CN110109077A - MIMO radar based on time reversal is concerned with angle estimating method - Google Patents

MIMO radar based on time reversal is concerned with angle estimating method Download PDF

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CN110109077A
CN110109077A CN201910341673.6A CN201910341673A CN110109077A CN 110109077 A CN110109077 A CN 110109077A CN 201910341673 A CN201910341673 A CN 201910341673A CN 110109077 A CN110109077 A CN 110109077A
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CN110109077B (en
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张娟
樊宏宝
王晨红
张林让
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Xidian 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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/418—Theoretical aspects

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  • Computer Networks & Wireless Communication (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Noise Elimination (AREA)

Abstract

The invention discloses a kind of relevant angle estimating methods of MIMO radar based on time reversal, and mainly solving the problems, such as the prior art, radar is low to target angle Parameter Estimation Precision in a multi-path environment.Its scheme is: obtaining radar echo signal；Inverted signal when being obtained to echo-signal progress energy normalized and time reversal；Back echo data when inverted signal obtains when repeating transmission；Clock synchronization back echo data carry out space smoothing decorrelation LMS, before obtaining to it is smooth revised when anti-covariance matrixAccording to when anti-covariance matrixTarget angle is estimated using multiple signal classification MUSIC method.Echo data is carried out energy normalized and time reversal and re-emitted by the present invention, by when inverted signal energy accumulation is formed at target, back echo signal-to-noise ratio when improving, and utilize MIMO radar system, the virtual aperture of array is increased, so that angular resolution is higher, angle measurement accuracy is higher, and cost is relatively low, the target angle estimation that can be used under the multi-path environment of low latitude.

Description

MIMO radar based on time reversal is concerned with angle estimating method
Technical field
The invention belongs to Radar Technology field, in particular to a kind of MIMO radar angle estimating method can be used for low latitude The angle measurement of target under multi-path environment.
Background technique
Radar when carrying out angle measurement to low target, will receive the shadow of multipath effect in sea low-altitude detection environment It rings, i.e., the echo that radar receives includes the direct-path signal from target and the multipath signal from reflective surface.Multipath Effect causes echo signal amplitude to be decayed, and reduces echo-signal signal-to-noise ratio, and multipath signal and the direct-path signal of target away from Delocalization and angle domain are very close, each other strong coherent signal, this brings serious influence to the angle estimation of low target, causes The accuracy decline of target angle estimated result even can not accurately measure the real angle of target when serious.
In order to improve angle measurement accuracy, weaken the influence that multipath effect estimates radar angular, existing method is mainly from airspace Accurate angle estimation is realized by multipaths restraint in terms of time domain two.In terms of airspace, by designing reasonable aerial position, So that multipath signal cannot be introduced into radar receiving antenna, although can inhibit the influence of multipath effect, nothing to a certain extent Method is suitable for all situations, and cost of implementation is higher, and flexibility is poor.In terms of time domain, mainly improved using narrow the relevant technologies The hardware configuration of radar receiver inhibits the influence of multipath effect, but this can introduce evaluated error again.
Summary of the invention
It is an object of the invention to be directed to the deficiency of the above method, propose that a kind of MIMO radar based on time reversal is relevant Angle estimating method increases the virtual aperture of array, to change to efficiently use the signal-to-noise ratio that multi-path information improves echo-signal Kind radar angle measurement performance.
To achieve the above object, technical solution of the present invention includes the following:
(1) radar generates transmitting signal s (t) and is emitted in environment, obtains the received echo-signal s of radar arrayr (t)；
(2) by the received echo-signal s of radar arrayr(t) it carries out energy normalized and carries out time reversal processing, obtain Radar when counter emit signal
(3) by when counter emit signalIt is re-emitted into environment, makesDay is propagated to after target scattering Linear array, obtain radar array it is received when back echo signal be
(4) back echo signal when received to radar arrayCarry out matched filtering, the letter after obtaining matched filtering NumberAccording to the signal after matched filteringObtain the Virtual array number M of array；
(5) the MUSIC angle estimation of space smoothing decorrelation LMS is carried out to target:
Interlaced different submatrixs 5a) are partitioned the array into, the array number of each submatrix is m, according to the void of array The submatrix number that quasi- array number M and the array number m of submatrix are divided: L=M-m+1；
Back echo signal when 5b) received according to each submatrix, find out each submatrix it is received when back echo signal data assist Variance matrix, and averaging to these covariance matrixes, before obtaining to it is smooth revised when anti-covariance matrix
5c) according to it is preceding to it is smooth revised when anti-covariance matrixUsing multiple signal classification MUSIC algorithm, estimate Count out target angle.
