CN108445442A - A kind of near-field signals source localization method based on the singular value decomposition blocked - Google Patents
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Abstract
The present invention discloses a kind of near-field signals source localization method based on the singular value decomposition blocked, and includes the following steps：1. the electrical angle of estimation of near field signalInitial value, and calculate initial covariance matrix R；2. calculating the oblique projection operator of electrical angle initial value；3. obtaining updated covariance matrix according to oblique projection operator4. according to electrical angle initial value and updated covariance matrix, electric angle angle value is updated；5. if update electric angle angle value and the difference of electrical angle initial value are less than given threshold, the positioning that final electric angle angle value completes near-field signals source is obtained, otherwise using updated electric angle angle value as initial value, step 2 to 5 is repeated and is iterated.The floating error caused by the characteristic value by noise subspace is eliminated, precision of prediction is improved.Effectively eliminate influencing each other between multiple near-field signals, by iteration for several times can within the scope of certain allowable error approaching to reality value.
Description
Technical field
The invention belongs to array signal processing technologies, are related to a kind of localization method of near field multisignal source, specially
A kind of near-field signals source localization method based on the singular value decomposition blocked.
Background technology
Signal source positioning is the root problem of field of signal processing, and it is in microphone array, radar, sonar, wireless
The fields such as communication, seismology and robot are all widely used.Therefore, educational circles proposes a large amount of algorithm and solves far field scene
Under narrow band signal arrival bearing's estimation problem.Wherein, array received to wave be considered as plane wave.However, near field
Under scene, the wave for being incident on array has spherical corrugated, this also cause signal that array received arrives should by direction of arrival and
Two parameters of distance describe simultaneously.
The algorithm of most of near-field signals source positioning is all based on does approximation with Taylor's second order expension to spherical corrugated.Recently,
Also it has been proposed that some are based on high-order statistic, the algorithm of Cyclostationarity and maximal possibility estimation.Compared to above-mentioned
These three algorithms, path following algorithm, the algorithm of Hu Tianyu high-precision signals subspace, the algorithm based on tensor and based on rotation
The algorithm computation burden for turning the Signal parameter estimation of invariance is smaller, without calculating high-order statistic or multi-dimensional search.
By using the special property of the second-order statistics for the signal observed from symmetrically and evenly linear array, there is
Person proposes a kind of algorithm of the linear prediction of weighting.However, in order to take the covariance matrix of signal into account, it is necessary to about incidence
The priori of the design feature of signal covariance matrix, and this is only just effective when number of snapshots are larger.So this method
The poor performance when number of snapshots are smaller because the error of covariance estimation cause the Mutual coupling near field signal-to-noise ratio it is low and
All occurs saturated phenomenon in the case of height.Here " it is saturated " evaluated error for referring to direction of arrival in the case of high s/n ratio still
Keep higher value.
Invention content
For problems of the prior art, the present invention provides a kind of near-field signals based on the singular value decomposition blocked
Source localization method is utilized the anti-diagonal element of covariance matrix this design feature, passes through the iteration based on oblique projection operator
Algorithm, saturated phenomenon is obtained for effective solution in the case of lower signal-to-noise ratio and smaller number of snapshots.
The present invention is to be achieved through the following technical solutions：
A kind of near-field signals source localization method based on the singular value decomposition blocked, includes the following steps：
Step 1, the electrical angle of estimation of near field signalWithInitial value, and calculate initial covariance square
Battle array R；
Step 2, the oblique projection operator of electrical angle initial value is calculated；
Step 3, updated covariance matrix is obtained according to oblique projection operator
Step 4, according to electrical angle initial value and updated covariance matrix, electric angle angle value is updated；
Step 5, if update electric angle angle value and the difference of electrical angle initial value are less than given threshold, final electric angle is obtained
Angle value completes the positioning in near-field signals source, otherwise using updated electric angle angle value as initial value, repeats step 2 to 5 and changes
Generation.
Preferably, which is characterized in that in the step 1, estimated using the singular value decomposition and linear prediction method blocked
The initial value of the electrical angle of near-field signals.
