CN106405487A - General spatial spectrum estimation method based on extended ESPRIT - Google Patents
General spatial spectrum estimation method based on extended ESPRIT 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
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Abstract
The invention relates to a general spatial spectrum estimation method based on extended ESPRIT. The method introduces a virtual reference array; the virtual reference array is determined by positions of array elements of an actual array, and a phase compensation matrix is defined by position difference between corresponding array elements of the actual array and the virtual array and one phase compensation angle; the phase compensation matrix is a diagonal unitary matrix; the unitary matrix is utilized to carry out phase compensation on an original signal feature space, and the signal feature space obtained after compensation is subjected to a classic ESPRIT algorithm to obtain a plurality of angle estimation values; but only one angle estimation value is output, and the angle is closest to the input phase compensation angle; and meanwhile, characteristic values of a fitting matrix corresponding to the angle estimation are output. Newly-defined general ESPRIT spatial spectrum can be calculated by utilizing the output angle estimation value and the corresponding characteristic values, and the general ESPRIT spatial spectrum has one spectrum peak at and only at the place of the real signal incident angle, so that direction-of-arrival estimation of the space signal can be obtained by searching the spectrum peak of the general ESPRIT spatial spectrum in a parameter space.
Description
Technical field
The invention belongs to Estimation of Spatial Spectrum technical field, it is related to a kind of general estimate based on the spatial spectrum of extension ESPRIT technology
Meter method.
Background technology
DoA estimation technique, through the development of nearly 40 years, has gradually formed perfect theoretical system.DoA estimation technique is big
Cause defines three developing stage.Earliest radar angle measurement uses mechanical scanning technology, and directional beam directive is aerial, if receiving
To echo-signal, then can determine whether in a transmit direction with the presence of target；Beam-forming technology assigns power to each transmitting antenna, finally
Form narrow directional beam, then by the way of electric scanning, the DoA of target can be estimated, this technology is referred to as conventional ripple
Bundle formation method (Conventional BF, CBF), is Bartlett Beam Expansion again.Due to being limited by Rayleigh limit, this skill
Art can not tell the multiple echo signals in a beam angle.For example for a standard M unit linear array (adjacent array element distance
Even linear array for half-wavelength), conventional beamformer method can only tell the space letter that angular interval is more than or equal to 2/M radian
Number.
1969, Capon proposed the undistorted response of minimum variance (Minimum Variance Distortionless
Response, MVDR) method, it is otherwise known as Capon or MVM (Minimum Variance Method) method.Capon method
Breach Rayleigh limit, the direction of arrival of multiple signals can be told in a beam angle.In addition it is based on linear prediction to promote
Maximum entropy (Maximum Entropy Method, MEM) method, and Pisarenko harmonic analysis method etc. is optimum based on certain
The method of Wave beam forming principle can obtain similar estimated result, they and be based on Adaptive beamformer (Adaptive
BF) the DoA algorithm for estimating of method all can tell multiple targets in a wave beam, and high-resolution DoA that is therefore otherwise known as is estimated
Meter technology.
The appearance of super-resolution (Super-resolution) DoA algorithm for estimating is then the important breakthrough of DoA estimation technique.Generation
Table algorithm has maximum likelihood method (Maximum Likelihood, ML), multiple signal classification method (MUltipleSIgnal
Classification, MUSIC) and ESPRIT algorithm, wherein latter two method is all subspace class DoA algorithm for estimating.Institute
It is because that they, so that DoA estimated accuracy has the raising of geometric progression, obtain with needle-like spectral peak to be referred to as super-resolution
Spatial spectrum.Maximum likelihood is the optiaml ciriterion in a kind of statistical significance, and it is introduced in DoA estimation.ML DoA estimates to calculate
Method typically will carry out multidimensional nonlinear search although there being Newton method, quasi- Newton method, alternating projection method, and maximum expected value method etc. is calculated
Method solving, but amount of calculation still very big thereby increases and it is possible to obtain locally optimal solution.
