CN117630808A - MIMO radar target DOA estimation method - Google Patents
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Abstract
The invention discloses a MIMO radar target DOA estimation method, which relates to the technical field of radar target estimation and comprises the following steps: the method comprises the steps of adopting a sparse circular array as a MIMO radar receiving and transmitting antenna, constructing a mirror multipath reflection signal model, utilizing the mirror multipath reflection signal model to receive a signal matrix, filtering the signal matrix to obtain a vectorization matrix, calculating a transmitting and receiving direct wave and a reflection waveguide vector to obtain a composite guiding vector and a real value composite guiding vector, carrying out dimension reduction on the composite guiding vector and the real value composite guiding vector, and carrying out basic algorithm spectrum peak search and real value processing algorithm spectrum peak search to obtain a target two-dimensional DOA. The invention realizes the expansion of the effective aperture on the premise of a certain number of physical array elements, so that compared with a uniform circular array, the invention improves the angle resolution and the estimation precision and reduces the fluctuation of the angle estimation error.
Description
Technical Field
The invention relates to the technical field of radar target estimation, in particular to a MIMO radar target DOA estimation method.
Background
The direction of arrival (DirectionOfArrival, DOA) estimation is an important research direction in spatial spectrum estimation, mainly realizes the position estimation of a target information source in space, and has wide application in the military and economic fields of radar sonar detection, radio communication, biomedical engineering and the like. The Mitsui radar is focused on the aspect of excellent performance on the anti-stealth target and the anti-radiation missile, however, the pitching dimension wave beam is wider, and serious multipath effect exists due to the fact that the wave beam is landed when DOA estimation is carried out on the low-altitude target. The direct wave and the ground multipath reflected wave have strong coherence and are equivalent to two strong coherent point sources which are close to each other in space, so that the DOA estimation problem of a low-altitude target can be equivalent to the super-resolution problem of the two strong coherent point sources. The array super-resolution technology is an important means for improving the DOA estimation performance of a low-altitude target of the meter wave radar, but at the moment, the echo signal subspace has the phenomenon of diffusing to the noise subspace, so that the performance of the subspace super-resolution algorithm is rapidly deteriorated.
In order to reduce the influence of multipath effect, the strong coherence between the direct wave and the reflected wave of the low-altitude target is removed, the direction of the direct wave and the direction of the reflected wave are effectively resolved, the performance of the subspace super-resolution algorithm is recovered, the decorrelation processing can be carried out by adopting decorrelation algorithms such as space smoothing, matrix reconstruction and the like at present, but the improvement of the DOA estimation performance of the pitch dimension of the low-altitude target is limited. The literature comprehensively analyzes that a forward-backward smoothing (Forward Backward Spatial Smoothing, FBSS) decoherence algorithm is applied to the problem of low-altitude target height measurement of the meter wave radar, and indicates that the decoherence failure and the large elevation error can occur even under the condition that the covariance matrix of the received signal is full rank. The document adopts the Toeplitz matrix reconstruction method to solve the rank deficiency problem of the covariance matrix of the coherent signal and realize DOA estimation of the coherent information source, but the matrix reconstruction method is not unbiased estimation, so that the error is larger. The vast majority of expert scholars then estimate the elevation angle of the low-altitude target in turn using either a maximum likelihood (Maximum Likelihood, ML) algorithm without decorrelation or a generalized multiple signal classification (Generalized Multiple Signal Classification, GMUSIC) algorithm. The literature closely combines the characteristics of the conventional meter wave array radar, summarizes and summarizes 3 meter wave radar height measurement methods based on the traditional ML algorithm on the basis of a mirror surface multipath reflection signal model, performs theoretical performance analysis on the methods, and combines the correlations among the 3 methods. The literature generalizes and analyzes various height measurement methods based on the GMUSIC algorithm, the essence of the effectiveness of the GMUSIC algorithm is that the basic spectrum peak search equation is weighted, a low elevation angle estimation method model based on the GMUSIC algorithm is provided on the basis, more reasonable algorithm weight is provided through simulation, and the estimation success probability is further improved.
The existing two-dimensional DOA estimation algorithm based on the circular array is mainly concentrated on a conventional array, less related research is conducted on a multi-input multi-output MIMO system, the research on low-altitude target two-dimensional DOA estimation of the meter wave circular array MIMO radar is still in a starting stage, and the problems of sharp decline of the ultra-low altitude target angle estimation precision, low resolution and larger fluctuation of angle measurement errors along with elevation angle change exist in the problem of low-altitude target two-dimensional positioning of the meter wave MIMO radar based on UCA.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a DOA estimation method for a MIMO radar target, which aims to solve the problems that in the prior art, the estimation precision of an ultra-low altitude target angle is rapidly reduced, the resolution is not high and the fluctuation of an angle measurement error along with the change of an elevation angle is large.
The invention specifically provides the following technical scheme: a MIMO radar target DOA estimation method comprises the following steps:
connecting the ends of the classical sparse arrays and arranging the classical sparse arrays according to a circle to obtain a sparse circular array;
adopting the sparse circular array as a receiving and transmitting antenna of a single-base meter wave MIMO radar, and constructing a mirror multipath reflection signal model based on the sparse circular array;
receiving a signal matrix Z (t, tau) of the single-base meter wave MIMO radar by using the mirror multipath reflection signal model, and carrying out matched filtering on the signal matrix Z (t, tau) to obtain a matrix Z;
Vectorizing the matrix Z to obtain a vectorized matrix Y;
based on the positions of the transmitting and receiving array elements, respectively calculating the transmitting and receiving direct waves and the reflecting waveguide vector by utilizing the transmitting array element guide vector and the receiving array element guide vector in the vectorization matrix Y;
the composite guiding vector is obtained through the calculation of the transmitting and receiving direct wave and the reflecting waveguide vectorAnd calculates a real-valued complex director vector +.>
For composite steering vectorsAnd real value composite guide vector +.>Performing dimension reduction, and utilizing the composite guide vector after dimension reduction +.>And real value composite guide vector +.>And performing basic algorithm spectrum peak search and real value processing algorithm spectrum peak search to obtain the target two-dimensional DOA.
Preferably, the sparse circular array is used as a transceiver antenna of a single-base meter wave MIMO radar, and a mirror multipath reflection signal model based on the sparse circular array is constructed, which comprises the following steps:
adopting a sparse circular array with an array plane inclination angle beta as a receiving and transmitting antenna, and obtaining projection of the receiving and transmitting antenna in a circular array on a horizontal plane by adjusting the height of the receiving and transmitting antenna;
and constructing a mirror multipath reflection signal model based on a sparse circular array through the relation between the receiving and transmitting antenna and the projection.
