CN114371441A - Virtual array direction of arrival estimation method, device, product and storage medium - Google Patents

Virtual array direction of arrival estimation method, device, product and storage medium Download PDF

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CN114371441A
CN114371441A CN202210052422.8A CN202210052422A CN114371441A CN 114371441 A CN114371441 A CN 114371441A CN 202210052422 A CN202210052422 A CN 202210052422A CN 114371441 A CN114371441 A CN 114371441A
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CN114371441B (en
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黄丽君
周骞
廖书寒
张舒皓
马军虎
周毓昌
王志高
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Hunan University
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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
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    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
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Abstract

The invention discloses a method, a device, a product and a storage medium for estimating the direction of arrival of a virtual array, which utilize matched filtering to filter out-of-band noise and improve the signal-to-noise ratio of an M-element real array received signal; based on the first-order statistical characteristics of the filtered received signals, the effective estimation of N-element forward and backward virtual position array element signals is realized by utilizing the linear prediction idea; on the basis of first-order linear prediction of virtual array element signals, solving a second-order covariance matrix of the virtual array element signals for a topopritz average, and further expanding the aperture of the virtual array according to the one-to-one correspondence relationship between phase differences and wave path differences among the array elements; the beam scanning method is used to perform azimuth estimation on the spatial incoherent source signal. The invention can realize the expansion of the array aperture in the virtual sense without adding additional physical array elements, thereby improving the target resolution; the invention has strong interference suppression capability, can be applied to non-ideal working environments with low signal-to-noise ratio, low fast beat number and the like, and has strong practicability and wide application adaptability.

Description

Virtual array direction of arrival estimation method, device, product and storage medium
Technical Field
The present invention relates to the field of array signal processing, and in particular, to a method, an apparatus, a product, and a storage medium for estimating a direction of arrival of a virtual array.
Background
Array signal processing is an important branch of the signal processing field, compared with a single sensor, the array space signal processing technology based on a plurality of sensors has the advantages of flexible beam control, high signal gain, strong interference suppression capability, high spatial resolution capability and the like, has important military and civil application values, is widely applied to various fields, and is sufficiently developed. Direction of Arrival (DOA) estimation is an important research content of array signal processing, and relates to various national economy and military application fields such as radar, sonar, communication, seismic exploration, radio astronomy, medical diagnosis and the like.
With the progress of modern information technology, the signal processing environment is increasingly complex, the traditional DOA estimation method has the defects of weak target resolution, low estimation precision and the like, and the high-resolution DOA estimation technology with strong resolution and high estimation precision is urgently needed to be developed. Under the influence of Rayleigh limit criterion, when the frequency of an incident signal is constant, the target space resolution of the array is positively correlated with the aperture of the array. The array aperture can be expanded by increasing the number of array elements forming the array or expanding the spacing between the array elements, so as to achieve the purpose of improving the target resolution. However, in practical application scenarios, increasing the number of array elements means increasing hardware cost and complexity of system design; expanding the array element spacing will lead to the appearance of grating lobes, and introduce a "false target" in the detection result. Therefore, the number and the pitch of the array elements cannot be increased without limit due to the layout cost and the space of the array. The virtual array expansion technology can obtain expanded array apertures equivalent to the increase of physical array elements through specific matrix transformation on the basis of an original array without increasing the physical array elements in a virtual sense, thereby realizing high-resolution DOA estimation, and simultaneously increasing the freedom degree of the array, inhibiting background noise and improving the target resolution precision.
As for the DOA estimation method of array signal processing, a lot of research has been conducted by scholars at home and abroad, and there are mainly a beam scanning method typically applied to a Minimum Variance Distortionless Response (MVDR) beam former and a subspace algorithm represented by a Multiple signal classification algorithm (MUSIC). The MVDR algorithm has higher target resolution than the conventional CBF algorithm, but is still limited by Rayleigh limit, and cannot distinguish two targets in one beam width; although the subspace algorithm breaks through the limit of the rayleigh limit, under the conditions of low signal-to-noise ratio and few snapshots, the signal subspace and the noise subspace mutually permeate, and the spatial resolution performance of the subspace algorithm is greatly influenced and reduced.
At present, the common virtual array expansion method mainly focuses on equivalent virtual aperture expansion by using first order/second order or high order statistics of array received data, effective information of original received data cannot be fully utilized, and the expanded equivalent array aperture is limited. Although the array expansion method based on the high-order cumulant contains a large amount of abundant information which is not available in the first-order and second-order statistics, the application of the method in a scene with high real-time requirement is limited by the computational complexity brought by the algorithm. The existing wave arrival direction estimation method based on the real array is limited by cost and layout space, the number of array elements and the array aperture cannot be greatly increased, and the contradiction between the high-spatial target resolution requirement on the ground and the limited array aperture cannot be avoided.