Further, which is characterized in that utilize the singular value decomposition and linear prediction method estimation of near field signal blocked
The initial value of electrical angle, is as follows：
It is poised for battle and is listed in the near-field signals data that moment n is received
It is handled as follows, wherein 2M+1 is array element element number of array, ()TIndicate transposition；
Step 1.1, initial covariance matrix R is calculated；
X (n) is expressed as vector matrix form：
Wherein, K indicates the total number of near-field signals, θkAnd rkIndicate k-th of incoming signal incident angle and it is incident away from
From a (θk,rk) it is direction vector, sk(n) sampled value of k-th of the signal of expression in moment n；A is direction matrix, is expressed asS (n) indicates sampled value of the near-field signals vector in moment n of incidence,
It is expressed asω (n) indicates additive noise vector in the sampled value of moment n, table
It is shown as
R=E { x (n) x (n)H}；
Wherein, expectation, () are asked in E { } expressionsHIndicate Ai Er meter Te transposition；
Step 1.2, linear prediction model is built according to the back-diagonal element of R；
P-th of element of the b articles back-diagonal vector of R can be expressed as,
Wherein,Indicate the power of k-th of near-field signals, σ2Indicate the power of noise signal, electrical angle ψkAnd φkRespectively
It is defined asD is array element spacing, and λ is near-field signals wavelength,
B=0, ± 1 ..., ± 2M, p=-M+b-,…M-b+,δ () indicates Crow
Interior gram of function；
And then linear prediction model is obtained,
Wherein,The M-b of the b articles back-diagonal of representing matrix R+- l-1 elements, ()TIndicate transposition,It is the coefficient vector of linear prediction model,
Q representative model exponent numbers；
Step 1.3, the coefficient vector of linear prediction model is estimated using the singular value decomposition blocked；
First, it is R to the Matrix-Vector form of linear prediction model(b)a(b)=g(b)Singular value decomposition is carried out to obtain,
Wherein, ()HAi Er meter Te transposition are represented,
Then, coefficient vector is calculated by following formula,
Wherein, the preceding K characteristic value of representation signal subspace is larger, represents the rear q-1-K characteristic value of noise subspace
It is smaller, i.e.,
Step 1.4, according to coefficient vector a(b), structure linear prediction multinomial D(b)(z)；
Wherein, z=2j (ψk-bφk),
Step 1.5, according to D(b)(z) justify K nearest zero in z-plane parasang to estimate to obtain the electricity of near-field signals
Angle ψkAnd φkInitial value.
Preferably, which is characterized in that in the step 2, K oblique projection operator of electrical angle initial value is as follows,
Wherein, Indicate k-th of direction vector,Expression remove direction to
AmountDirection matrix afterwards.
Preferably, which is characterized in that in step 3, using oblique projection operator Separation of Coherent Signals and incoherent signal, obtain
Updated covariance matrix
Wherein, I2M+1Indicate the unit matrix of 2M+1 dimensions,Indicate the estimated value of initial covariance matrix R,Indicate kth
The signal power of a near-field signals, It is RwEstimated value,
Indicate the surplus of non-signal part in initial covariance matrix.
Further, which is characterized in that the estimated value of initial covariance matrix RIndicate as follows,
Wherein, { }*Conjugate operation is sought in expression,Indicate the signal power of k-th of near-field signals,Indicate k-th of side
To vector,Direction vector is removed in expressionDirection matrix afterwards,N is indicated
Total hits,Signal s is removed in representativek(n) near-field signals vector,Representative and AkCorresponding signal covariance square
Battle array.
Preferably, which is characterized in that step 5 is as follows,
Judge whether update electric angle angle value and the difference of electrical angle initial value is less than given threshold ε according to the following formula,
Iteration is terminated if setting up, exports final electric angle angle value
Otherwise, incremented circulation index index (i=i+1) continues iteration.
Preferably, according to mapping relations following between actual parameter and electrical angle, final electrical angle is done and is mapped
Direction of arrival to multisignal source and incident distance, complete the positioning in near-field signals source；
Wherein, d is array element spacing, and λ is the wavelength in incident near-field signals source.
Compared with prior art, the present invention has technique effect beneficial below：
In the localization method of near-field signals source of the present invention, the singular value decomposition blocked only utilizes and near-field signals son sky
Between relevant characteristic value calculate linear predictor coefficient, eliminate the floating error caused by the characteristic value by noise subspace, carry
High precision of prediction.The introducing of oblique projection operator, on the one hand so that the facing arrays aperture of each signal increases, improving can profit
Information content；On the other hand, due to only considering a signal every time, the mutual shadow between multiple near-field signals is effectively eliminated
Ring, by iteration for several times can within the scope of certain allowable error approaching to reality value.So as in the lower feelings of number of snapshots
Also superior performance can be kept under condition, therefore robustness is stronger, successfully solve the " full of parameter Estimation in the case of high s/n ratio
With " phenomenon.