Preferably, the receiving signal matrix z (t, τ) by using the specular multipath reflection signal model includes the following steps:
transmitting multipath signals by using the MIMO radar to obtain transmitting signals which reach a target through air medium propagationIs represented by the expression:
where j is an imaginary unit, k 0 =2pi/λ, ρ is the ground reflectance, [.] T The transpose of the matrix is represented, Δr is the wave path difference between the direct wave and the reflected wave, and the calculation formula is:
ΔR≈2h a sinθ d
wherein,for transmitting array element steering vectors, the expression is:
the signal expression received by the nth array element is as follows:
βx(t)+v n (t,τ)
wherein beta is the target complex reflection coefficient, v n (t, τ) is additive white gaussian noise;
the signal received by the entire array can be written as:
where v (t, τ) is an additive Gaussian white noise vector,for receiving the array element steering vector, the expression is:
wherein,is azimuth angle, theta i Is the pitch angle.
Preferably, the signal matrix Z (t, τ) is matched filtered to obtain a matrix Z, which includes the following steps:
using transmitted signalsAnd carrying out matched filtering, wherein the specific expression is as follows:
wherein V is noise after matched filtering and vectorization operation.
Preferably, the vectorization operation is performed on the matrix Z to obtain a vectorized matrix Y, where the specific expression is:
Where vec represents the vectorization operation, represents kron product->Is a composite steering vector, and the expression is as follows:
if K incoherent targets with equal distances exist in the wave beam width of the MIMO radar, each target azimuth angle isThe incidence angles of the direct wave and the reflected wave are respectively theta dk And theta sk Where k=1, 2, …, K, the vectorized echo signal matrix expression is:
wherein, as follows, the product Khatri-Rao is represented by, ψ= [ beta ] 1 ,β 2 ,…β K ]For the target complex reflection coefficient matrix, the expression of the composite guide vector A is as follows:
wherein:
for a co-located transmit receive array, the steering vectors have the following relationship:
preferably, the composite guiding vector is obtained by calculating the transmitting and receiving direct wave and the reflecting waveguide guiding vectorThe method comprises the following steps:
obtaining projection to steering vector matrixIs a spatial projection matrix formed by column vectors of (a)>
By the space projection matrixMaximum likelihood estimate of azimuth and pitch angle obtained +.>And->
Wherein,is an estimate of the output covariance matrix;
inputting the maximum likelihood estimation value into Y after vectorization operation of signals, wherein the specific expression is as follows:
wherein,
wherein,transposed by β, γ is the time delay, β is the target complex reflection coefficient, and V is the noise matrix.
Preferably, a composite steering vector is obtained at the calculationPreviously, calculating the estimation of a covariance matrix, and carrying out eigenvalue decomposition on the estimation of the covariance matrix to obtain a noise subspace E n The method comprises the following steps:
by combining steering vectorsIs obtained by the calculation process of->Then the estimation of covariance matrix +.>The calculated expression of (2) is:
wherein L is the snapshot number;
the spectral peak search formula of the ML algorithm at this time is:
wherein det represents determinant operations and trace represents trace operations;
the spectral peak search formula for GMUSIC at this time is:
wherein E is n And a noise subspace obtained by eigenvalue decomposition for the estimation of the covariance matrix.
Preferably, the real value composite guide vector is calculated during real value processingThe method comprises the following steps:
for the covariance matrixPerforming real value processing to obtain real value covariance matrix +.>And +.>Performing eigenvalue decomposition to obtain a noise subspace U n ；
The covariance matrix R is calculated, and the concrete expression is as follows:
wherein:and->Respectively represent signal powerAnd noise power, p=mn, M and N are the number of transmit and receive array elements, respectively;
real-valued processing is performed on the covariance matrix R by using the unitary matrix, wherein the P×P-dimensional unitary matrix is as follows:
Wherein: pi (II) KP For K P ×K P The dimensional transformation matrix has the expression:
performing one-time bidirectional smoothing on the covariance matrix R to convert the covariance matrix R into a Centro-Hermitian matrix;
wherein [ (S)] * Representing the conjugate operation of the matrix;
unitary transformation is carried out on the Centro-Hermitian matrix to obtain a real matrix;
R U ＝U p H R fb U P
estimation using covariance matrixPerforming unitary transformation after bidirectional smoothing, and calculating real-value covariance matrix +.>
For composite steering vectorsReal value processing is carried out to obtain:
in the method, in the process of the invention,representing a real valued composite steering vector.
Preferably, the pair of composite steering vectorsAnd real value composite guide vector +.>The specific expression of the dimension reduction is as follows:
θ s ＝-arcsin(sin(θ d )+2h a /R)≈-θ d
wherein h is a For the center height of the circular array antenna, R comprises R d And R is R s ，R d And R is R s The path lengths of the direct wave and the multipath reflected wave are respectively.
Preferably, the composite guide vector after the dimension reduction is utilizedAnd real value composite steering vectorPerforming basic algorithm spectrum peak search and real value processing algorithm spectrum peak search to obtain a target two-dimensional DOA, wherein the method comprises the following steps of:
the ML algorithm and the GMUSIC which are subjected to real value processing are defined as UML algorithm and UGGUSIC algorithm, the target two-dimensional DOA is estimated, and the final azimuth angle estimated value of the target is obtainedAnd pitch angle estimation +.>
The UML algorithm spectral peak search function is as follows:
In the formula, the real value space projection matrix is as follows:
the UGGUS algorithm spectral peak search function is as follows:
in U n Is thatAnd (5) a real noise subspace obtained by characteristic decomposition.
Compared with the prior art, the invention has the following remarkable advantages:
according to the invention, a sparse circular array is used for replacing a uniform circular array as a receiving and transmitting antenna, a universal single-base meter-wave circular array MIMO radar mirror multipath reflection signal model based on array element positions is deduced and constructed, a two-dimensional DOA estimation method suitable for the model is provided by combining an ML algorithm and a GMUSIC algorithm, and the expansion of effective aperture is realized on the premise that the number of physical array elements is fixed, so that compared with the uniform circular array, the angle resolution and the estimation precision are improved, and meanwhile, the fluctuation degree of angle estimation errors is reduced.