Disclosure of Invention
The invention aims to solve the technical problems that the prior art is insufficient, a virtual array direction of arrival estimation method, a device, a product and a storage medium are provided, and the problems that the existing DOA estimation method is insufficient in spatial resolution and the existing virtual array equivalent aperture expansion is insufficient in utilization of original array received data information, complex in calculation and high in spatial spectrum side lobe are solved.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a virtual array direction of arrival estimation method comprises the following steps:
s1, performing matched filtering on the original receiving signals of the uniform linear arrays of the M array elements;
s2, performing N-element forward linear prediction and backward linear prediction based on first-order statistics on the matched and filtered signals to obtain output signals of M +2N virtual array elements;
s3, obtaining second-order statistical characteristics of the output signals of the M +2N virtual array elements, and carrying out topiraz averaging to obtain the output signals of the 2M +4N-1 virtual array elements;
and S4, performing spatial spectrum calculation on the output signals of the 2M +4N-1 virtual arrays, wherein the angle corresponding to the spatial spectrum peak value is the target angle result obtained by estimation.
In the invention, for the linear array which is uniformly distributed, firstly, the out-of-band noise is filtered by using matched filtering, and the signal-to-noise ratio of the M-element real array receiving signal is improved; then, based on the first-order statistical characteristics of the filtered received signals, the effective estimation of N-element forward and backward virtual position array element signals is realized by utilizing the idea of linear prediction; further, on the basis of first-order linear prediction of virtual array element signals, a second-order covariance matrix is subjected to topiralzem averaging, and the aperture of the virtual array is further expanded according to the one-to-one correspondence relationship between the phase difference and the wave path difference between the array elements; finally, the beam scanning method is used for carrying out azimuth estimation on the spatial incoherent source signal.
According to the method, on the basis of expanding the array aperture by using the first-order linear prediction result of the array received data, the Tupletzian average is further carried out according to the second-order covariance matrix, the method can obtain a larger array aperture expanding effect without adding extra physical array elements, the space resolution capability of a target can be improved, meanwhile, lower side lobes are obtained, in addition, the calculation amount of the method is small, and the real-time performance is good. The invention has strong interference suppression capability, can be applied to non-ideal working environments with low signal-to-noise ratio, low fast beat number and the like, and has strong practicability and wide application adaptability.
The specific implementation process of step S1 includes: using the transmitted signal s (n) as a copy signal for the received real signal
Figure BDA0003474802140000031
Performing matched filtering processing, and then performing array matched filtering on the output signal xl(n) the expression is:
Figure BDA0003474802140000032
wherein, denotes a convolution operation, sT is a transmission signal pulse width [, ]]HThis is expressed as conjugation, l ═ 1,2, 3, …, M. By means of the algorithm of matched filtering, out-of-band noise is filtered, and the signal-to-noise ratio of the received signal is improved.
In step S2, the specific implementation process of obtaining the output signals of M +2N virtual array elements includes: the forward prediction implementation process comprises the following steps:
array element number 1 x using a real array (i.e., matched filtered signal)1As a reference array element
Figure BDA0003474802140000033
Taking array element signals from No. 2 to No. P +1 as P-order observed values of linear prediction:
Figure BDA0003474802140000034
[]Trepresenting and taking a transposition;
calculating a forward prediction coefficient alpha according to a wiener-Hough equation:
Figure BDA0003474802140000035
wherein,
Figure BDA0003474802140000036
Figure BDA0003474802140000037
as P-order observed value xFSelf-phase ofThe relation matrix, RijA correlation matrix of the ith array element and the jth array element representing the P-order observation value;
Figure BDA0003474802140000038
for reference array elements in forward prediction
Figure BDA0003474802140000039
P-order observation x used for forward predictionFThe cross-correlation vector of (a) is,
Figure BDA00034748021400000310
representing reference array elements in forward prediction
Figure BDA00034748021400000311
A cross-correlation matrix with the i-th array element used for forward prediction; i is 1,2, … …, P; j ═ 1,2, … … P;
p-order observed value x needed when estimating received signal of forward nth virtual array element positionFThe updating is as follows:
Figure BDA00034748021400000312
xM+n-P ... xM+n-1the signals of array elements M + n-P to M + n-1;
according to the forward prediction coefficient alpha and the updated P-order observed value
Figure BDA00034748021400000313
Calculating to obtain a receiving signal of a forward nth virtual array element position: x is the number ofM+n＝xFα；
And a backward prediction implementation process:
using the M-th array element of the real array as the reference array element
Figure BDA00034748021400000314
Taking the M-P + 1-M array element signals as P-order observed values of linear prediction:
Figure BDA0003474802140000041
calculating a backward prediction coefficient beta according to a wiener-Hough equation:
Figure BDA0003474802140000042
wherein,
Figure BDA0003474802140000043
Figure BDA0003474802140000044
is xBThe autocorrelation matrix of (a) is then determined,
Figure BDA0003474802140000045
for referencing array elements in backward prediction
Figure BDA0003474802140000046
P-order observation x used for backward predictionBThe cross-correlation vector of (a);
p-order observed value x needed when estimating received signals at the position of the back nth virtual array elementBThe updating is as follows:
Figure BDA0003474802140000047
according to the backward prediction coefficient beta and the updated P-order observed value
Figure BDA0003474802140000048
Calculating to obtain a receiving signal of the backward nth virtual array element position: x is the number of1-n＝xBβ；
In summary, the output signal x of M +2N virtual array elementsLPThe method comprises three parts: backward prediction virtual position array element signals, original receiving real signals and forward prediction virtual position array element signals: x is the number ofLP＝[x1-N ... x1 ... xM+N]T。
The invention expands the M array element real array with uniform array to M +2N array element virtual array through the first-order linear prediction algorithm, and the array aperture is expanded equivalently in the virtual sense.
