CN109254272B - Two-dimensional angle estimation method of concurrent polarization MIMO radar - Google Patents
Two-dimensional angle estimation method of concurrent polarization MIMO radar Download PDFInfo
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- CN109254272B CN109254272B CN201811134025.5A CN201811134025A CN109254272B CN 109254272 B CN109254272 B CN 109254272B CN 201811134025 A CN201811134025 A CN 201811134025A CN 109254272 B CN109254272 B CN 109254272B
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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
Abstract
The invention discloses a two-dimensional angle estimation method of a concurrent polarization MIMO radar, which adopts the following scheme: 1) The received data X (t) is processed by matched filtering to obtain
Then to
Carrying out vectorization processing to obtain y (t); 2) Calculating the covariance matrix of y (t), and performing eigenvalue decomposition on the covariance matrix to obtain a signal subspace E S (ii) a 3) According to the signal subspace E S Constructing a rotation invariant equation, and calculating by using a total least square method to obtain a rotation invariant factor matrix psi i,j Carrying out characteristic value decomposition on the estimated value of (1) to obtain a rotation invariant factor; 4) Pairing the rotation invariant factors to obtain 5 paired rotation invariant factors; 5) Performing vector cross product on the paired rotation invariant factors, and obtaining 3 directional cosines by normalization
And
an estimated value of (d); 6) Using 3 directional cosines
And
calculating to obtain azimuth angle and pitchAn estimate of the angle. The method does not need angle search and array structure information, has good adaptability and can fully utilize polarization information.
Description
Technical Field
The invention belongs to the technical field of radars, relates to the estimation of the arrival angle of a radar, and particularly relates to a two-dimensional angle estimation method of a concurrent polarization MIMO radar, which can be used for target positioning and tracking of the radar.
Background
Because a polarization MIMO (Multiple-Input Multiple-Output) radar has polarization diversity and MIMO radar waveform diversity at the same time, the main methods for estimating the angle of the polarization MIMO radar are super-resolution and sparse recovery-based methods. Bistatic polarization MIMO radar estimates DOD (Direction of Departure) and DOA (Direction of Arrival) and polarization parameters by using an ESPRIT algorithm, needs extra pairing processing during estimation, and also has a combined ESPRIT-RootMUSIC algorithm without parameter pairing. And a dimension reduction DOA estimation method based on MUSIC, which reduces the calculation amount of the estimation process. In addition, the bistatic polarization MIMO radar two-dimensional DOD and two-dimensional DOA joint estimation method based on the parallel factor analysis method is used for estimating the angle and/or polarization parameters of the polarization MIMO radar by utilizing the traditional vector cross product and polarization smoothing by using an electromagnetic vector sensor which expands a receiving cross dipole to six components. Most of the research results are based on classical super-resolution algorithms, and the estimation methods play an important role in effectively utilizing the polarization diversity advantages of the polarization MIMO radar and improving the angle parameter estimation capability.
As is known, a six-component electromagnetic vector sensor can obtain more physical information than a cross dipole polarized array, and creates more favorable conditions for estimation of the direction of arrival from the information dimension, but the existing polarized MIMO radar does not take the sensor as an object, researches the problem of two-dimensional DOA and polarization joint estimation, and cannot obtain more effective physical information.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a two-dimensional angle estimation method of a concurrent polarization MIMO radar, can solve the problem that the information of the traditional polarization MIMO radar is not fully utilized, and utilizes polarization-airspace combined information to construct a rotation invariant equation and a vector cross product algorithm of an electric field vector and a magnetic field vector to obtain DOA angle estimation. The method does not need angle search and array structure information, has good adaptability and can fully utilize polarization information.
In order to achieve the purpose, the technical idea of the invention is as follows: the vector array is divided into scalar arrays formed by six sub-arrays, and a rotation invariant equation is constructed by utilizing the polarization-airspace joint information, so that the joint estimation of the target angle and the polarization parameters can be realized. The concrete implementation steps comprise:
1) The received data X (t) is processed by matched filtering to obtain
Then to
And carrying out vectorization treatment to obtain y (t).
2) Computing covariance matrix of y (t)
And performing eigenvalue decomposition on the covariance matrix to obtain a signal subspace E of the covariance matrix S 。
3) According to signal subspace E S Constructing a rotation invariant equation, and calculating by using a total least square method to obtain a rotation invariant factor matrix psi i,j Estimated value of [ p ], [ n ] i,j And decomposing the characteristic value to obtain a rotation invariant factor.
4) And pairing the rotation invariant factors to obtain 5 paired rotation invariant factors.
