CN108845325A - Towed linear-array sonar submatrix error misfits estimation method - Google Patents
Towed linear-array sonar submatrix error misfits estimation method Download PDFInfo
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- 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
- G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
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Abstract
A kind of towed linear-array sonar submatrix error misfits estimation method disclosed by the invention, position error can be reduced by providing one kind, and can obtain accurate azimuth estimation value, the estimation method of more high angular resolution, the technical scheme is that：In array manifold matrix model, by the true full linear combination that array manifold matrix is expressed as the displacement error amount of each submatrix and each submatrix margin of error contributes full array manifold matrix；Location error between submatrix is introduced into direction finding model, data fusion model is established with bayes rule between containing the full Array Model for being displaced mismatch submatrix, submatrix position error vector and target true bearing are carried out while being solved, estimate submatrix displacement error and direction of arrival how soon clapped the likelihood function of observation simultaneously using bayesian algorithm according to the collected data of merge sensor node；The azimuth estimation value and displacement error estimated value that root-mean-square error changes with signal-to-noise ratio are obtained with posteriority function.
Description
Technical field
The present invention relates to a kind of hydrophone are embedded on cable to form linear array, is dragged after stern in water by trailing cable
Detect the sonar of target.There are submatrix displacement error feelings when more particularly to a kind of sonar towing line array progress passive synthetic aperture
Under condition, while to submatrix bit array shift error and Wave arrival direction estimating method.
Background technique
Towed sonar (towed sonar) is that sidelong glance target sound is visited in transducer array towing after carrying platform tail in water
It receives.Dragging line battle array sonar transducer array is flexible.Since ship manoeuvre and ocean current influence and itself shake resonance during towing,
Its formation is difficult to keep stable, and formation distortion will be so that dragging line battle array sonar be difficult to reach theoretical performance, and this problem is especially being adopted
It is even more serious in the modern times such as Estimation of Spatial Spectrum battle array processing method with Adaptive Signal Processing.Because conventional battle array processing method is only right
Array element energy adds up, and modern battle array processing method is also to array element signal correlation, signal covariance matrix characteristic value etc. into
Row calculates, more stringent to formation stabilization although modern battle array processing method can greatly improve precision and target resolution capability.
In addition, dragging line battle array does not have vertical aperture, underwater surface target cannot distinguish between, a large amount of mesh at the intensive sea area of shipping or cooperative combat
Mark generates severe jamming to its performance, and can generate is target " babysbreath " phenomenon everywhere.Low frequency active starboard ambiguity of towed linear array sonar
It is the current detection most effective means of quiet submarine.Since starboard ambiguity of towed linear array sonar basic matrix is far from this warship, and it is flexible battle array, visits
There are large errors in the orientation of survey.Modern towed linear-array sonar system is gradually intended to work in low-frequency range, and detection range is not
It is disconnected to improve, develop towards higher operating distance and detection accuracy.Under such environment, to obtain preferable spatial discrimination energy
Power is needed using the biggish array in aperture, this in practice, generally mean that bigger system complexity and higher equipment at
This.In the case where not changing towed array parameter, passive synthetic aperture (PSA) is carried out using towing line array, has been increased
A possibility that imitating aperture.PSA technology is motion information, the position using signal time and correlation and array spatially
Information constructs the array containing multiple virtual submatrixs to obtain higher azimuth resolution.Currently, common line of motion
Battle array PSA method has：Yen, Carey passive synthetic aperture method, the passive synthetic aperture based on Fast Fourier Transform, and
Extend towed array measurement method etc..Although the PSA with multiple virtual submatrixs has been widely applied to sonar wave beams shape
At and wave up to fields such as orientation (DOA) estimations, but target numbers are more and target naval vessel and this warship kinematic parameter with
In the case that full-scale condition is inconsistent, performance can sharply decline.Specifically, when only existing single goal, PSA method can be opposite
Working under error condition occurs in speed, and true phase correction factor is directly obtained from data, and synthesis element position is not overlapped
When, it still can accurately carry out DOA estimation；But in multiple target, if relative velocity is error free, PSA method can work, if relatively
There are errors for speed, then DOA at this time as a result, can even be worse than the DOA of single gust of conventional beamformer as a result, array extension not only
Benefit is not brought, increases position error instead.In addition to this, there are also the estimated accuracies that other factors influence DOA, such as battle array
Differential seat angle, the coherence of signal between first spacing (usually taking the half of operation wavelength), target incoming wave etc..In the base of PSA
On plinth, usually estimated using the accurate angle of the available target of high resolution DOA method.Many High Resolution Methods, such as more letters
Number classification MUSIC (Multiple Signal Classification) multiple signal classification method, invariable rotary subspace side
Method, evacuated space Power estimation etc. can be accurately known in array parameter situation, improve the spatial resolution of array.MUSIC is calculated
Method is a kind of method based on matrix character spatial decomposition, is said from geometric angle, from geometric angle, the observation space of signal processing
It is orthogonal signal subspace and noise subspace that two spaces, which can be decomposed into,.MUSIC algorithm utilizes the two complementary spaces
Between orthogonal property come the orientation of estimation space signal.Institute's directed quantity of noise subspace is used to construction spectrum, all spaces
For peak position in azimuth spectrum to the incoming wave orientation of induction signal, basic thought is the covariance square to General Cell output data
Battle array carries out feature decomposition, to obtain signal subspace corresponding with Modulation recognition and the noise mutually orthogonal with signal component.