Description of the drawings
Fig. 1 is to indicate corrected symmetrical uniform linear array according to the ... of the embodiment of the present invention.
Fig. 2 a are the variations for indicating near-field signals Mutual coupling performance with signal-to-noise ratio.
Fig. 2 b are the variations for indicating near-field signals Mutual coupling performance with number of snapshots.
Specific implementation mode
With reference to specific embodiment, the present invention is described in further detail, it is described be explanation of the invention and
It is not to limit.
Data model of the present invention and problem are described as follows.
As shown in Figure 1, it is contemplated that K near field narrowband incoherent signal { sk(n) } one is incident on by 2M+1 in moment n
On the uniform linear array that the array element that a spacing is d forms, and assume that the array of these array elements composition is calibrated completely.If
The center array element for determining array is phase reference point, then the near-field signals x with noise that m-th of array element receivesmIt (n) can be with table
It is shown as
Wherein, m=-M ..., M, sk(n) indicate k-th of signal in the sampled value of moment n, ωm(n) be additive noise when
Carve the sampled value of n, τmkIt is k-th of signal phase delay caused by time delay between reference array element and m-th of array elementWherein θkAnd rkIndicate k-th of signal direction of arrival angle and
Distance, λ are the wavelength of incident near-field signals.When k-th of signal is in Fresnel region, time delay item τmkIt can be by second order
Taylor expansion obtains good approximation, i.e.,
Wherein,Since they are actual parameter
It is mapped to simpler form, so being called electrical angle.Ignored exponent number is represented to be equal to or more thanItem.So, the near-field signals vector received
It can be expressed as again with the form of vector sum matrix in the sampled value of moment n
Wherein, ()TRepresent transposition, s (n) and ω (n) be byWithGiven incoming signal vector sum additive noise vector respectively.A is
By the direction matrix of the uniform linear array by calibration, it is expressed as
It is the direction vector of array, can be expressed as
In the present invention, it is assumed that the response matrix A full ranks (for example, the order of A is K) of array, incoming signal { sk(n) } it is
The stationary stochastic process of the zero-mean of broad sense, additive noise { ωm(n) } be space-time complex field white Gaussian random process, mean value
It is zero, variance σ2, and with signal { sk(n) } uncorrelated.The number K of incoming signal is it is known that and meet K≤M.
Near-field signals source of the present invention localization method is described below, is included the following steps：
1) electrical angle of estimation of near field signalWithInitial value, and calculate initial covariance matrix R；
2) the oblique projection operator of electrical angle initial value is calculated；
3) updated covariance matrix is obtained according to oblique projection operator
4) according to electrical angle initial value and updated covariance matrix, electric angle angle value is updated；
5) if updated electric angle angle value and the difference of electrical angle initial value are less than given threshold, final electric angle is obtained
Angle value completes the positioning in near-field signals source, otherwise using updated electric angle angle value as initial value, repeats step 2 to 5 and changes
Generation.
In the step 1), the electrical angle of the singular value decomposition and linear prediction method estimation of near field signal blocked is utilized
Initial value is as follows：The near-field signals data that 2M+1 is clapped
It is handled as follows,
A, initial covariance matrix R is calculated
R=E { x (n) x (n)H} (4)
Wherein, expectation, () are asked in E { } expressionsHIndicate Ai Er meter Te transposition.
B, linear prediction model is built according to the back-diagonal element of R
Wherein,Indicate p-th of element of the vector being made of the b row back-diagonal elements of covariance matrix R, K tables
Show near-field signals number, b=-M+b-..., M-b+, p=-M+b_... M-b+, δ () indicate Kronecker function.
All elementsConstitute vector r(b).Vector r(b)Before being divided into that L is overlapped and being made of q element
To vector, then entryIt can predict to obtain from the linear combination by other vector elements
Wherein,
(6) the Matrix-Vector form of formula is R(b)a(b)=g(b) (7)
Wherein,It is the coefficient vector of linear prediction model,
q
Representative model exponent number.
C, the coefficient vector of linear prediction model described above is estimated using the singular value decomposition blocked.Formula (7) is done very
Different value decomposes to obtain
Wherein, ()HAi Er meter Te transposition are represented,
Further, coefficient vector can be calculated by following formula
Wherein, the preceding K characteristic value of representation signal subspace is larger, represents the rear q-1-K characteristic value of noise subspace
It is smaller, i.e.,
D, according to coefficient vector a(b), structure linear prediction multinomial D(b)(z)。
Wherein, z=2j (ψk-bφk),
The electrical angle ψ of near-field signalskAnd φkφkInitial value can be from D(b)(z) justify nearest K in z-plane parasang
A zero is estimated to obtain.
