CN111060885B - Parameter estimation method of MIMO radar - Google Patents

Parameter estimation method of MIMO radar Download PDF

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CN111060885B
CN111060885B CN201911281621.0A CN201911281621A CN111060885B CN 111060885 B CN111060885 B CN 111060885B CN 201911281621 A CN201911281621 A CN 201911281621A CN 111060885 B CN111060885 B CN 111060885B
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CN111060885A (en
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胡居荣
田颖
詹蕾
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Hohai University HHU
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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
    • 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
    • G01S7/411—Identification of targets based on measurements of radar reflectivity
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract

The invention discloses a parameter estimation method of MIMO radar, which utilizes a pre-constructed bistatic signal model under the condition of considering array errors to acquire a received signal; performing sparse representation on the received signal by using a pre-constructed sparse signal model; projecting and adopting the sparse representation of the received signals by using a random Gaussian observation matrix to obtain measurement signals; and reconstructing the measurement signal by using an OMP reconstruction algorithm, and determining the azimuth angle and the pitch angle of the target. The advantages are that: the method is suitable for high-resolution parameter estimation, can accurately estimate the two-dimensional angle of the target, can overcome array noise to realize the accurate estimation of the reflection amplitude of the target, and has the advantages of low data sampling rate and small data operand based on the OMP algorithm under the conditions of low signal-to-noise ratio and array error.

Description

Parameter estimation method of MIMO radar
Technical Field
The invention relates to a parameter estimation method of a MIMO radar, and belongs to the technical field of MIMO radar signal processing.
Background
The concept of MIMO radar and its associated signal processing techniques have received increased attention from various nations, and many have studied about the performance of estimating parameters of MIMO radar. In recent years, the field of signal processing has developed the theory of compressed sensing (Compressive Sensing) that solves the problem of high-rate analog-to-digital conversion by using existing classical methods (such as transform coding, optimization algorithms, etc.), by exploiting the sparse nature of the signal, taking discrete samples of the signal with random sampling at much less than the Nyquist sampling rate, and then perfectly reconstructing the signal by a nonlinear reconstruction algorithm.
Whether conventional algorithms or compressed sensing-based target reconstruction methods, the preconditions are precisely known for array manifold. However, in practical situations, the error of the array is often unavoidable, so it is very important to investigate how to realize robust target angle estimation when the array has an error.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a parameter estimation method of a MIMO radar.
In order to solve the technical problems, the invention provides a parameter estimation method of MIMO radar,
acquiring a received signal by using a pre-constructed bistatic signal model under the condition of considering array errors;
performing sparse representation on the received signal by using a pre-constructed sparse signal model;
projecting and adopting the sparse representation of the received signals by using a random Gaussian observation matrix to obtain measurement signals;
and reconstructing the measurement signal by using an OMP reconstruction algorithm, and determining the azimuth angle and the pitch angle of the target.
Further, the bistatic signal model under the condition of considering array errors is as follows:
Figure BDA0002316912340000011
wherein ,Xn-error Representing the received signal, the target angle of the received signal spatially discretizes into P 1 ×P 2 Direction P 1 For the number of discrete space wave departure angles of the target angle, P 2 For the number of discrete spatial angles of arrival of the target angle,
Figure BDA0002316912340000021
p representing the target angular discrete space 1 Wave separation angle->
Figure BDA0002316912340000022
P representing the target angular discrete space 2 Angle of arrival A Mr-error () A matrix of steering vectors representing errors in the receive array, < >>
Figure BDA0002316912340000023
A steering vector matrix representing the transmit array containing errors,
Figure BDA0002316912340000024
representing a reflection amplitude matrix, S representing M orthogonal independent waveforms transmitted by the system, W representing complex Gaussian white noise, and T being a matrix transposed symbol.
