CN105445698B - High-accuracy time delay estimation method between a kind of bilinear battle array - Google Patents

High-accuracy time delay estimation method between a kind of bilinear battle array Download PDF

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CN105445698B
CN105445698B CN201510846752.4A CN201510846752A CN105445698B CN 105445698 B CN105445698 B CN 105445698B CN 201510846752 A CN201510846752 A CN 201510846752A CN 105445698 B CN105445698 B CN 105445698B
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CN105445698A (en
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刘雄厚
孙超
刘振
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Northwestern Polytechnical 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
    • G01S3/00—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
    • G01S3/80—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 ultrasonic, sonic or infrasonic waves
    • G01S3/802—Systems for determining direction or deviation from predetermined direction
    • G01S3/808—Systems for determining direction or deviation from predetermined direction using transducers spaced apart and measuring phase or time difference between signals therefrom, i.e. path-difference systems
    • G01S3/8083—Systems for determining direction or deviation from predetermined direction using transducers spaced apart and measuring phase or time difference between signals therefrom, i.e. path-difference systems determining direction of source
    • 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
    • G01S3/00—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
    • 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
    • G01S3/14—Systems for determining direction or deviation from predetermined direction
    • G01S3/46—Systems for determining direction or deviation from predetermined direction using antennas spaced apart and measuring phase or time difference between signals therefrom, i.e. path-difference systems
    • 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
    • G01S3/00—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
    • G01S3/78—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 electromagnetic waves other than radio waves
    • G01S3/782—Systems for determining direction or deviation from predetermined direction

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  • Electromagnetism (AREA)
  • Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)

Abstract

The present invention relates to high-accuracy time delay estimation method between a kind of bilinear battle array, every line array in bilinear battle array is divided into multiple overlapped submatrixs by this method, after the angle measurement result of multiple target is obtained using bilinear battle array, angle obtains multiple wave beams and exported where all submatrixs are pointed into some target.These wave beams are exported with progress processing and builds new covariance matrix and time sweep vector, the output along time dimension is obtained, search peak responds to estimate the time delay between bilinear battle array.This method in order to improve bilinear battle array between time delay measurement accuracy, eliminate azimuth ambiguity of the line array in angle measurement.

Description

High-precision time delay estimation method between double linear arrays
Technical Field
The invention belongs to the field of array signal processing, and relates to a high-precision time delay estimation method between double linear arrays.
Background
The single linear array has the disadvantage of orientation ambiguity in performing goniometry (Van Trees H L. optimal orientation: part 4 of detection, and modulation the term. Hoboken: John Wiley & Sons Inc., 2002.). The double linear arrays can overcome the defect of the single linear array, and the target orientation can be judged by estimating the time delay between the double linear arrays (Lexus. preliminary analysis of the resolution performance of the targets on the left and right sides of the double linear arrays, acoustic report 2006, 31(5): 385-. However, in the prior art, when the double linear arrays are used to overcome the azimuth ambiguity in angle measurement, an interpolation method is used to estimate the time delay between the double linear arrays (Lihuan. a time delay estimation method for distinguishing port and starboard targets by using the double linear arrays and the realization thereof. Acoustics reports 2006; 31(6):485 and 487.). The interpolation method carries out numerical interpolation on the relevant output sequence output by the single linear array wave beam in the double linear array, and estimates the time delay value of the double linear array according to the peak value of the relevant output sequence after interpolation, the precision is difficult to satisfy, and the method is not ideal for eliminating the azimuth ambiguity.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: in order to improve the measurement precision of the time delay between the double linear arrays, the invention provides a method for estimating the high-precision time delay by utilizing sub-array processing. According to the method, each linear array in the double linear arrays is divided into a plurality of mutually overlapped sub-arrays. After the angle measurement result of the multiple targets is obtained by using the double linear arrays, all the sub-arrays point to the angle of a certain target to obtain multiple beam outputs. Processing the beam outputs to construct a new covariance matrix and a time scanning vector, obtaining outputs along a time dimension, and searching a peak response to estimate time delay between the double linear arrays.
