting the method of the invention, and comparing the estimated value with the true value, wherein the result is shown in figure 2;
analysis of simulation results
Referring to fig. 2, fig. 2(a) is a transmit array amplitude error estimation result. The abscissa is the number of sequences of the transmit array elements and the ordinate is the true and estimated values of the magnitude of the steering vector for each transmit array element. Fig. 2(b) is the transmit array phase error estimation result. The abscissa is the number of the sequence of the transmitting array elements, and the ordinate is the true value and the estimated value of the steering vector phase of each transmitting array element, and the diagram shows
Figure BDA0001569694400000164
The true value of the amplitude and phase error of the transmitting array is shown, and the + value of the amplitude and phase error of the transmitting array is shown.
As can be seen from FIG. 2(a), the estimated value of the amplitude error of the transmitting array obtained by the method of the present invention approaches the true value, the amplitude error estimation of the transmitting array is realized, and the amplitude error correction of the transmitting array is realized by modifying the steering vector of the transmitting array by the estimated value.
As can be seen from fig. 2(b), the estimated value of the phase error of the transmitting array obtained by the method of the present invention approaches the true value, the phase error estimation of the transmitting array is realized, and the phase error correction of the transmitting array is realized by correcting the steering vector of the transmitting array by using the estimated value.
Example 9
The clutter MIMO radar-based receiving and transmitting array amplitude-phase error correction method is the same as the embodiments 1-7, and the simulation scene is the same as that of the embodiment
Example 8.
Emulated content
Assuming that the noise-to-noise ratio is 30dB, the method of the invention is adopted to estimate the amplitude-phase error of the MIMO radar receiving array, and the estimated value is compared with the true value, and the result is shown in figure 3.
And (3) simulation result analysis:
referring to fig. 3, fig. 3(a) is a received array amplitude error estimation result. The abscissa is the number of the sequence of the receiving array elements and the ordinate is the true and estimated values of the magnitude of the steering vector of each receiving array element. Fig. 3(b) is the receive array phase error estimation result. The abscissa is the number of the sequence of the receiving array elements and the ordinate is the true and estimated values of the steering vector phase of each receiving array element, as shown in the figure
Figure BDA0001569694400000171
The true value of the amplitude and phase error of the receiving array is shown, and the + value of the amplitude and phase error of the receiving array is shown.
As can be seen from fig. 3(a), the estimated value of the amplitude error of the receiving array obtained by the method of the present invention approaches the true value, so that the amplitude error estimation of the receiving array is realized, and the amplitude error correction of the receiving array is realized by correcting the steering vector of the receiving array by using the estimated value.
As can be seen from fig. 3(b), the estimated value of the phase error of the receiving array obtained by the method of the present invention approaches the true value, so that the phase error estimation of the receiving array is realized, and the phase error correction of the receiving array is realized by correcting the steering vector of the receiving array by using the estimated value.
Example 9
The clutter MIMO radar-based receiving and transmitting array amplitude-phase error correction method is the same as the embodiments 1-7, and the simulation scene is the same as that of the embodiment
Example 8.
Emulated content
The echo noise ratio was changed from 0dB to 40dB at 5dB intervals. Each noise-to-noise ratio was independently subjected to 1000 monte carlo experiments, and the root mean square error of the transmit-receive error estimation is shown in fig. 4.
Analysis of simulation results
Referring to fig. 4, fig. 4 is a graph of echo noise ratio versus transmit-receive error root mean square. The abscissa is the magnitude of the noise-to-noise ratio in the echo, and the ordinate is the root mean square error of the amplitude phase of the radar transmitting and receiving array.
It can be seen from fig. 4 that, when the amplitude-phase error of the transmitting and receiving arrays is estimated by the method of the present invention, the root mean square error becomes smaller as the noise-to-noise ratio in the echo becomes larger, and the estimation performance is gradually improved.
When pulse compression and matching separation are carried out on radar data Y, echo data of a distance unit with stronger clutter energy is selected to estimate the amplitude-phase error of the receiving and transmitting array, and the stronger the clutter energy is, the more accurate the estimation on the amplitude-phase error of the receiving and transmitting array is, and the better the correction effect on the amplitude-phase error of the radar receiving and transmitting array is.
In summary, the clutter-based MIMO radar transmit-receive array amplitude-phase error correction method disclosed by the invention mainly solves the problem that radar detection performance is reduced due to inconsistent array element amplitudes and phases. The implementation process comprises the following steps: constructing a receiving guide vector, a transmitting guide vector, a receiving and transmitting joint guide vector, a receiving guide vector of a receiving sub-array and a receiving and transmitting joint guide vector of the receiving sub-array; calculating a projection matrix of the receiving and transmitting joint guide vector and a projection matrix of the receiving subarray receiving and transmitting joint guide vector; extracting echo data of a receiving array and echo data of a receiving sub-array; respectively constructing a cost function of the transmitting array error compensation coefficient and a cost function of the receiving array error compensation coefficient, and solving an optimal solution of the cost function of the transmitting array error compensation coefficient and an optimal solution of the cost function of the receiving array error compensation coefficient; obtaining a transmitting amplitude-phase error matrix and a receiving amplitude-phase error matrix; and correcting the transmitting array guide vector and the receiving array guide vector to realize the amplitude-phase error correction of the radar transmitting-receiving array. The method does not need to estimate the number of information source targets, can effectively estimate the amplitude-phase error of the MIMO radar receiving and transmitting array only by a single echo sample, has small calculated amount and low complexity, and is suitable for the error correction real-time processing of the MIMO radar receiving and transmitting array.

