CN106646344B - A kind of Wave arrival direction estimating method using relatively prime battle array - Google Patents
A kind of Wave arrival direction estimating method using relatively prime battle array Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract
The present invention provides a kind of Wave arrival direction estimating methods using relatively prime battle array, it is related to array signal processing field, based on the sparse reconstruct thought in compressed sensing, Wave arrival direction estimating method based on OMP algorithm is constructed for relatively prime battle array, overcome the problem of smooth MUSIC algorithm in airspace causes Virtual array to reduce, so that detection target numbers are more than MN, due to using this novel nested battle array of relatively prime battle array, so that Mutual coupling performance significantly improves the destination number of estimation, there is estimation performance well in the estimation of array multiple target, when equally using relatively prime battle array, so that the target numbers of estimation are more than NM target, under same array element quantity, further improve the estimation target numbers of relatively prime battle array, what can be simple and efficient is reconstructed sparse signal, finally the direction of arrival that provides rapidly and efficiently is estimated For meter as a result, in high s/n ratio, the estimated accuracy of the method for the present invention is better than the MUSIC algorithm of space smoothing.
Description
Technical field
The present invention relates to array signal processing field, especially a kind of Wave arrival direction estimating method.
Background technique
Mutual coupling has and is widely applied very much in radar, sonar and wireless communication, however traditional direction of arrival
Estimation method can only solve the case where number of targets is less than array number, therefore how to detect more targets with a small amount of array element is one
A good problem to study.In practice, general common N member concentrating rate, can only at most estimate the incoming wave of N-1 target
Direction.In recent years, propose a kind of linear array of new geometric structure --- relatively prime battle array so that estimation target numbers far more than
Array element number N, in fact, the target numbers for having the relatively prime battle array of N+M array element that can estimate can achieve O (MN), i.e., and MN
The target numbers of same order size, since the ingenious distribution of relatively prime battle array element position can be formed after mathematical operation is handled
The bigger virtual array in aperture.Specifically, the relatively prime battle array of N+2M-1 physics array element mentioned above can fictionalize aperture and be
The concentrating rate of 2MN+1.
For relatively prime battle array, it has been proposed that a kind of smooth MUSIC algorithm in airspace based on relatively prime battle array, for using N+2M-1
The relatively prime battle array of a physics array element, MN target is at most estimated that using this method, although the target that this algorithm estimates
Number has been much larger than the concentrating rate of equal number physics array element, but due to having used airspace smoothing method, leads
Virtual array is caused to be reduced to MN+1, detection performance reduces.Recent years, by D.Donoho, E.Candes and scientist of Chinese origin
T.Tao et al. proposes a kind of new acquisition of information guiding theory, i.e. compressed sensing, the theory once proposition, just information theory,
The fields such as signal processing, pattern-recognition, wireless communication are paid high attention to, which thinks, for a sparse signal or
It is that can be carried out after observing on a small quantity to the signal with the signal of rarefaction representation, it is then former using the reconstruct of specific restructing algorithm
Beginning signal meets y=Ax, observing matrix in formula for the finite observation y of signal xM < N, if meeting certain item
Part can reconstruct original sparse signal x from finite observation y.
Summary of the invention
For overcome the deficiencies in the prior art, the present invention is based on the sparse reconstruct thoughts in compressed sensing, for relatively prime battle array
The Wave arrival direction estimating method based on OMP algorithm is constructed, overcoming the smooth MUSIC algorithm in airspace leads to asking for Virtual array reduction
Topic so that detection target numbers be more than MN, and emulate proof this method have good estimated accuracy in high s/n ratio.