The technical scheme of the invention is as follows: a high-precision time delay estimation method between double linear arrays comprises the following steps:
the method comprises the following steps: the method comprises the following substeps of measuring an angle of a target through a double-linear array, forming a beam and obtaining the output quantity of the beam:
the first substep: the double linear array is composed of a linear array 1 and a linear array 2. The linear array 1 and the linear array 2 are both M-element uniform linear arrays with array element spacing of d, and are parallel to each other and have a distance of d0(ii) a The double linear array receives signals transmitted by P (P is 1,2,3 … …) targets, and forms an angle on the double linear array; the double linear array carries out multi-target angle measurement to obtain multi-target angle measurement results and a spatial spectrum b (theta), wherein theta is a scanning angle and the value range is-180 degrees to 180 degrees; the peak response angle theta of the pth target on the spatial spectrump(P is 1,2,3 … P), at which time it is difficult to directly determine from the angle measurement results whether the target is port or starboard due to the influence of azimuth ambiguity;
and a second substep: dividing the linear array 1 and the linear array 2 into N mutually overlapped sub-arrays respectively, namely the two linear arrays have 2N sub-arrays in total; the array element of each subarray is M0(M0Less than or equal to M); within each M-element linear array, the number N of array elements of adjacent sub-arrays which are mutually overlapped0It can be expressed as:
wherein,representing the smallest integer number equal to or greater than the value therein, f being the centre frequency of the signal subband being processed, fDThe frequency is designed for the array corresponding to the array element spacing d, denoted fDC/(2d), where c is the signal propagation speed;
pointing 2N sub-arrays to corresponding peak response angles theta of P targets on a space spectrump(p ═ 1,2,3 … …) to perform beamforming, obtaining 2N beam output vectors; the beam output vector of the nth sub-array in the linear array 1 isThe beam output vector of the nth sub-array in the linear array 2 is
Step three: the method comprises the following substeps:
the first substep: according to the wave beam output vector in the step two, solving N cross-spectrum outputs of the two linear arrays, wherein the formula is
Wherein R isn(θp) The nth cross spectrum obtained by the linear array 1 and the linear array 2;
wherein]HThe method comprises the steps of calculating a conjugate transpose, wherein L represents the snapshot number of beam output;represents the first k (k ═ 1,2, …, N) of the N co-spectra.
And a second substep: constructing a covariance matrix R (theta) for the obtained N cross-spectral outputsp)
And a third substep: design a weight vector that varies in the time dimension, a (Δ t):
wherein, Δ t is time delay and its value range is Δ t ∈ [ -d ]0/c,d0/c](ii) a f is the center frequency of the signal subband being processed.
Step four: the R (theta) obtained in the third stepp) Substituting a (delta t) into a time delay estimation formula to obtain a p-th target (corresponding to theta on a space spectrum)p) And (4) corresponding double linear array time delay, judging whether the target is from a port or a starboard according to the time delay, and eliminating the azimuth ambiguity.
Effects of the invention
The invention has the technical effects that: the basic principle and the implementation scheme of the invention are verified by computer numerical simulation, and the result shows that: the method for processing the divided subarrays can accurately estimate the time delay between the double linear arrays and eliminate the orientation ambiguity of the linear arrays during angle measurement.
Drawings
FIG. 1 is a diagram of a coordinate system of a dual linear array during angle measurement;
FIG. 2 is a flow chart of the main steps in the present invention;
FIG. 3 is a flow chart of time delay estimation using a bi-linear array to divide a subarray according to the present invention;
FIG. 4 is a diagram illustrating the results of multi-target angle measurements for a dual linear array in an exemplary embodiment;
fig. 5 is a diagram of the delay estimation result obtained by the method of the present invention in the embodiment.