MUSIC algorithm process task is to try to estimate the number D for the spacing wave for being incident on array and the intensity in spacing wave source
And its arrival bearing.In actual treatment, the data that the array output data complex vector Y observed is obtained are in finite time section
Finite number of time sample, also referred to as snap or take the photograph fastly, but it is incoherent that prototype MUSIC algorithm, which requires incoming wave signal,.With
MUSIC be representative algorithm there are a disadvantages, i.e., to the undesirable of coherent signal processing.In the system for being directed to coherent signal source
In column processing scheme, more classical is Search Space Smoothing, as space smoothing (SS) and modified space smoothing (MSS) are calculated
Method.However, Search Space Smoothing is and to be only applicable to equidistant even linear array to lose array effective aperture as cost
(ULA).When there are array element error, it is assumed that Clutter Model and the practical data that receive mismatch, in the feelings of model parameter mismatch
Under condition, the echo signal for originally belonging to signal subspace can be divided into noise subspace by mistake, destroy MUSIC algorithm target
The orthogonality of function, cause positioning failure and.Similarly, remaining all kinds of high resolution DOA algorithm is also very quick to the error of array manifold
Sense, and when low signal-to-noise ratio, few number of snapshots, the relevant situation of sound source occur, the performance of high resolution algorithm will greatly degenerate.Due to
Reconstruct clutter covariance matrix depend on Clutter Model accuracy, if it is assumed that Clutter Model and actual data mismatch
When, it will lead to algorithm performance decline and even fail.Therefore in towing line array PSA application, array element error, signal coherence, battle array
First mutual coupling, Channel Mismatch etc. can be such that ideal model no longer sets up.It is how more effectively actual to estimate using data are received
True array prevalence vector, and accurate orientation estimation is carried out, become a highly important project.
Currently, having been carried out a series of exploration in such issues that solve both at home and abroad.These documents are according to each self-application
Actual error source present in field, never ipsilateral is corrected array error.Such as Weiss and Friedlander
A kind of method based on maximal possibility estimation array self-correcting is proposed, this method divides target bearing and displacement amount of mismatch
Block alternative optimization iteration.Since such method is modeled to all array elements, it is being applied to Long baselines, extensive, long-time
When in PSA, it will lead to dimension and sharply increase, objective function convergence is extremely slow, computational efficiency sharply declines.Therefore, it is necessary to send out
Exhibition is for Long baselines, extensive, the array prevalence self-correcting of long-time situation towing line array PSA and direction estimation method.
Starboard ambiguity of towed linear array sonar is also referred to as " towed array sonar " (can abbreviation dragging line battle array).It is that hydrophone is embedded on cable
Linear array is formed, the sonar of the hydrospace detection target after naval vessels tail is dragged by trailing cable.It is mainly used for listening and surveys submarine radiated noise,
It is remotely monitored, direction finding and identification, some can also be used for ranging.By linear array, trailing cable, draw off gear and capstan winch,
The composition such as electronics rack.Towing line array again by lead-in cable, instrument section, basic matrix section, after lead section and endpiece is constituted, the tens of rice of array length
To hundreds of meters, working depth is variable.With basic matrix size is big, working frequency is low, be conducive to line-spectrum detection, can snugly send out at a distance
The advantages that existing target；But it is motor-driven to the cycle of traction naval vessels and reversing etc. to adversely affect.Sound source, ocean channel and hydrophone array
It is three fundamentals in Hydroacoustic survey.Sound source radiates acoustical signal in water, is the source to form sound field；Ocean channel is then
Determine propagating characteristic of the sound wave in ocean；Hydrophone array samples the sound-filed simulation in water to receive acoustical signal.