MUSIC algorithm is proposed respectively by Schimidt, Bienvenu and Kopp.Thereafter rooting MUSIC (Root-MUSIC),
Tenth of the twelve Earthly Branches root MUSIC (Unitary-Root-MUSIC), minimum modulus (Minimum Norm Method, MNM are also called weighting MUSIC)
It is proposed out respectively Deng also.MUSIC is that plain method is searched in a kind of exhaustion, mutually orthogonal with noise subspace using signal subspace
Characteristic is so that needle-like crest in the MUSIC spatial spectrum in spatial domain, then by searching plain crest location thus obtaining DoA's
Estimate.Weighted Sub-Space Fitting Direction (Weighted Subspace Fitting, WSF) is by searching for generated subspace and sample
Estimate a kind of spatial fit algorithm under least square (LS, the Least Square) criterion of subspace.WSF obtains in the case of asymptotic
To the object function of optimum power and direction determining method (MODE, the Method of that is given of Stoica and Sharman
Direction Estimation) object function the same, WSF is thus by maximum likelihood and MUSIC method from spatial fit
Angle is united.For unrelated signal source, the MUSIC algorithm of large sample is the realization of maximum likelihood estimate, therefore estimates
Meter result is consistent.There are a large amount of MUSIC correction algorithms at present, to search strategy and search plain interval and be optimized, such as gold-
MUSIC method, compression MUSIC method (Compressed MUSIC, C-MUSIC) and real-valued MUSIC algorithm (Real Valued-
MUSIC, RV-MUSIC) etc..MUSIC algorithm has versatility, and the DoA that can be used for arbitrary geometry array estimates.
ESPRIT algorithm is another kind of subspace class DoA algorithm for estimating, Toeplitz approximate data (Toeplitz
Approximation Method, TAM) be ESPRIT algorithm the other form of expression.ESPRIT algorithm provides DoA and estimates to close
The algebraic solution of conjunction form, therefore computational efficiency are very high, have milestone property meaning.This algorithm utilizes the rotation of signal subspace
Turn invariance principle that DoA is estimated, it requires array can mark off identical two subarrays (referred to as to move constant
Property).Array is divided into two identical submatrixs first, then estimates two submatrix signal subspaces, and according to two subspaces
The phase information of the characteristic value of fit metric just can estimate DoA parameter.Least square typically be can be utilized to fit metric
Or total least square (TLS, Total LS) criterion, to solve, therefore has LS-ESPRIT and TLS-ESPRIT algorithm accordingly.
If array also has centrosymmetric vandermonde (Vandermonde) form structure, tenth of the twelve Earthly Branches ESPRIT (Unitary- can be utilized
ESPRIT) algorithm is calculated in real-valued domain, and efficiency will obtain bigger raising.Although ESPRIT provides efficient algebraic solution
Method, but its condition premised on the motion immovability of array, therefore application scenarios are greatly limited.Occur in that various bases afterwards
In the innovatory algorithm of ESPRIT, purpose is exactly that this efficient Algebraic Method is used for the array of arbitrary structures.Dogan and
Mendel proposes the virtual ESPRIT algorithm (VESPA, Virtual ESPRIT Algorithm) based on Higher Order Cumulants, both carries
The high effective aperture of array, effectively can suppress gauss heat source model again, be studied much.But Higher Order Cumulants operand
Larger, more sensitive to model error.Virtual array technology based on interpolation (Interpolation) is to arbitrary geometry array
DoA estimates to provide another kind of solution, and actual Array Mapping is in a space set in advance angular domain block by it
One virtual array with vandermonde structure, then carries out DoA estimation using ESPRIT or Root-MUSIC algorithm.But this
Plant mapping only approximately equal in predetermined angular domain, become greatly in the outer mapping error of angular domain.Manifold isolation technics (Manifold
Separation Technique, MST) it is that another is used for arbitrary geometry array DoA approximate evaluation technology, MST is discrete
Fourier (Discrete Fourier Transform, DFT) beam space is interior to be a sampling matrix by manifold matrixing
(Sampling Matrix) and the product of a generalized circular matrix, array manifold matrix is common by array structure and sense
With decision, impact receipt signal being applied for characterization array.Using MST, one-dimensional DoA is estimated, sampling matrix only by
Array structure determines, the measured value (as recorded in darkroom) that therefore can be calibrated by some is through inverse discrete Fourier transformer inverse-discrete
(Inverse Discrete Fourier Transform, IDFT) off-line calculation draws.For arrival direction estimation, square of sampling
Battle array comprises pitching angular dimensions to be estimated, and therefore typically also needs to carry out spheric harmonic function (Spherical Harmonics) expansion, meter
Calculate complex and inevitably have truncated error.For Random sparseness array, MST to block modulus value higher, therefore
Do not only exist truncated error, solve high-order algebraic equation operand itself than larger yet.