Detailed Description
The technical scheme of the invention is further explained by combining specific implementation examples.
The method comprises the steps of carrying out multi-target angle measurement by adopting double linear arrays (comprising a linear array 1 and a linear array 2 which are both M-element uniform linear arrays and are parallel to each other), dividing each linear array into N sub-arrays which are overlapped with each other, and obtaining 2 groups of 2N sub-arrays by 2 linear arrays. And obtaining a multi-target angle measurement result by using the double linear arrays, and pointing the 2 groups of sub-arrays to the angle measurement result corresponding to a certain target, wherein the 2 groups of sub-arrays are 2N in total, so as to obtain 2N wave beam output vectors. And (3) performing conjugate transpose on the nth (N is 1,2, …, N) sub-array beam output vector in the linear array 1, and multiplying the nth sub-array beam output vector in the linear array 2 by the conjugate transpose result to obtain the nth cross spectrum 2N sub-arrays so as to obtain N cross spectra in total.
The first k (k ═ 1,2, …, N) of the N co-spectra are multiplied, and the product result is divided by the conjugate of the 1 st co-spectrum, thus obtaining a total of N outputs. And constructing a covariance matrix by using the N outputs, and designing a weighting vector changing in a time dimension to obtain output responses on different time delay values. And searching a time delay value corresponding to the peak response to obtain the time delay value between the double linear arrays.
The angle measurement result obtained by using the method of the invention is provided through computer numerical simulation, thereby proving that the method of the invention can obtain a double linear array time delay difference estimation result with higher precision.
The technical scheme adopted by the invention for solving the existing problems can be divided into the following steps:
the method comprises the steps of carrying out multi-target angle measurement by adopting a double linear array (comprising a linear array 1 and a linear array 2 which are both M-element uniform linear arrays and are parallel to each other), and obtaining a multi-target angle measurement result by utilizing the double linear array, wherein port and starboard fuzziness exists in the angle measurement result. Each linear array is divided into N mutually overlapped sub-arrays, and 2 linear arrays can obtain 2 groups of 2N sub-arrays. When azimuth ambiguity of a certain target is eliminated, the 2 groups of subarrays are pointed to the angle of the target to form beams, and 2N beam outputs are obtained in total.
And (3) solving a conjugate transpose for the nth (N is 1,2, …, N) sub-array beam output vector in the linear array 1, and multiplying the nth sub-array beam output vector in the linear array 2 by the conjugate transpose to obtain the nth cross-spectrum output. The 2N subarrays obtain N cross-spectrum outputs. The first k (k ═ 1,2, …, N) of the N cross spectra are multiplied, and the product result is divided by the conjugate of the 1 st cross spectrum, thus obtaining N phase difference factors. And constructing a covariance matrix by using the N phase difference factors, and designing a weighting vector changing along with the delay value of the double linear arrays.
And (3) obtaining response outputs on different time delay values by using the covariance matrix and the weighting vector in the step 2). And searching the time delay value of the peak response to obtain the time delay difference of a certain target signal between the double linear arrays. And judging whether a certain target is from a port or a starboard according to the time delay difference so as to achieve the purpose of eliminating the azimuth ambiguity.
Each step of the present invention is described in detail below:
the relevant theory and details of step 1) are as follows:
and measuring angles by using a double linear array. Let the distance between the two linear arrays be d0Each linear array is an M-element Uniform Linear Array (ULA) with an array element spacing of d, as shown in fig. 1. The double linear arrays receive signals with certain bandwidth radiated by P targets in a far field, and the sampling signals on the double linear arrays are processed by adopting a molecular band processing method. In order to simplify the analysis, specific processing steps are given below by taking the sampling signal in a certain sub-band as an example. The processing of the signals on the other subbands may refer to the processing step for that subband.