It mutually maintains close ties with, constitutes indivisible unified whole between this three.Known wherein the two, so that it may infer the third party,
Here it is the basic foundations of underwater sound Matched-field processing.If it is known that hydrophone array receives signal and ocean channel information, it is to be solved
Be sound source information including sound source position, here it is Matched Field Passive Positionings.If it is known that be hydrophone array receive
Signal and the sound source information including sound source position, to be solved is ocean channel information, and here it is Matched Field inverting (MFI：
MatchedField Inversion).They are all the important contents of underwater sound Matched-field processing research.
Matched Field Processing Technique target detection, Passive Positioning, ocean environment parameter inverting etc. under water in recent years
Using widely being paid close attention to.Matched Field Matched-field processing (the MFP of sonar array signal：Matched Field
It Processing) is that reception base is calculated by underwater sound-field model using ocean environment parameter harmony propagation channel characteristics
The sound field amplitude and phase of battle array form copy field vector, and receive data with basic matrix and matched, to realize submarine target
The accurate estimation of Passive Positioning and ocean environment parameter.Dragging line battle array sonar platforms based on far and near field acoustic propagation characteristic, far field mesh
The plane wave propagation characteristic for marking signal combines Matched Field location technology peace wave target horizontal DOA Estimation, in far field plane
Under wave is assumed, having N number of angular frequency is that the sound-source signal of ω is incident in the linear array with P submatrix.Assuming that inside each submatrix
There is MpThe array number of a array element, entire array isElement position in submatrix is accurately known, the mould of p-th of submatrix
Type can be expressed as
xp(t)=Aps(t)+ep(t), (1)
Wherein, pth sub- battle array array manifold matrix Ap=[ap(θ1),ap(θ2),...,ap(θN)], θnIt is n-th of incoming wave
Orientation；Vector ap(θn)=[1, exp (- j ω dcos (θn)/c),...,exp(-jω(M-1)dcos(θn)/c)]TIt is pth sub-
Battle array θnThe corresponding array manifold vector in direction, c are the velocity of sound, and subscript T indicates transposition；Vector s (t)=[s1(t),s2(t),...,sN
(t)]TIndicate the corresponding signal waveform vector of t moment；Vector ep(t)=[e1(t),e2(t),...,eM(t)]TRepresent t moment
The corresponding noise of p submatrix.Under normal conditions, sound source quantity N is less than element number of array M, and incoming wave has sparsity in airspace.Assuming that
Scalar rpBe p-th of submatrix first array element to first submatrix first array element distance, the array manifold of full battle array to
Amount can be expressed as
aw(θ)=V (θ) h (θ), (2)
In formulaFor array prevalence matrix, a in submatrixp(θ) is p-th of submatrix
Array prevalence vector, h approximate array prevalence vector between submatrix, θ is the azimuth of incoming wave.Although ap(θ) is accurately known, real
The submatrix relative position vector of border measurementGenerally not equal to pre-set submatrix relative position vector r, so true full battle array
Array manifold vectorWith pre-built array manifold vector awThere can be deviation between (θ).There are the arrays that mismatch is displaced between submatrix
Model and a kind of Bearing method.
Summary of the invention
The present invention in view of the shortcomings of the prior art place, position error can be reduced by providing one kind, and can obtain standard
True azimuth estimation value, more high angular resolution can improve the sonar towing line array submatrix error misfits of robustness simultaneously
The method of the target positioning of model.
Above-mentioned purpose of the invention can be achieved by the following technical programs, a kind of towed linear-array sonar submatrix mistake
Mistake matches estimation method, it is characterised in that includes the following steps：There are between submatrix be displaced mismatch array manifold matrix model
In, the displacement error amount and each submatrix margin of error that true full array manifold matrix is expressed as each submatrix are to full array stream
The linear combination of shape matrix contribution；By between submatrix location error introduce direction finding model, between containing submatrix be displaced mismatch it is complete
Array Model establishes data fusion model with bayes rule, to submatrix position error vector β and target true bearing angle α-1
It carries out while solving, according to the collected data of merge sensor node, using bayesian algorithm simultaneously to submatrix displacement error
Estimated the likelihood function for how soon clapping observation is calculated with direction of arrival；With posteriority function obtain root-mean-square error with
The azimuth estimation value and displacement error estimated value of signal-to-noise ratio variation.
The present invention has the advantages that compared with the prior art：
The displacement that true complete a burst of column matrix in the case of submatrix displacement error is approximately each submatrix will be present in the present invention
The linear combination of the margin of error and each submatrix margin of error to the contribution of full battle array array manifold matrix, then using Bayesian frame into
Row solves, and submatrix position error vector and target true bearing can be carried out while be solved in low signal-to-noise ratio, when depositing
The self-correcting and the accurate direction finding of target that array can be achieved at the same time in submatrix displacement error, by missing the position between submatrix
Difference introduces direction finding model, estimates while realization by bayesian algorithm to submatrix displacement error and direction of arrival, to array stream
The error of shape is insensitive, and robustness is improved while reducing position error.
