CN103760527B

CN103760527B - Single base MIMO radar coherent source Wave arrival direction estimating method

Info

Publication number: CN103760527B
Application number: CN201410032063.5A
Authority: CN
Inventors: 曹运合; 王胜华; 苏洪涛; 谢荣; 王敏; 张子敬
Original assignee: Xidian University
Current assignee: Xidian University
Priority date: 2014-01-23
Filing date: 2014-01-23
Publication date: 2015-12-09
Anticipated expiration: 2034-01-23
Also published as: CN103760527A

Abstract

The invention belongs to Radar Technology field, disclose a kind of single base MIMO radar coherent source Wave arrival direction estimating method, can be used for goal orientation and the tracking of single base MIMO radar of General Cell stream shape.Implementation step is: step 1, writes out the steering vector of single base MIMO radar according to array manifold; Step 2, arranges M Wei Fandemeng vector, obtains transition matrix G; Step 3, obtains the steering vector after converting by smooth transformation matrix F; Step 4, matched filtering is carried out to the reception data of MIMO radar, reception data after matched filtering are designated as X (k), obtain data Y (the k)=FGX (k) after conversion, then form autocorrelation matrix by transition matrix G and level and smooth transformation matrix F; Step 5, carries out feature decomposition to autocorrelation matrix, forms noise subspace; Step 6, utilizes noise subspace to form space zero spectral function; Step 7, adopts polynomial rooting method to obtain azimuth of target.

Description

Method for estimating direction of arrival of coherent source of single-base MIMO radar

Technical Field

The invention belongs to the technical field of radars, and particularly relates to a method for estimating the direction of arrival of coherent sources of any single-base MIMO radar, which can be used for target orientation and tracking of the single-base MIMO radar with any array manifold.

Background

The multi-input multi-output radar (namely the MIMO radar) fully utilizes the waveform diversity gain to improve the spatial resolution, improve the parameter estimation precision and increase the maximum number of the targets which can be positioned by the system. In recent years, MIMO radar has been developed very rapidly, wherein a direction of arrival estimation (i.e., DOA) method is a major issue in the research of MIMO radar. In various array structures, the uniform linear array is the foundation of the research of the current MIMO radar DOA algorithm due to the simple structure and easy realization, and various rapid DOA algorithms can be adopted. However, one-dimensional uniform lines can only provide 180 degrees of unambiguous azimuthal information, and the resolution in different directions is different, and sometimes the need for a particular system makes the array likely not to be uniform. For the MIMO radar, a space beam is not formed during transmission, an array element directional diagram covers the whole space domain and is used for detecting the whole space information of 360 degrees, and at the moment, the linear array is adopted, so that the ambiguity can occur in the range of 360 degrees, and the requirement cannot be met. Therefore, estimation of the direction of arrival for any array manifold is a problem that needs to be studied.

At present, the most basic angle super-resolution estimation method adopts a multi-signal classification MUSIC method, which can work under any array manifold, but needs to carry out full-space domain search on angles, and has very large computation amount. In addition, the subspace-like high-resolution DOA estimation algorithm represented by the MUSIC algorithm has good resolution performance and high estimation accuracy for incoherent spatial sources, but the resolution performance thereof gradually deteriorates as the degree of correlation between the spatial sources increases.

The traditional array space smoothing algorithm is a common preprocessing method for processing coherent sources, and then a sub-array covariance algorithm and a weighted space smoothing algorithm appear on the basis of a forward and backward space smoothing technology, and the improved algorithms reduce the aperture loss of the array to a certain degree, improve the resolving power of the coherent sources, but bring larger calculation amount. The various smoothing-technology-based solution coherence methods mentioned above are all based on a uniform linear array structure, and cannot process any array manifold; in addition, the algorithms obtain the decoherence capability by sacrificing the effective aperture of the array, and the resolution capability of the coherent source is greatly reduced after the decoherence.

Disclosure of Invention

In view of the above shortcomings in the prior art, the present invention aims to provide a method for estimating direction of arrival of coherent source of monostatic MIMO radar, which can be used for coherent source decorrelation processing of MIMO radar arrays of any array manifold, and can realize monostatic MIMO radar coherent source DOA estimation of any array manifold while reducing the amount of computation by using polynomial root-finding algorithm instead of spectral peak search algorithm.