In step S3, the output signals of 2M +4N-1 virtual array elements are represented as:
D＝[D-(M+2N-1) … D0 … DM+2N-1]Twherein
Figure BDA0003474802140000049
|n|≤M+2N-1
Figure BDA00034748021400000410
denotes taking the conjugate transpose.
Figure BDA00034748021400000411
The output signals of array elements No. 1-N, …, 1, …, M + N, which are shown as expanded virtual arrays.
The invention further expands the virtual array of the M +2N array elements in the step 2 to 2M +4N-1 array elements by a second-order topopritz average algorithm, thereby further expanding the equivalent aperture of the virtual array.
Compared with the original real array, the virtual array jointly expanded based on the first-order and second-order statistics of the uniform linear array has the advantages that the number of array elements is increased by M +4N-1, the width of a spatial spectrum-3 dB main lobe is reduced to M/(2M +4N-1) of the original real array, and therefore the spatial resolution capability of the method is remarkably improved.
In step S4, the formula for performing spatial spectrum calculation on the output signals of the 2M +4N-1 virtual arrays is: p (θ) ═ a (θ) Rvira*(θ)；
a(θ)＝[1 e-j2πfdcos(θ)/c e-j2πf2dcos(θ)/c ... e-j2πf(2M+4N-2)dcos(θ)/c]TWherein theta is the scanning azimuth of the target of interest, f is the central frequency of the narrow-band signal, c is the sound velocity, and d is the array element spacing;
Figure BDA0003474802140000051
denotes taking the conjugate transpose, D-(M+2N-1) ... D1 ... DM+2N-1Respectively represents signals of array elements No. (M +2N-1), …, 1, … and M + 2N-1.
Under ideal and non-ideal conditions (low snapshot number and low signal-to-noise ratio), the method adopts a beam scanning method to calculate the spatial spectrum of the interested direction for the virtual array element signals based on the combined expansion of the first-order and second-order statistics, obtains a better spatial resolution advantage than the spatial spectrum calculation result by adopting real array signals, and proves the effectiveness of the method.
As an inventive concept, the present invention also provides a computer arrangement comprising a memory, a processor and a computer program stored on the memory; the processor executes the computer program to implement the steps of the method of the present invention.
As an inventive concept, the present invention also provides a computer-readable storage medium having stored thereon a computer program/instructions; wherein the computer program/instructions, when executed by a processor, performs the steps of the method of the present invention.
As an inventive concept, the present invention also provides a computer program product comprising computer programs/instructions; which when executed by a processor implement the steps of the method of the present invention.
Compared with the prior art, the invention has the beneficial effects that: according to the method, on the basis of expanding the array aperture by using the first-order linear prediction result of the array received data, the Tupletzian average is further carried out according to the second-order covariance matrix, the method can obtain a larger array aperture expanding effect without adding extra physical array elements, the space resolution capability of a target can be improved, and a lower side lobe suppression effect is obtained. The invention has strong interference suppression capability, can be applied to non-ideal working environments with low signal-to-noise ratio, low fast beat number and the like, and has strong practicability and wide application adaptability.
Drawings
FIG. 1 is a block diagram of a method flow of an embodiment of the present invention;
FIG. 2 is a schematic diagram of an expansion structure of a virtual array element according to an embodiment of the present invention;
FIGS. 3(a) and 3(b) are graphs showing the influence of the first-order linear prediction array element number on the main lobe width of the spatial spectrum under different signal-to-noise ratios and snapshot numbers; FIG. 3(a) is a graph showing the influence of different signal-to-noise ratios, and FIG. 3(b) is a graph showing the influence of different snapshot numbers;
fig. 4(a) and fig. 4(b) are graphs of the spatial spectrum and-3 dB main lobe width of a single target under fixed signal-to-noise ratio (SNR ═ 10dB) and fast beat number (S _ N ═ 400), respectively; FIG. 4(a) single target space spectrum, FIG. 4(b) -3dB main lobe width plot;
fig. 5(a) and 5(b) are the spatial spectrograms of a single target under the conditions of fixed fast beat number (S _ N ═ 400) and different signal-to-noise ratio, respectively; fig. 5(a) is a space spectrum of a single target under the condition of-12 dB SNR, and fig. 5(b) is a space spectrum of a single target under the condition of 0dB SNR;
fig. 6(a) and fig. 6(b) are the spatial spectrograms of a single target under a fixed signal-to-noise ratio (SNR ═ 10dB) and different snapshot conditions, respectively; fig. 6(a) shows a space spectrum of a single target with a fast beat number S _ N of 10, and fig. 6(b) shows a space spectrum of a single target with a fast beat number S _ N of 20;
FIGS. 7(a) and 7(b) are the spatial spectrograms of 3 targets under different fast beat number and signal-to-noise ratio, respectively; fig. 7(a) shows a space spectrum of 3 targets under the conditions of fast beat S _ N being 400 and SNR being 15dB, fig. 7(b) shows a space spectrum of 3 targets under the conditions of fast beat S _ N being 400 and SNR being 0dB, fig. 7(c) shows a space spectrum of 3 targets under the conditions of fast beat S _ N being 8 and SNR being 15dB, and fig. 7(d) shows a space spectrum of 3 targets under the conditions of fast beat S _ N being 20 and SNR being 0 dB.