Drawings
FIG. 1 is a block diagram of each sparse circular array; wherein (a) is nested circular array NCA, (b) is simple mutual circular array SCCA, (c) is expanded mutual circular array ECCA, and (d) is expanded mutual circular array UCCA;
FIG. 2 is a diagram of a meter wave circular array MIMO radar mirror multipath reflection signal model provided by the invention;
FIG. 3 is a spatial spectrum provided by the present invention;
FIG. 4 is a graph of comparing the angular resolution provided by the present invention; wherein (a) is a two-dimensional spatial spectrum, (b) is a pitch dimensional spatial spectrum, (c) is an azimuth dimensional spatial spectrum, and (a 1), (a 2), (a 3), (a 4) and (a 5) in (a) are two-dimensional spatial spectrums of uniform circular arrays UCA, NCA, SCCA, ECCA and UCCA respectively;
FIG. 5 is a contour diagram provided by the present invention; wherein (a) and (b) are each an array meter wave MIMO radar two-dimensional spatial spectrum contour map when snr=0 and 10db, respectively, and (a) is a contour map of uniform circular array UCA, NCA, SCCA, ECCA and UCCA when (a 1), (a 2), (a 3), (a 4), and (a 5) are each 10db, and (a) is a contour map of uniform circular array UCA, NCA, SCCA, ECCA and UCCA when (a 1), (a 2), (a 3), (a 4), and (a 5) are each 0 db;
FIG. 6 is a graph of the influence of pitch angle on resolution success probability provided by the invention;
FIG. 7 is a graph of the impact of target elevation on goniometric performance provided by the present invention; wherein (a) is the variation of the pitch angle RMSE along with the pitch angle, and (b) is the variation of the azimuth angle RMSE along with the pitch angle;
FIG. 8 is a graph of the influence of the signal-to-noise ratio on the angular accuracy provided by the present invention; wherein (a) is the variation of a pitch angle RMSE along with the signal to noise ratio, and (b) is the variation of an azimuth angle RMSE along with the signal to noise ratio;
FIG. 9 is a graph showing the influence of the number of snapshots on the angular accuracy provided by the invention; wherein (a) is the variation of the pitch angle RMSE along with the number of shots, and (b) is the variation of the azimuth angle RMSE along with the number of shots;
fig. 10 is a graph of a relationship between a low-altitude target two-dimensional angle RMSE and an amplitude-phase error of each array meter wave MIMO radar provided by the present invention; wherein (a) is the variation of the pitch angle RMSE with the amplitude error, (b) is the variation of the azimuth angle RMSE with the amplitude error, (c) is the variation of the pitch angle RMSE with the phase error, and (d) is the variation of the azimuth angle RMSE with the phase error.
Detailed Description
The following description of the embodiments of the present invention, taken in conjunction with the accompanying drawings, will clearly and completely describe the embodiments of the present invention, and it is evident that the described embodiments are some, 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 present invention without making any inventive effort, shall fall within the scope of the present invention.
The traditional linear array radar can only estimate one-dimensional angle parameters, cannot meet the requirements of modern war, and if two-dimensional DOA estimation of a low-altitude target is to be realized, a cross-shaped, L-shaped and other two-dimensional array structures are adopted, which is actually equivalent to the fact that a one-dimensional linear array is added in the azimuth dimension to realize the estimation of azimuth information. The current coherent signal high-resolution spatial spectrum estimation algorithm based on a Uniform linear array (Uniform LinearArray, ULA) only can estimate the azimuth information of [ -pi/2, pi/2 ], the Uniform circular array (Uniform Circular Array, UCA) can estimate the two-dimensional information of [ -pi, pi ] azimuth angle and [0, pi/2 ] pitch angle, and the beam shape robustness of the directional pattern is good when the array plane rotates due to the symmetrical characteristic of the array structure, the same direction finding performance is achieved in all the azimuth, and the phase ambiguity phenomenon does not exist. Based on the excellent performance of UCA two-dimensional DOA estimation, literature provides a meter wave circular array radar model of a MIMO system, the model not only can estimate the azimuth angle of a target, but also can separate a real target and a mirror image target from the pitching dimension, thereby realizing the two-dimensional DOA estimation of a low-altitude target, improving the parameter estimation performance, but only analyzing the two-dimensional DOA estimation performance under the conditions of horizontal placement and vertical placement. The literature builds a meter wave uniform circular array MIMO radar specular reflection signal model which is obliquely arranged, and provides a low-altitude target two-dimensional DOA estimation method suitable for the model by combining a GMUSIC algorithm.
The sparse array is a novel antenna array which appears in recent years, and different from the traditional ULA, the sparse array can obtain larger array aperture when having the same physical array element number as the ULA, so that the sparse array has better parameter estimation performance.
Referring to fig. 1-2, an embodiment of the present application provides a MIMO radar target DOA estimation method, including the steps of:
step S1: and connecting the ends of the classical sparse arrays and arranging the classical sparse arrays according to a circle to obtain a sparse circular array.
Classical sparse linear arrays are mainly composed of three types, namely a minimum redundant Array (Minimum Redundancy Array, MRA), a Nested Array (NA) and a prime Array (Co-prime Array, CPA). The MRA array element positions cannot be solved by the unified expression, so that the MRA array element positions are difficult to apply to engineering practice, and the NA and CPA array element positions are convenient to apply due to the unified expression. This section summarizes the Nested circular array (Nested CircularArray, NCA) and the reciprocal circular array (Co-prime Circular Array, CPCA) structures by referencing NA and CPA array structures, as described in detail below.
NA is formed by connecting uniform linear arrays with different array element distances in series, and the array element positions can be determined by the following formula:
in the method, in the process of the invention,here->Represents a positive integer set, Q is the order of NA, N i The number of array elements in the i-th order uniform subarray is represented. When q=2, a classical second-order NA structure can be obtained, and the array element position set expression is:
Typical CPAs are mainly composed of three types, simple Co-prime Array (SCPA), extended Co-prime Array (ECPA), and Extended Co-prime Array (UCPA). Each mutual matrix array is composed of two subarrays with mutual matrix element intervals, and when the two subarrays all take an origin as a reference zero point, the array element position set expression of each array is as follows:
the typical sparse arrays are connected end to end and are arranged in a circular mode to obtain the sparse circular array which is improved in a generalized mode, and the sparse circular array mainly comprises four types of Nested Circular Arrays (NCA) shown in fig. 1 (a), simple mutual circular arrays (Simple Co-prime CircularArray, SCCA) shown in fig. 1 (b), expanded Co-prime CircularArray, ECCA shown in fig. 1 (c) and expanded mutual circular arrays (UnfoldedCo-prime Circular Array, UCCA) shown in fig. 1 (d). Each sparse circular array structure is shown in fig. 1, where d=0.5λ, and λ is a signal wavelength.