Claims (6)

1. A clutter-based MIMO radar transmit-receive array amplitude-phase error correction method is characterized by comprising the following steps:
(1) construction of receive steering vectors a using radar parametersr(theta) and a transmit steering vector at(θ): number of elements N of radar transmitting arraytAnd the number of receiving array elements Nr，NtIs the total number of transmitting array elements, NrFor receiving the total number of array elements, the spacing d between array elementstAnd the spacing d of receiving array elementsrThe radar operating wavelength lambda, the reception guide vector a being constructed using these radar parametersr(theta) and a transmit steering vector at(θ), θ is the direction angle of arrival;
(2) constructing a receiving and transmitting joint guide vector: based on received steering vector ar(theta) and a transmit steering vector at(theta) construction of transmit-receive joint steering vectors
Figure FDA0002987294130000011
Figure FDA0002987294130000012
Represents the Kronecker product;
(3) calculating a projection matrix of the receiving and transmitting joint guide vector: by joint steering vectors a in both transmit and receivev(theta) calculating a projection matrix P⊥Make the projection matrix P⊥Joint steering vector a with transmit-receivevThe product of (theta) is 0, and P is satisfied⊥av(θ)＝0；
(4) And constructing a receiving guide vector of the receiving sub-array: according to the number p of the array elements of the calibrated receiving arrayrConstructing a receiving guide vector b (theta) of the receiving subarray, wherein the receiving subarray is an array formed by calibrated array elements of which the guide vectors have no amplitude-phase errors in the receiving array;
(5) constructing a receiving and transmitting joint guide vector of a receiving subarray: constructing a by using a receiving guide vector b (theta) of a receiving sub-array and a transmitting guide vector of the receiving arrayt(theta) Transmit-receive Joint steering vector for constructing receive subarrays
Figure FDA0002987294130000013
(6) Calculating a projection matrix of the receiving subarray receiving and transmitting combined guide vector: transmit-receive joint steering vector a with receive subarrayssub(theta) computing the projection matrix of the receiving subarray
Figure FDA0002987294130000014
Projection matrix of reception subarrays
Figure FDA0002987294130000015
Transmit-receive joint steering vector a with receive subarrayssubMultiplication by (theta)The product is 0, satisfy
Figure FDA0002987294130000016
(7) Extracting echo data of a receiving array and echo data of a receiving sub-array: performing pulse compression and matching separation on radar echo data Y, selecting echo data of a distance unit with stronger clutter energy in the radar echo data Y as echo data x of a receiving array, and extracting the echo data x of the receiving subarray from the echo data x of the receiving arraysub；
(8) Constructing a cost function of the error compensation coefficient of the transmitting array: echo data x using receiving subarrayssubAnd a projection matrix of the receiving sub-array
Figure FDA0002987294130000021
And estimating the error compensation coefficient of the transmitting array, wherein the cost function of the error compensation coefficient of the transmitting array is expressed as:
Figure FDA0002987294130000022
Figure FDA0002987294130000023
wherein q isTThe elements of the error compensation coefficient vector of the transmitting array respectively correspond to the reciprocal of the amplitude-phase error of the transmitting array elements, wherein gamma (·) is a function for converting the vector into a diagonal matrix, and IprRepresentative dimension is pr×prIdentity matrix of hT＝[1,0,···,0]TWith a representation dimension of NtX 1 column vector, NtFor transmitting array element number [ ·]TThe transpose is represented by,
Figure FDA0002987294130000024
represents the square of the Frobenius norm of the vector;
(9) obtaining transmit array error compensation coefficient vectorsqT: obtaining a closed-form solution of the cost function by using a Lagrange multiplier method according to the cost function of the error compensation coefficient of the transmitting array, namely a vector q of the error compensation coefficient of the transmitting arrayT；
(10) Constructing a cost function of the error compensation coefficients of the receiving array: compensating coefficient vector q using transmit array errorsTEcho data x of a receiving array and a projection matrix P⊥And realizing the estimation of the error compensation coefficient of the receiving array, wherein the cost function of the error compensation coefficient of the receiving array is expressed as:
Figure FDA0002987294130000025
Figure FDA0002987294130000026
wherein q isRFor receiving array error compensation coefficient vector, its elements respectively correspond to reciprocal of amplitude-phase error of receiving array element, Γ (-) is function for converting vector into diagonal matrix, hR＝[1,0,···,0]TRepresents NrX 1 column vector, NrIn order to receive the number of array elements,
Figure FDA0002987294130000027
represents the square of the Frobenius norm of the vector;
(11) obtaining a receiving array error compensation coefficient vector qR: obtaining a closed-form solution of the cost function by using a Lagrange multiplier method according to the cost function of the error compensation coefficient of the receiving array, namely receiving the error compensation coefficient vector q of the receiving arrayR；
(12) Compensating coefficient vector q using transmit array errorsTAnd receiving the array error compensation coefficient vector qRObtaining a transmitting amplitude-phase error matrix GTAnd a received amplitude-phase error matrix GRRespectively as follows: gT＝[Γ(qT)]-1And GR＝[Γ(qR)]-1；