Detailed Description
The invention provides a virtual array high-resolution direction of arrival estimation method based on first-order and second-order statistic joint expansion, and a flow chart is shown in figure 1. The basic idea of the invention is: after the real array receiving signal is processed by matched filtering, the out-of-band noise is filtered, and the signal-to-noise ratio of the receiving signal is improved. According to the characteristics of a narrow-band transmitting signal and an array structure, a received signal after filtering processing forms a virtual array formed by a plurality of virtual array elements after first-order linear prediction and second-order topopritz averaging, and the phase difference between signals of each virtual array element is consistent with the phase difference between real array elements caused by the wave path difference. The virtual array element expansion based on first-order linear prediction is based on the linear superposition of a plurality of array element signals, and the correlation between the noise in the obtained virtual array element expansion signal and the received noise of each real array element is weakened; the virtual array element expansion based on the second-order topiralzer mean is equivalent to performing space noise mean, and effectively inhibits background noise. Therefore, the invention utilizes the first-order and second-order statistical characteristics of the real array to virtually expand the aperture of the array according to the relationship between the signal phase difference and the wave path difference between the array elements, thereby improving the spatial resolution of the target. Compared with the prior art, the method provided by the invention can realize high-resolution target azimuth estimation under the application environment of low signal-to-noise ratio and low fast beat number without adding additional actual physical array elements.
The following detailed description of the steps of embodiments of the present invention is made with reference to the accompanying drawings:
the method comprises the following steps: considering that the channel characteristics between the transmitting end and the receiving end do not change in a short time, the array received signal can be regarded as a sampling sequence of a stationary random process. The invention takes the uniform linear array as an example for analysis.
Under the far-field condition, K targets are totally arranged, the receiving and transmitting combination is considered, narrow-band signals are transmitted by a transmitting end, and echo signals radiated back to a receiving end after reaching the targets through a channel are received by a receiving array. The incident direction of the echo signal is thetakIf the No. 1 real array element is used as the reference array element, the received signal of the No. l array element can be expressed as
Figure BDA0003474802140000071
Wherein,
Figure BDA0003474802140000072
the time delay of the echo signal reflected by the kth target in the space to the first array element is shown, d is the uniform array spacing of the linear array, c is the sound velocity, n isl(n) is additive noise, l ═ 1,2, 3, …, M.
And performing matched filtering processing on the received real signal by using the transmitting signal as a copy signal, wherein the output signal after array matched filtering is as follows:
Figure BDA0003474802140000073
wherein, denotes a convolution operation, sT is a transmission signal pulse width [, ]]HIndicating that conjugation was taken.
Step two: the received signals of the forward and backward virtual array element positions are estimated according to the known first-order statistical characteristics of the original received signals of each array element of the linear array, and the method is realized by means of the idea of linear prediction. The virtual aperture expanding structure of the uniform linear array is shown in fig. 2.
The original array elements of the basic array are represented by solid circles and are marked as i real1,2, 3, …, M, backward and forward expanding virtual array elements are distributed on two sides of the original array element, and are represented by hollow circles and respectively marked as iB…, -1, 0 and iF＝M+1，M+2，…。
Considering that the principles of forward prediction and backward prediction are consistent, only forward prediction is taken as an example for specific analysis. Based on the linear prediction idea, the received signals of the first P array elements of the known array elements are used for estimating the received signals of the forward P +1 array element position. Estimation of array element received signal
Figure BDA0003474802140000074
And the actual value xP+1Error of (n) is eP+1(n) then:
Figure BDA0003474802140000081
Figure BDA0003474802140000082
wherein, { α [ [ alpha ] ]iIs the linear prediction forward coefficient. By e is denoted eP+1(n), x represents xP+1(n)，
Figure BDA0003474802140000083
To represent
Figure BDA0003474802140000084
xiDenotes xi(n), then the error power can be expressed as:
Figure BDA0003474802140000085
based on the principle of orthogonality of linear minimum mean square errors, in equation (4), E (E) is calculated2) Minimum { alpha }iE should be made to correspond to all observed values xiOrthogonal, where i is 1,2, …, P. The following two equivalent systems of equations can be obtained:
E[exi]＝0,i＝1,2,...,P (6)
Figure BDA0003474802140000086
let E (x)ixj)＝Rij，
Figure BDA0003474802140000087
Equation (7) can be rewritten as:
Figure BDA0003474802140000088
namely:
Figure BDA0003474802140000089
equation (9) is a linear-predictive Wiener-Hopf equation which reflects the relationship between the correlation function and the optimum linear prediction coefficient, and by solving this equation, the forward prediction coefficient { α [ alpha ] can be solvedi}。