Compared with prior art, the present invention having the advantage that
One, robustness is stronger.
To weaken influence of the multipath effect to angle measurement, conventional method takes the method for inhibiting multipath effect, detects at low angle In environment, multi-path information complexity increases, therefore the inhibitory effect of multipath signal can degenerate, so as to cause entire angle measuring system Echo-signal is carried out time reversal and resend in environment by the deterioration of performance, the present invention, is effectively utilized multipath signal, Inverted signal generates adaptive focusing effect to channel when being made by time reversal, and this adaptive operation enhances the steady of model Property, to improve the robustness of angle estimation result.
Two, angle measurement performance is higher.
In a multi-path environment, it is influenced by noise, if signal-to-noise ratio is too low, target detection performance decline is believed by multipath The influence of number coherence, traditional angle-measuring method effect can seriously degenerate and even fail, and the present invention realizes MIMO radar system With effective combination of time reversal technology, the virtual aperture of array is increased, by carrying out time reversal to echo-signal, is utilized The signal-to-noise ratio of back echo signal when the energy of multipath signal increases, then clock synchronization back echo signal carry out space smoothing amendment and MUSIC angle estimation, available higher angular resolution and lower angle error, possess better angle measurement performance.
Detailed description of the invention
Fig. 1 is implementation flow chart of the invention；
Fig. 2 is to carry out the wave of angle estimation using two kinds of conventional methods and the method for the present invention respectively under no multipath conditions Up to direction DOA estimated result figure；
Fig. 3 is to carry out the wave of angle estimation using two kinds of conventional methods and the method for the present invention respectively under 1 multipath conditions Up to direction DOA estimated result figure；
Fig. 4 is to carry out the wave of angle estimation using two kinds of conventional methods and the method for the present invention respectively under 2 multipath conditions Up to direction DOA estimated result figure；
Fig. 5 is to carry out the wave of angle estimation using two kinds of conventional methods and the method for the present invention respectively under 3 multipath conditions Up to direction DOA estimated result figure；
Fig. 6 is to carry out angle estimation under no multipath conditions using two kinds of conventional methods and the method for the present invention respectively and obtain Angle measurement mean square error curve graph；
Fig. 7 is to carry out angle estimation under 1 multipath conditions using two kinds of conventional methods and the method for the present invention respectively and obtain Angle measurement mean square error curve graph；
Fig. 8 is to carry out angle estimation under 2 multipath conditions using two kinds of conventional methods and the method for the present invention respectively and obtain Angle measurement mean square error curve graph；
Fig. 9 is to carry out angle estimation under 3 multipath conditions using two kinds of conventional methods and the method for the present invention respectively and obtain Angle measurement mean square error curve graph.
Specific embodiment
With reference to the accompanying drawing, the embodiment of the present invention and effect are described in further detail:
It is referring to Fig.1, of the invention that the specific implementation steps are as follows:
Step 1: radar generates transmitting signal s (t) and is emitted in environment, obtains the received echo-signal s of radar arrayr (t)。
It sets MIMO radar aerial array 1a) as even linear array, includes N number of array element, the transmitting signal that radar generates are as follows: s (t) =[s1(t),s2(t)…,sN(t)]T, wherein s1(t), s2(t)…sN(t) it indicates the signal that each array element generates, emits signal Meet s (t) sH(t)=IN, []HIndicate conjugate transposition, INIndicate N-dimensional unit matrix；
1b) transmitting signal s (t) is propagated at target by medium, the composite signal s at targettarget(t) are as follows:
Wherein, P indicates that signal s (t) propagates to the multipath transmisstion total number of target, X by mediumlIndicate l paths Synthesis path decay factor, sn(t) indicate that the transmitting signal of n-th of array element, τ (n, l) indicate the transmitting signal of n-th of array element Pass through the transmission time delay difference that l paths are propagated, τ relative to first array element transmitting signallIndicate signal along l paths Propagation delay；
1c) the composite signal s at targettarget(t) aerial array is propagated to again by target scattering, in the aerial array The received echo-signal of h-th of array elementAre as follows:
Wherein, τ (h, l) indicates that h-th of array element is believed relative to the reception of its first array element along l paths, array Number transmission time delay difference, nh(t) the reception noise of h-th of array element is indicated；
The reception signal of N number of array element in array 1d) is lined up into vector, obtains the echo-signal s of antenna array receiverr (t):
Wherein, []TIndicate transposition；
1e) by the echo-signal s of above-mentioned antenna array receiverr(t) be written as follow matrix form:
sr(t)=A (θ) X Γ (t) Γ (t)TXA(θ)Ts(t)+N(t)
Wherein, A (θ) indicates the direction matrix of aerial array；X indicates that synthesis path decay factor matrix, the matrix include P The synthesis path decay factor of multipath signal, P >=0；Γ (t) indicates that propagation delay time matrix, the matrix include P multipath signal Propagation delay time；N (t) is to receive noise matrix.