Step S2: and (3) adopting the sparse circular array as a receiving and transmitting antenna of the single-base meter wave MIMO radar, and constructing a mirror multipath reflection signal model based on the sparse circular array.
In this step, as shown in fig. 2, consider that a single-base metric wave MIMO radar uses a circular array disposed obliquely as a transmitting/receiving antenna, where the tilt angle of the array plane is β, and the height of the transmitting/receiving array element is adjusted so that the projection of the array element on the horizontal plane is a circular array, so that the transmitting/receiving array element is kept on the same plane, and the lower part of the array plane faces the focal direction of the detection. The system adopts a classical mirror plane multipath reflection signal model, wherein a radar is positioned at A, a target is positioned at T, B is a multipath reflection point, C is a circular array center, and h a Is the central height of the circular array antenna (the heights of the receiving and transmitting first array elements are consistent with the central height), h t For the target height, R d And R is R s The path lengths of the direct wave and the multipath reflected wave respectively,for the target azimuth angle, θ d ' and theta s ' separateTo transmit the direct wave and the reflected wave, pitch angle, theta d And theta s The pitch angles of the received direct wave and the reflected wave are respectively the same, namely theta is approximately the same for the incidence angle of the far-field target receiving and transmitting direct wave and the reflected wave d ＝θ' d And theta s ＝θ s '. The number of the transmitting and receiving array elements is M and N respectively, the first array element is taken as a reference, and the positions of the transmitting and receiving array elements on the circumference are d respectively em And d rn Where m=1, 2, …, M, n=1, 2, …, N, and d e1 ＝d r1 ＝0。
For any element m on the transmit circular array, the coordinates are (x em ,y em ,z em ) From the geometrical relationship, it can be seen that:
here, r e For the radius of the transmitting circular array,and the radian corresponding to the arc connecting with the first array element is used for transmitting the array element m.
Similarly, the coordinates (x rn ,y rn ,z rn ) The method comprises the following steps:
here, r r In order to receive the radius of the circular array,for receiving the radian corresponding to the arc connected with the first array element.
Then atIn the direction, the delay corresponding to the wave path difference between the mth transmitting array element and the nth receiving array element and the reference array element is as follows:
where c is the propagation speed of the electromagnetic wave in free space, and i=d, s represent the direct signal wave direction and the reflected wave direction, respectively.
Then, the transmit receive steering vector component expression is:
where f 0 For the transmit signal frequency.
Transmitting signal of MIMO radarAre mutually orthogonal, which satisfies the following formula:
here I M Is a unit array, T is a pulse duration, [] H Representing the conjugate transpose of the matrix.
Step S3: and receiving a signal matrix Z (t, tau) of the single-base meter wave MIMO radar by using a mirror multipath reflection signal model, carrying out matched filtering on the signal matrix Z (t, tau) to obtain a matrix Z, and setting the snapshot number for sampling.
For MIMO radar, transmission multipath is considered, so that the target echo signal has four propagation paths of A-T-A, A-B-T-A, A-T-B-A and A-B-T-B-A, and the obtained transmission signal propagates through air medium to reach the targetThe expression of (2) is:
wherein j is an imaginary unit, k 0 =2pi/λ, ρ is the ground reflectance, [ ·] T The transpose of the matrix is represented, Δr is the wave path difference between the direct wave and the reflected wave, and the calculation formula is:
ΔR≈2h a sinθ d (18)
for transmitting array element steering vectors, the expression is:
thus, after considering the received multipath, the signal received by the nth array element has the following expression:
wherein beta is the target complex reflection coefficient, v n (t, τ) is additive white gaussian noise.
The signal received by the entire array can be written as:
Where v (t, τ) is an additive Gaussian white noise vector,for receiving the array element steering vector, the expression is:
wherein,is azimuth angle, theta i Is the pitch angle.
Using transmitted signalsAnd carrying out matched filtering on Z (t, tau) to obtain a matrix Z, wherein the specific expression is as follows:
wherein V is noise after matched filtering and vectorization operation.
Step S4: and carrying out vectorization operation on the matrix Z to obtain a vectorized matrix Y.
Vectorizing the signal matrix Z to obtain:
here vec represents the vectorization operation, represents kron product->Is a composite steering vector, and the expression is as follows: />
V is noise after matched filtering and vectorizing operation, and the original noise is assumed to be Gaussian white noise, so that the literature shows that V is still Gaussian white noise after matched filtering and vectorizing operation.
For ease of discussion, a single-target model is assumed, with only one reflection point. The incoherent multi-objective situation is similar, and the echo signal matrix expression derivation process is not repeated, so that a conclusion is directly given here.
Assume that there are K incoherent targets within the beam width of a milwave circular array MIMO radar, whose distances are equal, i.e., the radar cannot resolve it from the time domain. Each target azimuth angle is The incidence angles of the direct wave and the reflected wave are respectively theta dk And theta sk Where k=1, 2, …, K.
The vectorized echo signal matrix expression is:
wherein, as follows, the product Khatri-Rao is represented by, ψ= [ beta ] 1 ,β 2 ,…β K ]For the target complex reflection coefficient matrix, the composite guide vectorThe expression A is:
wherein:
the single-base MIMO radar can be divided into two types, i.e., co-transmit and receive and transmit. For far-field narrowband signals, the incidence angles of the receiving and transmitting separated direct wave and the reflected wave are the same, and only the transmitting and receiving arrays are different. The transmitting and receiving arrays are the same array when the transmitting and receiving are co-arranged, the transmitting and receiving arrays are different arrays when the transmitting and receiving are separated, the visible signal models are not essentially different, and only the composite guiding vector is adoptedDifferent, and thus different, pore size expansion results. For a co-located transmit receive array, the steering vectors have the following relationship:
step S5: based on the positions of the transmitting and receiving array elements, the transmitting array element guiding vector and the receiving array element guiding vector in the vectorization matrix Y are utilized to calculate the transmitting and receiving direct wave and the reflecting waveguide guiding vector through formulas (19) and (22) respectively.
Step S6: obtaining a composite guiding vector by transmitting and receiving direct wave and reflecting waveguide vector calculationAnd calculates a real-valued complex director vector +. >
The conventional MUSIC algorithm mainly utilizes the principle of signal subspace and noise subspace orthogonality to perform angle estimation, but in the metric wave MIMO radar, serious coherent multipath signals exist in the received signals, and meanwhile, the transmitting and receiving guide vectors also exist such asWhich causes the steering vector to lose orthogonality with the noise subspace. Although there are methods of decoherence such as spatial smoothing, matrix reconstruction, etc., these methods have limited improvement in DOA estimation performance under low-altitude multipath reflection conditions and are not applicable to sparse circular arrays. Therefore, the invention adopts ML algorithm and GMUSIC algorithm without decoherence to realize two-dimensional DOA estimation of the low-altitude target of the meter wave MIMO radar based on the sparse circular array.