Generally speaking, MUSIC method is applicable to the array of various structures, and classical ESPRIT algorithm is only applied to tool
There is the array of motion immovability, lack versatility, want to make ESPRIT algorithm be suitable for irregular array, then need using various approximate
Method.Therefore the present invention will design a kind of extension ESPRIT algorithm, then define a kind of space being applied to arbitrary geometry array
Spectrum, thus obtain the unbiased esti-mator of signal DoA.
Content of the invention
In view of this, it is an object of the invention to provide a kind of general based on extension ESPRIT technology Estimation of Spatial Spectrum side
Method, specifically includes following technical scheme：
A kind of general Estimation of Spatial Spectrum method based on extension ESPRIT technology, the method is applied to General Cell, including
But it is not limited to Random sparseness array；The method comprises the following steps：
S1：By classical ESPRIT (Estimation of Signal Parameters via Rotational
Invariance Techniques, ESPRIT estimate signal parameter technology) algorithm be modified as extend ESPRIT algorithm；
S2：Output using extension ESPRIT algorithm defines a kind of general ESPRIT spatial spectrum；
S3：The DoA obtaining final signal by searching for the spectrum peak position of general ESPRIT spatial spectrum estimates.
Further, in step sl, described extension ESPRIT algorithm refers to obtain characteristic signal from receiving data first
The estimation of subspace；Then introduce an auxiliary input variable being referred to as phase compensation angle, based on this variable and element position
A phase compensation matrix can be calculated, thus unitary transformation is carried out to original characteristic signal subspace；To through conversion
Signal space after renewal implements classical ESPRIT algorithm, obtains one (mono signal situation) or multiple (multi signal situation) angle
Degree is estimated, but only output and that angle valuation immediate of input phase offset angle, and export this angle valuation pair simultaneously
The characteristic value of the two sub-array signal spatial fit matrixes answered.
Further, in step s 2, the described output using extension ESPRIT algorithm defines a kind of general ESPRIT space
Spectrum includes：First calculate angle valuation and the absolute value of the difference at input phase compensation angle of extension ESPRIT algorithm output, count simultaneously
Calculate the mould of character pair value of extension ESPRIT algorithm output and the absolute value of 1 difference；General ESPRIT spatial spectrum is mended in phase place
Repay the inverse that the spectrum on angle direction is equal to this two absolute value sums；
The spectrum size of general ESPRIT spatial spectrum characterizes the signal subspace institute after phase compensation in some directions
The power of the motion immovability matter having, and if only if produces a needle-like spectrum in the true incident direction of signal for general ESPRIT spectrum
Peak.
The beneficial effects of the present invention is：This method introduces a virtual reference array, and this virtual array is by actual array
Element position determine, and by the alternate position spike between actual array array element corresponding with virtual array and a phase compensation angle
To define a phase compensation matrix.Phase compensation matrix is a diagonal unitary, special to primary signal using this unitary matrice
Levy space and carry out phase compensation, the ESPRIT algorithm then implementing classics to the signal characteristic space after overcompensation obtains multiple
Angle estimation, but only export an angle estimation, this angle is closest with the phase compensation angle of input, exports this angle simultaneously
Degree estimates the characteristic value of corresponding fit metric.Angle valuation and corresponding characteristic value using output just can calculate newly
The general ESPRIT spatial spectrum of definition, and and if only if at actual signal incident angle, and this general ESPRIT spatial spectrum has
One spectral peak, the spectral peak therefore searching plain general ESPRIT spatial spectrum in parameter space just can obtain the direction of arrival of spacing wave
Estimate.