Step 2: echo-signal is subjected to energy normalized and carries out time reversal processing, it is anti-when obtaining to emit signal.
2a) according to transmitting signal s (t) and echo-signal sr(t), energy normalized factor K is calculated:
Wherein, K is positive number；
2b) to echo sr(t) energy normalized and time reversal are carried out, it is anti-when obtaining to emit signal
Wherein []*For conjugate operation.
Step 3: by when counter emit signalIt is re-emitted into environment, back echo signal is when obtaining
3a) by when counter emit signalIt is propagated at target by medium, the composite signal s at targetTRtarget (t) are as follows:
Wherein, N indicates that transmitting element number of array, P indicate signalThe multipath transmisstion for propagating to target by medium is total Item number, XlIndicate the synthesis path decay factor of l paths,Indicate n-th of array element when it is counter emit signal, τ (n, L) indicate n-th array element when anti-anti- when emitting signal relative to first array element emit what signal was propagated by l paths Transmission time delay difference, τlIndicate signal along the propagation delay of l paths；
3b) the composite signal s at targetTRtarget(t) aerial array is propagated to by target scattering, h-th gust in array Back echo signal is denoted as when member is receivedIts expression formula are as follows:
Wherein, τ (h, l) is indicated along l paths, biography of h-th of the array element relative to the reception signal of its first array element Defeated delay inequality, wh(t) the reception noise of h-th of array element is indicated；
3c) the when reversal connection of N number of array element in aerial array is collected mail and number lines up vector, obtain antenna array receiver when it is anti- Echo-signal
Wherein []TIndicate transposition；
Back echo signal when 3d) will be above-mentionedBe written as follow matrix form are as follows:
Wherein, K indicates the energy normalized factor, and A (θ) indicates the direction matrix of aerial array；X indicates synthesis path decaying Factor matrix, the matrix include the synthesis path decay factor of P multipath, P >=0；Γ (t) indicates propagation delay time matrix, the square Battle array includes the propagation delay time of P multipath；W (t) is to receive noise matrix, []*For conjugate operation, []HIndicate conjugate transposition.
Step 4: back echo signal when received to radar arrayMatched filtering is carried out, after obtaining matched filtering Signal
The turning operation in time domain 4a) is carried out to the transmitting signal s (t) of aerial array and obtains sT(-t)；
4b) by when back echo signalWith sT(- t) carries out matched filtering, the signal after obtaining matched filtering
Wherein, K indicates the energy normalized factor, and A (θ) indicates that the direction matrix of aerial array, X indicate synthesis path decaying Factor matrix, the matrix include the synthesis path decay factor of P multipath, P >=0；Γ (t) indicates propagation delay time matrix, the square Battle array includes the propagation delay time of P multipath；Indicate Kronecker product, C (θ)=[c (θ1),c(θ2),…c(θP)] indicate array Virtual direction matrix,Indicate the virtual steering vector of kth multipath signal, a (θk) indicate kth multipath signal practical steering vector, θ1,θ2,…θPIndicate the angle of arrival of P multipath signal, c (θk) in Unequal element number is equal to the Virtual array number M of MIMO radar.