The technical idea for realizing the invention is as follows: firstly, decomposing the MIMO radar steering vector into a structure of multiplying a matrix and a Van der Waals vector by using an array interpolation technology; then, the thought of space smoothing is used for reference, and the coherent source is subjected to decoherence; and finally, a polynomial root-finding method is adopted to replace a spectral peak searching mode in the traditional method to obtain target angle information, so that the quick estimation of the direction of arrival is realized.

The technical scheme of the invention is a coherent source direction-of-arrival estimation method of a single-base MIMO radar, which is characterized by comprising the following steps:

step 1, obtaining an array steering vector A (theta) according to an array manifold of the single-base MIMO radar, wherein the array has N array elements, and the polar coordinate of each array element is (r)_n，β_n) N is 1, 2,. N; n is the number of array elements;

step 2, setting an M-dimension vandermonde vector B (theta), and setting the M-dimension vandermonde vector B (theta) A according to a formula G^H(θ)[A(θ)A^H(θ)]^-1Solving a conversion matrix G; wherein, it is madeSelecting the dimension M of the Van der Monte guide vector B (theta) to be approximately equal to 4kR, k to be 2 pi/lambda, wherein lambda is the wavelength of the emission signal;

step 3, performing similar space smoothing processing on the van der waals guide vector B (theta), wherein if F is a smooth transformation matrix, the smoothed guide vector C (theta) is FB (theta);

step 4, performing matched filtering on the received data of the MIMO radar, recording the matched filtered received data as X (k), converting the matrix G and the smooth transformation matrix F to obtain a transformed data matrix Y (k) ═ FGX (k), and forming an autocorrelation matrix R by using the data matrix Y (k)_y；

Step 5, for the autocorrelation matrix R_yPerforming feature decomposition to obtain noise subspace

Step 6, utilizing noise subspaceForming a MUSIC spatial zero spectrum function:

wherein | | | purple hair²The expression is given in the 2-norm,representation matrixThe conjugate transpose of (1);

step 7, let z equal to e^jθThen f (θ) can be converted to:

f (z) = C^{H} (z) {\hat{E}}_{n} {\hat{E}}_{n}^{H} C (z)

and f (z) is equal to 0, and a polynomial root solving method is adopted to obtain a complex exponential form z of P azimuth angles which are closest to a unit circle and have amplitudes less than 1_pP ═ 1, 2.. P; wherein P is the number of targets in the same range gate, theta_pAzimuth for the p-th target;

step 8, using the complex exponential form z of the acceptance angle_pObtaining the p-th acceptance azimuth angle theta_p：

θ_p＝angle(z_p)

Wherein, angle () represents the phase angle;

p＝1，2...P。

and solving the azimuth angles of the P targets, namely finishing the estimation of the direction of arrival of the MIMO radar coherent source.

Compared with the prior art, the invention has the following advantages: (1) the existing DOA estimation method independent of the array manifold is an MUSIC spectrum estimation method, but the method cannot process coherent source signals, the existing subspace type coherent source processing method has requirements on the array manifold, the array is required to be a linear uniform array or a two-dimensional linear uniform array, and the irregular array manifold cannot be processed; (2) the method capable of processing coherent source signals is a maximum likelihood method at present, but the method needs multidimensional search, the calculation amount is large, and particularly under the condition of multiple sources, the calculation amount is exponentially increased, and the engineering realization is difficult. The invention can change the MIMO radar steering vector into a Van der Mongolian form, and the DOA estimation adopts a polynomial root-solving form, thereby greatly reducing the operation amount.

Drawings

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

FIG. 1 is a flow chart of an implementation of a coherent source direction of arrival estimation method of a monostatic MIMO radar of the invention;

FIG. 2 is a graph of simulation results obtained using the present invention for 100 independent experiments on a target;

FIG. 3 is a graph of the mean square error of the target angle as a function of the SNR for locating a target 1 using the present invention;

fig. 4 is a graph of the mean square error of the target angle as a function of the signal-to-noise ratio SNR when the target 2 is positioned using the present invention.

Detailed Description

Referring to fig. 1, the method for estimating the direction of arrival of coherent source of single-base MIMO radar of the present invention comprises the following steps:

step 1, obtaining the array steering vector A (theta) according to the array manifold of the single-base MIMO radar.