Substituting i into 1,2, … and P into formula (9) and reacting
Figure BDA00034748021400000810
Represents a matrix of correlation functions, namely:
Figure BDA00034748021400000811
respectively order
α＝[α1 α2 ... αP]T (11)
Figure BDA0003474802140000091
Equation (9) can be expressed in matrix form as:
Figure BDA0003474802140000092
wherein
Figure BDA0003474802140000093
Is referred to as xiThe autocorrelation matrix of (a) is then determined,
Figure BDA0003474802140000094
referred to as x and xiThe cross-correlation vector of (a). The best forward prediction coefficient can be solved by equation (12):
Figure BDA0003474802140000095
similarly, based on linear prediction idea, estimating the received signal of the backward M-P array element position by using the received signals of M-P + 1-M array elements of the known array, and backward prediction coefficient { betaiThe expression of is:
Figure BDA0003474802140000096
therefore, the received signals of the forward and backward n-th virtual array element positions can be respectively obtained by iterative estimation in sequence by using the known array element data of the P order:
xM+n＝[xM+n-P ... xM+n-1]Tα (16)
x1-n＝[xM-n+2-P ... xM-n+1]Tβ (17)
in summary, the extended array received signal based on forward and backward linear prediction is composed of three parts: the backward prediction virtual position array element signal, the original receiving real signal and the forward prediction virtual position array element signal are expressed as follows:
xLP＝[x1-N ... x1 ... xM+N]T (18)
step three: and (3) further expanding the array aperture by using the second-order statistical characteristic of the received signals at the virtual array element positions expanded in the step (II), namely azimuth information in the covariance matrix, so as to realize effective estimation of the far-field plane wave incident azimuth, wherein the schematic diagram of the expanded structure of the virtual array element is shown in FIG. 2.
In order to simplify the formula, the output signals of the array elements 1-N, …, 1, … and M + N of the expanded virtual array obtained in the step two are respectively rewritten into
Figure BDA0003474802140000097
The covariance matrix between the array elements is:
Figure BDA0003474802140000098
where denotes taking the conjugate transpose. As can be seen from the above equation, the diagonal elements of the covariance matrix between the array elements have the same target azimuth information. Averaging matrix elements with the same target azimuth information component, namely, performing Topriz averaging on R, and converting a two-dimensional covariance matrix into one-dimensional data with space distribution characteristics:
Figure BDA0003474802140000101
wherein | N | is less than or equal to M +2N-1, q is less than or equal to 0 and less than or equal to M +2N-1- | N | M is the actual array element number, and 2N is the effective array element number of forward and backward expansion. The Toeplitz average is equivalent to the spatial average of noise, so the method provided by the invention has higher noise suppression capability.
D (N) has 2M +4N-1 elements in total, and can be equivalently expanded into 2M +4N-1 virtual array elements. Constructing a virtual array through multiple snapshots to receive data, represented as:
D＝[D-(M+2N-1) … D0 … DM+2N-1]T (21)
step four: and (3) performing spatial spectrum calculation on the virtual array element received signals obtained in the third step based on the first-order and second-order statistic joint expansion by using a conventional beam scanning method (CBF).
The array manifold vector corresponding to the virtual array is:
a(θ)＝[1 e-j2πfdcos(θ)/c e-j2πf2dcos(θ)/c ... e-j2πf(2M+4N-2)dcos(θ)/c]T (22)
where θ is the target scan bearing of interest.
And (3) carrying out phase compensation summation processing on the large-aperture virtual uniform linear array received data obtained in the third step in an interested angle range by using CBF, and obtaining the spatial spectrum output as follows:
P(θ)＝a(θ)Rvira*(θ) (23)
wherein, the angle corresponding to the space spectrum peak is the target angle result obtained by estimation, the expression is the conjugate transpose, x-(M+2N-1) ... x1 ... xM+2N-1Respectively represents signals of array elements No. (M +2N-1), …, 1, … and M + 2N-1. The covariance matrix among the array elements of the virtual array after the second-order joint expansion is as follows:
Figure BDA0003474802140000102
compared with the original real array, the virtual array jointly expanded based on the first-order and second-order statistics has the advantages that the number of array elements is increased by M +4N-1, and the width of a spatial spectrum-3 dB main lobe is reduced to M/(2M +4N-1) of the original real array.
And in the second step, when forward and backward virtual array element expansion is carried out based on the first-order cumulant, the actual array element receiving signals are utilized for linear superposition, and the correlation between the noise in the obtained virtual array element expansion signals and the receiving noise of each actual array element is weakened. The array aperture is expanded to M +2N in a virtual sense, and the main lobe width of a wave beam is favorably sharpened. However, the number N of virtual array elements cannot be increased indefinitely. When the virtual array elements are constructed by adopting a linear prediction method, the signal of each virtual array element is obtained by linearly superposing the data of the signals of the first P array elements. When the number of virtual array elements is larger, the effective real signal data in the observation data for constructing the array element signal is less, and the sharpening of the beam width gradually tends to be stable due to the accumulation of prediction errors and the influence of an actual noise signal.