The root-mean-square error of displacement error estimated value as shown in Figure 2 is calculated using bayesian algorithm with letter by the present invention
It makes an uproar the variation of ratio, it can be seen that the root-mean-square error of displacement error estimator reduces with the increase of signal-to-noise ratio.Azimuth estimation value
Root-mean-square error with signal-to-noise ratio as shown in Figure 3 variation, than the root mean square for using multiple signal classification MUSIC algorithm to obtain
Error is stablized near 1 degree.
The root-mean-square error that the present invention is calculated using bayesian algorithm reduces with the increase of signal-to-noise ratio, and small
In 1 degree, performance improves a lot compared with MUSIC algorithm.Signal-to-noise ratio be 0dB when using full battle array CBF algorithm, full battle array MUSIC algorithm with
And the positioning result of the method for the present invention is as shown in figure 4, by comparing as can be seen that the present invention can not only obtain accurate orientation
Estimated value also has angular resolution more higher than other methods.
Obvious reality is achieved in estimating using the array with submatrix displacement error the azimuth of coherent sound sources
Apply effect.Compared with directly carrying out orientation estimation using full battle array CBF method and full battle array MUSIC method, advantage is essentially consisted in：
(1) by the way that submatrix error is introduced Array Model, can simultaneously to submatrix displacement error and target direction of arrival into
Row estimation；
(2) by the way that Bayesian frame, available more steady, precision will be introduced containing the Array Model of submatrix displacement error
Higher positioning performance.
The present invention is suitable for the scenes such as the processing of sensor submatrix, radio-frequency antenna array extension, sonar passive synthetic aperture, main
It is used to listening and surveys submarine radiated noise, remotely monitored, ranging, direction finding and identify array signal processing, signal processing
Method,
Detailed description of the invention
Fig. 1 is the array extension schematic diagram that the present invention has submatrix displacement error.
Fig. 2 is the root-mean-square error of displacement error estimated value of the present invention with the change curve schematic diagram of signal-to-noise ratio.
Fig. 3 is the root-mean-square error of azimuth estimation value of the present invention with the change curve schematic diagram of signal-to-noise ratio.
Fig. 4 be signal-to-noise ratio of the present invention be 0dB when positioning result curve synoptic diagram.
The invention will be further described with reference to the accompanying drawing.
Specific embodiment
- Fig. 4 refering to fig. 1.According to the present invention, there are between submatrix be displaced mismatch array manifold matrix model in, will be true
The displacement error amount and each submatrix margin of error that real full array manifold matrix is expressed as each submatrix are to full array manifold matrix
The linear combination of contribution；Location error between submatrix is introduced into direction finding model, between the full array mould for containing displacement mismatch submatrix
Type, establish data fusion model and the collected data of merge sensor node with Bayesian Method calculate the position of target and
Speed, to submatrix position error vector β and target true bearing angle α-1It carries out while solving, be calculated and how soon clap observation
Likelihood function；Submatrix displacement error and direction of arrival are carried out while being estimated, obtains root-mean-square error with noise with posteriority function
Than the azimuth estimation value and displacement error estimated value of variation.The specific steps are
Step 1：Array prevalence vector between true submatrix after mismatchTrue
First order Taylor expansion is carried out at the default submatrix relative position vector r of real submatrix relative position vector to approach, and is obtained close between submatrix
Like array prevalence vector
In formula, vector h approximate array prevalence vector between submatrix, e is Euler's constant, and j is imaginary unit's constant, and k is wave
Number, subscript T indicate that transposition, P are submatrix number, and θ is the azimuth for indicating incoming wave, vectorFor true submatrix phase
To position vector,For the true relative position of p-th of submatrix, vector r=[r1,...,rP]TFor preset submatrix relative position
Vector, rpFor the default relative position of p-th of submatrix, β=[β1,...,βP]TFor submatrix position error vector,For
P-th of submatrix displacement error, diag (β) indicate the diagonal matrix using the element of vector β as diagonal entry.
It, will true full battle array array manifold according to approximate array prevalence vector between the submatrix approached of first order Taylor expansion
Vector awIt is approximately
Array prevalence matrix between submatrix
In formula,Be incoming wave orientation be θ when pth be classified as vp(θ) remaining be classified as null vector
Matrix, vector vpThe pth column of array prevalence matrix V (θ), a between submatrixp(θ) is the array prevalence vector of p-th of submatrix.