Step 5: space smoothing decorrelation LMS is carried out to target, before asking to it is smooth revised when anti-covariance matrix
5a) by antenna array partition at interlaced different submatrixs, the array number of each submatrix is m, according to array Virtual array number M and submatrix the submatrix number that is divided of array number m: it is received to acquire L submatrix respectively by L=M-m+1 When back echo signal, wherein back echo signal x when i-th of submatrix is receivedi(t) are as follows:
Wherein,Indicate that back echo signal when i-th of array element is received in array, B (θ) indicate first submatrix Direction matrix；λ is the wavelength for emitting signal, and P indicates multipath letter Number amount, θ1,θ2,…θPIndicate that P multipath signal reaches the angle of arrival of array；X indicates synthesis path decay factor matrix, The matrix includes the synthesis path decay factor of P multipath signal；Γ (t) indicates that propagation delay time matrix, the matrix include that P item is more The propagation delay time of diameter signal；W (t) is to receive noise matrix,Indicate i-th of submatrix when it is counter emit signal, L is submatrix Number；
5b) acquire respectively L submatrix it is received when back echo signal data covariance matrix, wherein i-th of submatrix connects Receipts when back echo signal data covariance matrix are as follows:
Ri=xi(t)xi(t)H, i=1,2 ... L
The mean value of the data covariance matrix of back echo signal when 5c) L submatrix of calculating is received, obtains flat by space Anti- covariance matrix when sliding revised
Step 6: using it is preceding to it is smooth revised when anti-covariance matrixCarry out target angle estimation.
Carrying out angle estimation to target in the prior art has multiple signal classification MUSIC algorithm, invariable rotary subspace ESPRIT algorithm and a variety of methods of maximum likelihood ML algorithm, this step sample multiple signal classification MUSIC algorithm and carry out target angle Degree estimation, the specific steps of which are as follows:
6a) the anti-covariance matrix of clock synchronizationFeature decomposition is carried out, P big characteristic value and m-P small characteristic values is obtained, uses P The corresponding characteristic vector of a big characteristic value constitutes signal subspaceIt is made an uproar with the corresponding characteristic vector composition of m-P small characteristic value Phonon spaceWherein P indicates multipath signal quantity, and m indicates the transmitting array number of submatrix；
6b) use search vector a (θ) to noise subspaceIt projects, projection result are as follows:
Wherein PnIndicate that projection matrix, θ are search angle, viIt is worth corresponding characteristic vector for ith feature；
6c) according to 6b) in projection relation, obtain spatial spectrum STRmusic(θ):
Wherein, | | | | expression asks norm to operate；
6d) according to spatial spectrum STRmusic(θ) estimates target angle
Complete the relevant angle estimation of the MIMO radar based on time reversal.
Effect of the invention can further be verified by following emulation experiment.
1. experiment scene
The mutually orthogonal chirp pulse signal of radar emission, signal center frequency 4GHz, antenna height 50m, Object height is 60m, and target range 1km, element number of array 16, submatrix element number of array is 8, and multipath signal number is respectively 0 Item, 1,2,3, it is as shown in table 1 that multipath signal corresponds to parameter.
1 multipath signal of table corresponds to parameter
2. experiment content and analysis of experimental results
Experiment 1, under no multipath conditions, uses the smooth Conv-SSMUSIC algorithm of Traditional Space, MIMO radar space Smooth MIMO-SSMUSIC algorithm and the method for the present invention carry out angle estimation, obtained direction of arrival DOA estimated result, such as Fig. 2 It is shown.
Experiment 2, it is flat using the smooth Conv-SSMUSIC algorithm of Traditional Space, MIMO radar space under 1 multipath conditions Sliding MIMO-SSMUSIC algorithm and the method for the present invention carry out angle estimation, obtained direction of arrival DOA estimated result, such as Fig. 3 institute Show.
Experiment 3, it is flat using the smooth Conv-SSMUSIC algorithm of Traditional Space, MIMO radar space under 2 multipath conditions Sliding MIMO-SSMUSIC algorithm and the method for the present invention carry out angle estimation, obtained direction of arrival DOA estimated result, such as Fig. 4 institute Show；
Experiment 4, it is flat using the smooth Conv-SSMUSIC algorithm of Traditional Space, MIMO radar space under 3 multipath conditions Sliding MIMO-SSMUSIC algorithm and the method for the present invention carry out angle estimation, obtained direction of arrival DOA estimated result, such as Fig. 5 institute Show.