Simulation result
In order to verify the effectiveness of the virtual array high-resolution direction-of-arrival estimation method based on the first-order and second-order statistic joint expansion, simulation verification is carried out. And (4) investigating the influence of the signal-to-noise ratio and the snapshot number on the uniform linear array virtual array element expansion algorithm. In simulation, five algorithms such as a CBF algorithm based on the actual array element number and the expanded array element number, a first-order statistic virtual array element expansion algorithm based on linear prediction, a virtual array element expansion algorithm based on second-order statistic topiralZ mean, the virtual array element high-resolution DOA estimation provided by the invention and the like are compared under an ideal condition.
The basic simulation parameters are as follows: the half-wavelength array frequency f of the uniform linear array design is 500 Hz; sampling frequency fsIs 4 k; the actual array element number is M is 8; the far-field space information source is an ideal point source target, and the target direction is a horizontal forward included angle with the array. In order to simplify analysis, ideal equal sound velocity free far field propagation conditions are considered, energy loss, waveform distortion and the like do not occur in the signal propagation process, the influence of spatial reverberation is ignored, and noise on a receiving array element is set to be additive white Gaussian noise.
(1) Influence of first-order linear prediction array element number on spatial spectrum main lobe width under different signal-to-noise ratios and snapshot numbers
From the above analysis, the number of virtual array elements is determined by the first order linear prediction and the second order topolitz mean. Wherein, the expansion ratio coefficient of the second-order topolitz average virtual array aperture is fixed to be 2 times of the array aperture before expansion. Therefore, the variation parameter of the virtual array element aperture expansion of the invention is mainly determined by the array element number N of the first-order linear prediction.
And carrying out simulation verification by adopting two groups of parameters. Basic parameters: the number K of far-field space information sources is 1, the included angle between the direction and the horizontal forward direction of the array is 60 degrees, the first-order linear prediction order P is 7, and the number N of forward and backward prediction array elements is consistent.
A first set of parameters: the fast beat number S _ N is 400 sampling points, the SNR is respectively set to be 20dB/0dB/-10dB, and the trend that the main lobe width of the space spectrum-3 dB changes along with the predicted array element number N under the conditions of different SNR is given in figure 3 (a). It can be seen that the main lobe width shows a trend of overall narrowing with the increase of the number of linear prediction array elements, and the main lobe width sharpening trend is less and less obvious and finally tends to be stable with the increase of the number of virtual array elements due to the influence of prediction errors and actual noise. The lower the signal-to-noise ratio, the lower the sharpening effect of the main lobe width, and as the signal-to-noise ratio decreases, the faster the plateau region where the sharpening of the main lobe width becomes slow comes.
The second set of parameters: the SNR is 20dB, the number of snapshots S _ N is set to 8/12/16/40, respectively, and fig. 3(b) shows the trend of the spatial spectrum-3 dB main lobe width varying with the number of predicted array elements N under different fast-beat conditions. It can be seen that under the condition of extremely low fast beat number, the main lobe width changes towards the increasing direction along with the increase of the number of linear prediction array elements. At this time, the robustness of the algorithm is affected by the extremely low fast beat number, and the prediction error is large. When the number of snapshots increases to 40, the main lobe width tends to narrow overall as the number of linear prediction array elements increases.
Therefore, according to the two sets of simulation analysis, the linear prediction array element number is limited by the signal-to-noise ratio and the fast beat number, and can not be increased without limit. Under the conditions of good signal-to-noise ratio and fast beat number, the linear prediction array element number N is preferably not more than 2.5 times of the actual array element M. According to the simulation analysis below, the linear prediction array element number N is taken as M.
(2) Single target simulation at fixed signal-to-noise ratio and snapshot number
Basic parameters: the number K of far-field space information sources is 1, and the included angle between the direction and the horizontal forward direction of the array is 90 degrees; the first-order linear prediction order P is taken as 7, the number N of forward and backward prediction array elements is consistent, and the number N is taken as 8; the fast beat number S _ N is 400 samples and the signal-to-noise ratio SNR is set to 10 dB.
Fig. 4(a) and fig. 4(b) respectively compare the spatial spectrum calculation results of a single signal element by five algorithms, namely, a CBF algorithm based on the actual array element number and the expanded array element number, a first-order statistic virtual array element expansion algorithm based on linear prediction, a virtual array element expansion algorithm based on a second-order statistic topolitzier average, and the virtual array element high-resolution DOA estimation provided by the invention.
Fig. 4(a) shows that compared with a first-order statistic virtual array element expansion algorithm based on actual array element number and linear prediction and a virtual array element expansion algorithm based on second-order statistic topolitz average, the spatial spectrum main lobe width sharpening effect is remarkable, the side lobe level is lower, and the spatial spectrum main lobe width sharpening effect is equivalent to a spatial spectrum result obtained by a CBF algorithm based on the array element number after expansion.
As the source incidence direction changes from near-array end-fire direction to transverse direction in fig. 4(b), the main lobe width of the spatial spectrum estimation result gradually narrows, which is determined by the characteristics of the array structure itself, which indicates that the spatial resolution of the array decreases when the target incidence direction is near the end-fire direction. However, the virtual array element algorithm provided by the invention can solve the defect that the array spatial resolution is reduced when the target is in the end-fire direction through the expansion of the virtual aperture on the basis of not increasing the actual array elements.