The single-base MIMO radar array has N array elements (the N array elements are shared by transmitting and receiving), and the polar coordinate of each array element can be obtained according to the array element distribution as (r)_n，β_n) N is 1, 2,. N, N is an array element number;

according to the polar coordinates (r) of each array element_n，β_n) Obtaining the transmitting guide vector a of the MIMO radar array_t(theta) and the received steering vector a_r(θ) is:

where k is 2 pi/λ, λ is the wavelength of the emitted signal, r_nAnd beta_nThe distance between the nth array element and the origin of the coordinate and the angular position of the nth array element relative to the x axis in the polar coordinate are respectively, theta is an azimuth angle]^TRepresenting a matrix transposition;

according to the transmission steering vector a_t(theta) and the received steering vector a_r(theta) obtaining a MIMO radar arrayThe column steering vector A (θ) is:

<math> <mrow> <mi>A</mi> <mrow> <mo>(</mo> <mi>θ</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>a</mi> <mi>t</mi> </msub> <mrow> <mo>(</mo> <mi>θ</mi> <mo>)</mo> </mrow> <mo>&CircleTimes;</mo> <msub> <mi>a</mi> <mi>r</mi> </msub> <mrow> <mo>(</mo> <mi>θ</mi> <mo>)</mo> </mrow> </mrow> </math>

in the formula,representing a Kronecker product operation;

step 2, setting an M-dimension vandermonde vector B (theta), and setting the M-dimension vandermonde vector B (theta) A according to a formula G^H(θ)[A(θ)A^H(θ)]^-1And solving a conversion matrix G.

2a) Obtaining dimension M of Van der Monte vector B (theta)

Order toN is 1, 2, N is the number of array elements, the dimension M of the van der mond guide vector B (θ) is selected to be approximately equal to 4kR, k is 2 pi/λ, and λ is the wavelength of the transmitted signal;

neglecting the truncation error, the van der waals steering vector B (θ) is:

wherein, the [ alpha ], [ beta ]]^TRepresenting a matrix transpose and j an imaginary number.

2b) Obtaining a transformation matrix G

Taking J angles at equal intervals in the observation range, namely: theta₁，θ₂，...，θ_J；

According to theta₁，θ₂，...，θ_JRespectively form a steering vector matrixAnd vandermonde matrix

According to a steering vector matrixAnd vandermonde matrixObtaining a conversion matrix G by using a least square method:

G = \tilde{B} {\tilde{A}}^{H} {(\tilde{A} {\tilde{A}}^{H})}^{- 1}

wherein,representation matrixConjugate transpose of (c) ()^-1Representing the matrix inversion.

And step 3, performing similar space smoothing processing on the van der waals guide vector B (theta), wherein if F is a smooth transformation matrix, the smoothed guide vector is represented as C (theta) being FB (theta).

Dividing a van der waals guide vector B (θ) (equivalent to a uniform linear array) into L mutually overlapped sub-arrays, wherein the dimension of each sub-array is Q-M-L + 1; wherein M is the dimension of B (θ);

constructing a smooth transformation matrix according to Q: f_l＝[0_Q×(l-1)|I_Q|0_Q×(L-l)]Wherein L is 1, 2_Q×(l-1)Denotes the zero matrix of Q × (l-1), I_QDenotes an identity matrix of order Q, 0_Q×(_l-1)Represents zero matrix of Q × (L-L);

the smooth transformation matrix F can be obtained by:

the transformed steering vector C (θ) can be obtained by:

C(θ)＝FB(θ)

4a) Matched filtering of received data for radar

Assuming that the radar cross-sectional areas RCS of the targets are the same, the received signals are:

wherein P is the number of targets in the same range gate, theta_pAzimuth of the p-th target, f_dpIs the doppler frequency (P ═ 1, 2,. P) of the pth target, and V is the receive noise matrix of the MIMO radar array.

And performing matched filtering on the received data of the MIMO radar array, wherein the received data after matched filtering is recorded as X (k).