(13) Using transmitted amplitude-phase error matrix GTAnd a received amplitude-phase error matrix GRSeparately modifying transmit array steering vectors
Figure FDA0002987294130000028
And receiving array steering vectors
Figure FDA0002987294130000029
Comprises the following steps:
Figure FDA00029872941300000210
and
Figure FDA00029872941300000211
and amplitude and phase error correction of the radar receiving and transmitting array is realized.
2. The clutter-based MIMO radar transmit-receive array amplitude-phase error correction method according to claim 1, wherein the calculating of the projection matrix of the transmit-receive joint steering vector in step (3) is specifically performed by using the following formula:
(3a) the range of azimuth angle [ - π/2]Evenly dividing K parts by K > NtNrConstructing a transmit-receive joint steering matrix AV：
Figure FDA0002987294130000031
Where K is the number of azimuthal divisions, θiIs the azimuth angle, i ═ 1,2tIs the number of transmitting array elements, NrIs the number of receiving array elements;
(3b) calculating its projection matrix P⊥
Figure FDA0002987294130000032
Wherein the content of the first and second substances,
Figure FDA0002987294130000033
with a representation dimension of NtNr×NtNrIdentity matrix of AVIs a transmit-receive joint steering matrix [ ·]TRepresents a transposition [ ·]-1Indicating inversion.
3. The clutter-based MIMO radar transmit-receive array amplitude-phase error correction method according to claim 1, wherein the calculating of the projection matrix of the receive sub-array transmit-receive joint steering vector in step (6) is specifically performed by the following formula:
(6a) the range of azimuth angle [ - π/2]Evenly dividing K parts by K > NtPrConstructing a transmit-receive joint steering matrix Asub
Figure FDA0002987294130000034
Where K is the number of azimuthal divisions, θiIs the azimuth angle, i ═ 1,2tIs the number of transmitting array elements, prThe number of array elements which are calibrated for the receiving array;
(6b) calculating its projection matrix
Figure FDA0002987294130000035
Figure FDA0002987294130000036
Wherein the content of the first and second substances,
Figure FDA0002987294130000041
is dimension NtPr×NtPrThe identity matrix of [ ·]TRepresents a transposition [ ·]-1Indicating inversion.
4. The method for correcting the amplitude-phase error of the clutter-based MIMO radar transmit-receive array according to claim 1, wherein the step (7) of extracting the echo data of the receive array and the echo data of the receive sub-array is performed by the following formula:
(7a) MIMO radar radiates an orthogonal signal s, then thetaiThe echo Y of a direction can be expressed as:
Figure FDA0002987294130000042
wherein beta isiIs thetaiDirectional clutter scattering coefficient, gTAnd gRRepresenting the amplitude-phase error of the transmitting and receiving arrays respectively, wherein gamma (-) is a function for converting the vector into a diagonal matrix, and N is the noise of the receiver;
(7b) performing pulse compression on the echo Y by using a radiation waveform s, and vectorizing the obtained matrix to obtain echo data x of the receiving array:
Figure FDA0002987294130000043
wherein vec represents a function converting the matrix into a column vector, and n is noise;
(7c) selecting the echo x of the receiving subarray according to the echo data x of the receiving arraysubExpressed as:
Figure FDA0002987294130000044
wherein n issubIs noise, IprThe expression dimension is Pr×PrThe identity matrix of (2).
5. The method according to claim 1, wherein the obtaining of the transmit array error compensation coefficient vector q in step (9) is performed by using the clutter based MIMO radar transmit/receive array amplitude and phase error correction methodTSpecifically, the calculation is performed through the following steps:
(9a) simplifying the cost function:
due to the fact that
Figure FDA0002987294130000045
Wherein the content of the first and second substances,
Figure FDA0002987294130000046
represents prX 1 dimensional all 1 column vectors, the cost function can be simplified as:
Figure FDA0002987294130000051
Figure FDA0002987294130000052
wherein the content of the first and second substances,
Figure FDA0002987294130000053
[·]Hrepresents a conjugate transpose;
(9b) by the Lagrange multiplier method, qTThere is a unique closed-form solution:
Figure FDA0002987294130000054
6. the method according to claim 1, wherein the obtaining of the received array error compensation coefficient vector q in step (11) is performed by using the clutter based MIMO radar transmit/receive array amplitude and phase error correction methodRSpecifically, the calculation is performed through the following steps:
(11a) simplifying the cost function:
due to the fact that
Figure FDA0002987294130000055
The cost function is simplified as follows:
Figure FDA0002987294130000056
Figure FDA0002987294130000057
wherein the content of the first and second substances,
Figure FDA0002987294130000058
(11b) by the Lagrange multiplier method, qRExpressed as:
Figure FDA0002987294130000059
CN201810112602.4A 2018-02-05 2018-02-05 Clutter-based MIMO radar transmit-receive array amplitude-phase error correction method Active CN108459307B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201810112602.4A CN108459307B (en) 2018-02-05 2018-02-05 Clutter-based MIMO radar transmit-receive array amplitude-phase error correction method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201810112602.4A CN108459307B (en) 2018-02-05 2018-02-05 Clutter-based MIMO radar transmit-receive array amplitude-phase error correction method