In full Array Model, by the array manifold vector of full battle arrayAlong N number of θ1-θNIncoming wave orientation swept
It retouches, the approximate array prevalence matrix A of battle array is helped in combination1, then by the displacement error amount of each submatrix and each submatrix margin of error pair
The linear combination of the contribution of full array manifold matrix is:
And preset full battle array array manifold matrix A when setting error without submatrix meta positionw=[aw(θ1),...,aw(θN)], p-th
Submatrix error pro matrix Bp=-jk [Vp(θ1)h(θ1,r),...,Vp(θN)h(θN, r)],
In formula, N is scan position number of grid, awFor preset full battle array array manifold vector, βpBpIt is p-th of submatrix position
The single order for setting full battle array array manifold matrix error caused by error approaches product.
Step 2. is in based on the Bayes's positioning for being displaced misfit array model between submatrix, using bayesian algorithm to full battle array
The β of position error vector containing submatrix and target true bearing α between column model submatrix-1It carries out while solving, obtain indicating approximate complete
The popular matrix of a burst of columnWith the full battle array received signal vector x (t) of Array Model=Φ of approximate full battle array
(β) s (t)+e (t), according to full battle array received signal vector x (t)=[x1(t),x2(t),...,xN(t)]TT moment array received arrives
Signal, t moment correspond to sound source vector s (t)=[s of echo signal waveform1(t),s2(t),...,sN(t)]TWith t moment
Noise vector e (t)=[e of full battle array noise1(t),e2(t),...,eM(t)]T, when how soon clapping, by the array mould of full battle array
Type is rewritten as array received signal matrix X=Φ (β, θ) S+E under multiple number of snapshots, wherein T is number of snapshots, matrix X=[x
(1), x (2) ..., x (T)], x (t) is the array received signal vector of array t moment, matrix S=[s (1), s (2) ..., s
(T)] indicate that sound-source signal matrix, s (t) are the sound-source signal vector of t moment, E=[e (1), e (2) ..., e (T)] expression is made an uproar
Sound matrix, e (t) indicate that the noise vector of t moment, θ indicate the azimuth vector of scanning incoming wave.
The scan position of incoming wave is angularly measuredFor L azimuth scan grid vector, and L > > N, t moment
The signal vector of all scanning directions isMatrixIt is L to sweep
The echo signal matrix for retouching the T moment under the conditions of grid, according to how soon the array received signal matrix formula X=under umber of beats
The full array under the conditions of L azimuth scan grid of the array manifold matrix for being displaced mismatch between submatrix will be present in Φ (β, θ) S+E
Model can be expressed as
In formula, matrixFor there are the full battle array scanning array prevalence matrix of error between submatrix, vectorsIndicate that the scan position of scanning incoming wave is angularly measured,For first of scan position,
The full battle array scanning array manifold matrix of error, vector are set for no submatrix meta positionIt is true full when for first of scan position
Battle array scanning array manifold vector, matrixFor sweeping for p-th submatrix error
Retouch projection matrix, matrixIt is θ for scan positionlWhen pth be classified asRemaining is classified as the matrix of null vector, and β is submatrix
Position error vector,It is the echo signal matrix at T moment under the conditions of L scanning grid,For the signal vector of all scanning directions of t moment, E indicates noise matrix.
Each array element noise independence and to meet mean value be 0 variance is the true initial azimuth of targetMultiple Gauss
When distribution, the likelihood function for how soon clapping observation acquired
In formula, I is L dimension unit matrix, and det () representing matrix seeks determinant, and exponential function is sought in exp () expression, | | () |
|2Two norm of vector is sought in expression.Noise precision α0The gamma that parameter is a and b is obeyed to be distributed
p(α0| a, b)=Gamma (α0|a,b)
In formula, functionΓ (a) indicates that variable is the gamma function of a.
Information source vectorMultiple Gauss distribution is obeyed, the probability density function of echo signal matrix is
In formula,
Covariance matrix
α2For the precision in first of orientation.Signal accuracy vector parameter α=[α1,α2,...,αL] parameter is obeyed as c's and d
Gamma distribution
Echo signal matrixPosterior probability distribution be
In formula, α0For initial noisc precision parameter, μ (t) is indicatedPosterior Mean vector, Σ are indicatedPosteriority association side
Poor matrix.
