JPH0474985A - Elimination of noise - Google Patents

Abstract

PURPOSE:To enable elimination of noise with high accuracy even if the covariance matrix of sound source signal is decomposed into factors for the factor matrix consisting of column vector elements not crossing perpendicularly be renewing a noise matrix with the use of vector decomposition of a mode matrix. CONSTITUTION:There is a signal receiver 2 receiving source signal S1 from a multitude of sound sources 1 existing at arbitrary locations in the air and its output side is connected to a covariance matrix calculator 3. During eliminating noise added to the input signal from a certain initial noise added to the input signal from a certain initial noise in turn, an eigen value and an eigen vector are calculated from the eigen value decomposition of the covariance matrix in the input signal and that of reference signal. Noise matrix is renewed with the use of the vector decomposition of a mode matrix utilizing the eigen value and the eigen vector. And the noise is eliminated based on the result of the renewal. With this method, even if the common disperse matrix of the source signal S1 is decomposed into factors for the factor matrix consisting of column vector elements not crossing perpendicularly, noise elimination is possible with high accuracy.

Description

DETAILED DESCRIPTION OF THE INVENTION (Industrial Application Field) The present invention is directed to the characteristics of a sound source signal from a sound source located anywhere in space. The present invention relates to a noise removal method for extracting (S width, frequency, direction:), etc. even under high noise.

(Prior Art) Conventionally, as a technique in this field, there is a technique described in Masaru Okaki, "Fundamentals of Factor Analysis J (1986-3-6), Hiyori Giren Shuppansha, P, 1-8-28. There was.

Conventionally, in a noise removal method for removing noise added to an input signal, for example, as described in the above-mentioned document, the covariance matrix Σ of the input signal is expressed as Σ=△ by the factor matrix Δ and the noise matrix ψ. △ 士ψ... (1) However, *
; When performing conjugate transposition and factorization, use the cyclic method (cyclicproc
edure) algorithm, the noise matrix type is sequentially updated and noise is removed.

The two-trowel, circulation algorithm consists of the following first to fourth stages.

First stage: Start from an appropriate initial value of the city (0).

Let the repetition number be t-〇.

(1) is a diagonal matrix consisting of the largest eigenvalues of Dl(Σ-weight(t))Aa in the second stage iteration of matrix A, and ■ is the corresponding orthonormal eigenvector matrix, 9)-A'V is > (D (t) > 1/
'2 is set.

3rd stage city”1)-D i ag (Σ-Δ(1)Δ (℃))
If the difference between weight (11) and city (1) is small enough, proceed to the fourth stage, otherwise proceed to the second stage with t:=t-i-1.
Proceed to step.

End of the 4th stage.

(Problems to be Solved by the Invention) However, the noise removal method using the above-mentioned cyclic algorithm has the following problems.

The cyclic algorithm requires that the matrix △*WΔ be diagonal for a given P-order positive definite matrix W, and if we set it as W-1 (weight), △"Δ is diagonal. From the angular matrix, the factor matrix Δ is expressed as a column vector Δ−(5,...,
The column vectors of ) must be orthogonal.

Therefore, if the covariance matrix of the input signal is factorized by a factor matrix consisting of non-orthogonal column vector elements,
Noise added to the input signal cannot be removed.

For example, when removing noise contained in a sound source signal from a sound source that exists underwater, if you apply a conventional cyclic algorithm, the algorithm will be able to remove the noise contained in the sound source signal because the constituent column vectors of the factor matrix are orthogonal vectors Noise cannot be removed The problem that the present invention had with the prior art is that because the factor matrix consists of column vectors or orthogonal vectors, the noise contained in the incoming sound source signal cannot be removed. This paper provides a noise removal method that solves the problem.

(Means for Solving the Problems) In order to solve the problems, a first invention provides a noise removal method in which, when sequentially estimating and removing noise added to an input signal from a certain initial noise, Eigenvalues and eigenvectors are calculated by eigenvalue decomposition of the covariance matrix of the input signal and eigenvalue decomposition of the reference signal, and the noise matrix is updated using vector l-Herr decomposition of the mode matrix using the eigenvalues and eigenvectors, The noise is removed based on the updated results.

In a second invention, in the first invention, the noise matrix is updated optimally using a least squares method.