The technical solution adopted by the present invention to solve the technical problems specifically comprises the following steps:
Step 1: relatively prime battle array structure design
Relatively prime battle array, which is respectively that Md is nested with the concentrating rate of Nd by two spacing, to be formed, and wherein M and N is two matter each other
Several constants, d indicate the half-wavelength of reception signal, and a concentrating rate has N number of array element, and array element spacing is Md, another
Concentrating rate has 2M array element, and array element spacing is Nd, and first array element of two concentrating rates is overlapped, and shares N+2M-1
Array element, since M and N is prime number, so this linear array is referred to as relatively prime battle array, relatively prime battle array is a kind of heterogeneous line of special construction
Array；
Step 2: estimating that relatively prime battle array receives the covariance matrix of signal
Relatively prime battle array receives the covariance matrix R of signalxxEstimated by formula (1):
In formula (1),Indicate that relatively prime battle array received signal vector, T indicate array number of snapshots；
Step 3: constructing the received vector y of virtual concentrating rate
Construct the element b that size is the i-th row jth column in (N+2M-1) × (N+2M-1) identity matrix B, Bij=i-j, mark
Matrix B and covariance matrix RxxIt is straightened, obtains by column respectivelyMark vectorThe position that element value is-MN to MN is successively found according to sequence from small to large from mark vector b
It sets, and is sequentially recorded lower 2MN+1 location information, then successively come out the element extraction of corresponding position from vector z, structure
Produce the received vector of virtual concentrating rate
Step 4: angular regions subdivision grid to be detected, constructs array manifold matrix A
By angular regions discretization subdivision grid to be detected, grid vector θ=[θ is formed1,θ2,…,θD]T, wherein θkTable
Showing discrete grid angle, k=1 ..., D, D indicates lattice number, and the lattice number D of subdivision is made to be greater than signal number, by
Formula (2) and formula (3) construct array manifold matrix A:
A(θ1,θ2,…,θD)=[a (θ1),a(θ2),…a(θk),...,a(θD)] (2)
In formula (2), a (θk) be corresponding array array manifold vector, k=1,2 ..., D, in formula (3), j indicates imaginary number
Unit, d indicate to receive the half-wavelength of signal, the wavelength of λ expression reception signal, θkIndicate discrete grid angle；
Step 5: estimating sparse signal using OMP algorithm
Array manifold matrix A (θ1,θ2,…,θD) and the received vector y of virtual concentrating rate meet following equation:
P is corresponding to subdivision grid θ=[θ in formula (4)1,θ2,…,θD]TSparse vector,Indicate noise vector, it is dilute
Sparse vector estimated value can be obtained using the OMP algorithm solution in compressed sensing by dredging vector p
Step 6: obtaining signal direction of arrival by sparse vector
If sparse vector estimated valueIn i-th it is non-zero, then it represents that corresponding θiDirection has signal, otherwise indicates do not have
Signal.
The present invention uses concentrating rate compared to traditional Mutual coupling, this novel due to using relatively prime battle array
Nested battle array has so that Mutual coupling performance significantly improves the destination number of estimation in the estimation of array multiple target
Estimation performance well；When equally using relatively prime battle array, this method is for the MUSIC algorithm of space smoothing, due to making
With the OMP algorithm of compressed sensing, so that the target numbers of estimation are more than NM target, under same array element quantity, further
Improve the estimation target numbers of relatively prime battle array；Due to having used OMP algorithm, what can be simple and efficient carries out weight to sparse signal
Structure, finally rapidly and efficiently provide Mutual coupling result；In high s/n ratio, the estimated accuracy of the method for the present invention is better than sky
Between smooth MUSIC algorithm, in general, performance of the invention is not less than the MUSIC algorithm of space smoothing.
Detailed description of the invention
Fig. 1 is the method flow diagram that the present invention carries out Mutual coupling.
Fig. 2 is the geometry of the relatively prime battle array of the present invention.
Fig. 3 is the Mutual coupling result of the present invention with space smoothing MUSIC algorithm.
Fig. 4 is Mutual coupling result of the present invention to 16 incoming wave signals.
Fig. 5 is the estimated accuracy comparing result of the present invention with the single goal of space smoothing MUSIC algorithm.
The smooth MUSIC algorithm of MUSIC representation space in Fig. 5, OMP indicate that the wave proposed by the present invention based on OMP algorithm reaches
Direction determining method.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and examples.
Step 1: relatively prime battle array structure design
The constant M and N for choosing two prime numbers each other indicate the half-wavelength for receiving signal with constant d, and relatively prime battle array is by between two
Away from respectively Md composition nested with the concentrating rate of Nd, one of even linear array has N number of array element, and array element spacing is Md, separately
An outer linear array has 2M array element, and array element spacing is Nd, and two linear arrays, first array element is overlapped, a total of N+2M-1 battle array
Member, since M and N is prime number, so this linear array is referred to as relatively prime battle array, the structure of relatively prime battle array is as shown in Figure 1, relatively prime battle array is one
The unequally spaced linear array of kind special construction, therefore can further be derived on the model of linear array；
The linear array comprising N number of array element, element position l are considered firsti, it is assumed that K target bearing isAnd
And K echo signal is set as narrow band signal, then array received signal indicates are as follows:
1≤t≤T, s in formulakIt (t) is k-th of incoming wave signal, n (t) is independent identically distributed white noise, It is array manifold vector, and
I-th of element represent k-th of signal phase change brought by the time delay of i-th of array element.