(3) Single target simulation under different signal-to-noise ratio conditions
Basic parameters: the number K of far-field space information sources is 1, and the included angle between the direction and the horizontal forward direction of the array is 90 degrees; the first-order linear prediction order P is taken as 7, the number N of forward and backward prediction array elements is consistent, and the number N is taken as 8; the fast beat number S _ N is 400 samples, and the SNR is set to 10dB/-12dB, respectively.
Fig. 5(a) and 5(b) compare the spatial spectrum estimation results of the above five algorithms on a single signal element under the same fast beat number and different signal-to-noise ratios, respectively. Under the condition of a lower signal-to-noise ratio, the estimation capability of a virtual array element expanding algorithm based on the actual array element number and the second-order statistic topolitz average on a target is sharply reduced, the main lobe width of a spatial spectrum is seriously widened, side lobes are increased, and the suppression of interference in a non-target direction is not facilitated. The method provided by the invention can still keep a space spectrum estimation result equivalent to a CBF algorithm based on the actual array element number after expansion under the condition of low signal to noise ratio, which shows that the method provided by the invention has strong applicability under the condition of low signal to noise ratio.
(4) Single target simulation under different snapshot number conditions
Basic parameters: the number K of far-field space information sources is 1, and the included angle between the direction and the horizontal forward direction of the array is 90 degrees; the first-order linear prediction order P is taken as 7, the number N of forward and backward prediction array elements is consistent, and the number N is taken as 8; the signal-to-noise ratio SNR is 10dB and the number of snapshots S _ N is set to 10/20, respectively.
Fig. 6(a) and fig. 6(b) compare the spatial spectrum estimation results of the above five algorithms on a single signal element under the same signal-to-noise ratio and different fast beat numbers, respectively. Under the condition of a lower fast beat number, the estimation capability of a virtual array element expanding algorithm based on the actual array element number and the second-order statistic topolitz average on a target is sharply reduced, the main lobe width of a spatial spectrum is seriously widened, side lobes are increased, and the suppression of interference in a non-target direction is not facilitated. The method provided by the invention can still keep a space spectrum estimation result equivalent to a CBF algorithm based on the actual array element number after expansion under the condition of low signal to noise ratio, which shows that the method provided by the invention has strong applicability under the condition of low signal to noise ratio.
It can be seen that under the condition of extremely low fast beat number, the method provided by the invention is influenced by the increase of prediction error, and the sidelobe suppression effect is weakened to a certain extent compared with the ideal condition. However, from the overall trend observation, the method provided by the invention can still maintain the spatial spectrum estimation result equivalent to the CBF algorithm based on the actual array element number after the expansion under the condition of low snapshot number, which shows that the method provided by the invention has strong applicability under the condition of low snapshot number.
(5) Multiple target resolution simulation at fixed signal-to-noise ratio and snapshot number
Basic parameters: the number K of far-field space information sources is 3, and the included angles between the direction and the horizontal forward direction of the array are respectively set to be 75 degrees, 80 degrees and 110 degrees; the first-order linear prediction order P is 7, the number N of the forward and backward prediction array elements is consistent, and the number N is 8.
As can be seen from fig. 7(a) -7 (d), when the incidence angles of the two spatial sources are within one beam width, the real array-based DOA estimation algorithm has failed, and cannot distinguish between the spatial targets of 75 ° and 80 °.
A first set of parameters: the fast beat number S _ N is 400 sampling points, and the SNR is set to 15dB/0dB respectively. Comparing fig. 7(a) and fig. 7(b), the method of the present invention can still resolve 75 ° and 80 ° spatial objects well under low snr condition, and has good sidelobe suppression effect.
The second set of parameters: the signal-to-noise ratio SNR was 15dB and the fast beat number S _ N was set to 400/8 sample points, respectively. Compared with fig. 7(a) and fig. 7(c), the method provided by the invention can still well distinguish the spatial targets of 75 ° and 80 ° under the condition of low snapshot count, and has good side lobe suppression effect.
The third set of parameters: the signal-to-noise ratio SNR of fig. 7(d) is 0dB, and the fast beat number S _ N is set to 20 sampling points. Comparing fig. 7(a) and fig. 7(d), the method of the present invention can still resolve 75 ° and 80 ° spatial objects well under the conditions of low fast beat number and low signal-to-noise ratio, and has good side lobe suppression effect.

Claims (8)

1. A virtual array direction of arrival estimation method is characterized by comprising the following steps:
s1, performing matched filtering on the original receiving signals of the uniform linear arrays of the M array elements;
s2, performing N-element forward linear prediction and backward linear prediction based on first-order statistics on the matched and filtered signals to obtain output signals of M +2N virtual array elements;
s3, obtaining second-order statistical characteristics of the output signals of the M +2N virtual array elements, and carrying out topiraz averaging to obtain the output signals of the 2M +4N-1 virtual array elements;
and S4, performing spatial spectrum calculation on the output signals of the 2M +4N-1 virtual arrays, wherein the angle corresponding to the spatial spectrum peak value is the target angle result obtained by estimation.