Brief description
In order that the purpose of the present invention, technical scheme and beneficial effect are clearer, the present invention provides drawings described below to carry out
Explanation：
Fig. 1 is any linear array schematic diagram of M array element；
Fig. 2 is a M unit virtual uniform linear array schematic diagram；
Fig. 3 is extension ESPRIT algorithm block diagram；
Fig. 4 is to general during the constant power incidence simultaneously of 3 signals using a M=10 array element linear random arraya determining
ESPRIT spatial spectrum；
Fig. 5 be using array shown in Fig. 4 under two signal condition of incidence DoA estimate absolute deviation with SNR change
Situation；
Fig. 6 is the change feelings with SNR for the root-mean-square error of the DoA estimation that two signal incidence emulation experiments described in Fig. 5 obtain
Condition.
Specific embodiment
The invention provides a kind of phased array using arbitrary structures form is estimated to the direction of arrival of spacing wave
The method of meter.Classical ESPRIT algorithm is modified as extending ESPRIT algorithm by the method first；Then using extension ESPRIT
The output of algorithm defines a kind of general ESPRIT spatial spectrum；Obtain finally by the spectrum peak position searching for general ESPRIT spatial spectrum
The DoA of final signal estimates.
Described extension ESPRIT algorithm refers to obtain the estimation of characteristic signal subspace first from receiving data；Then draw
Enter an auxiliary input variable being referred to as phase compensation angle, a phase place can be calculated based on this variable and element position
Compensation matrix, thus carry out unitary transformation to original characteristic signal subspace；Signal space after conversion updates is implemented
Classical ESPRIT algorithm, obtains one (mono signal situation) or multiple (multi signal situation) angle estimation, but only output with defeated
That the angle valuation immediate of applying aspect offset angle, and export the corresponding two sub-array signal spaces of this angle valuation simultaneously
The characteristic value of fit metric.
Described general ESPRIT spatial spectrum is defined on the output of extension ESPRIT algorithm, first calculates extension ESPRIT
The angle valuation of algorithm output compensates the absolute value of the difference at angle with input phase, calculates the right of extension ESPRIT algorithm output simultaneously
Answer the mould of characteristic value and the absolute value of 1 difference；Spectrum on phase compensation angle direction for the general ESPRIT spatial spectrum is equal to
The inverse of this two absolute value sums.The spectrum size of general ESPRIT spatial spectrum characterizes in some directions after phase compensation
The power of the motion immovability matter that signal subspace has, and if only if for general ESPRIT spectrum in the true incident direction of signal
Produce a needle-like spectral peak, then pass through the estimation that search spectral peak obtains signal direction of arrival.
Below in conjunction with accompanying drawing, the preferred embodiments of the present invention are described in detail.
Fig. 1 is any linear array schematic diagram of M array element；Fig. 2 is a M unit virtual uniform linear array schematic diagram, and it is taken as
The referential array of true array, the end array element of true array and virtual array overlaps；Fig. 3 is extension ESPRIT algorithm block diagram；Fig. 4
It is shown that using a M=10 array element linear random arraya determining to the general ESPRIT during constant power incidence simultaneously of 3 signals
Spatial spectrum, sets noise as white Gaussian noise and signal to noise ratio as 30dB, the incident direction of three signals be respectively 172.96 °,
54.55 ° and 156.85 °, hits is 1000；Fig. 5 is using array shown in Fig. 4, the DoA under two signal condition of incidence to be estimated
Absolute deviation with SNR situation of change, the spatial spectrum scouting interval be 0.1 degree, two signal incident angles be 61.1 °, 71.5 °,
Hits is 1000；Fig. 6 is the change with SNR for the root-mean-square error of the DoA estimation that two signal incidence emulation experiments described in Fig. 5 obtain
Change situation, the scouting interval is 0.1 degree.