Further, the sparse representation of the received signal by using the pre-constructed sparse signal model is as follows:
Figure BDA0002316912340000025
X n-error ＝(ψ n σ) T
Figure BDA0002316912340000026
wherein ,α1 ,α 2 …α P1 The angle representing the wave departure angle space, together with P 1 And (b) wherein
Figure BDA0002316912340000027
The angle representing the angle of arrival space, together with P 2 And sigma represents a sparse vector matrix of the received signal after sparse representation, and sigma represents the received signal after sparse representation ij Representing the reflection amplitude corresponding to the object in which the discrete space corresponding to the i-th angle of arrival and the j-th angle of departure exists, i=1, 2, …, P 2 ，j＝1,2，…，P 1 。
Further, the receiving signals with sparse representation are projected and adopted by utilizing a random Gaussian observation matrix, and the obtained measuring signals are expressed as:
y n ＝Θ n σ
wherein ,Θn Representing a perception matrix, wherein sigma represents a sparse vector matrix of a received signal after sparse representation;
Θ n ＝φ n ψ n
wherein ,φn Representing a stationary, and transformed basis matrix ψ n Uncorrelated m×l-dimensional random gaussian observation matrix, n=1, 2, … M, M<L；
Further, the reconstruction process is as follows:
1) Selecting an index lambda corresponding to a column having the greatest correlation with the residual signal vector r from the perceptual matrix Θ k ，λ k ＝argmax(Θ n H r)，Θ n Column N representing Θ,1 < N < N, H representing the transpose conjugate, argmax () representing the Θ n H r is a set of variable points corresponding to the maximum value;
2) Update index set Ω=Ω ≡λ k ；
3) By means ofThe least squares estimation yields an approximate solution:
Figure BDA0002316912340000031
in (I)>
Figure BDA0002316912340000032
For the iterative kth least squares approximation solution, Θ Ω Is a matrix of columns indicated by Ω in Θ, ||y n -Θ Ω X′ n || 2 2 norms representing the equation, argmin () represents the equation y n -Θ Ω X′ n || 2 Acquiring a set of minimum solutions;
4) Updating residual signal vectors
Figure BDA0002316912340000033
5) Judging whether the iteration satisfies the stop condition k=k or r|| 2 Epsilon, and stopping outputting when the epsilon is satisfied
Figure BDA0002316912340000034
Figure BDA0002316912340000035
Otherwise let k=k+1, go to step 1).
Further, the OMP reconstruction algorithm iteratively determines the positions of K non-zero elements represented by the index set Ω, the values of the elements corresponding to the projection coefficients at that time
Figure BDA0002316912340000036
k=1, 2, … K, measuring signal y n Projection coefficients of subspaces formed by the K atoms are corresponding to X' n Wherein the position index of the non-zero element indicates the angle of the target, the magnitude of which is the reflection amplitude of the target, and the azimuth angle and the pitch angle of the target are determined by the angle and the reflection amplitude of the target.
The invention has the beneficial effects that: according to the method, even if the signal model has array error, the two-dimensional angle of the target can be estimated accurately, and the algorithm can also overcome array noise to realize accurate estimation of the reflection amplitude of the target.
The method is suitable for high-resolution parameter estimation, can accurately estimate the two-dimensional angle of the target, can overcome array noise to realize the accurate estimation of the reflection amplitude of the target, and has the advantages of low data sampling rate and small data operand based on the OMP algorithm under the conditions of low signal-to-noise ratio and array error.
Drawings
FIG. 1 is a bistatic uniform linear array MIMO radar signal model;
fig. 2 is a flow chart of parameter estimation based on OMP algorithm.
Detailed Description
In order to make the objects, features and advantages of the present invention more comprehensible, the technical solutions in the embodiments of the present invention are described in detail below with reference to the accompanying drawings, and it is apparent that the embodiments described below are only some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The technical scheme of the invention is further described below by the specific embodiments with reference to the accompanying drawings.
A bistatic signal model is built as in fig. 1. The transmitting antenna array and the receiving antenna array are equidistant linear arrays, and the transmitting array and the receiving array are remotely separated. The radar system has M transmitting antennas, N receiving antennas, and the array element spacing between the transmitting and receiving antennas is d t and dr In order to ensure that the received signals of each received signal unit do not generate resolution ambiguity, the spacing of the received array elements should satisfy the half-wavelength condition, namely d r Lambda/2 (lambda is the wavelength). Assuming K targets in the far field, the orientation of the kth target is
Figure BDA0002316912340000041
And K is<MN (M is the emission)The number of antennas, N is the number of receive arrays). Wherein θ is k Is wave departure angle (DOD),>
Figure BDA0002316912340000042
is the angle of arrival (DOA).