X(k)＝E(SX_r)

Where E () represents the mathematical expectation, S ═ S₁ ^T，...S_i ^T...，S_N ^T]^TRepresenting a matrix of N transmit signals,S_iwhich represents the ith transmission signal, is transmitted,denotes S_iTranspose of (i ═ 1.. N);

4b) obtaining a transformed data matrix Y (k) by converting the matrix G and the smooth transformation matrix F

Y(k)＝FGX(k)

4c) Then, the transformed data matrix Y (k) is used to form an autocorrelation matrix R_y

Where K is the number of sampling points, Y^H(k) Denotes the conjugate transpose of Y (k).

For autocorrelation matrix R_yPerforming characteristic decomposition to obtain a series of characteristic values lambda_mAnd its corresponding feature vector e_m(m ═ 1, 2,. Q), the characteristic value λ is calculated_mCarry out the order from big to small lambda₁≥λ₂≥...≥λQ，e₁，...，e_QSelecting P large eigenvalues lambda for corresponding eigenvectors₁，...，λ_pP is the number of targets, and the eigenvectors e corresponding to the eigenvalues are taken₁，e₂，...，e_pForming a signal subspace

Then the noise subspaceSatisfies the following conditions:

{\hat{E}}_{n} {\hat{E}}_{n}^{H} = I - {\hat{E}}_{s} {\hat{E}}_{s}^{H}

wherein I is an identity matrix with dimension Q.

Step 6, utilizing noise subspaceForming a MUSIC spatial zero spectrum function:

wherein | | | purple hair²The expression is given in the 2-norm,representation matrixThe conjugate transpose of (c).

Step 7, let z equal to e^jθThen f (θ) can be converted to:

f (z) = C^{H} (z) {\hat{E}}_{n} {\hat{E}}_{n}^{H} C (z)

and f (z) is equal to 0, and a polynomial root solving method is adopted to obtain a complex exponential form z of P azimuth angles which are closest to a unit circle and have amplitudes less than 1_p(p＝1，2...P)。

Step 8, using the complex exponential form z of the acceptance angle_pFinding the azimuth angle theta of the p-th target_p；

θ_p＝angle(z_p)

Wherein, angle () represents the phase angle;

p＝1，2...P

The effects of the present invention are further illustrated by the following simulation test.

(1) Simulation conditions are as follows:

according to the derivation steps of the invention, the method has no limitation of the array manifold and is suitable for any array manifold. Without loss of generality, assuming that the MIMO radar array is a uniform circular array, the wavelength of a transmitting signal is 0.75M, the array element number is 10, the array radius is 0.45M, the transmitting signal is in the form of a phase coding signal orthogonal to a carrier frequency, two coherent signal sources are arranged, the azimuth angle of a signal source 1 is 22 degrees, the azimuth angle of a signal source 2 is 45 degrees, the repetition period number of a receiving pulse is 100 degrees, the signal-to-noise ratio SNR is 20dB, the van der monster steering vector dimension M is 11 degrees, the length of a spatial smoothing sub-array is Q9 degrees, 100 independent monte carlo experiments are performed, and the mean square error calculation of a signal source p adopts a formulaWhereinAs an estimate of the azimuth angle of the signal source p, theta_pIs the azimuth angle of the signal source p.

(2) Simulation content:

simulation 1, the target orientation angle is subjected to target positioning simulation by adopting the method, and the results of 100 independent simulation experiments on the target are shown in fig. 2. As can be seen from FIG. 2, the invention can realize the fast direction-of-arrival estimation of the single-base MIMO radar of any array manifold.

Simulation 2, when the signal source 1 is positioned by adopting the method, the simulation result of the variation of the target angle mean square error along with the signal-to-noise ratio SNR is shown in FIG. 3;

simulation 3, when the signal source 2 is positioned by adopting the method, the simulation result of the variation of the target angle mean square error along with the signal-to-noise ratio SNR is shown in figure 4.

It can be seen from fig. 3 and 4 that the mean square error of the target angle estimation decreases as the signal-to-noise ratio SNR increases, and the mean square error of the target angle estimation can reach below 0.1 ° when the signal-to-noise ratio is 5dB, and the positioning accuracy is high, indicating that the present invention is practical.

In summary, the invention can realize the estimation of the direction of arrival of the coherent source of the single-base multiple-input multiple-output (MIMO) radar with any array manifold, and has high positioning precision.