Publications (2)

Publication Number Publication Date
CN108459307A CN108459307A (en) 2018-08-28
CN108459307B true CN108459307B (en) 2021-07-20

Family

ID=63239685

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201810112602.4A Active CN108459307B (en) 2018-02-05 2018-02-05 Clutter-based MIMO radar transmit-receive array amplitude-phase error correction method

Country Status (1)

Country Link
CN (1) CN108459307B (en)

Families Citing this family (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109507651B (en) * 2018-11-02 2020-10-20 北京遥测技术研究所 MIMO imaging system calibration method and device
CN109490828B (en) * 2018-11-28 2020-10-30 中国电子科技集团公司第五十四研究所 Positioning method based on homologous baseline array
CN109709514B (en) * 2019-01-10 2020-09-04 燕山大学 Array model error estimation value calibration method
JP2020165725A (en) * 2019-03-28 2020-10-08 パナソニックＩｐマネジメント株式会社 Radar system and radar signal processing method
CN110376560B (en) * 2019-06-03 2021-05-07 西安电子科技大学 Airborne bistatic MIMO radar amplitude-phase error correction method based on single range gate
CN110208762B (en) * 2019-07-05 2023-06-16 西安电子科技大学 Clutter-based multi-input multi-output radar array error correction method
CN111487478B (en) * 2020-03-27 2022-04-01 杭州电子科技大学 Angle-dependent complex array error calibration method based on deep neural network
CN112083385B (en) * 2020-08-28 2023-06-23 西安电子科技大学 Array amplitude-phase error self-correction method based on point target echo
CN112649799B (en) * 2020-12-04 2022-09-23 浙江大学 MIMO radar amplitude-phase error correction method
CN112782663B (en) * 2021-02-03 2023-07-21 海南大学 Target parameter estimation method of FDA-MIMO radar under amplitude-phase error condition
CN112986935B (en) * 2021-02-24 2022-12-20 湖北中南鹏力海洋探测系统工程有限公司 Multi-element array channel passive calibration method based on landform conformal arrangement
CN113314832B (en) * 2021-06-15 2022-10-25 东南大学 Millimeter wave vehicle-mounted MIMO radar antenna array device and design method

