CN105044453B - A kind of harmonic frequency signal method of estimation suitable for Complex Noise background - Google Patents

A kind of harmonic frequency signal method of estimation suitable for Complex Noise background Download PDF

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CN105044453B
CN105044453B CN201510489544.3A CN201510489544A CN105044453B CN 105044453 B CN105044453 B CN 105044453B CN 201510489544 A CN201510489544 A CN 201510489544A CN 105044453 B CN105044453 B CN 105044453B
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CN105044453A (en
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杨世永
冯玉文
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Shandong Taikai Electric Automation Co ltd
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Abstract

The present invention discloses a kind of a kind of harmonic frequency signal method of estimation suitable for Complex Noise background of high, the achievable super-resolution estimation of computational accuracy；It, which comprises the following steps, is achieved：1) circulation covariance is calculated；2) construction circulation covariance matrix；3) Eigenvalues Decomposition is carried out；4) secondary structural matrix；5) singular value decomposition is carried out；6) it is basic structural matrix R, S, T with step 5)；7) structural matrix W=RHGT；8) structural matrix beam { S, W }, and carry out generalized eigenvalue decomposition；9) frequency estimation is calculated.

Description

A kind of harmonic frequency signal method of estimation suitable for Complex Noise background
Technical field
The present invention relates to field of signal processing, more particularly to a kind of harmonic frequency signal suitable for Complex Noise background to estimate Meter method.
Background technology
The Parameter Estimation Problem of harmonic signal has a wide range of applications in multiple field of signal processing, mainly from by noise The frequency of harmonic signal is estimated in the observation signal of pollution.According to noise pollution different situations generally can be divided into additive noise and Two kinds of situations of complex background noise (also known as multiplying property and additive noise).
At present, in Complex Noise background the method for estimation of harmonic frequency signal mainly have Cyclic Statistics method (Li Hongwei, Cheng Qian life " the Cyclic Statistics method of Harmonic retrieval in multiplying property and additive noise ", electronic letters, vol, volume 26, the 7th phase, 1998 Year) and general covariance matrix method (" harmonic wave in multiplying property and additive noise based on general covariance matrix is extensive by forever for poplar generation It is multiple ", signal processing, volume 28, the 2nd phase, 2012).Cyclic Statistics method is to be based on Cyclic Statistics, using in quick Fu Leaf transformation and peak value searching method are realized, due to being influenced by Rayleigh limit, the estimated accuracy and frequency point of Cyclic Statistics method Resolution is not high.General covariance matrix method estimates the frequency of harmonic signal using the constant technology of Subspace Rotation, but it is realized Process is complicated, and the resolution ratio of Frequency Estimation is low.Therefore, it is necessary to above-mentioned technical problem is solved.
The content of the invention
It is an object of the invention to overcome the deficiencies in the prior art, real needs are adapted to, there is provided a kind of computational accuracy height, can Realize the harmonic frequency signal method of estimation suitable for complex background noise of super-resolution estimation.
In order to achieve the object of the present invention, the technical solution adopted in the present invention is：
A kind of harmonic frequency signal method of estimation suitable for Complex Noise background is designed, it comprises the following steps：
1) circulation covariance c (k) is calculated；
2) two circulation covariance matrix A and matrix B are constructed；
3) Eigenvalues Decomposition is carried out to matrix A, the minimum value of gained characteristic value is denoted as λmin；
4) F and G, wherein F=A- λ are constructedminI, G=B- λminZ；
5) singular value decomposition is carried out to matrix F, the left singular vector matrix of gained is denoted as U, singular value matrix is denoted as Σ, right Singular value vector matrix is denoted as V；
6) preceding P row one new matrix of composition of the left singular vector matrix U in step 5) is denoted as R, by singular value square The preceding P rows and preceding P row one new matrix of composition of battle array Σ is denoted as S, and the preceding P row composition one of right singular value vector matrix V is new Matrix be denoted as T；
7) structural matrix W=RHGT, wherein ()HRepresent conjugate transposition computing；
8) structural matrix beam { S, W }, and generalized eigenvalue decomposition is carried out to pencil of matrix { S, W }；
9) frequency estimation is calculated.
Further, the method for the calculating circulation covariance c (k) is：If N number of data measurement of harmonic signal is x (1), x (2) ..., x (N), P are harmonic component number, and for integer K of the value range in [P+1, N/2], calculating follows Ring covariance c (k), wherein k=0,1,2 ..., K, then：
Wherein ()*Expression takes conjugate operation；
Further, described two circulation covariance matrix A of construction and matrix B method are：Using circulating covariance c (0), C (1), c (2) ..., c (K) construct the matrix A and B of two K × K, i.e.,：
Further, in the step 4), wherein：
Further, after carrying out generalized eigenvalue decomposition to pencil of matrix { S, W }, P generalized eigenvalue of gained is denoted as ω1, ω2..., ωP。
Further, the method for the calculating frequency estimation is：IfFor the estimate of harmonic frequency signal, then：K=1,2 ..., P ..., wherein ∠ represent to take argument computing.
The beneficial effects of the present invention are：
The method of the present invention can realize the Frequency Estimation that super-resolution is carried out to complex background noise harmonic signal, and this The precision of method harmonic frequency signal estimation is high, solves existing method and realizes process complexity, the low skill of Frequency Estimation resolution ratio Art problem.
Brief description of the drawings
Fig. 1 is the flow diagram of the method for the present invention；
Embodiment
The present invention is further described with reference to the accompanying drawings and examples：
Embodiment 1：A kind of harmonic frequency signal method of estimation suitable for Complex Noise background, referring to Fig. 1, this method it Comprise the following steps and be achieved：
1) circulation covariance c (k) is calculated；If N number of data measurement of harmonic signal is x (1), x (2) ..., x (N), P are Harmonic component number, for integer K of the value range in [P+1, N/2], calculates circulation covariance c (k), wherein k= 0,1,2 ..., K, then：
Wherein ()*Expression takes conjugate operation.
2) two circulation covariance matrix A and matrix B are constructed；Using circulating covariance c (0), c (1), c (2) ..., c (K) The matrix A and B of two K × K is constructed, i.e.,：
3) Eigenvalues Decomposition is carried out to matrix A, the minimum value of gained characteristic value is denoted as λmin；
4) F and G, wherein F=A- λ are constructedminI, G=B- λminZ；Wherein：
5) singular value decomposition is carried out to matrix F, the left singular vector matrix of gained is denoted as U, singular value matrix is denoted as Σ, right Singular value vector matrix is denoted as V；
6) preceding P row one new matrix of composition of the left singular vector matrix U in step 5) is denoted as R, by singular value square The preceding P rows and preceding P row one new matrix of composition of battle array Σ is denoted as S, and the preceding P row composition one of right singular value vector matrix V is new Matrix be denoted as T；
7) structural matrix W=RHGT, wherein ()HRepresent conjugate transposition computing；
8) structural matrix beam { S, W }, and generalized eigenvalue decomposition is carried out to pencil of matrix { S, W }, and P broad sense of gained is special Value indicative is denoted as ω1, ω2..., ωP；
9) frequency estimation is calculated：IfFor the estimate of harmonic frequency signal, then：K=1, 2 ..., P, wherein ∠ represent to take argument computing.
Although what the embodiment of the present invention was announced is preferred embodiment, it is not limited thereto, the common skill of this area Art personnel, easily according to above-described embodiment, understand the spirit of the present invention, and make different amplification and change, but as long as not taking off From the present invention spirit, all within the scope of the present invention.