It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, it is intended that the present invention cover the modifications and variations of this invention provided they come within the scope of the appended claims and their equivalents.

Claims

1. A coherent source direction-of-arrival estimation method for a single-base MIMO radar is characterized by comprising the following steps:

step 1, obtaining an array steering vector A (theta) according to an array manifold of the single-base MIMO radar, wherein the array has N array elements, and the polar coordinate of each array element is (r)_n，β_n) N is 1, 2, … N, N is array element number;

step 3, performing similar space smoothing processing on the van der mond guide vector B (theta), wherein F is a smooth transformation matrix, and the smoothed guide vector C (theta) is FB (theta);

step 4, performing matched filtering on the received data of the MIMO radar, recording the matched filtered received data as X (k), obtaining a transformed data matrix Y (k) ═ FGX (k) by converting the matrix G and the smooth transformation matrix F, and forming an autocorrelation matrix R by using the data matrix Y (k)_y；

Step 6, utilizing noise subspaceForming a MUSIC spatial zero spectrum function:

wherein |)²The expression is given in the 2-norm,representation matrixThe conjugate transpose of (1);

step 7, let z equal to e^jθThen f (θ) can be converted to:

and f (z) is equal to 0, and a polynomial root solving method is adopted to obtain a complex exponential form z of P azimuth angles which are closest to a unit circle and have amplitudes less than 1_pP is 1, 2 … P; wherein P is the number of targets in the same range gate, theta_pAzimuth for the p-th target;

step 8, using the complex exponential form z of the acceptance angle_pFinding the azimuth angle theta of the p-th target_p：

θ_p＝angle(z_p)

Wherein, angle () represents the phase angle;

p＝1，2…P

2. The method of estimating the direction of arrival of a coherent source of a monostatic MIMO radar according to claim 1, wherein the M-dimensional vandermonde vector B (θ) and the transformation matrix G in step 2 are obtained by:

first, letr_nThe distance between the nth array element and the origin of coordinates is defined, N is 1, 2, … N, N is the number of the array elements, the dimension M of the Van der Menu vector B (theta) is selected to be approximately equal to 4kR, k is 2 pi/lambda, and lambda is the wavelength of the emission signal;

neglecting truncation errors, the vandermonde vector B (θ) is:

wherein, the [ alpha ], [ beta ]]^TRepresenting a matrix transpose, j represents an imaginary number,

secondly, taking J angles at equal intervals in the observation range, namely: theta₁，θ₂，…，θ_J(ii) a According to theta₁，θ₂…，θ_JRespectively forming steering matricesAnd vandermonde matrix

According to a steering matrixAnd vandermonde matrixObtaining a conversion matrix G by using a least square method:

3. The method for estimating direction of arrival of coherent source of monostatic MIMO radar according to claim 1, wherein the smooth transformation matrix F in step 3 is obtained by the following steps:

firstly, dividing a van der waals guiding vector B (theta) into L mutually overlapped sub-arrays, wherein the dimension of each sub-array is Q-M-L + 1; wherein M is the dimension of B (θ);

next, a smooth transformation matrix is constructed from Q: f_l＝[O_Q×(l-1)|I_Q|O_Q×(L-l)]Wherein L is 1, 2, … L, O_Q×(l-1)Denotes the zero matrix of Q × (l-1), I_QRepresenting an identity matrix of order Q, O_Q×(L-1)Represents zero matrix of Q × (L-L);

finally, the smooth transformation matrix F can be obtained by:

。

4. the coherent source direction-of-arrival estimation method for monostatic MIMO radar according to claim 1, wherein the detailed substeps of step 4 are as follows:

4a) matched filtering of received data for radar

wherein P is the number of targets in the same range gate, theta_pAzimuth of the p-th target, f_dpIs the doppler frequency of the pth target, P1, 2, … P, V is the receive noise matrix of the MIMO radar array,

carrying out matched filtering on the received data of the MIMO radar array, and recording the received data after matched filtering as X (k);

X(k)＝E(SX_r)

wherein E () represents the mathematical expectation,representing a matrix, s, consisting of N transmitted signals_iWhich represents the ith transmission signal, is transmitted,denotes s_i1, i is 1 … N;

Y(k)＝FGX(k)