(Operation) According to the first invention, since the noise removal method is configured as described above, an input signal containing noise is subjected to eigenvalue decomposition of its covariance matrix, and the input signal corresponding to the input signal is Eigenvalue decomposition of the reference signal is performed. The eigenvalues and eigenvectors calculated by these eigenvalue decompositions are used to perform spectral decomposition of the Maumley matrix, and based on the decomposition results, the noise matrix is updated to remove noise in the input signal.

In the second invention, by optimal updating using the square method,
The noise matrix is updated in a short time and accurately.

Therefore, the above problem can be eliminated.

(Embodiment) FIG. 1 is a functional block diagram of a noise removal device using a noise removal method showing an embodiment of the present invention.

This noise removal device has a signal receiving section 2 that receives sound source signals S1 from a plurality of sound sources 1 existing at arbitrary locations in space, and a covariance matrix calculating section 3 is connected to the output side of the signal receiving section 2.
are doing. The signal receiving unit 2 has a plurality of receivers that receive the sound source signal S1 and convert it into an electrical signal, and samples the received signal of the receivers at a predetermined sampling frequency to generate a discrete time series signal X (n). , covariance matrix calculation unit 3I
＼It has the function of giving.

The covariance matrix calculation unit 3 has a function of calculating a covariance matrix from the discrete time series signal X(n), and has a real component covariance matrix calculation unit 22a and An imaginary component covariance matrix calculation unit 22b is connected.

The noise removal unit 10 includes a noise initialization unit 11 that operates only once at the beginning, a noise matrix setting unit 12, a noise removal unit 13 that removes noise from the covariance matrix, a noise matrix calculation unit 14, and a noise update unit 15. ,It is configured.

Further, this noise removal method is provided with a mode matrix calculation unit 20 that calculates a mode matrix consisting of an amplitude and a direction vector corresponding to sound source information.

The mode matrix calculation unit 20 is connected to an imaginary component covariance matrix calculation unit 21a and a real component covariance matrix calculation unit 21b, which output an imaginary component covariance matrix and a real component covariance matrix of the mode matrix. There is. The imaginary component covariance matrix calculation section 21a and the real component covariance matrix calculation section 21b include a real component covariance matrix calculation section 22a and a real component covariance matrix calculation section 22a, which respectively calculate the real component covariance matrix and the imaginary component covariance matrix after noise removal. An imaginary component covariance matrix calculation unit 22b is also connected.

Eigenvalue decomposition units 23a and 23b that calculate eigenvector eigenvalues and singular values of the covariance matrix are connected to the real component covariance matrix calculation unit 22a and the imaginary component covariance matrix calculation unit 22b, respectively. Eigenvalue decomposition units 25a and 25b that calculate eigenvector eigenvalues and singular values of the Gaussian transformation matrix are connected to the moat matrix calculation unit 20 via Gaussian transformation matrix calculation units 24a and 24b, respectively.

A mode matrix updating section 27 is connected to the eigenvalue decomposition sections 23a, 25a and 23b, 25b via spectral decomposition sections 26a and 26b, respectively.

The spectral decomposition units 26a, 26b and the mode matrix update unit 27 estimate the mode matrix using the eigenvectors and singular values of the input covariance matrix and the eigenvectors and singular values of the Gaussian transformation matrix, and )t.

The spectrum decomposition units 26a and 26b are also connected to the noise update unit 5 via the noise matrix calculation unit 4.

The noise matrix calculation unit 14 calculates, from the eigenvectors and singular values of the input covariance matrix and the eigenvectors of the Gaussian transformation matrix,
It has a function to calculate a new noise matrix. The noise update unit 15 updates the noise matrix and applies it to the noise removal unit 13/
＼It has the function of giving.

Next, a noise removal method using the noise removal apparatus configured as described above will be explained.

For example, if there are 0 sound sources 1 in space, the waves generated from each sound source 1 are considered to be plane waves, and their amplitude, angular frequency, and wave number vector (spatial direction) are expressed as bj, ω1, kj (j=1.
..., D).

The number of receivers is M, and the position vector of each receiver from the same reference point is r. (i=1..9M).