T moment initial noisc precision parameter α is acquired according to Bayesian model update method0Update Posterior Mean vector μ
(t) and posteriority covariance matrix Σ, wherein
Posterior Mean vector
Posteriority covariance matrix
In formula,Full battle array scanning array prevalence matrix when error between submatrix, H are conjugate transposition, and β is submatrix location error
Vector,For the received signal vector that t moment is unknown, matrix Λ is priori covariance matrix, matrix Λ-1For the inverse of matrix Λ.
T moment signal accuracy parameter alpha is acquired according to Bayesian model update methodiWith noise precision parameter α0Update make an uproar
Sound precision parameterUpdate noise precision parameter calculation formula
Update variances sigma
In formula, σ is variance, | | ()F| | the Frobenius norm operator of representation vector, Mean Matrix H=[μ (1), μ
(2) ..., μ (T)], ΣiiIt is i-th of diagonal element of covariance matrix Σ, scalar γi=1- αiΣii。
The estimated value of submatrix position error vector β is acquired according to Bayesian model iteration update method
First intermediary matrix T=G+Q,
Second intermediary matrix
Third intermediary matrix
4th intermediary matrix
First intermediate vector
Second intermediate vector
Entire Bayesian model, which updates iterative process, to be summarized as follows：This model iteration update method of leaf is to initial noisc
Precision parameter α0, signal accuracy vector α and submatrix position error vector β assign initial value, use and update Posterior Mean vector μ
(t) formula (8) and posteriority covariance matrix Σ formula (9) update mean vector μ and covariance matrix Σ, then use according to public affairs
(the σ that formula updates noise precision parameter calculation formula (10), updates variances sigma2)newCalculation formula (11) and submatrix location error to
Measure the estimated value of βCalculation formula (12) updates initial noisc precision parameter α0, signal accuracy vector α and submatrix location error
Vector β repeats above procedure, until convergence.Initial noisc precision parameter α after the completion of iteration0, signal accuracy vector α and son
Battle array position error vector β shows respectively the displacement error of noise energy, the signal energy of particular orientation and each virtual submatrix.
Illustrated below with concrete example：
Refering to fig. 1.The predeterminated position of the array extension of submatrix displacement error includes virtual submatrix 1, virtual submatrix 2, virtual
Submatrix 3, the physical location of virtual submatrix 2 deviate β=0.11, and the physical location of virtual submatrix 3 deviates β=0.2, there is number of targets K
=2 far field narrow band signals are incident on array number M=4 member even linear array, centre frequency f=250Hz, sound-source signal incidence angle
Spend θ1And θ2Respectively 60 ° and 65 °, linear array array element spacing is 0.68 meter.The predeterminated position difference of P=3 virtual submatrix head array element
Apart from initial position 0m, 3.4m and 6.8m, submatrix displacement error β1,β2And β3Respectively 0 meter, 0.11m and 0.2m.Each position
The number of snapshots T=200 of array acquisition obtains echo signal matrix X.P-th of submatrix location error is calculated according to formula (5) to cause
Full battle array array manifold matrix Bp。
Initial noisc precision parameter α0Hyper parameter be set to a=b=1 × 10-4, the hyper parameter difference of signal accuracy vector
It is set as c=1, d=0.01；Iterative process initial noisc precision parameter α0Initial value be set as
The initial value of signal accuracy vector is set asThe initial value of submatrix position error vector β is set as β
=0.
It is σ to each array element received signal addition variances sigma2Independent white Gaussian noise, define signal-to-noise ratioThe SNR ranges of emulation are 0-10dB, the simulation times R=under each signal-to-noise ratio
200。
Posterior Mean vector μ is updated according to Posterior Mean vector μ (t) formula (8) and posteriority covariance matrix Σ formula (9)
With posteriority covariance matrix the Σ, (σ for then updating noise precision parameter calculation formula (10) according to formula, updating variances sigma2)new
The estimated value of calculation formula (11) and submatrix position error vector βCalculation formula (12) updates initial noisc precision parameter
α0, signal accuracy vector α and submatrix position error vector β, repeat above procedure, until convergence, obtain the position of i-th emulation
Shift error vector estimated valueAnd azimuth estimation valueWhereinIt is signal essence
The vector that the inverse of the degree the smallest K component of vector α intermediate value is composed.
The direction of arrival root-mean-square error under given signal-to-noise ratio, according to direction of arrival root-mean-square error calculation formulaIt calculates,
Displacement error root-mean-square error is according to displacement error root-mean-square error calculation formula
It calculates, R indicates simulation times in formula, and P indicates submatrix number.