5) Carrying out vector cross product on 5 paired rotation invariant factors, and obtaining 3 direction cosines through normalization
And
an estimate of (d).
6) Using said 3 directional cosines
And
and calculating to obtain the estimated values of the azimuth angle and the pitch angle.
Compared with the prior art, the invention has the following advantages:
(1) Since no array information is used in the angle estimation process, the algorithm is applicable to any array.
(2) The algorithm does not need array element information of the array antenna.
(3) The algorithm does not need angle search and has lower calculation amount.
(4) The effective area of the algorithm angle estimation is 360 degrees full airspace.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a plot of RMS error as a function of SNR for an azimuth angle in accordance with the present invention;
fig. 3 is a plot of root mean square error of pitch angle as a function of signal to noise ratio in the present invention.
Detailed Description
Referring to fig. 1, the specific implementation steps of the present invention are as follows:
Consider a monostatic MIMO radar, its transmission array element is M scalar quantity antennas of horizontal polarization or vertical polarization, the receiving end is N six-component electromagnetic vector sensor composition. Defining the position of the transmitting array element m as (x) tm ,y tm ,z tm ) M =1, \8230;, M. Wherein x is tm ,y tm ,z tm The numerical values of the m-th transmitting array element on the X axis, the Y axis and the Z axis are respectively. The position of the nth receiving electromagnetic vector sensor is (x) rn ,y rn ,z rn ) N =1, \8230, N, wherein x rn ,y rn ,z rn The numerical values of the nth electromagnetic vector sensor on the X axis, the Y axis and the Z axis are respectively. M transmit elements transmit M orthogonal signals with the same carrier frequency and bandwidth:
wherein s is i (i =1, \8230;, M) denotes the ith transmission code signal, s i T Denotes s i T denotes a transposed symbol, and P denotes a code length. According to the characteristics of the MIMO radar, the transmitting signals satisfy the following conditions:
then SS H ＝I M Where H is the conjugate transposed symbol,
representing the conjugate transpose of the jth transmitted encoded signal, I M Representing an M × M identity matrix. Assume that there are K far-field point targets. The two-dimensional directions of arrival of the target are an azimuth angle phi and a pitch angle theta respectively, the azimuth angle phi belongs to [0,2 pi ], the pitch angle theta belongs to [0, pi ]]. Polarization auxiliary angle gamma for polarization state angle belongs to [0, pi/2 ]]And a polarization phase difference eta ∈ [ -pi, pi]To indicate. The received signal of the radar system can be represented by:
in the formula, t represents a slow time dimension number.
Spatial steering matrix representing a receiving array, a r (θ k ,φ k ) (K =1, \8230;, K) represents a reception steering vector of the kth target, θ k Denotes the pitch angle, phi, of the kth target k Indicating the azimuth of the k-th object,
spatial steering matrix representing the transmit array, a t (θ k ,φ k ) (K =1, \8230;, K) denotes a transmission steering vector of the kth target. A. The pol (θ,φ,γ,η)＝[a pol (θ 1 ,φ 1 ,γ 1 ,η 1 ),…,a pol (θ K ,φ K ,γ K ,η K )]Representing the response of a single electromagnetic vector sensor in the spatial-polarization domain, a pol (θ k ,φ k ,γ k ,η k ) Representing the polarization steering vector of the kth target. And diag denotes the operation of diagonalization,
representing the vector of the reflected signal at the target, the component gamma of which k (t)＝α k exp(j2πf k t)(k＝1,2,...,K)。α k Representing the amplitude of the reflected signal, whose value depends on the RCS (radar cross-section) of the target, the phase of the reflected signal being related to the Doppler frequency, f k Which is indicative of the doppler frequency of the target,
representing additive white gaussian noise. Right multiplying X (t) by S H And M transmitting signals are utilized to carry out matched filtering processing, and the output result is as follows:
wherein N (t) is a noise vector matrix, N (t) = W (t) S H ，
Representing the Khatri-Rao product. Vectorization operation is performed on equation (2), so that 6 MN-dimensional received vector data can be obtained:
wherein the content of the first and second substances,
its column vector is defined as the final virtual steering vector
Wherein, the K =1, \8230, the K column can be expressed as
Representing the Kronecker product and n (t) representing noise.
Computing covariance matrix of y (t)
L represents the number of fast beats. Then, the characteristic value decomposition is carried out on the obtained product to obtain
Wherein E is S Represents 6MN × K signal subspaces, Σ S Representing a matrix of signal energies, E N Representing a noise subspace. If there is no noise at this time, the signal subspace and the steering vector { a (θ) } k ,φ k ,γ k ,η k ) K =1, \ 8230;, K } constitutes the same subspace, i.e. E S = a (θ, Φ, γ, η) T. Where T represents a unique non-singular matrix.