The maximum likelihood estimation is a common and effective parameter estimation method, and the estimation criteria are as follows:
wherein,and->Maximum likelihood estimates for azimuth and pitch angle, respectively, < >>For the estimation of the output covariance matrix, +.>For guiding vector matrix, ++>For projection to the steering vector matrix +.>A spatial projection matrix of column vectors of (a) that can be expressed as:
the received signal Y in the equation (24) is collated:
wherein:
wherein,transposed by β, γ is the time delay, β is the target complex reflection coefficient, and V is the noise matrix.
Calculating to obtain a composite steering vectorPreviously, calculating the estimation of a covariance matrix, and carrying out eigenvalue decomposition on the estimation of the covariance matrix to obtain a noise subspace E n The method comprises the following steps:
from the above derivation, it can be seen that the maximum likelihood criterion is thatAccording to maximum likelihood estimation criterion->Can be obtained from the following formula:
here, L is the snapshot number.
The spectral peak search formula of the ML algorithm at this time is:
where det represents a determinant operation and trace represents a trace operation.
A generalized MUSIC algorithm is proposed that proposes a new steering vector matrix that is still orthogonal to the noise subspace. Above, the aboveI.e. the proposed steering vector matrix, which is still orthogonal to the noise subspace under multipath coherent signal interference, unlike the steering vector in the normal MUSIC algorithm. The spectral peak search formula for GMUSIC at this time is: />
Wherein E is n To pair(s)And carrying out characteristic value decomposition to obtain a noise subspace.
Since the estimation process involves three-dimensional search, dimension reduction of the search can be realized by introducing a mathematical relationship between the angle of the direct wave and the angle of the reflected wave, and the mathematical relationship is as follows:
θ s ＝-arcsin(sin(θ d )+2h a /R)≈-θ d (40)
step S7: for composite steering vectorsAnd real value composite guide vector +.>And performing dimension reduction, and performing basic algorithm spectrum peak search and real value processing algorithm spectrum peak search by using the vector after dimension reduction to obtain low-altitude target azimuth angle and pitch angle estimated values.
The dimensionality reduction of the search can be achieved by introducing a mathematical relationship of the direct wave and reflected wave angles (equation (40)).
Calculating real-valued complex steering vectors during real-valued processingThe method comprises the following steps:
the MIMO radar greatly increases the operation amount while enhancing the DOa estimation performance, and can reduce the calculation amount of the algorithm by using a real-value processing algorithm, as described below.
The covariance matrix R is calculated from equation (24) as follows:
wherein:and->Respectively representing signal power and noise power, p=mn, and M and N are respectively the numbers of transmitting and receiving array elements.
The observation of equation (41) shows that the signal covariance matrix R is a complex matrix, which is now subjected to real-valued processing by means of a unitary matrix. The P x P dimensional unitary matrix is defined as follows:
wherein:for K P ×K P The dimensional transformation matrix has the expression:
if P is odd, performing real value processing by using formula (42), and K P = (P-1)/2; if P is even, performing real value processing by using formula (43), and K P ＝P/2。
According to the nature of the unitary matrix, the unitary matrix can change the Centro-Hermitian matrix into a real matrix through unitary transformation, but R is not the Centro-Hermitian matrix, so that it needs to be subjected to a bi-directional smoothing to be converted into the Centro-Hermitian matrix:
here, [] * Representing the conjugate operation of the matrix.
And then unitary transformation is carried out on the matrix to obtain a real matrix:
R U ＝U P H R fb U P (46)
according to the maximum likelihood estimation criterion, the real value echo data covariance matrix estimation valueCan be calculated by formula (37)>The unitary transformation is obtained after bidirectional smoothing, and the specific calculation process is as follows:
for composite steering vectorsAnd (3) real value processing to obtain:
in the method, in the process of the invention,representing a real valued composite steering vector.
After the real value processing, the ML algorithm or the GMUSIC algorithm can be used for estimating the target two-dimensional DOA, and the ML algorithm and the GMUSIC algorithm which are subjected to the real value processing are respectively and simply called UML algorithm and UGGUMUSIC algorithm.
The UML algorithm spectral peak search function is as follows:
in the formula, the real value space projection matrix is as follows:
the UGGUS algorithm spectral peak search function is as follows:
in U n Is thatAnd (5) a real noise subspace obtained by characteristic decomposition.
The above-mentioned spectral peak search is three-dimensional, and similarly, it can be reduced to a two-dimensional search by using the geometric relational expression (40). Performing final azimuth estimation of the target after conversion by equation (32)And pitch angle estimation +.>And (5) calculating.
The algorithm calculation complexity provided by the invention mainly comprises the following three parts: (1) constructing a covariance matrix; (2) covariance matrix feature decomposition; (3) and searching a spectrum peak. The real value processing algorithm needs to add the complexity of the real value processing algorithm, and compared with the basic algorithm, the real value processing algorithm needs to additionally calculate the real value composite guide vector And real-valued covariance matrix->Due to the switching matrix pi P Unitary transformation matrix U P Are sparse, so the added computational complexity is small, and is ignored here. In addition, addition is omitted here, only multiplication being considered. Further, one complex multiplication corresponds to four real multiplications. The various algorithm complexity calculation formulas are as follows:
C GMUSIC ＝4P 2 L+4P 3 +4Θ(8P+2P 2 ) (52)
C ML ＝4P 2 (L+P)+4Θ(8P+2P 2 +P 3 ) (53)
C UGMUSIC ＝P 2 L+P 3 +Θ(8P+2P 2 ) (54)
C UML ＝P 2 (L+P)+Θ(8P+2P 2 +P 3 ) (55)
wherein: Θ is the number of spectral peak searches.
Fig. 3 is a graph showing the complexity of the algorithm provided by the invention along with the number of array elements under the condition of co-transmitting and receiving, wherein the number of targets is assumed to be 1, the snapshot number is l=30, and the spectrum peak searching frequency Θ=1000. As can be seen from fig. 3, the GMUSIC algorithm has a lower computational complexity than the ML algorithm, and the real-valued processing algorithm has a significant advantage over the basic algorithm. Obviously, the calculation complexity can be greatly reduced through real-value processing, the calculation complexity of one order of magnitude can be reduced, the calculation time is saved by about 75%, and the effect is better along with the increase of the number of array elements.