Step 2: estimating that relatively prime battle array receives the covariance matrix of signal
Relatively prime battle array receives the covariance matrix R of signalxxEstimated by formula (1):
In formula,Indicate that relatively prime battle array received signal vector, T indicate array number of snapshots；
If signal sk(t) obeying variance isIndependent Gaussian distribution, consider that each array element receives the second-order statistics of data
Amount solves the covariance matrix R of array received signal x (t)xx
σ in formula2It is noise power, by matrix RxxIt is straightened by column, according to the operation of matrix Padé approximants (also referred to as direct product)
Property obtains vector z by formula (7):
Wherein, Indicate the variance of k-th of transmitting signal,Expression formula is as follows:
Represent in addition to i-th of position be all as 1 remaining element 0 column vector, letter as is regarded vector z according to (8) formula
The signal that source vector q is received after matrix Φ observation, matrixIt is middle that there are an array manifold matrixes, and
And this matrix is the array manifold matrix of a linear array with more Virtual arrays.
Step 3: constructing the received vector y of virtual concentrating rate
Construct the element b that size is the i-th row jth column in (N+2M-1) × (N+2M-1) identity matrix B, Bij=i-j, mark
Matrix B and covariance matrix RxxIt is straightened, obtains by column respectivelyMark vector
Sequence from mark vector b from small to large successively finds the position that element value is-MN to MN, is sequentially recorded lower total 2MN+1
A location information, it is assumed that b=[- 3, -1,1,5,0] successively finds the position that element value is -1 to 1 to big sequence from b with small
It sets, the corresponding position information recorded is exactly [2,5,3], then successively the element extraction of corresponding position come out from vector z,
Construct the received vector of virtual concentrating rate
Step 4: angular regions subdivision grid to be detected, constructs array manifold matrix A
By angular regions discretization subdivision grid to be detected, grid vector θ=[θ is formed1,θ2,…,θD]T, wherein θk(k
=1 ..., D) indicate discrete grid angle, D indicates lattice number, and the lattice number D of subdivision is made to be greater than signal number,
Taking D is 10 times or more of signal number, constructs array manifold matrix A by following formula:
A(θ1,θ2,…,θD)=[a (θ1),a(θ2),…,a(θD)] (2)
In formula (2), a (θk) be corresponding array array manifold vector, k=1,2 ..., D, in formula (3), j indicates imaginary number
Unit, d indicate to receive the half-wavelength of signal, the wavelength of λ expression reception signal, θkIndicate discrete grid angle；
Step 5: estimating sparse signal using OMP algorithm
Array manifold matrix A (θ1,θ2,…,θD) and the received vector y of virtual concentrating rate meet following equation:
P is corresponding to subdivision grid θ=[θ in formula (4)1,θ2,…,θD]TSparse vector,Indicate noise vector, it is dilute
Sparse vector estimated value can be obtained using the OMP algorithm solution in compressed sensing by dredging vector p
Step 6: obtaining signal direction of arrival by sparse vector
If sparse vector estimated valueIn i-th it is non-zero, then it represents that θiDirection has signal, otherwise indicates no signal.
In the present invention, more specifically assume that this linear array is relatively prime battle array as shown in Figure 1, be respectively by two spacing
Md composition nested with the concentrating rate of Nd, a shared N+2M-1 physics array element, one of even linear array have N number of array element,
Another linear array has 2M array element, and first array element of two linear arrays is overlapped.Assuming that the covariance matrix R of signalxxIt is known that square
Battle array size is (N+2M-1) × (N+2M-1), according to formula (4), by the property of direct product it is recognised that matrix Φ shares (N+2M-
1)2A row vector, it has been demonstrated that, if N, M are prime numbers, the subset of these row vectors corresponds to bigger equal in an aperture
The array manifold matrix A of even linear array, element position is from-MNd to MNd, and array element spacing is d, at this moment virtual concentrating rate
Aperture can achieve (2MN+1) d, below by matrixConstruct the array manifold matrix of concentrating rate
Corresponding row vector is selected from Φ, and these row vectors are ranked up to obtain A, so that array manifold matrix A
In (n, k) a element beK=1,2 ..., K, n=-MN ..., 0 ..., MN ultimately form size
For the matrix A of (2NM+1) × K, A is just the array manifold matrix of the concentrating rate of (2MN+1) d for an aperture at this time,
For the vector z of formula (8) left end, according to the corresponding item of method choice that vector y is constructed described in step 3 and sorting obtain to
Y is measured, y is the received vector corresponding to this virtual concentrating rate, then A, y meet
Vector in formulaIt is vector 1nRemove the vector that corresponding entry sorts, and NM+1 are 1, remaining is 0.