And setting the space spectrum in the sub-band, and measuring the angle by using double ULAs to obtain a space spectrum b (theta), wherein the theta is a scanning angle and the value range is-180 degrees to 180 degrees. As shown in FIG. 1, with θpWhen the corresponding direction vector is coincident with the positive direction of the y axis, theta is 0 degree; when the direction vector corresponding to theta p is coincident with the negative direction of the y axis, theta is 180 degrees and-180 degrees; theta is 90 DEG when the direction vector corresponding to theta p is aligned with the positive direction of the x-axis, and theta is-90 DEG when the direction vector corresponding to theta p is aligned with the negative direction of the x-axis. In the spatial spectrum b (θ), the peak response corresponding to the P-th (P-1, 2, …, P) target is θ ═ θpTo (3). Due to the existence of port and starboard blur, the target can not be directly judged to be positioned at theta according to the spatial spectrum resultpIn terms of angle.
Respectively carrying out subarray division on the two M-element ULAs, wherein each ULA is divided into N mutually overlapped sub-ULAs, and the number of array elements of each sub-ULA is M0(M0Less than or equal to M). Within each M-element ULA, the number of array elements, N0, where adjacent sub-ULA coincide with each other, may be expressed as:
wherein,representing the smallest integer number equal to or greater than the value therein, f being the centre frequency of the signal subband being processed, fDC/(2d) is the array design frequency corresponding to the array element spacing d, and c is the signal propagation speed.
The two M-membered ULAs together divided 2N sub-ULAs. Pointing the 2N sub-ULAs to the corresponding peak response angle theta of the P targets on the spatial spectrump(P ═ 1,2, …, P) for beamforming, 2N sub-ULA result in 2N beam output vectors. For the 1 st ULA, the beam output complex vector of the nth (N ═ 1,2, …, N) th sub-ULA during this time isWhen discretized expression is used, it is a 1 × L-dimensional complex row vector, where L represents the fast beat number of the beam output, accordingly, the beam output complex vector of the nth sub-ULA in the 2 nd ULA isWhich is also a 1 × L-dimensional complex row vector.
The relevant theory and the concrete content of the step 2) are as follows:
outputting vector to the N (N is 1,2, …, N) th sub-array beam in the 1 st ULACalculating a conjugate transpose to obtainWherein]HRepresenting the conjugate transpose. Using beam output vectors of the n-th sub-ULA in the 2 nd ULAAndmultiplying to obtain the nth cross spectrum, Rn(θp) The expression is as follows:
the 2N beam outputs on the 2N sub-ULA are processed according to equation (2) to obtain N co-spectra in total. The first k (k ═ 1,2, …, N) of the N co-spectra are multiplied and the product is divided by the conjugate of the 1 st co-spectrum [ R ═ R1(θp)]*(wherein [, ]]*Representing conjugation) to yield the kth value, Xk(θp) The expression is as follows:
wherein,represents multiplying the first k values and represents taking the absolute value. The N cross spectra are processed according to equation (3) to obtain a total of N outputs.
Constructing a covariance matrix, R (θ), using the N outputs obtained in equation (3)p)：
Design a weight vector that varies in the time dimension, a (Δ t):
wherein, Δ t is time delay and its value range is Δ t ∈ [ -d ]0/c,d0/c]。
The relevant theory and details of step 3) are as follows:
and (3) obtaining estimation results under different time delays by using the covariance matrix and the weighting vector constructed in the step 2). If the time delay between the two linear arrays is estimated using conventional methods, the output in the time dimension, b (Δ t), can be expressed as:
b(Δt)＝[a(Δt)]HR(θp)a(Δt) (6)
if Capon beamforming is used to estimate the time delay between the two linear arrays, the output in the time dimension, b (Δ t), can be expressed as:
wherein, the [ alpha ], [ beta ]]-1Representing the inversion of the matrix.