Specific embodiment：
(1) the position vector x=[x according to actual array bay1, x2..., xM] T to be determining phase compensation matrix
Γ (θ), wherein θ are phase compensation angle.
Calculate the distance between adjacent two array elements of virtual reference array d=(x firstM-x1)/(M-1), then obtain virtual
Position vector x '=[the x ' of each array element of referential array1, x '2..., x 'M] T, wherein x '1=x1, x 'j=x1+ d (j-1), j=
2 ..., M, thus can calculate the position difference vector Δ=[Δ of true array and virtual reference array1, Δ2..., ΔM]：=
x-x′.In tenth of the twelve Earthly Branches diagonal matrix Γ (θ) being defined in phase compensation angle θ it is：
(2) signal characteristic subspace is obtained according to the snapshot data receivingEstimation
First according to snapshot data z (k) receiving, k=1 ..., K is calculated sample covariance matrixHere K is total number of samples.Then rightCarry out feature decomposition, maximum N number of characteristic value is corresponding
The signal characteristic subspace obtaining as is estimated in the space of characteristic vector composition
HereFor the characteristic vector of sample covariance matrix,It is characterized vectorCorresponding feature
Value, and
(3) classical ESPRIT algorithm is extended, obtains the angle estimation output based on input phase offset angle θ
The signal characteristic subspace first estimation being obtainedCarry out phase compensation renewal (unitary transformation), after being updated
Signal subspace
Then selectFront M-1 row form the signal subspace of subarray 1SelectRear M-1 row composition submatrix
The signal subspace of row 2Solution fit equationObtain fit equation ⊙
Then feature decomposition is carried out to fit metric ⊙, obtain N number of characteristic value μJ, j=1 ..., N, true according to following relation
Fixed N number of estimation angle value
The angle valuation of finally output extension ESPRIT algorithm
Above formula shows, extension ESPRIT algorithm only exports and compensates that closest angle valuation of angle with input phase,
And export this angle valuation simultaneouslyCorresponding characteristic value μ.
(4) calculate the general ESPRIT space spectrum at phase compensation value θ
WhereinIt is the output angle valuation of the extension ESPRIT that corresponding phase compensates angle θ in step (3), μ isCorresponding
Fit metric characteristic value.
(5) interval travels through θ angular domain at an angle, and obtains the general ESPRIT of total space angular domain according to step (3)
Space spectrum.Choose the corresponding angle value of maximum N number of spectral peak for finally N number of signal Mutual coupling.
Finally illustrate, preferred embodiment above only in order to technical scheme to be described and unrestricted, although logical
Cross above preferred embodiment the present invention to be described in detail, it is to be understood by those skilled in the art that can be
In form and various changes are made to it, without departing from claims of the present invention limited range in details.
Claims (3)
1. a kind of general based on extension ESPRIT technology Estimation of Spatial Spectrum method it is characterised in that：The method is applied to arbitrarily
Array, including but not limited to Random sparseness array；The method comprises the following steps：
S1：By classical ESPRIT (Estimation of Signal Parameters via Rotational
Invariance Techniques, ESPRIT estimate signal parameter technology) algorithm be modified as extend ESPRIT algorithm；
S2：Output using extension ESPRIT algorithm defines a kind of general ESPRIT spatial spectrum；
S3：The DoA obtaining final signal by searching for the spectrum peak position of general ESPRIT spatial spectrum estimates.
2. a kind of general Estimation of Spatial Spectrum method based on extension ESPRIT technology according to claim 1, its feature exists
In：In step sl, described extension ESPRIT algorithm refers to obtain the estimation of characteristic signal subspace first from receiving data；
Then introduce an auxiliary input variable being referred to as phase compensation angle, one can be calculated based on this variable and element position
Individual phase compensation matrix, thus carry out unitary transformation to original characteristic signal subspace；Empty to the signal after conversion updates
Between implement the ESPRIT algorithm of classics, obtain one (mono signal situation) or multiple (multi signal situation) angle estimation, but only defeated
Go out that angle valuation immediate with input phase offset angle, and export the corresponding two subarray letters of this angle valuation simultaneously
The characteristic value of number spatial fit matrix.