Be calculated using root-mean-square error calculation formula the root-mean-square error of displacement error estimated value as shown in Figure 2 with
The variation of signal-to-noise ratio, it can be seen that the root-mean-square error of displacement error estimator reduces with the increase of signal-to-noise ratio.Orientation estimation
The root-mean-square error of value with signal-to-noise ratio as shown in Figure 3 variation, it is more square than use that multiple signal classification MUSIC algorithm obtains
Root error is stablized near 1 degree.The root-mean-square error being calculated using the method for the present invention is reduced with the increase of signal-to-noise ratio, and
Respectively less than 1 degree, performance improves a lot compared with MUSIC algorithm.It is calculated when signal-to-noise ratio is 0dB using full battle array CBF algorithm, full battle array MUSIC
The positioning result of method and the method for the present invention is as shown in figure 4, by comparing as can be seen that the method for the present invention can not only obtain standard
True azimuth estimation value also has angular resolution more higher than other methods.
Claims (10)
1. a kind of towed linear-array sonar submatrix error misfits estimation method, it is characterised in that include the following steps：There is son
It is displaced between battle array in the array manifold matrix model of mismatch, the displacement that true full array manifold matrix is expressed as each submatrix is missed
The linear combination that residual quantity and each submatrix margin of error contribute full array manifold matrix；Location error between submatrix is introduced into direction finding
Model establishes data fusion model with bayes rule to containing the full Array Model for being displaced mismatch submatrix, to submatrix position
Set error vector β and target true bearing angle α-1It carries out while solving, according to the collected data of merge sensor node, use
Bayesian algorithm estimates submatrix displacement error and direction of arrival the likelihood letter for how soon clapping observation is calculated simultaneously
Number；The azimuth estimation value and displacement error estimated value that root-mean-square error changes with signal-to-noise ratio are obtained with posteriority function.
2. towed linear-array sonar submatrix error misfits estimation method as described in claim 1, it is characterised in that：After mismatch
Array prevalence vector between true submatrixIn true submatrix relative position vector
Default submatrix relative position vector r at carry out first order Taylor expansion and approach, obtain approximate array prevalence vector between submatrix
In formula, vector h approximate array prevalence vector between submatrix, e is Euler's constant, and j is imaginary unit's constant, and k is wave number, on
Marking T indicates that transposition, P are submatrix number, and θ is the azimuth for indicating scanning incoming wave, vectorIt is opposite for true submatrix
Position vector,For the true relative position of p-th of submatrix, vector r=[r1,...,rP]TFor preset submatrix relative position to
Amount, rpFor the default relative position of p-th of submatrix, β=[β1,...,βP]TFor submatrix position error vector,It is
P submatrix displacement error, diag (β) indicate the diagonal matrix using the element of vector β as diagonal entry.
3. towed linear-array sonar submatrix error misfits estimation method as claimed in claim 2, it is characterised in that：According to single order
Approximate array prevalence vector between the submatrix that Taylor expansion is approached, will true full battle array array manifold vectorIt is approximate
For
Array prevalence matrix between submatrix
In formula,Be incoming wave orientation be θ when pth be classified as vp(θ) remaining is classified as the matrix of null vector,
Vector vpThe pth column of array prevalence matrix V (θ), a between submatrixp(θ) is the array prevalence vector of p-th of submatrix.
4. towed linear-array sonar submatrix error misfits estimation method as claimed in claim 3, it is characterised in that：In full array
In model, by the array manifold vector of full battle arrayAlong N number of (θ1To θN) incoming wave orientation be scanned, combination help battle array
Approximate array prevalence matrix A1, then by the displacement error amount of each submatrix and each submatrix margin of error to full array manifold matrix
The linear combination of contribution be:
And preset full battle array array manifold matrix A when setting error without submatrix meta positionw=[aw(θ1),...,aw(θN)], p-th of submatrix
Error pro matrix Bp=-jk [Vp(θ1)h(θ1,r),...,Vp(θN)h(θN, r)],
In formula, N is scan position number of grid, awFor preset full battle array array manifold vector, βpBpIt is that p-th of submatrix position is missed
The single order of full battle array array manifold matrix error caused by difference approaches product.
P-th of submatrix error pro matrix Bp=-jk [Vp(θ1)h(θ1,r),...,Vp(θN)h(θN, r)],
In formula, N is scan position number of grid, awFor preset full battle array array manifold vector, Aw=[aw(θ1),...,aw(θN)]
It is that no submatrix meta position sets preset full battle array array manifold matrix, β when errorpBpIt is complete a burst of caused by p-th of submatrix location error
The single order of column manifold matrix error approaches product.