If the time delay between the two linear arrays is estimated by the MUSIC method, since the beam output mainly includes the signal component of the pth target, the number of targets can be directly assumed to be 1, and the output in the time dimension, b (Δ t), can be expressed as:
wherein, Unoise(θp) Is to R (theta)p) The characteristic matrix formed by the characteristic vectors corresponding to the N-1 small characteristic values after decomposition is carried out, and the corresponding characteristic decomposition expression is as follows:
R(θp)＝U(θp)(θp)UH(θp) (9)
wherein U (theta)p) And (theta)p) Are respectively R (theta)p) The eigenvector matrix and the eigenvalue matrix.
According to the equations (6), (7) and (8), the double linear array time delay corresponding to the pth target (corresponding to θ p in the spatial spectrum) can be obtained. According to the time delay, whether a certain target is from a port or a starboard can be judged, and finally the aim of eliminating the azimuth ambiguity is achieved.
The flow of the main steps of the invention is shown in fig. 2, and the flow of the double linear array time delay estimation by using the sub-array is shown in fig. 3.
The embodiment of the invention is given by taking a typical underwater target angle measurement as an example.
The linear arrays in the double linear arrays are all 36-element ULAs, the array element spacing is d equal to 1.5 meters, and the spacing between the double linear arrays is d0 equal to 1.5 meters. The 2 targets were located at-60 ° and 150 °, respectively, and each radiated a broadband signal of 200Hz to 800 Hz. And measuring angles of the molecular bands, and extracting a sub-band (the bandwidth is 10Hz) with the center frequency of 500Hz to perform time delay estimation. Within the 500Hz sub-band, the power snr at each receiving element is set to 10 dB. Each 36-membered ULA was divided into 8 sub-ULA, and the sub-arrays were all 29-membered ULA.
The results of the angle measurements using the dual linear arrays are shown in fig. 4. although peak responses can be seen at-60 deg. and 30 deg., respectively, it is also possible for the targets to come from-120 deg. and 150 deg., respectively, due to the presence of spatial blurring.
The results of the delay estimation using the method of the present invention according to the flow of fig. 2 and fig. 3 are shown in fig. 4. When the subarray beam points at-60 degrees, the corresponding delay estimation result is shown in fig. 4, and at this time, the delay estimation results obtained by the conventional delay estimation method, the Capon delay estimation method and the MUSIC experiment estimation method are 0.4986 milliseconds, which is close to 0.5 millisecond of the true value. Because the estimated time delay value is a positive number, the signal can be judged to arrive at the linear array 1 first and then arrive at the linear array 2, and the target is known to be positioned at 60 degrees below zero. When the subarray beam is pointed at 30 °, the corresponding delay estimation results are shown in fig. 4. At the moment, the time delay estimation results obtained by the conventional time delay estimation method, the Capon time delay estimation method and the MUSIC experimental estimation method are all-0.8679 milliseconds, and are close to-0.8660 milliseconds of the true value. Since the estimated delay value is a negative number, it can be determined that the signal reaches the linear array 2 first and then reaches the linear array 1, and the target is known to be located at 150 °.
According to the implementation example, the method for dividing the double linear arrays and estimating the time delay can obtain the time delay estimation result which is closer to the true value, and the azimuth ambiguity during angle measurement can be eliminated according to the time delay estimation result.