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101251597A (en) * 2008-04-08 2008-08-27 西安电子科技大学 Method for self-correction of array error of multi-input multi-output radar system
CN101770022A (en) * 2009-12-30 2010-07-07 南京航空航天大学 Multiple input multiple output (MIMO) radar array position error self-correcting method based on genetic algorithm
CN102540162A (en) * 2011-12-12 2012-07-04 中国船舶重工集团公司第七二四研究所 Method for estimating low-altitude electromagnetic wave propagation characteristic on basis of sea clutter
CN103885048A (en) * 2014-03-20 2014-06-25 西安电子科技大学 Bistatic MIMO radar transceiver array amplitude phase error correction method
CN104111448A (en) * 2014-07-29 2014-10-22 电子科技大学 Method for united correction of MIMO radar transceiving array errors
CN106443610A (en) * 2016-11-16 2017-02-22 西安电子科技大学 Self-correcting method for mutual coupling errors of MIMO radar receiving and transmitting arrays

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7106243B2 (en) * 2004-11-23 2006-09-12 Raytheon Company Technique for enhanced quality high resolution 2D imaging of ground moving targets

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101251597A (en) * 2008-04-08 2008-08-27 西安电子科技大学 Method for self-correction of array error of multi-input multi-output radar system
CN101770022A (en) * 2009-12-30 2010-07-07 南京航空航天大学 Multiple input multiple output (MIMO) radar array position error self-correcting method based on genetic algorithm
CN102540162A (en) * 2011-12-12 2012-07-04 中国船舶重工集团公司第七二四研究所 Method for estimating low-altitude electromagnetic wave propagation characteristic on basis of sea clutter
CN103885048A (en) * 2014-03-20 2014-06-25 西安电子科技大学 Bistatic MIMO radar transceiver array amplitude phase error correction method
CN104111448A (en) * 2014-07-29 2014-10-22 电子科技大学 Method for united correction of MIMO radar transceiving array errors
CN106443610A (en) * 2016-11-16 2017-02-22 西安电子科技大学 Self-correcting method for mutual coupling errors of MIMO radar receiving and transmitting arrays

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
基于杂波的收发分置MIMO雷达阵列位置误差联合校正方法;刘源 等;《电子与信息学报》;20151231;第37卷(第12期);第2956-2963页 *

Also Published As

Publication number Publication date
CN108459307A (en) 2018-08-28

Similar Documents

Publication Publication Date Title
CN108459307B (en) Clutter-based MIMO radar transmit-receive array amplitude-phase error correction method
CN107064892B (en) MIMO radar angle estimation algorithm based on tensor subspace and rotation invariance
Ma et al. Three-dimensional imaging of targets using colocated MIMO radar
CN108303683B (en) Single-base MIMO radar real-value ESPRIT non-circular signal angle estimation method
CN105445709B (en) A kind of thinning array near field passive location amplitude and phase error correction method
CN104111448A (en) Method for united correction of MIMO radar transceiving array errors
CN102135617A (en) Multi-target positioning method of bistatic multi-input multi-output radar
CN107390197B (en) Radar self-adaption sum-difference beam angle measurement method based on feature space
CN107607915B (en) Active phased array radar receiving channel correction method based on fixed ground object echo
CN113189592B (en) Vehicle-mounted millimeter wave MIMO radar angle measurement method considering amplitude mutual coupling error
CN107576947B (en) L-shaped array pair coherent information source two-dimensional direction of arrival estimation method based on time smoothing
CN112379327A (en) Two-dimensional DOA estimation and cross coupling correction method based on rank loss estimation
CN108828504B (en) MIMO radar target direction fast estimation method based on partial correlation waveform
Feng et al. Jointly iterative adaptive approach based space time adaptive processing using MIMO radar
CN112255629A (en) Sequential ESPRIT two-dimensional incoherent distribution source parameter estimation method based on combined UCA array
CN110196417A (en) The bistatic MIMO radar angle estimating method concentrated based on emitted energy
CN108828586B (en) Bistatic MIMO radar angle measurement optimization method based on beam domain
CN112612013B (en) FDA-MIMO radar incremental distance-angle two-dimensional beam forming method
CN104459680B (en) Method for rapidly estimating target direction through MIMO radar
CN115932824A (en) FMCW radar ranging method and system based on multiple antennas
CN115436909A (en) FMCW radar ranging method based on matrix reconstruction Root-MUSIC algorithm
Zhao et al. Multiple-target localization by millimeter-wave radars with trapezoid virtual antenna arrays
RU2752878C2 (en) Method of direction finding for broadband signals with increased resolution
KR102331907B1 (en) Apparatus for processing signal of radar for estimating joint range and angle and method thereof
Han et al. MIMO radar fast imaging algorithm based on sub-image combination

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant