CN105301354A - Harmonic signal frequency estimation method in multiplicative and additive noise - Google Patents

Abstract

The invention discloses a harmonic signal frequency estimation method in multiplicative and additive noise. The method comprises the following steps: cyclic covariance is calculated; a cyclic covariance matrix is built; a characteristic value is decomposed; a noise sub space matrix is built; spatial spectrum is calculated; and a frequency estimation value is calculated. The harmonic signal frequency estimation method in multiplicative and additive noise can improve the frequency estimation precision and the frequency resolution, and is easy to realize.

Description

Harmonic frequency signal method of estimation in a kind of multiplicative and additive noise

Technical field

The present invention relates to signal transacting field, particularly relate to harmonic frequency signal method of estimation in a kind of multiplicative and additive noise.

Background technology

In multiplicative and additive noise background, the Parameter Estimation Problem of harmonic signal has a wide range of applications in multiple field, and its fundamental purpose is from being estimated the harmonious wave frequency of the harmonic component number of harmonic signal the signal of noise pollution.

At present, in multiplicative and additive noise, the method for estimation of harmonic frequency signal mainly contains circle statistics metering method (Li Hongwei, Cheng Qiansheng. the circle statistics metering method of Harmonic retrieval " in multiplicative and the additive noise ", electronic letters, vol, the 26th volume, 7th phase, 1998) and general covariance matrix method (Yang Shiyong. " Harmonic retrieval based in the multiplicative of general covariance matrix and additive noise ", signal transacting, the 28th volume, 2nd phase, 2012).Circle statistics metering method is based on Cyclic Statistics, utilizes Fast Fourier Transform (FFT) and peak value searching method to realize.Due to the impact by Rayleigh limit, the estimated accuracy of circle statistics metering method and frequency resolution are not high.General covariance matrix method utilizes the constant technology of Subspace Rotation to estimate humorous wave frequency, but its implementation procedure is more complicated, and the resolution of Frequency Estimation is not high yet.

Summary of the invention

The invention provides harmonic frequency signal method of estimation in a kind of multiplicative and additive noise, to reach that computational accuracy is high, frequency resolution is high and to be easy to the object that realizes.

The present invention realizes above-mentioned purpose by the following technical solutions.Harmonic frequency signal method of estimation in a kind of multiplicative and additive noise, it comprises the following steps:

Step 1: computation cycles covariance;

Step 2: structure circulation covariance matrix;

Step 3: Eigenvalues Decomposition;

Step 4: build noise subspace matrix;

Step 5: computer memory is composed;

Step 6: calculated rate estimated value.

The method of described computation cycles covariance is: set N number of data measurement of harmonic signal as x (1), x (2) ... x (N), P is harmonic component number, for the integer M of a span in [P+1, N/2], computation cycles covariance c (α), α=0,1,2,, M-1:

Wherein () ^*represent and get conjugate operation.

The method of described structure circulation covariance matrix C is:

The method of described Eigenvalues Decomposition is: carry out Eigenvalues Decomposition to circulation covariance matrix C, the eigenwert of gained is denoted as λ by order from big to small ₁, λ ₂..., λ _m, corresponding feature value vector is denoted as e ₁, e ₂..., e _m.

The method of described structure noise subspace matrix Z is: Z=[e _p+1, e _p+2..., e _m].

The method of described computer memory spectrum is: a given positive integer K (span for (2P, M]), makes ω _x=2 π (k-1)/K; K=1,2 ..., K, first calculates β (ω _k):

Then by following formulae discovery spatial spectrum W (ω _k):

Wherein () ^hrepresent conjugate transpose operation.

The method of described calculated rate estimated value is: find out spatial spectrum W (ω successively _k) P peak value, first find out first peak value and the ω value of correspondence be designated as ω ₁, next is found out second largest peak value and the ω value of correspondence is designated as ω ₂, by parity of reasoning, finally finds out P large peak value and the ω value of correspondence is designated as ω _p; Calculate the estimated value of harmonic frequency signal for: m=1,2 ..., P.

Described second largest peak value is the peak value being only second to described first peak value.

Harmonic frequency signal method of estimation in multiplicative of the present invention and additive noise, its advantage is: precision and the frequency resolution that can improve Frequency Estimation, and is easy to realize.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention.

Embodiment

Be described principle of the present invention and feature below in conjunction with accompanying drawing, example, only for explaining the present invention, is not intended to limit scope of the present invention.

As shown in Figure 1, harmonic frequency signal method of estimation in a kind of multiplicative and additive noise, comprises the following steps:

Step 1: computation cycles covariance 101;

If N number of data measurement of harmonic signal is x (1), x (2) ..., x (N), P are harmonic component number, for the integer M of a span in [P+1, N/2], computation cycles covariance c (α), α=0,1,2 ..., M-1:

Wherein () ^*represent and get conjugate operation.

Step 2: structure circulation covariance matrix 102;

The method of structure circulation covariance matrix 102C is:

Step 3: Eigenvalues Decomposition 103;

Eigenvalues Decomposition 103 is carried out to circulation covariance matrix C, the eigenwert of gained is denoted as λ by order from big to small ₁, λ ₂..., λ _m, corresponding feature value vector is denoted as e ₁, e ₂..., e _m;

Step 4: build noise subspace matrix 104;

The method building noise subspace matrix 104Z is: Z=[e _p+1, e _p+2..., e _m].