2) K oblique projection operator of electrical angle initial value is calculated；
The estimated value of initial covariance matrix RIt is expressed as following form
Wherein, { }*Conjugate operation is sought in expression,Indicate the signal power of k-th of near-field signals,Indicate k-th of side
To vector,Direction vector is removed in expressionDirection matrix afterwards,N is indicated
Total hits,Signal s is removed in representativek(n) near-field signals vector,Representative and AkCorresponding signal covariance square
Battle array.
In order to eliminate influencing each other between signal and noise, i.e. Section 2, Section 3 and Section 4 in formula (11), count
Calculate K new oblique projection operators
Wherein,
Wherein, I2M+1Indicate the unit matrix of 2M+1 dimensions.
3) oblique projection operator Separation of Coherent Signals and incoherent signal, the covariance matrix obtained after update are utilized
To formula (11), premultiplication and the right side multiply projection operator respectively, and wherein Section 2, Section 3 and Section 4 are due to projection operator
Characteristic be eliminated, i.e.,
Wherein, I2M+1Indicate the unit matrix of 2M+1 dimensions,Indicate the estimated value of initial covariance matrix R, It is RwEstimated value, indicate non-near in initial covariance matrix
The surplus of field signal and noise signal portions.When signal-to-noise ratio is sufficiently large,It is sufficiently small, then
It is obvious that at this timeOnly include the ψ of k-th of near-field signalsk-bφkInformation.
4) according to electrical angle initial value and updated covariance matrix, electric angle angle value is updated；
Updated covariance matrix substitution step 1) can be calculated to the estimated value of this iteration.
5) if update electric angle angle value and the difference of electrical angle initial value are less than given threshold, final electric angle angle value is obtained
The positioning for completing near-field signals source repeats step 2 to 5 and is iterated otherwise using updated electric angle angle value as initial value.
Specifically, being decided whether to carry out next step iteration according to the difference of electrical angle between iteration twice, if iteration is poor
Value is less than a certain small threshold, such as：
Wherein, ε is arbitrary a smaller normal number, terminates iteration, exports final electric angle angle valueOtherwise, incremented circulation index index (i=i+1) continues iteration.Because of actual parameter and electricity
Meet certain mapping relations between angle, i.e., So right
Electrical angle, which does corresponding mapping, can solve the direction of arrival of multisignal source and incident distance.
Numerical simulation demonstrates the validity of the method for the present invention,
The symmetrical uniform linear array that method proposed in this paper is made of by one array element that 9 spacing are d
Carry out simulating, verifying.It is assumed that two incident near-field signals power are equal, wavelength λ, incident angle and distance is respectively
(6 °, 2.5 λ), (20 °, 3.5 λ).The threshold value of iterative algorithm is set as 10-6.Fixed signal-to-noise ratio and number of snapshots are respectively set to
10dB and 200.
Fig. 2 a and Fig. 2 b indicate the estimation performance of angle and distance in the positioning of near-field signals source with signal-to-noise ratio and snap respectively
Several change curves.As can be seen that in signal-to-noise ratio and larger number of snapshots, method (solid line in figure) proposed in this paper and performance are estimated
The theory lower bound (dotted line in figure) of meter closely, illustrates that iterative algorithm effectively eliminates saturated phenomenon, greatly improves
Parameter Estimation Precision.
Claims (8)
1. a kind of near-field signals source localization method based on the singular value decomposition blocked, which is characterized in that include the following steps：
Step 1, the electrical angle of estimation of near field signalWithInitial value, and calculate initial covariance matrix R；
Step 2, the oblique projection operator of electrical angle initial value is calculated；
Step 3, updated covariance matrix is obtained according to oblique projection operator
Step 4, according to electrical angle initial value and updated covariance matrix, electric angle angle value is updated；
Step 5, if update electric angle angle value and the difference of electrical angle initial value are less than given threshold, final electric angle angle value is obtained
The positioning for completing near-field signals source repeats step 2 to 5 and is iterated otherwise using updated electric angle angle value as initial value.
2. a kind of near-field signals source localization method based on the singular value decomposition blocked according to claim 1, feature
Be, in the step 1, using the singular value decomposition and linear prediction method estimation of near field signal blocked electrical angle it is initial
Value.