Claims (1)

1. A high-precision time delay estimation method between double linear arrays is characterized by comprising the following steps:
the method comprises the following steps: the method comprises the following substeps of measuring an angle of a target through a double-linear array, forming a beam and obtaining the output quantity of the beam:
the first substep: the double linear arrays consist of linear arrays 1 and 2; the linear array 1 and the linear array 2 are both M-element uniform linear arrays with array element spacing of d, and are parallel to each other and have a distance of d0(ii) a The double linear array receives the signals transmitted by P targets and forms an angle on the double linear arrayDegrees, where P ═ 1,2,3 … …; the double linear array carries out multi-target angle measurement to obtain multi-target angle measurement results and a spatial spectrum b (theta), wherein theta is a scanning angle and the value range is-180 degrees to 180 degrees; the peak response angle theta of the pth target on the spatial spectrumpWhen P is 1,2,3 … P, it is difficult to directly determine whether the target is from port or starboard from the angle measurement result due to the influence of azimuth ambiguity;
and a second substep: dividing the linear array 1 and the linear array 2 into N mutually overlapped sub-arrays respectively, namely the two linear arrays have 2N sub-arrays in total; the array element of each subarray is M0And M is0Less than or equal to M; within each M-element linear array, the number N of array elements of adjacent sub-arrays which are mutually overlapped0It can be expressed as:
wherein,representing the smallest integer number equal to or greater than the value therein, f being the centre frequency of the signal subband being processed, fDThe frequency is designed for the array corresponding to the array element spacing d, denoted fDC/(2d), where c is the signal propagation speed;
pointing 2N sub-arrays to corresponding peak response angles theta of P targets on a space spectrumpPerforming beamforming to obtain 2N beam output vectors, where p is 1,2,3 … …; the beam output vector of the nth sub-array in the linear array 1 isThe beam output vector of the nth sub-array in the linear array 2 is
Step three: the method comprises the following substeps:
the first substep: according to the wave beam output vector in the step two, solving N cross-spectrum outputs of the two linear arrays, wherein the formula is
<mrow> <msub> <mi>X</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mo>&amp;lsqb;</mo> <munderover> <mi>&amp;Pi;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>k</mi> </munderover> <msub> <mi>R</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>/</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mo>*</mo> </msup> </mrow> <mrow> <mo>&amp;lsqb;</mo> <munderover> <mi>&amp;Pi;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>k</mi> </munderover> <mo>|</mo> <msub> <mi>R</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>|</mo> <mo>&amp;rsqb;</mo> <mo>/</mo> <mo>|</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>|</mo> </mrow> </mfrac> </mrow>
Wherein R isn(θp) The nth cross spectrum obtained by the linear array 1 and the linear array 2;
<mrow> <msub> <mi>R</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>b</mi> <mi>n</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <msup> <mrow> <mo>&amp;lsqb;</mo> <msubsup> <mi>b</mi> <mi>n</mi> <mn>1</mn> </msubsup> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>H</mi> </msup> <mo>/</mo> <mi>L</mi> </mrow>
wherein]HThe method comprises the steps of calculating a conjugate transpose, wherein L represents the snapshot number of beam output;represents the first k cross-products of N co-spectra, where k is 1,2, …, N;
and a second substep: constructing a covariance matrix R (theta) for the obtained N cross-spectral outputsp)
<mrow> <mi>R</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>X</mi> <mn>1</mn> </msub> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>p</mi> </msub> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>X</mi> <mi>k</mi> </msub> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>p</mi> </msub> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>X</mi> <mi>N</mi> </msub> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>p</mi> </msub> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>X</mi> <mn>1</mn> </msub> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>p</mi> </msub> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>X</mi> <mi>k</mi> </msub> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>p</mi> </msub> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>X</mi> <mi>N</mi> </msub> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>p</mi> </msub> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced> <mi>H</mi> </msup> </mrow>
And a third substep: design a weight vector that varies in the time dimension, a (Δ t):
<mrow> <mi>a</mi> <mrow> <mo>(</mo> <mi>&amp;Delta;</mi> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mi>j</mi> <mn>2</mn> <mi>&amp;pi;</mi> <mi>f</mi> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mi>&amp;Delta;</mi> <mi>t</mi> <mo>)</mo> </mrow> </mrow>
wherein, Δ t is time delay and its value range is Δ t ∈ [ -d ]0/c,d0/c](ii) a f is the center frequency of the signal subband being processed;
step four: the R (theta) obtained in the third stepp) Substituting a (delta t) into a time delay estimation formula to obtain a p-th target corresponding to theta on a space spectrumpCorresponding double linear array time delay, according to whichAnd judging whether the target is from a port or a starboard, and eliminating the azimuth ambiguity.
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