For a bistatic MIMO radar, when there are multiple targets in space, and the MIMO radar transceiver array contains an amplitude-phase error, its received data is expressed as:
Figure BDA0002316912340000043
wherein ,
Figure BDA0002316912340000044
and />
Figure BDA0002316912340000045
Representing the steering vector matrix of the transmit and receive arrays, respectively, containing errors. Diagonal matrix
Figure BDA0002316912340000046
Representing the amplitude and phase errors of N receiving array elements, wherein ρ Mri and φMri Respectively representing the amplitude error and the phase error of the ith receiving array element>
Figure BDA0002316912340000047
Figure BDA0002316912340000048
Respectively represent the amplitude-phase errors of M transmitting array elements, wherein ρ Mti and φMti Respectively representing the amplitude error and the phase error of the ith transmit element. />
Figure BDA0002316912340000051
and AMt (θ k ) Representing the ideal receive steering vector and transmit steering vector matrices for the K targets, respectively.
Figure BDA0002316912340000052
Figure BDA0002316912340000053
Figure BDA0002316912340000054
Figure BDA0002316912340000055
η＝[η 1 η 2 … η k ] T For the amplitude of K target reflected signals, S is M orthogonal independent waveforms transmitted by the system, W is C N×L Is complex gaussian white noise.
We spatially discretize each target angle into P 1 ×P 2 The directions. Define alpha as P separating the signal wave from the angular space 1 Angle, defining beta as P of the signal angle of arrival space 2 The corners, i.e
Figure BDA00023169123400000514
Figure BDA00023169123400000515
Definition of the definition
When (when)
Figure BDA0002316912340000056
When there is a K-th object +.>
Figure BDA0002316912340000057
When->
Figure BDA0002316912340000058
When there is no target at the position,
Figure BDA0002316912340000059
the received signal of the bistatic uniform linear array MIMO radar under the array error can be written as
Figure BDA00023169123400000510
Recording device
Figure BDA00023169123400000511
Figure BDA00023169123400000512
Figure BDA00023169123400000513
Then
X′ n ＝(ψ n σ) T
ψ n The (n=1, 2, … L) transform basis matrix has been determined, knowing ψ n (n=1, 2, … L) is the sparse basis containing the phase information of the array element, σ is the sparse vector of the signal under the sparse basis, wherein the position index P of the non-zero element 2 P 1 The angle of the target is indicated, and the value of the angle is the reflection amplitude of the target. The number of the targets is sparsity, and the reflection amplitude of the targets is the non-zero coefficient of each received signal in a transformation domain. Then a stable and transformed base matrix psi is taken n Uncorrelated M x L-dimensional random Gaussian observation matrix phi n (n=1, 2, … M), where M<L. Thus, the reception signal X 'of the nth reception antenna' n (n=1, 2, … L) in the observation matrix phi n The projection vector on is y n ＝φ n X′ n T ＝φ n ψ n σ＝Θ n σ
Θ n (n=1, 2, … M) is the sensing matrix.
Fig. 2 is a flowchart of a MIMO radar parameter estimation method based on OMP algorithm, and the specific steps are summarized as follows:
input a sensing matrix Θ, measuring vector y n Signal sparsity K, error threshold epsilon;
and (3) outputting: residual component r=y n (n=1, 2 … N), index set Ω=Φ, number of iterations k=1, estimation of signal sparseness factor
Figure BDA0002316912340000061
Support domain->
Figure BDA0002316912340000062
Step 1: selecting an index lambda corresponding to a column having the greatest correlation with the residual signal vector r from the perceptual matrix Θ k ，λ k ＝argmax(Θ n H r)(1＜＜n＜＜N)，Θ n An nth column representing Θ;
step 2: update index set Ω=Ω ≡λ k ；
Step 3: obtaining an approximate solution by using least square estimation:
Figure BDA0002316912340000063
wherein ,
Figure BDA0002316912340000064
for the iterative kth least squares approximation solution, Θ Ω Is a matrix made up of columns indicated by Ω in Θ;
step 4: updating the margin
Figure BDA0002316912340000065
Step 5: judging whether the iteration satisfies the stop condition k=k or r|| 2 Epsilon, and stopping outputting when the epsilon is satisfied
Figure BDA0002316912340000066
Figure BDA0002316912340000067
If not, let k=k+1, turn to step1;
iterative determination of the position of the K non-zero elements represented by the index set Ω, the values of which correspond to thisProjection coefficient at the time
Figure BDA0002316912340000071
Observation signal y n The projection coefficient of the subspace formed by the K atoms by the (n=1, 2 … N) is also corresponding to X' n (n=1, 2 … L), wherein the position index of the non-zero element indicates the angle of the target, and the magnitude of the value is the reflection amplitude of the target. Such that the sparse signal X 'to be reconstructed' n (n=1, 2 … L) is also determined, as are the azimuth and pitch angles of the target.