Simulation experiment:
the superiority of the sparse circular array structure and the effectiveness of the method are verified through simulation experiments. The simulation experiment conclusion of the document 1 shows that the DOA estimation performance of the GMUSIC algorithm is similar to that of the ML algorithm, the simulation experiment conclusion of the document 2 shows that the DOA estimation performance of the real value processing algorithm is similar to that of the prototype algorithm, the GMUSIC algorithm is adopted in the following simulation without losing generality.
The experimental basic conditions were set as follows: assume that five single-base co-located meter wave MIMO radars adopt a circular array which is obliquely arranged as a receiving and transmitting antenna, the inclination angle is beta=30°, and the central height h of the circular array a The antenna 1 is UCA, the antenna 2 is second-order NCA, the antenna 3 is SCCA, the antenna 4 is ECCA, the antenna 5 is UCCA, the number of array elements of each array is 9, the initial positions of the array elements are consistent, and the array elements are rotated anticlockwise by taking the reference point of the invention as a reference; the positions of the physical array elements of each array on the circumference are as follows: UCA is {0, d,2d,3d,4d,5d,6d,7d,8d,9d }, second order NCA is {0, d,2d,3d,4d,5d,11d,17d,23d,29d }, SCCA is {0,5d,6d,10d,12d,15d,18d,20d,24d,25d }, ECCA is {0,3d,5d,6d,9d,10d,12d,15d,20d,25d }, UCCA is {0,6d,12d,18d,24d,29d,34d,39d,44d,49d }, where d=0.5λ, and head-tail array elements overlap; radar operating frequency f 0 The echo signal is a horizontally polarized wave, the ground reflection coefficient ρ= -0.98, and the additive noise is gaussian white noise. The invention adopts Monte Carlo repeated experiments to compare the angle measurement precision of different arrays, the experiment times are 100 times, and the formula of the angle root mean square error (Root Mean Square Error, RMSE) is as follows:
wherein I is the number of Monte Carlo tests, And->For the i-th measured target elevation and azimuth.
Simulation 1 spatial spectrum contrast experiment:
the experimental condition is that the number of space targets is 1, the distance R d =200 km, pitch angle θ d =6° azimuthThe snapshot number l=30, the signal-to-noise ratio snr=20 dB, the pitch angle and azimuth angle search ranges are 0 ° to 10 ° and 0 ° to 20 °, respectively, and the search intervals are 0.1 °. Fig. 4 is a spatial spectrum diagram of each array of the metlbond MIMO radar, and can be seen from the figure: each array can accurately estimate the target two-dimensional DOA, the spectral peak becomes more sharp along with the enlargement of the array aperture, the sharpness is UCCA & gtNCA & apprxeq SCCA & apprxeq ECCA & gtUCA, and the superiority of the improved sparse circular array structure is verified.
The experimental condition is that the number of the space incoherent targets is 2, and the pitch angle and the azimuth angle of the target 1 are respectively theta d1 =4° sumThe pitch angle and the azimuth angle of the target 2 are respectively theta d2 =9° and->The distance between two targets is 200km, the snapshot number is L=30,the signal-to-noise ratio SNR takes 10dB and 0dB respectively, the pitch angle and azimuth angle search ranges are 0 DEG to 10 DEG and 0 DEG to 20 DEG respectively, and the search interval is 0.1 deg. Fig. 5 is a two-dimensional spatial spectrum contour diagram of each array of the metrewave MIMO radar, from which it can be seen: when the signal-to-noise ratio SNR is 10dB, each sparse circular array can successfully resolve two targets, the UCA only barely resolves the two targets, when the signal-to-noise ratio SNR is 0dB, the UCA spatial spectrum contour map only has 1 spectrum peak, the two targets cannot be resolved accurately, the sparse circular array can still resolve the two targets clearly, and the angular resolution capability is ordered as UCCA & gtNCA & apprxeq SCCA & gtUCA along with the enlargement of the array aperture, so that the superiority of the improved sparse circular array structure is verified.
The experimental condition is that the number of space targets is 1, the distance R d =200 km, azimuthThe signal-to-noise ratio snr=20 dB, the snapshot number l=30, the elevation angle range is 0.3 ° to 4.8 °, the variation interval is 0.3 °, the pitch angle and azimuth angle search ranges are 0 ° to 10 ° and 0 ° to 20 °, respectively, and the interval is 0.05 °. And when the spatial spectrum curve generates obvious spectrum peaks near the direct wave direction and the multipath signal direction and the spatial spectrum curve between the two peaks is a concave curve, the resolution is considered to be successful. Fig. 6 is a graph of the relationship between the resolution success probability of each array meter wave MIMO radar direct wave and reflected wave with the change of elevation angle, and it can be seen from the graph: (1) for two coherent sources, namely direct wave and reflected wave, in the beam width, the success probability of each array resolution is in positive correlation with the target elevation angle, and when the elevation angle is larger than a certain range, the probability can reach 100%; (2) in the figure, the resolution success probability of the direct wave and the reflected wave with the pitch angle of about 2.5 degrees is suddenly reduced, which is caused by the multipath effect, and the direct wave and the reflected wave cancel each other due to the combined action of the wave path difference and the ground reflection at the pitch angle, so that the target echo intensity is suddenly reduced to influence the resolution success probability; (3) under the condition of the same pitch angle, the overall sequence of the resolution success probability of each array is UCCA & gtNCA & apprxeq SCCA & apprxeq ECCA & gtUCA, because the resolution success probability of each array direct wave and reflected wave and the array are effective The aperture is proportional, and the excellent angle resolution performance of the sparse circular array benefits from the fact that the sparse circular array has larger array aperture and non-uniform array element spacing.