It can be seen that from Fig. 2, Fig. 3, Fig. 4, Fig. 5 in identical array number and SNR, in no multipath, more than 1 Diameter, 2 multipaths, the method for the present invention all has more sharp compared to the spatial spectrum of other two methods in the case where 3 multipaths Spectral peak illustrates that the method for the present invention has higher angular resolution compared to other two methods.
Experiment 5, under no multipath conditions, uses the smooth Conv-SSMUSIC algorithm of Traditional Space, MIMO radar space Smooth MIMO-SSMUSIC algorithm and the method for the present invention carry out angle estimation, obtained angle measurement mean square error curve, such as Fig. 6 institute Show.
Experiment 6, it is flat using the smooth Conv-SSMUSIC algorithm of Traditional Space, MIMO radar space under 1 multipath conditions Sliding MIMO-SSMUSIC algorithm and the method for the present invention progress angle estimation, obtained angle measurement mean square error curve, as shown in Figure 7.
Experiment 7, it is flat using the smooth Conv-SSMUSIC algorithm of Traditional Space, MIMO radar space under 2 multipath conditions Sliding MIMO-SSMUSIC algorithm and the method for the present invention progress angle estimation, obtained angle measurement mean square error curve, as shown in Figure 8.
Experiment 8, it is flat using the smooth Conv-SSMUSIC algorithm of Traditional Space, MIMO radar space under 3 multipath conditions Sliding MIMO-SSMUSIC algorithm and the method for the present invention progress angle estimation, obtained angle measurement mean square error curve, as shown in Figure 9.
The case where can be seen that from Fig. 6, Fig. 7, Fig. 8, Fig. 9 in no multipath, 1 multipath, 2 multipaths, 3 multipaths Under, when SNR is lower, the method for the present invention has minimum root-mean-square error compared to other both of which, illustrates the present invention With lower angle error and higher angle measurement performance.

Claims (7)

  1. The angle estimating method 1. a kind of MIMO radar based on time reversal is concerned with, which is characterized in that include the following:
    (1) radar generates transmitting signal s (t) and is emitted in environment, obtains the received echo-signal s of radar arrayr(t)；
    (2) by the received echo-signal s of radar arrayr(t) it carries out energy normalized and carries out time reversal processing, obtain radar When counter emit signal
    (3) by when counter emit signalIt is re-emitted into environment, makesAntenna array is propagated to after target scattering Column, obtain radar array it is received when back echo signal be
    (4) back echo signal when received to radar arrayCarry out matched filtering, the signal after obtaining matched filteringAccording to the signal after matched filteringObtain the Virtual array number M of array；
    (5) the MUSIC angle estimation of space smoothing decorrelation LMS is carried out to target:
    Interlaced different submatrixs 5a) are partitioned the array into, the array number of each submatrix is m, according to the virtual array of array The submatrix number that first number M and the array number m of submatrix are divided: L=M-m+1；
    Back echo signal when 5b) received according to each submatrix, find out each submatrix it is received when back echo signal data covariance Matrix, and averaging to these covariance matrixes, before obtaining to it is smooth revised when anti-covariance matrix
    5c) according to it is preceding to it is smooth revised when anti-covariance matrixUsing multiple signal classification MUSIC algorithm, estimate Target angle.
  2. 2. the method according to claim 1, wherein the received echo-signal s of radar array in (1)r(t), table Up to formula are as follows:
    sr(t)=A (θ) X Γ (t) Γ (t)TXA(θ)TS (t)+N (t),
    Wherein, A (θ) indicates the direction matrix of array；X indicates synthesis path decay factor matrix, and it includes the synthesis of P multipath The path attenuation factor, P >=0；Γ (t) indicates propagation delay time matrix, and it includes the propagation delay time of P multipath, N (t) is to receive to make an uproar Sound matrix.
  3. 3. the method according to claim 1, wherein by radar echo signal s in (2)r(t) energy normalizing is carried out Change and carry out time reversal processing, realizes that steps are as follows:
    2a) according to transmitting signal s (t) and echo-signal sr(t) energy normalized factor K is calculated:
    Wherein, K is positive number；
    It is anti-when being obtained by following formula to emit signal 2b) according to energy normalized factor K pair
    Wherein []*For conjugate operation.