5. towed linear-array sonar submatrix error misfits estimation method as described in claim 1, it is characterised in that：Based on son
It is displaced between battle array in Bayes's positioning of misfit array model, using bayesian algorithm between position containing submatrix full Array Model submatrix
Error vector β and target true bearing α-1It carries out while solving, obtain indicating the approximate popular matrix of complete a burst of columnWith the full battle array received signal vector x (t) of Array Model=Φ (β) s (t)+e (t) of approximate full battle array,
According to full battle array received signal vector x (t)=[x1(t),x2(t),...,xN(t)]TSignal that t moment array received arrives, t moment
Sound source vector s (t)=[s of corresponding echo signal waveform1(t),s2(t),...,sN(t)]TWith making an uproar for the full battle array noise of t moment
Sound vector e (t)=[e1(t),e2(t),...,eM(t)]T, when how soon clapping, the Array Model of full battle array is rewritten as multiple
Array received signal matrix X=Φ (β, θ) S+E under number of snapshots, wherein T is number of snapshots, matrix X=[x (1), x (2) ...,
X (T)], x (t) is the array received signal vector of array t moment, and matrix S=[s (1), s (2) ..., s (T)] indicates sound source letter
Number matrix, s (t) are the sound-source signal vector of t moment, and E=[e (1), e (2) ..., e (T)] indicates that noise matrix, e (t) indicate
The noise vector of t moment, θ indicate the azimuth vector of scanning incoming wave.
6. towed linear-array sonar submatrix error misfits estimation method as claimed in claim 5, it is characterised in that：According to multiple
The array manifold square of displacement mismatch between submatrix will be present in array received signal matrix formula X=Φ (β, θ) S+E under number of snapshots
The unknown receipt signal matrix in incoming wave orientation are expressed as under the conditions of L azimuth scan grid of battle array
Wherein, matrixFor there are the full battle array scanning array prevalence matrix of error between submatrix,
In formula, vectorIndicate that the scan position of scanning incoming wave is angularly measured,For first of scan position,Full battle array scanning array manifold matrix, vector when setting error for no submatrix meta positionIt is first
True full battle array scanning array manifold vector when scan position, matrix
For the scanning projection matrix of p-th of submatrix error, matrixIt is θ for scan positionlWhen pth be classified asRemaining is classified as zero
The matrix of vector, β are submatrix position error vector, and E indicates noise matrix.
7. towed linear-array sonar submatrix error misfits estimation method as claimed in claim 5, it is characterised in that：Information source vectorObeying mean value is 0, echo signal battle arrayWherein priori covariance matrixα2For the precision in first of orientation, signal accuracy vector α=[α1,α2,...,αL] obey parameter
It is distributed for the gamma of c and d
Echo signal matrixPosterior probability distribution be
In formula, α0For initial noisc precision parameter, μ (t) is indicatedPosterior Mean vector, Σ are indicatedPosteriority covariance square
Battle array.
8. towed linear-array sonar submatrix error misfits estimation method as described in claim 1 or 6, it is characterised in that：Every
The noise independence of a array element and meet mean value be 0 when, variance be initial noisc precision parameterMultiple Gauss distribution when how soon clap
The likelihood function of observation
Noise precision α0Obey the gamma distribution p (α that parameter is a and b0| a, b)=Gamma (α0| a, b), and function
In formula, I is L dimension unit matrix, and det () representing matrix seeks determinant, and exponential function is sought in exp () expression, | | () | |2Table
Show and seek two norm of vector, Γ (a) indicates that variable is the gamma function of a.
9. towed linear-array sonar submatrix error misfits estimation method as claimed in claim 7, it is characterised in that：According to pattra leaves
This model update method acquires t moment noise precision parameter α0Update Posterior Mean vector μ (t) and posteriority covariance matrix
Σ, wherein
Posterior Mean vector
Posteriority covariance matrix
In formula,For there are full battle array scanning array prevalence matrix when error between submatrix, H is conjugate transposition, β is submatrix location error
Vector,For the received signal vector that t moment is unknown, Λ is priori covariance matrix, matrix Λ-1For the inverse of matrix Λ.
10. towed linear-array sonar submatrix error misfits estimation method as claimed in claim 9, it is characterised in that：Ye Simo
Type iteration update method is to initial noisc precision parameter α0, signal accuracy vector α and submatrix position error vector β assign just
Value updates mean vector μ and association using update Posterior Mean vector μ (t) formula (8) and posteriority covariance matrix Σ formula (9)
Then variance matrix Σ uses the (σ for updating noise precision parameter calculation formula (10) according to formula, updating variances sigma2)newIt calculates
The estimated value of formula (11) and submatrix position error vector βCalculation formula (12) updates initial noisc precision parameter α0, signal essence
Vector α and submatrix position error vector β is spent, above procedure is repeated, until convergence.
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