The experimental condition is that the number of space targets is 1, the distance R d =200 km, azimuthSignal to noise ratio snr=10 dB, snapshot l=30, pitch angle θ d The range of values is 0.5-8 degrees, the change interval is 0.5 degrees, the pitch angle and azimuth angle searching ranges are 0-10 degrees and 0-20 degrees respectively, and the interval is 0.05 degrees. Fig. 7 is a graph showing the relationship between the two-dimensional angle RMSE of the low-altitude target of each array meter wave MIMO radar and the pitch angle, and it can be seen from the graph: (1) the two-dimensional DOA estimation errors of the arrays and the target elevation angle are in a negative correlation relationship to a certain extent, but have certain fluctuation in the interval along with the change of the elevation angle, and the main reason is that the change of the target elevation angle brings about the periodic change of the multipath attenuation coefficient phase, so that the target echo intensity is periodically changed to further influence the DOA estimation performance; (2) under the condition of the same target elevation angle, the two-dimensional DOA of each array estimates that the RMSE and the waviness are generally ordered as UCCA < NCA (geometric center of gravity) and SCCA (geometric center of gravity) are less than UCA, the two-dimensional DOA estimates that the RMSE is inversely proportional to the effective aperture of the circular array, the larger the effective aperture is, the smaller the RMSE is, and the smaller the sparse circular array angle RMSE is because of the non-uniformity of the array element spacing, and the direct wave and the reflected wave cannot be offset in all array elements; (3) the pitch angle and the angle measurement precision of the same array are lower than those of azimuth angles, which are caused by that the equivalent aperture of the pitch dimension array is smaller than that of the azimuth dimension due to the inclination of the circular array.
The experimental condition is that the number of space targets is 1, the distance R d =200 km, pitch angle θ d =5° azimuthThe snapshot number L=15, the signal-to-noise ratio SNR range is-10 dB to 10dB, the change interval is 2dB, the pitch angle and azimuth angle searching range are respectively 0 DEG to 10 DEG and 0 DEG to 20 DEG, and the interval is 0.05 deg. Fig. 8 is a graph of a relationship between a low-altitude target two-dimensional angle RMSE and a signal-to-noise ratio of each array of meter wave MIMO radar, and it can be seen from the graph: equivalent messageUnder the condition of a noise ratio, the overall sequence of the two-dimensional DOA estimation precision of each array is UCCA & gtNCA & apprxeq SCCA & apprxeq ECCA & gtUCA, and the pitch angle and the angle measurement precision of the same array are lower in azimuth angle, so that the reason is the same as that of experiment 4.
The experimental condition is that the target quantity is 1, the distance R d =200 km, pitch angle θ d =5° azimuthThe SNR=10dB, the snapshot L is in the range of 3 times to 30 times, the change interval is 3 times, the pitch angle and azimuth angle searching ranges are respectively 0 DEG to 10 DEG and 0 DEG to 20 DEG, and the interval is 0.05 deg. Fig. 9 is a graph of a relationship between a low-altitude target two-dimensional angle RMSE and a snapshot number of each array meter wave MIMO radar, and it can be seen from the graph: under the condition of the same snapshot number, the overall sequence of the two-dimensional DOA estimation precision of each array is UCCA & gtNCA & apprxeq SCCA & apprxeq ECCA & gtUCA, and the pitch angle and the angle measurement precision of the same array are lower in azimuth angle, for the same experiment 4.
The experimental condition is that the number of space targets is 1, the distance R d =200 km, pitch angle θ d =5° azimuthThe snapshot number l=30, the signal-to-noise ratio snr=10 dB, the amplitude and phase errors are uniformly distributed, the amplitude error variation range is 5% to 30%, the interval is 5%, the phase error variation range is 5 ° to 45 °, the interval is 5 °, the pitch angle and azimuth angle search ranges are 0 ° to 10 ° and 0 ° to 20 °, respectively, and the search interval is 0.05 °. Fig. 10 is a graph showing the relationship between the two-dimensional angle RMSE of the low-altitude target and the amplitude-phase error of each array of the metrewave MIMO radar, and it can be seen from the graph: as the amplitude and phase error increases, the angular measurement performance of each array decreases; under the condition of the same-amplitude phase error, the overall sequence of the two-dimensional DOA estimation precision of each array is UCCA & gtNCA & apprxeq SCCA & apprxeq ECCA & gtUCA, and the pitch angle and the angle measurement precision of the same array are lower in azimuth angle, for the same experiment 4.
In order to improve the low-altitude and ultra-low-altitude target two-dimensional angle estimation precision and angle resolution of a single-base meter wave MIMO radar based on a circular array and reduce the fluctuation degree of angle estimation errors, the invention combines a classical sparse array induction to improve several sparse circular array structures, replaces a uniform circular array as a receiving and transmitting antenna, deduces and constructs a universal single-base meter wave circular array MIMO radar mirror multipath reflection signal model based on array element positions, and provides a two-dimensional DOA estimation method suitable for the model by combining an ML algorithm and a GMUSIC algorithm. The method mainly utilizes the sparse structure of the sparse circular array to overlap the radar performance of the MIMO system, realizes the expansion of effective aperture on the premise of a certain number of physical array elements, and compared with a uniform circular array, improves the angle resolution and the estimation precision, reduces the fluctuation degree of angle estimation errors, and verifies the superiority of the generalized improved sparse circular array structure and the correctness of the method. However, the improved sparse circular array is to complete the improvement of the two-dimensional DOA estimation performance on the premise of expanding the physical aperture by using the same array element, and how to further improve the low-altitude target two-dimensional angle estimation performance under the multipath reflection condition by using the transceiving division and the array element layout optimization on the premise of limiting the physical aperture is the key point of the next research.
The present invention has been described in further detail with reference to specific preferred embodiments, and it should be understood by those skilled in the art that the present invention may be embodied with several simple deductions or substitutions without departing from the spirit of the invention.
Claims (10)
1. The MIMO radar target DOA estimation method is characterized by comprising the following steps:
connecting the ends of the classical sparse arrays and arranging the classical sparse arrays according to a circle to obtain a sparse circular array;
adopting the sparse circular array as a receiving and transmitting antenna of a single-base meter wave MIMO radar, and constructing a mirror multipath reflection signal model based on the sparse circular array;
receiving a signal matrix Z (t, tau) of the single-base meter wave MIMO radar by using the mirror multipath reflection signal model, and carrying out matched filtering on the signal matrix Z (t, tau) to obtain a matrix Z;
vectorizing the matrix Z to obtain a vectorized matrix Y;
based on the positions of the transmitting and receiving array elements, respectively calculating the transmitting and receiving direct waves and the reflecting waveguide vector by utilizing the transmitting array element guide vector and the receiving array element guide vector in the vectorization matrix Y;
the composite guiding vector is obtained through the calculation of the transmitting and receiving direct wave and the reflecting waveguide vector And calculates a real-valued complex director vector +.>
For composite steering vectorsAnd real value composite guide vector +.>Performing dimension reduction, and utilizing the composite guide vector after dimension reduction +.>And real value composite guide vector +.>And performing basic algorithm spectrum peak search and real value processing algorithm spectrum peak search to obtain the target two-dimensional DOA.