Mutual coupling is carried out to the sparse reconstruct thought of compressed sensing below to be illustrated:
First to angular regions discretization to be detected: θ=[θ1,θ2,…,θD]T, and D > > K, the i.e. grid number of subdivision
Mesh is greater than signal number, constructs array manifold matrix A (θ1,θ2,…,θD):
A(θ1,θ2,…,θD)=[a (θ1),a(θ2),…,a(θD)] (2)
In formula
It is the array manifold vector for the concentrating rate that an array number is 2NM+1.Therefore formula (4) can be rewritten as
Wherein, y is the received vector for the virtual concentrating rate being calculated according to the reception signal x (t) of relatively prime battle array, such as
The arrival bearing of k-th of signal of fruit is θi, then i-th of position of vector pAssuming that the lucky position in the position of all targets
In on the mesh point of subdivision, then being only non-zero on K arrival bearing, at this point, p is K sparse vector.For formula (9),
If given y and A, solves equation by the sparse restructing algorithm in compressed sensing.
According to compressive sensing theory, need to acquire the most sparse solution for meeting formula (10)Therefore sparse reconstruction indicates
Are as follows:
In formula | | | |0The number of vector nonzero term is indicated, in order to indicate to facilitate A=A (θ1,θ2,…,θD), it is assumed that noise
Variances sigma2Be it is unknown, in order to solve formula (10), the present invention is solved using OMP algorithm, and the iterative step of OMP algorithm is as follows:
Input: array manifold matrix A, the received vector y of virtual concentrating rate, echo signal quantity K；
Output: the K sparse bayesian learning of pError vector E；
Initialization: surplus E0=y, reconstruction signal p0=0, indexed setThe number of iterations n=0；
Step 1: calculating surplus and construction array manifold matrix A (θ1,θ2,…,θD) each column between inner product Gn=
ATEn-1, En-1It is the surplus of nth iteration, when n=1, En-1=E0；
Step 2: finding out GnThe corresponding position of the element of middle maximum absolute value, i.e.,
Step 3: updating indexed set Γn=Γn-1∪ { k } and atom set
Step 4: acquiring approximate solution using least square method
Step 5: updating surplus
Step 6: judging whether iteration meets stop condition, i.e., whether the number of iterations n is greater than K, when the number of iterations is greater than K then
Meet stop condition, if meeting stop condition,E=En, outputOtherwise n ← n+1 is enabled, step is turned
Rapid 1, whereinIt isI-th.
Method of the invention is further described below: implementing under the premise of the technical scheme of the present invention, provides
Detailed embodiment and specific operating process.
Consider the relatively prime battle array comprising 10 physics array element, i.e., N=5, M=3 is taken to the relatively prime battle array in Fig. 2, specifically, the
One layer of element position is in [0,3,6,9,12] d, and for second layer element position in [0,5,10,15,20,25] d, taking d is half-wave long value,
Several narrow band signals are chosen, arrival bearing is evenly distributed in -60 degree to 60 degree of section, and frequency is taken as f=1000Hz, adopts
Sample frequency fs=8192Hz, number of snapshots 500, signal-to-noise ratio 0dB.
The narrow band signal that 15 different directions are had chosen in Fig. 3 emulates the detection performance of two kinds of algorithms.In Fig. 4 left figure be by
The result obtained according to space smoothing matrix MUSIC algorithm.Right figure illustrates the Mutual coupling based on OMP algorithm in Fig. 3.It is first
It first spends to 60 degree with 0.5 degree from -60 for step-length grid division, i.e. then D=240 arrives (3) according to formula (1), calculate structural formula
(4) equation equation finally executes OMP algorithm, obtains Mutual coupling result.Dotted line indicates original signal direction in Fig. 4,
Solid line indicates estimated result.As can be seen that two kinds of algorithms can obtain good estimation effect, however space smoothing MUSIC is calculated
Method can only at most estimate the arrival bearing of MN=15 signal.For 10 yuan of relatively prime battle arrays mentioned above, when there is 16 incoming waves
When signal, space smoothing MUSIC algorithm will go wrong, and MUSIC algorithm can only at most estimate NM=15 signal, when 16
When a signal, method is without solution, if still solving according to the input of 15 signals, estimated result differs greatly with true value, at this time
Mutual coupling based on OMP algorithm will show advantage.