Claims (3)

  1. A kind of 1. harmonic frequency signal method of estimation suitable for Complex Noise background, it is characterised in that：It comprises the following steps：
    1) circulation covariance c (k) is calculated；
    2) two circulation covariance matrix A and matrix B are constructed；
    3) Eigenvalues Decomposition is carried out to matrix A, the minimum value of gained characteristic value is denoted as λmin；
    4) F and G, wherein F=A- λ are constructedminI, G=B- λminZ；
    5) singular value decomposition is carried out to matrix F, the left singular vector matrix of gained is denoted as U, singular value matrix is denoted as Σ, right unusual Value vector matrix is denoted as V；
    6) preceding P row one new matrix of composition of the left singular vector matrix U in step 5) is denoted as R, by singular value matrix Σ Preceding P rows and preceding P row one new matrix of composition be denoted as S, by the preceding P of right singular value vector matrix V row one new square of composition Battle array is denoted as T；
    7) structural matrix W=RHGT, wherein ()HRepresent conjugate transposition computing；
    8) structural matrix beam { S, W }, and generalized eigenvalue decomposition is carried out to pencil of matrix { S, W }；
    9) frequency estimation is calculated；
    It is described calculate circulation covariance c (k) method be：If N number of data measurement of harmonic signal is x (1), x (2) ..., x (N), P is harmonic component number, for integer K of the value range in [P+1, N/2], calculates circulation covariance c (k), Wherein k=0,1,2 ..., K, then：
    <mrow> <mi>c</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>M</mi> <mo>-</mo> <mi>k</mi> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mi>k</mi> </mrow> </munderover> <msup> <mi>x</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>(</mo> <mrow> <mi>n</mi> <mo>+</mo> <mi>k</mi> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>*</mo> <mo>-</mo> <mfrac> <mn>1</mn> <msup> <mrow> <mo>(</mo> <mi>M</mi> <mo>-</mo> <mi>k</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mi>k</mi> </mrow> </munderover> <msup> <mi>x</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mi>k</mi> </mrow> </munderover> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>(</mo> <mrow> <mi>n</mi> <mo>+</mo> <mi>k</mi> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>*</mo> <mo>,</mo> </mrow>
    Wherein ()*Expression takes conjugate operation；
    Described two circulation covariance matrix A of construction and matrix B method are：Using circulating covariance c (0), c (1), c (2) ..., C (K) constructs the matrix A and B of two K × K, i.e.,：
    In the step 4), wherein：
  2. 2. a kind of harmonic frequency signal method of estimation suitable for Complex Noise background as claimed in claim 1, its feature exist In：After carrying out generalized eigenvalue decomposition to pencil of matrix { S, W }, P generalized eigenvalue of gained is denoted as ω1, ω2..., ωP。
  3. 3. a kind of harmonic frequency signal method of estimation suitable for Complex Noise background as claimed in claim 1, its feature exist In：It is described calculate frequency estimation method be：IfFor the estimate of harmonic frequency signal, then：
    <mrow> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mi>k</mi> </msub> <mo>=</mo> <mo>&amp;angle;</mo> <msub> <mi>&amp;omega;</mi> <mi>k</mi> </msub> <mo>/</mo> <mn>2</mn> <mo>,</mo> </mrow>
    K=1,2 ..., P ..., wherein ∠ represent to take argument computing.
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