First using a selection matrix J i To select the steering vector of the ith matrix. There is the following guidance vector equation for the kth target:
selection matrix J i Is the key to the algorithm, having a value of
In which the vector
a pol,i (θ k ,φ k ,γ k ,η k ) Representing the ith component of the polarization steering vector. From equation (4), we can also choose the steering vector of the jth matrix, and the steering vectors of the ith and jth matrices can form a rotation invariant relationship as follows:
wherein i, j =1, \8230;, 6. The above formula is modified as follows:
if all K incident signals are considered at this time, the above equation can be converted into a matrix form as follows:
J i A(θ,φ,γ,η)＝J j A(θ,φ,γ,η)Φ i,j (7)
wherein
For ease of presentation, a sign of a rotation invariant factor is defined:
will E S If = a (θ, Φ, γ, η) T is substituted into equation (7), the signal subspace E can be obtained S Is given by the rotational invariant equation of (a):
J i E S ＝J j E S Ψ i,j (8)
in which Ψ i,j ＝(T i,j ) -1 Φ i,j T i,j ，T i,j Representing the unique non-singular matrix formed by the ith matrix and the jth matrix, and-1 representing the inversion operation. In the presence of noise, the above equation can be solved using least squares or total least squares to obtain the rotation invariant factor matrix Ψ i,j An estimate of (d). Then to psi i,j The estimated value is subjected to eigenvalue decomposition to obtain a rotation invariant factor
And 104, pairing the rotation invariant factors to obtain 5 paired rotation invariant factors.
Here, due to the matrix Φ i,j Is a rotation invariant factor
After the eigenvalue decomposition, the pairing process needs to be performed by other methods. Because of the rotation invariant factor
And the feature vector to which it corresponds, and therefore, is different
Matrix T which can be composed using feature vectors i,j To perform the pairing process.
To be provided with
And
as an example. Let k and f denote { T, respectively 2,1 ·(T 3,2 ) -1 The serial number corresponding to the row and the column of the maximum value element of each column in the matrix. Then the matrix T 2,1 Kth row and matrix T 3,2 The f-th row of (a) necessarily corresponds to the same target, and the pairing process can be realized according to the relationship. At this point in time,
and
pairing is completed, all rotation invariant factors
The pairing process can be accomplished in the same way. Since i, j =1, \ 8230;, 6, the rotation invariant factor
Total number of
And (4) respectively. Setting i = j +1, the rotation invariant factor is then set
The number of (2) is reduced to 5.
According to a rotation invariant factor
The following equation is easily derived.
According to maxwell's equations, the electric field vector cross-product magnetic field vector of the incident signal is equal to the poynting vector of the incident signal, and the expression above is shown as follows:
wherein e represents an electric field vector, h represents a magnetic field vector,
i.e. representing a poynting vector, the component of which is equal to u k ＝sinθ k cosφ k ，v k ＝sinθ k sinφ k And w k ＝cosθ k . Substituting formula (9) into the above formula, one can obtain:
rotation invariant factor derived from previous estimates
The value of the direction cosine is substituted into an expression (11) to finally obtain the estimation of the direction cosine
Using 3 directional cosines
And
and calculating to obtain the estimated values of the azimuth angle and the pitch angle. I.e. a two-dimensional estimate of the direction of arrival is obtained by some triangulation:
simulation content: the root mean square error changes with the signal-to-noise ratio;
simulation conditions are as follows: in the simulation, the numbers of transmitting array elements and receiving vector sensors of the radar system are considered as follows: m =6,n =6. Assuming that the transmitting antennas are distributed on an x axis, the array element interval is a uniform half-wavelength interval, the receiving vector antennas are arranged on a y axis, the array element interval is also a uniform half-wavelength interval, according to the above arrangement, the MIMO radar system is distributed in an L shape, and it needs to be noted that the array can be arranged in any form. Set fast beat number L =200, monte carlo experiment number 1000. Assume that there are two independent targets whose two-dimensional angles are: (theta) 1 ,φ 1 )＝(30°,40°)，(θ 2 ,φ 2 ) = (60 °,70 °), polarization parameters thereof are (γ) respectively 1 ,η 1 )＝(45°,90°)，(γ 2 ,η 2 ) = (45 °, -90 °). It can be seen that the first signal is left hand circular polarized and the second signal is right hand circular polarized, and that the two targets have the same value of the supplementary polarization angle.