2. The virtual array direction-of-arrival estimation method according to claim 1, wherein the specific implementation procedure of step S1 includes: using the transmitted signal s (n) as a copy signal for the received real signal
Figure FDA0003474802130000011
Performing matched filtering processing, and then performing array matched filtering on the output signal xl(n) the expression is:
Figure FDA0003474802130000012
wherein, denotes a convolution operation, sT is a transmission signal pulse width [, ]]HThis means taking the conjugate, where l is 1,2, 3, …, and M, n is the discrete sampling instant of the transmitted signal.
3. The method according to claim 1, wherein in step S2, the specific implementation process of obtaining the output signals of M +2N virtual array elements includes:
the forward prediction implementation process comprises the following steps:
array element number 1 x using real array1As a reference array element
Figure FDA0003474802130000013
Taking array element signals from No. 2 to No. P +1 as P-order observed values of linear prediction:
Figure FDA0003474802130000014
[]Trepresenting and taking a transposition;
according toWiener-hough equation, calculating the forward prediction coefficient alpha:
Figure FDA0003474802130000015
wherein,
Figure FDA0003474802130000016
Figure FDA0003474802130000017
as P-order observed value xFOf the autocorrelation matrix RijA correlation matrix of the ith array element and the jth array element representing the P-order observation value;
Figure FDA0003474802130000018
for reference array elements in forward prediction
Figure FDA0003474802130000019
P-order observation x used for forward predictionFThe cross-correlation vector of (a) is,
Figure FDA0003474802130000021
representing reference array elements in forward prediction
Figure FDA0003474802130000022
A cross-correlation matrix with the i-th array element used for forward prediction; i is 1,2, … …, P; j ═ 1,2, … … P;
p-order observed value x needed when estimating received signal of forward nth virtual array element positionFThe updating is as follows:
Figure FDA0003474802130000023
xM+n-P … xM+n-1the signals of array elements M + n-P to M + n-1;
according to the forward prediction coefficient alpha and the updated P-order observed value
Figure FDA0003474802130000024
Calculating to obtain a receiving signal of a forward nth virtual array element position: x is the number ofM+n＝xFα；
And a backward prediction implementation process:
using the M-th array element of the real array as the reference array element
Figure FDA0003474802130000025
Taking the M-P + 1-M array element signals as P-order observed values of linear prediction:
Figure FDA0003474802130000026
calculating a backward prediction coefficient beta according to a wiener-Hough equation:
Figure FDA0003474802130000027
wherein,
Figure FDA0003474802130000028
Figure FDA0003474802130000029
is xBThe autocorrelation matrix of (a) is then determined,
Figure FDA00034748021300000210
for referencing array elements in backward prediction
Figure FDA00034748021300000211
P-order observation x used for backward predictionBThe cross-correlation vector of (a);
p-order observed value x needed when estimating received signals at the position of the back nth virtual array elementBThe updating is as follows:
Figure FDA00034748021300000212
according to the backward prediction coefficient beta and the updated P-order observed value
Figure FDA00034748021300000213
Calculating to obtain a receiving signal of the backward nth virtual array element position: x is the number of1-n＝xBβ；
In summary, the output signal x of M +2N virtual array elementsLPThe method comprises three parts: backward prediction virtual position array element signals, original receiving real signals and forward prediction virtual position array element signals: x is the number ofLP＝[x1-N ... x1 … xM+N]T。
4. The method according to claim 1, wherein in step S3, the output signals of 2M +4N "1 virtual array elements are represented as:
D＝[D-(M+2N-1) … D0 … DM+2N-1]Twherein
Figure FDA0003474802130000031
|n|≤M+2N-1
Figure FDA0003474802130000032
denotes taking the conjugate transpose.
Figure FDA0003474802130000033
And (3) output signals of array elements 1-N, …, 1, …, M + N of the expanded virtual array.
5. The virtual array direction of arrival estimation method according to claim 1, wherein in step S4, the formula for performing spatial spectrum calculation on the output signals of 2M +4N "1 virtual arrays is:
P(θ)＝a(θ)Rvira*(θ)；
a(θ)＝[1 e-j2πfdcos(θ)/c e-j2πf2dcos(θ)/c ... e-j2πf(2M+4N-2)dcos(θ)/c]Twherein theta is the scanning azimuth of the target of interest, f is the central frequency of the narrow-band signal, c is the sound velocity, and d is the array element spacing;
Figure FDA0003474802130000034
denotes taking the conjugate transpose, D-(M+2N-1) ... D1 ... DM+2N-1Respectively represents signals of array elements No. (M +2N-1), …, 1, … and M + 2N-1.
6. A computer apparatus comprising a memory, a processor and a computer program stored on the memory; characterized in that the processor executes the computer program to carry out the steps of the method according to one of claims 1 to 5.
7. A computer readable storage medium having stored thereon a computer program/instructions; characterized in that the computer program/instructions, when executed by a processor, implement the steps of the method of one of claims 1 to 5.
8. A computer program product comprising a computer program/instructions; characterized in that the computer program/instructions, when executed by a processor, performs the steps of the method according to one of claims 1 to 5.
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