2. The method for estimating the target DOA of the MIMO radar according to claim 1, wherein the step of constructing a mirror multipath reflection signal model based on the sparse circular array by adopting the sparse circular array as a receiving and transmitting antenna of the single-base meter wave MIMO radar comprises the following steps:
adopting a sparse circular array with an array plane inclination angle beta as a receiving and transmitting antenna, and obtaining projection of the receiving and transmitting antenna in a circular array on a horizontal plane by adjusting the height of the receiving and transmitting antenna;
and constructing a mirror multipath reflection signal model based on a sparse circular array through the relation between the receiving and transmitting antenna and the projection.
3. A MIMO radar target DOA estimation method as claimed in claim 1, wherein the signal matrix z (t, τ) is received using the specular multipath reflection signal model, comprising the steps of:
transmitting multipath signals by using the MIMO radar to obtain transmitting signals which reach a target through air medium propagation Is represented by the expression:
where j is an imaginary unit, k 0 =2pi/λ, ρ is the ground reflectance, [ ·] T The transpose of the matrix is represented, Δr is the wave path difference between the direct wave and the reflected wave, and the calculation formula is:
ΔR≈2h a sinθ d
wherein,for transmitting array element steering vectors, the expression is:
the signal expression received by the nth array element is as follows:
βx(t)+v n (t,τ)
wherein beta is the target complex reflection coefficient, v n (t, τ) is additive white gaussian noise;
the signal received by the entire array can be written as:
where v (t, τ) is an additive Gaussian white noise vector,for receiving the array element steering vector, the expression is:
wherein,is azimuth angle, theta i Is the pitch angle.
4. A MIMO radar target DOA estimation method as claimed in claim 3, wherein the signal matrix Z (t, τ) is matched filtered to obtain a matrix Z, comprising the steps of:
using transmitted signalsAnd carrying out matched filtering on z (t, tau), wherein the specific expression is as follows:
wherein V is noise after matched filtering and vectorization operation.
5. The MIMO radar target DOA estimation method according to claim 4, wherein the vectorizing operation is performed on the matrix Z to obtain a vectorized matrix Y, and the specific expression is:
Where vec represents the vectorization operation, represents kron product->Is a composite steering vector, and the expression is as follows:
if K incoherent targets with equal distances exist in the wave beam width of the MIMO radar, each target azimuth angle isThe incidence angles of the direct wave and the reflected wave are respectively theta dk And theta sk Where k=1, 2, …, K, the vectorized echo signal matrix expression is:
wherein, as follows, the product Khatri-Rao is represented by, ψ= [ beta ] 1 ,β 2 ,…β K ]For the target complex reflection coefficient matrix, the expression of the composite guide vector A is as follows:
wherein:
for a co-located transmit receive array, the steering vectors have the following relationship:
6. a MIMO radar target DOA estimation method according to claim 5 wherein the composite steering vector is obtained by the transmit receive direct wave and reflected waveguide vector calculationThe method comprises the following steps:
obtaining projection to steering vector matrixIs a spatial projection matrix formed by column vectors of (a)>
By the space projection matrixMaximum likelihood estimate of azimuth and pitch angle obtained +.>And->
Wherein,is an estimate of the output covariance matrix;
inputting the maximum likelihood estimation value into Y after vectorization operation of signals, wherein the specific expression is as follows:
wherein,
wherein,is the transpose of beta, gamma is the time delay, beta is the target complex reflection coefficient, V is the noise A matrix.
7. A MIMO radar target DOA estimation method as recited in claim 6, wherein a composite steering vector is obtained at the calculationPreviously, calculating the estimation of a covariance matrix, and carrying out eigenvalue decomposition on the estimation of the covariance matrix to obtain a noise subspace E n The method comprises the following steps:
by combining steering vectorsIs obtained by the calculation process of->Estimation of covariance matrixThe calculated expression of (2) is:
wherein L is the snapshot number;
the spectral peak search formula of the ML algorithm at this time is:
wherein det represents determinant operations and trace represents trace operations;
the spectral peak search formula for GMUSIC at this time is:
wherein E is n And a noise subspace obtained by eigenvalue decomposition for the estimation of the covariance matrix.
8. A MIMO radar target DOA estimation method according to claim 7 wherein the real valued composite steering vector is calculated at real valued processingThe method comprises the following steps:
for the covariance matrixPerforming real value processing to obtain real value covariance matrix +.>And for the real-valued covariance matrixPerforming eigenvalue decomposition to obtain a noise subspace U n ；
The covariance matrix R is calculated, and the concrete expression is as follows:
wherein:and->Respectively representing signal power and noise power, wherein P=MN, M and N are respectively the numbers of transmitting and receiving array elements;
Real-valued processing is performed on the covariance matrix R by using the unitary matrix, wherein the P×P-dimensional unitary matrix is as follows:
wherein:for K P ×K P The dimensional transformation matrix has the expression:
performing one-time bidirectional smoothing on the covariance matrix R to convert the covariance matrix R into a Centro-Hermitian matrix;
wherein [ (S)] * Representing the conjugate operation of the matrix;
unitary transformation is carried out on the Centro-Hermitian matrix to obtain a real matrix;
R U ＝U P H R fb U P
estimation using covariance matrixPerforming unitary transformation after bidirectional smoothing, and calculating real-value covariance matrix +.>
For composite steering vectorsReal value processing is carried out to obtain:
in the method, in the process of the invention,representing a real valued composite steering vector.
9. A method of MIMO radar target DOA estimation as recited in claim 8 wherein the pair of composite steering vectorsAnd real value composite guide vector +.>The specific expression of the dimension reduction is as follows:
θ s ＝-arcsin(sin(θ d )+2h a /R)≈-θ d
wherein h is a For the center height of the circular array antenna, R comprises R d And R is R s ，R d And R is R s The path lengths of the direct wave and the multipath reflected wave are respectively.
10. A method for estimating a target DOA for a MIMO radar as recited in claim 9, wherein the reduced-dimension complex steering vectors are utilizedAnd real value composite guide vector +.>Performing basic algorithm spectrum peak search and real value processing algorithm spectrum peak search to obtain a target two-dimensional DOA, wherein the method comprises the following steps of:
The ML algorithm and the GMUSIC which are subjected to real value processing are defined as UML algorithm and UGGUSIC algorithm, the target two-dimensional DOA is estimated, and the final azimuth angle estimated value of the target is obtainedAnd pitch angle estimation +.>
The UML algorithm spectral peak search function is as follows:
in the formula, the real value space projection matrix is as follows:
the UGGUS algorithm spectral peak search function is as follows:
in U n Is thatAnd (5) a real noise subspace obtained by characteristic decomposition.
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