And (3) simulation results: FIG. 2 is a plot of RMS error in azimuth angle versus signal-to-noise ratio in the present invention, and FIG. 3 is a plot of RMS error in pitch angle versus signal-to-noise ratio in the present invention, which is compared to Cramer-Rainband (RCRB). From the simulation, it can be seen that the angle estimation accuracy of the algorithm of the present invention increases with the increase of the signal-to-noise ratio, which accords with the result of theoretical analysis, and from the results of fig. 2 and fig. 3, the accuracy estimation result has a certain distance from the RCRB. Because the angle estimation accuracy of the array signal depends heavily on the array aperture, the larger array aperture can effectively improve the angle estimation accuracy, the root cause of the application that the angle estimation accuracy has a certain distance compared with the RCRB is that the method only utilizes the internal information of the vector antenna and does not fully utilize the aperture information of the array, thereby bringing a certain estimation error, but the method of the application can be applicable to any array because the array information is not used in the angle estimation process; the angle search is not needed, and the calculation amount is low; and the structure information of the array is not needed, and the method has better adaptability.
Claims (2)
1. A two-dimensional angle estimation method for a co-point polarized MIMO radar, the method comprising the steps of:
1) The received data X (t) is processed by matched filtering to obtain
Then to
Performing vectorization processing to obtain y (t), wherein the received data can be represented by the following formula:
a t (θ k ,φ k ) (K =1, \8230;, K) represents a transmit steering vector of a kth target;
A pol (θ,φ,γ,η)＝[a pol (θ 1 ,φ 1 ,γ 1 ,η 1 ),…,a pol (θ K ,φ K ,γ K ,η K )]representing the response of the spatial-polarization domain of a single electromagnetic vector sensor, a pol (θ k ,φ k ,γ k ,η k ) The polarization steering vector of the kth target, diag the diagonalization operation,
representing a vector of reflected signals at the target, the component gamma of which k (t)＝α k exp(j2πf k t)(k＝1,2,...,K)，α k Representing the amplitude of the reflected signal, the value of which depends on the radar cross-section of the target, the phase of the reflected signal being related to the Doppler frequency, f k Indicating the Doppler frequency, f, of the target k ，
Representing additive white gaussian noise;
2) Computing covariance matrix of y (t)
And performing eigenvalue decomposition on the covariance matrix to obtain a signal subspace E of the covariance matrix S ；
3) According to the signal subspace E S Constructing a rotation invariant equation, and calculating by using a total least square methodObtaining a rotation invariant factor matrix Ψ i,j Estimated value of [ p ], [ n ] i,j Carrying out characteristic value decomposition on the estimated value of the (I) to obtain a rotation invariant factor, wherein i, j =1, \8230;, 6;
4) Pairing the rotation invariant factors to obtain 5 paired rotation invariant factors;
5) Carrying out vector cross product on 5 paired rotation invariant factors, and obtaining 3 direction cosines through normalization
And
an estimated value of (d);
6) Using said 3 directional cosines
And
and calculating to obtain the estimated values of the azimuth angle and the pitch angle.
2. The two-dimensional angle estimation method of a concurrent polarization MIMO radar according to claim 1, wherein the step 4) pairs the rotation invariant factors to obtain 5 pairs of rotation invariant factors, and the solution is performed according to the following steps:
(4a) Rotation invariant factor
And the feature vector to which it corresponds, and therefore, is different
Matrix T which can be composed using feature vectors i,j To perform a pairing process, wherein i, j =1, \8230;, 6;
(4b) At x degree 2,1 Hexix- 3,2 As an example, letk and f represent { T } 2,1 ·(T 3,2 ) -1 The serial number corresponding to the row and column of the maximum value element of each column in the matrix, and then the matrix T 2,1 Kth row and matrix T 3,2 The f-th row of (1) necessarily corresponds to the same target, so far, χ 2,1 Hexix- 3,2 The pairing is completed;
(4c) All rotation invariant factors χ i,j The pairing process can be completed by the (4 b) operation method for i, j =1, \8230 |, 6.
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| CN109959891B (en) * | 2019-04-11 | 2023-05-23 | 南京航空航天大学 | Dimension-reducing spectral peak searching method for space angle and polarization parameters of electromagnetic vector L array |
| CN111504952B (en) * | 2020-04-15 | 2021-09-07 | 成都飞机工业（集团）有限责任公司 | Low-scattering carrier with both horizontal polarization and vertical polarization and testing method thereof |
| CN111864347B (en) * | 2020-06-24 | 2021-04-13 | 宁波大学 | Polarization dynamic matching method of VICTS antenna |
| CN113359196B (en) * | 2021-05-26 | 2023-01-20 | 上海交通大学 | Multi-target vital sign detection method based on subspace method and DBF |
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