3. a kind of near-field signals source localization method based on the singular value decomposition blocked according to claim 2, feature
It is, utilizes the initial value of the electrical angle of the singular value decomposition and linear prediction method estimation of near field signal blocked, specific steps
It is as follows：
It is poised for battle and is listed in the near-field signals data that moment n is received
It is handled as follows, wherein 2M+1 is array element element number of array, ()TIndicate transposition；
Step 1.1, initial covariance matrix R is calculated；
X (n) is expressed as vector matrix form：
Wherein, K indicates the total number of near-field signals, θkAnd rkIndicate the incident angle of k-th of incoming signal and incident distance, a
(θk,rk) it is direction vector, sk(n) sampled value of k-th of the signal of expression in moment n；A is direction matrix, is expressed asS (n) indicates sampled value of the near-field signals vector in moment n of incidence,
It is expressed asω (n) indicates additive noise vector in the sampled value of moment n, table
It is shown as
R=E { x (n) x (n)H}；
Wherein, expectation, () are asked in E { } expressionsHIndicate Ai Er meter Te transposition；
Step 1.2, linear prediction model is built according to the back-diagonal element of R；
P-th of element of the b articles back-diagonal vector of R can be expressed as,
Wherein,Indicate the power of k-th of near-field signals, σ2Indicate the power of noise signal, electrical angle ψkWithkIt is respectively defined asD be array element spacing, λ be near-field signals wavelength, b=0,
± 1 ..., ± 2M, p=-M+b-,…M-b+,δ () indicates Kronecker letter
Number；
And then linear prediction model is obtained,
Wherein,The M-b of the b articles back-diagonal of representing matrix R+- l-1 elements, ()TIndicate transposition,It is the coefficient vector of linear prediction model,q
Representative model exponent number；
Step 1.3, the coefficient vector of linear prediction model is estimated using the singular value decomposition blocked；
First, it is R to the Matrix-Vector form of linear prediction model(b)a(b)=g(b)Singular value decomposition is carried out to obtain,
R(b)Hg(b)=U(b)Λ(b)V(b)H,
Wherein, ()HAi Er meter Te transposition are represented,
Then, coefficient vector is calculated by following formula,
Wherein, the preceding K characteristic value of representation signal subspace is larger, and the rear q-1-K characteristic value for representing noise subspace is smaller,
I.e.
Step 1.4, according to coefficient vector a(b), structure linear prediction multinomial D(b)(z)；
Wherein, z=2j (ψk-bφk),
Step 1.5, according to D(b)(z) justify K nearest zero in z-plane parasang to estimate to obtain the electrical angle ψ of near-field signalsk
And φkInitial value.
4. a kind of near-field signals source localization method based on the singular value decomposition blocked according to claim 1, feature
It is, in the step 2, K oblique projection operator of electrical angle initial value is as follows,
Wherein, Indicate k-th of direction vector,Direction vector is removed in expression
Direction matrix afterwards.
5. a kind of near-field signals source localization method based on the singular value decomposition blocked according to claim 1, feature
It is, in step 3, using oblique projection operator Separation of Coherent Signals and incoherent signal, obtains updated covariance matrix
Wherein, I2M+1Indicate the unit matrix of 2M+1 dimensions,Indicate the estimated value of initial covariance matrix R,Indicate k-th closely
The signal power of field signal, It is RwEstimated value, indicate
The surplus of non-signal part in initial covariance matrix.
6. a kind of near-field signals source localization method based on the singular value decomposition blocked according to claim 5, feature
It is, the estimated value of initial covariance matrix RIndicate as follows,
Wherein, { }*Conjugate operation is sought in expression,Indicate the signal power of k-th of near-field signals,Indicate k-th of direction to
Amount,Direction vector is removed in expressionDirection matrix afterwards,N expressions are always adopted
Sample number,Signal s is removed in representativek(n) near-field signals vector,Representative and AkCorresponding signal covariance matrix.
7. a kind of near-field signals source localization method based on the singular value decomposition blocked according to claim 1, feature
It is, step 5 is as follows,
Judge whether update electric angle angle value and the difference of electrical angle initial value is less than given threshold ε according to the following formula,
Iteration is terminated if setting up, exports final electric angle angle value
Otherwise, incremented circulation index index (i=i+1) continues iteration.
8. a kind of near-field signals source localization method based on the singular value decomposition blocked according to claim 1, feature
It is, according to mapping relations following between actual parameter and electrical angle, mapping is done to final electrical angle and obtains multisignal source
Direction of arrival and incident distance, complete the positioning in near-field signals source；
Wherein, d is array element spacing, and λ is the wavelength in incident near-field signals source.
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