Step 5: computer memory spectrum 105;

The method of computer memory spectrum 105 is: a given positive integer K (span for (2P, M]), makes ω _k=2 π (k-1)/K; K=1,2 ..., K, first calculates β (ω _k):

Then by following formulae discovery spatial spectrum W (ω _k):

Wherein () ^hrepresent conjugate transpose operation.

Step 6: calculated rate estimated value 106;

The method of calculated rate estimated value 106 is: find out spatial spectrum W (ω successively _k) P peak value, first find out first peak value and the ω value of correspondence be designated as ω ₁, next is found out second largest peak value and the ω value of correspondence is designated as ω ₂.First peak value is peak-peak.Second largest peak value is only second to first peak value.By parity of reasoning, finally finds out P large peak value and the ω value of correspondence is designated as ω _p.Calculate the estimated value of harmonic frequency signal for: ${\hat{f}}_m={\mathrm{\ω}}_m/2;m=1,2,\mathrm{...},P.$

Claims (8)

1. a harmonic frequency signal method of estimation in multiplicative and additive noise, it is characterized in that, it comprises the following steps:

Step 1: computation cycles covariance;

Step 2: structure circulation covariance matrix;

Step 3: Eigenvalues Decomposition;

Step 4: build noise subspace matrix;

Step 5: computer memory is composed;

Step 6: calculated rate estimated value.

2. harmonic frequency signal method of estimation in multiplicative according to claim 1 and additive noise, it is characterized in that, the method for described computation cycles covariance is: set N number of data measurement of harmonic signal as x (1), x (2) ..., x (N), P is harmonic component number, for the integer M of a span in [P+1, N/2], computation cycles covariance c (α), α=0,1,2,, M-1:

$c\left(\mathrm{\α}\right)=\frac{1}{M-\mathrm{\α}}\underset{n=1}{\overset{M-\mathrm{\α}}{\Σ}}{x}^2\left(n\right){\left(x^2\right(n+\mathrm{\α}\left)\right)}^{*}-\frac{1}{{(M-\mathrm{\α})}^2}\underset{n=1}{\overset{M-\mathrm{\α}}{\Σ}}{x}^2\left(n\right)\underset{n=1}{\overset{M-\mathrm{\α}}{\Σ}}{\left(x^2\right(n+\mathrm{\α}\left)\right)}^{*};$

Wherein () ^*represent and get conjugate operation.

3. harmonic frequency signal method of estimation in multiplicative according to claim 1 and additive noise, it is characterized in that, the method for described structure circulation covariance matrix C is:

4. harmonic frequency signal method of estimation in multiplicative according to claim 1 and additive noise, it is characterized in that, the method of described Eigenvalues Decomposition is: carry out Eigenvalues Decomposition to circulation covariance matrix C, the eigenwert of gained is denoted as λ by order from big to small ₁, λ ₂..., λ _m, corresponding feature value vector is denoted as e ₁, e ₂..., e _m.

5. harmonic frequency signal method of estimation in multiplicative according to claim 1 and additive noise, it is characterized in that, the method for described structure noise subspace matrix Z is: Z=[e _p+1, e _p+2..., e _m].

6. harmonic frequency signal method of estimation in multiplicative according to claim 1 and additive noise, is characterized in that, the method for described computer memory spectrum is: a given positive integer K (span for (2P, M]), makes ω _k=2 π (k-1)/K, k=1,2 ..., K, first calculates β (ω _k):

$\mathrm{\β}\left({\mathrm{\ω}}_k\right)=\left[\begin{array}{c}1\\ e^{-{\mathrm{j\ω}}_k}\\ e^{-j2{\mathrm{\ω}}_k}\\ .\\ .\\ .\\ e^{-j(M-1){\mathrm{\ω}}_k}\end{array}\right];$

Then by following formulae discovery spatial spectrum W (ω _k):

$W\left({\mathrm{\ω}}_k\right)=\frac{1}{{\mathrm{\β}}^H\left({\mathrm{\ω}}_k\right){\mathrm{ZZ}}^H\mathrm{\β}\left({\mathrm{\ω}}_k\right)};k=1,2,\mathrm{...},K,$

Wherein () ^hrepresent conjugate transpose operation.

7. harmonic frequency signal method of estimation in multiplicative according to claim 1 and additive noise, it is characterized in that, the method for described calculated rate estimated value is: find out spatial spectrum W (ω successively _k) P peak value, first find out first peak value and the ω value of correspondence be designated as ω ₁, next is found out second largest peak value and the ω value of correspondence is designated as ω ₂, by parity of reasoning, finally finds out P large peak value and the ω value of correspondence is designated as ω _p; Calculate the estimated value of harmonic frequency signal for: m=1,2 ..., P.

8. harmonic frequency signal method of estimation in multiplicative according to claim 7 and additive noise, it is characterized in that, described second largest peak value is the peak value being only second to described first peak value.