  4. 4. the method according to claim 1, wherein the when back echo signal in (3)Its expression formula are as follows:
    Wherein, K indicates the energy normalized factor, and A (θ) indicates the direction matrix of array；X indicates synthesis path decay factor square Battle array, it includes the synthesis path decay factor of P multipath, P >=0；Γ (t) indicates propagation delay time matrix, the biography comprising P multipath Defeated time delay；W (t) is to receive noise matrix, []TIndicate transposition operation, []*For conjugate operation, []HIndicate conjugate transposition.
  5. 5. the method according to claim 1, wherein the signal after matched filtering obtained in (4)Its Expression formula are as follows:
    Wherein, K indicates the energy normalized factor, and A (θ) indicates that the direction matrix of array, X indicate synthesis path decay factor square Battle array, the synthesis path decay factor comprising P multipath, P >=0；Γ (t) indicates propagation delay time matrix, the transmission comprising P multipath Time delay；Indicate Kronecker product, C (θ)=[c (θ1),c(θ2),…c(θP)] indicate array virtual direction matrix,Indicate the virtual steering vector of kth multipath signal, a (θk) indicate kth item The practical steering vector of multipath signal, θ1,θ2,…θPIndicate the angle of arrival of P multipath signal, []*For conjugate operation, [·]TIndicate transposition, c (θk) in unequal element number be equal to MIMO radar Virtual array number M.
  6. 6. the method according to claim 1, wherein the 5b) realize that steps are as follows:
    Back echo signal x when 5b1 is received by i-th of submatrixi(t) are as follows:
    Wherein,Indicate that back echo signal when i-th of array element is received in array, B (θ) indicate the direction of first submatrix Matrix；λ is the wavelength for emitting signal, and P indicates multipath signal number Amount, θ1,θ2,…θPIndicate that P multipath signal reaches the angle of arrival of array；X indicates synthesis path decay factor matrix, packet Synthesis path decay factor containing P multipath signal；Γ (t) indicates propagation delay time matrix, and it includes the transmission of P multipath signal Time delay；W (t) is to receive noise matrix, []*For conjugate operation, []TIndicate transposition,Indicate i-th of submatrix when Anti- transmitting signal, L are submatrix number；
    5b2) acquire respectively L submatrix it is received when back echo signal data covariance matrix, wherein i-th of submatrix is received When back echo signal data covariance matrix are as follows:
    Ri=xi(t)xi(t)H, i=1,2 ... L；
    The mean value of the data covariance matrix of back echo signal, is spatially smoothed when 5b3) L submatrix of calculating is received Anti- covariance matrix when revised
  7. 7. the method according to claim 1, wherein 5c) it is middle using multiple signal classification MUSIC algorithm, estimate Target angle out realizes that steps are as follows:
    5c1) the anti-covariance matrix of clock synchronizationFeature decomposition is carried out, P big characteristic value and m-P small characteristic values are obtained, with P The corresponding characteristic vector of characteristic value greatly constitutes signal subspaceNoise is constituted with the corresponding characteristic vector of m-P small characteristic value SubspaceWherein P indicates multipath signal quantity, and m indicates the transmitting array number of submatrix；
    5c2) use search vector a (θ) to noise subspaceIt projects, projection result are as follows:
    Wherein PnIndicate that projection matrix, θ are search angle, viIt is worth corresponding characteristic vector, [] for ith featureHIndicate conjugation Transposition；
    5c3) according to 5c2) in projection result, obtain spatial spectrum STRmusic(θ):
    Wherein, | | | | expression asks norm to operate；
    5c4) according to spatial spectrum STRmusic(θ) estimates target angle
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CN110596686A (en) * 2019-09-04 2019-12-20 电子科技大学 Frequency control array time focusing method based on time reversal technology
CN111693947A (en) * 2020-07-06 2020-09-22 羿升(深圳)电子装备有限公司 Improved MUSIC method based on co-prime array DOA estimation
CN112083423A (en) * 2020-09-16 2020-12-15 哈尔滨工程大学 Multi-base sound source high-precision positioning method

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