The above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (4)

1. A parameter estimation method of MIMO radar is characterized in that,
acquiring a received signal by using a pre-constructed bistatic signal model under the condition of considering array errors;
performing sparse representation on the received signal by using a pre-constructed sparse signal model;
projecting and adopting the sparse representation of the received signals by using a random Gaussian observation matrix to obtain measurement signals;
reconstructing the measurement signal by using an OMP reconstruction algorithm, and determining the azimuth angle and the pitch angle of the target;
the bistatic signal model under the array error consideration condition is as follows:
Figure QLYQS_1
wherein ,Xn-error Representing received signalsNumber, target angle space of the received signal is discretized into P 1 ×P 2 Direction P 1 For the number of discrete space wave departure angles of the target angle, P 2 For the number of discrete spatial angles of arrival of the target angle,
Figure QLYQS_2
p representing the target angular discrete space 1 Wave separation angle->
Figure QLYQS_3
P representing the target angular discrete space 2 Angle of arrival A Mr-error (indicating that the receive array contains a matrix of steering vectors with errors, ">
Figure QLYQS_4
A matrix of steering vectors representing errors in the transmit array, < >>
Figure QLYQS_5
Representing a reflection amplitude matrix, wherein S represents M orthogonal independent waveforms transmitted by a system, W represents complex Gaussian white noise, and T is a matrix transposed symbol;
the sparse representation of the received signal by using the pre-constructed sparse signal model is as follows:
Figure QLYQS_6
X n-error ＝(ψ n σ) T
Figure QLYQS_7
wherein ,
Figure QLYQS_8
the angle representing the wave departure angle space, together with P 1 Individual, wherein->
Figure QLYQS_9
The angle representing the angle of arrival space, together with P 2 And sigma represents a sparse vector matrix of the received signal after sparse representation, and sigma represents the received signal after sparse representation ij Representing the reflection amplitude corresponding to the object in which the discrete space corresponding to the i-th angle of arrival and the j-th angle of departure exists, i=1, 2, …, P 2 ，j＝1，2，…，P 1 。
2. The method for estimating parameters of MIMO radar according to claim 1, wherein the projecting and adopting the sparse representation of the received signal by using the random gaussian observation matrix, the obtained measurement signal is expressed as:
y n ＝Θ n σ
wherein ,Θn Representing a perception matrix, wherein sigma represents a sparse vector matrix of a received signal after sparse representation;
Θ n ＝φ n ψ n
wherein ,φn Representing a stationary, and transformed basis matrix ψ n Uncorrelated m×l-dimensional random gaussian observation matrices, n=1, 2, … M, M < L.
3. The method for estimating parameters of MIMO radar according to claim 2, wherein the reconstructing process is:
1) Selecting an index lambda corresponding to a column having the greatest correlation with the residual signal vector r from the perceptual matrix Θ k ，λ k ＝argmax(Θ n H r)，Θ n Column N representing Θ,1 < N < N, H representing the transpose conjugate, argmax () representing the Θ n H r is a set of variable points corresponding to the maximum value;
2) Update index set Ω=Ω ≡λ k ；
3) Obtaining an approximate solution by using least square estimation:
Figure QLYQS_10
in (I)>
Figure QLYQS_11
For the iterative kth least squares approximation solution, Θ Ω Is a matrix of columns indicated by Ω in Θ, ||y n -Θ Ω X′ n || 2 2 norms representing the equation, argmin () represents the equation y n -Θ Ω X′ n || 2 Acquiring a set of minimum solutions;
4) Updating residual signal vectors
Figure QLYQS_12
5) Judging whether the iteration satisfies the stop condition k=k or r|| 2 Epsilon, and stopping outputting when the epsilon is satisfied
Figure QLYQS_13
Otherwise let k=k+1, go to step 1).
4. A method for estimating parameters of a MIMO radar according to claim 3, characterized in that the positions of K non-zero elements represented by the index set Ω are iteratively determined by an OMP reconstruction algorithm, the values of these elements corresponding to the projection coefficients at that time
Figure QLYQS_14
k=1, 2,..k, measurement signal y n Projection coefficients of subspaces formed by the K atoms are corresponding to X' n Wherein the position index of the non-zero element indicates the angle of the target, the magnitude of which is the reflection amplitude of the target, and the azimuth angle and the pitch angle of the target are determined by the angle and the reflection amplitude of the target.
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