When Fig. 4 gives 16 incoming wave signals, the result of Mutual coupling is carried out using OMP algorithm, it can be seen that OMP
The Mutual coupling result of algorithm can provide accurate estimated result, and this result is that space smoothing MUSIC algorithm cannot
Reach.
In the analogous diagram that Fig. 5 is provided, when the present invention considers single target estimation, the estimated accuracy of two kinds of algorithms is with letter
It makes an uproar the situation of change of ratio.Different from the emulation of front, specifically in the range of -90 degree are to 90 degree, a signal side is randomly generated
To the SNR ranges that horizontal axis indicates are using 2dB as step-length, from -20dB to 10dB；The longitudinal axis indicate error using estimation angle with
The absolute value of real angle difference.Each point executes 5000 Monte Carlo Experiments, remaining condition is identical as front emulation.From figure
Result in 5 can be seen that the Mutual coupling for single goal, in low signal-to-noise ratio, the estimation performance base of two kinds of algorithms
This is the same, but in high s/n ratio, the estimated accuracy of OMP algorithm is better than the MUSIC algorithm of space smoothing.
Claims (1)
1. a kind of Wave arrival direction estimating method using relatively prime battle array, it is characterised in that include the following steps:
Step 1: relatively prime battle array structure design
Relatively prime battle array, which is respectively that Md is nested with the concentrating rate of Nd by two spacing, to be formed, and wherein M and N is two prime numbers each other
Constant, d indicate the half-wavelength of reception signal, and a concentrating rate has N number of array element, and array element spacing is Md, another is uniformly
Linear array has 2M array element, and array element spacing is Nd, and first array element of two concentrating rates is overlapped, and shares N+2M-1 battle array
Member, since M and N is prime number, so this linear array is referred to as relatively prime battle array, relatively prime battle array is a kind of non-homogeneous alignment of special construction
Battle array；
Step 2: estimating that relatively prime battle array receives the covariance matrix of signal
Relatively prime battle array receives the covariance matrix R of signalxxEstimated by formula (1):
In formula (1),Indicate that relatively prime battle array received signal vector, T indicate array number of snapshots；
Step 3: constructing the received vector y of virtual concentrating rate
Construct the element b that size is the i-th row jth column in (N+2M-1) × (N+2M-1) identity matrix B, Bij=i-j, identity matrix
B and covariance matrix RxxIt is straightened, obtains by column respectivelyMark vector
Element value is successively found according to sequence from small to large from mark vector b and is the position of-MN to MN, and is sequentially recorded down
Then 2MN+1 location information successively comes out the element extraction of corresponding position from vector z, construct virtual uniform alignment
The received vector of battle array
Step 4: angular regions subdivision grid to be detected, constructs array manifold matrix A
By angular regions discretization subdivision grid to be detected, grid vector θ=[θ is formed1,θ2,…,θD]T, wherein θkIndicate from
Scattered grid angle, k=1 ..., D, D indicate lattice number, and the lattice number D of subdivision is made to be greater than signal number, by formula
(2) and formula (3) constructs array manifold matrix A:
A(θ1,θ2,…,θD)=[a (θ1),a(θ2),…a(θk),...,a(θD)] (2)
In formula (2), a (θk) be corresponding array array manifold vector, k=1,2 ..., D, in formula (3), j indicates imaginary unit, d
Indicate the half-wavelength of reception signal, λ indicates to receive the wavelength of signal, θkIndicate discrete grid angle；
Step 5: estimating sparse signal using OMP algorithm
Array manifold matrix A (θ1,θ2,…,θD) and the received vector y of virtual concentrating rate meet following equation:
P is corresponding to grid vector θ=[θ in formula (4)1,θ2,…,θD]TSparse vector,Indicate noise vector, it is sparse to
Amount p can obtain sparse vector estimated value using the OMP algorithm solution in compressed sensing
Step 6: obtaining signal direction of arrival by sparse vector
If sparse vector estimated valueIn i-th it is non-zero, then it represents that corresponding θiDirection has signal, otherwise indicates not believe
Number.
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