3. a kind of general Estimation of Spatial Spectrum method based on extension ESPRIT technology according to claim 1, its feature exists
In：In step s 2, the described output using extension ESPRIT algorithm defines a kind of general ESPRIT spatial spectrum and includes：First calculate
The angle valuation of extension ESPRIT algorithm output compensates the absolute value of the difference at angle with input phase, calculates extension ESPRIT simultaneously and calculates
The mould of character pair value and the absolute value of 1 difference that method exports；General ESPRIT spatial spectrum is on phase compensation angle direction
Spectrum is equal to the inverse of this two absolute value sums；
The spectrum size of general ESPRIT spatial spectrum characterizes the signal subspace after phase compensation in some directions to be had
Motion immovability matter power, and if only if produces a needle-like spectral peak in the true incident direction of signal for general ESPRIT spectrum.
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| CN107479025A (en) * | 2017-08-15 | 2017-12-15 | 重庆邮电大学 | A kind of extensive linear array Estimation of Spatial Spectrum method of single snap |
| CN107870315A (en) * | 2017-11-06 | 2018-04-03 | 重庆邮电大学 | One kind utilizes iterative phase compensation technique estimation General Cell direction of arrival method |
| CN108710101A (en) * | 2018-04-10 | 2018-10-26 | 贵州理工学院 | A kind of DOA algorithm for estimating obtaining coherent signal subspace using orthogonality |
| CN109633520A (en) * | 2019-01-21 | 2019-04-16 | 重庆邮电大学 | A kind of uniform circular array super-resolution Estimation of Spatial Spectrum method |
| WO2019095912A1 (en) * | 2017-11-16 | 2019-05-23 | 华南理工大学 | Underwater direction of arrival estimation method and device based on uniform linear array with adjustable angle |
| CN112444810A (en) * | 2020-10-27 | 2021-03-05 | 电子科技大学 | Radar air multi-target super-resolution method |
| CN113422629A (en) * | 2021-06-17 | 2021-09-21 | 长安大学 | Covariance matrix reconstruction self-adaptive beam forming method and system |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN107479025A (en) * | 2017-08-15 | 2017-12-15 | 重庆邮电大学 | A kind of extensive linear array Estimation of Spatial Spectrum method of single snap |
| CN107870315A (en) * | 2017-11-06 | 2018-04-03 | 重庆邮电大学 | One kind utilizes iterative phase compensation technique estimation General Cell direction of arrival method |
| CN107870315B (en) * | 2017-11-06 | 2021-07-30 | 重庆邮电大学 | Method for estimating direction of arrival of any array by using iterative phase compensation technology |
| WO2019095912A1 (en) * | 2017-11-16 | 2019-05-23 | 华南理工大学 | Underwater direction of arrival estimation method and device based on uniform linear array with adjustable angle |
| CN108710101A (en) * | 2018-04-10 | 2018-10-26 | 贵州理工学院 | A kind of DOA algorithm for estimating obtaining coherent signal subspace using orthogonality |
| CN109633520A (en) * | 2019-01-21 | 2019-04-16 | 重庆邮电大学 | A kind of uniform circular array super-resolution Estimation of Spatial Spectrum method |
| CN112444810A (en) * | 2020-10-27 | 2021-03-05 | 电子科技大学 | Radar air multi-target super-resolution method |
| CN113422629A (en) * | 2021-06-17 | 2021-09-21 | 长安大学 | Covariance matrix reconstruction self-adaptive beam forming method and system |
| CN113422629B (en) * | 2021-06-17 | 2023-02-21 | 长安大学 | Covariance matrix reconstruction self-adaptive beam forming method and system |
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