First, the sound source signal S1 from the sound source 1 is received by the signal receiving section 2, and is converted into a discrete time series signal X.
(n). The discrete time-series signal X(n) can be expressed by the following equation, where W·(n) is the noise added to it in space.

x・(n) −): J EXP Ej (ω, ra−
8-J rH'+ 11J・1 W・ (n) ・・・(4) Here, X (n〉 is a−=bEXP [j (kJr, ! LIJ
J fj (n) = EXPlj fωjn) m,
Equation (4) is (n) When expressed as a matrix, the following equations (a) and (8) to (9) are obtained.

A f = w (n> The covariance matrix VfD(n) of the output of the signal receiving section 2 is calculated as follows: V=E <xx >fEc' ×H (10 ) However, E< n time unsampled average ○ (fJ≠j) (ensemble average) E < f J (n) (n)>−* conjugate transpose (fJ j), and furthermore, 9 (n); complex conjugate) E <fw ノE <w*f> = 0 (month) P3E<ff>2■ (■; identity matrix) Assuming that, VmiAEguff) A = E <ww/=APA
τ City (12〉)

(The covariance matrix type defined by Equation 13 means that the variance of the input noise of each receiver is C2, and the oscillation frequency PmiE<f of each sound source 1 is
f], 畢=E<ww/If the numbers are mutually uncorrelated, then from equation (8), it becomes.

If the oscillation frequencies of each sound source 1 are uncorrelated with each other, the covariance matrix P defined in equation (13) becomes from equation (5), and the covariance matrix type is a diagonal matrix. , ignoring noise, let the eigenvalues of the matrix ■ be λ1−λ1Ilax>A2 °〉λD=λmIn in descending order of magnitude, then equation (18) is expressed as The eigenvalue decomposition of the covariance matrix ■ is Vx=λ·X J JJ , and the changes in the elements of the column vector

Here, the covariance matrix ■ of the output of the signal receiving section 2 is (15
) Considering the sound source condition of the equation (the oscillation frequencies are mutually uncorrelated) and ignoring the presence of noise, D) ... (19) is obtained. When equation (17) is expressed in a matrix, it becomes the following equation (20).

XR=ARfRAI fr X■=ARf I I A4 f R V=AA* ・・・・・・(18) ・・・・・・(20) will be given.

ank (A>D, covariance: RR al(1°°゛aMJ"°°aHD) If we divide the covariance matrix X' defined by equation (18) into a real part and an imaginary part, ■EE< xx >EE< (XR-rjX■) (XRj XI)” >E
E<XRXR>+E<xIXRl> +j EE<xIXRl>E<xRXI'>=・
(21) 1, 1, (); Becomes a car device. Here, ■ is an identity matrix and 0 is a zero matrix. Therefore, the real covariance matrix X"8 and the imaginary covariance matrix V1 are VR=E<xRxR>-E<x■XI t ".

・・・・・・(22) 1 -.

Vy = E<XJ XR,>-E<XRXI 1>...
・(23> If defined as E<x x t>+E<x x t>RRII E< (ARfRAI fr HARfRAI fI
>1>÷E< (ARf I÷AIfR) (AR
fr l AI fR>'°>-ARE<fRfR>
AR1+ARE<flfI>ARt−+−AIE<f
RfR1>AI÷AIE<fr f, >AlE
Assuming <fRfR>=E<flfI1>=L/2, V■=E<XI XR>−E<XRXI t>So,
In the covariance matrix calculation unit 3, the discrete time series signal X・(n>
Based on this, the covariance matrix VR of equation (24) is calculated, and the calculation result is provided to the noise matrix setting section 12 and the noise removal section 13'\ in the noise removal means 10. The noise initial setting section 11 in the noise removing means 10 sets the S/'N ratio (signal to noise ratio) I-
An approximate value r0 of is set in the noise matrix setting section 12. The noise matrix setting unit 12 calculates the covariance matrix V calculated by the covariance matrix calculation unit 3. For R, the sum of diagonal elements,
is calculated, and the noise matrix W(0) is set.

The noise removal unit 13 calculates
a and the imaginary component covariance matrix calculation unit 22b.

The moat matrix calculation unit 20 calculates R(k) of the estimated mode matrix (reference signal) input (k) corresponding to the feature amount (amplitude, magnitude) of the sound source 1 defined by equations (-5) and (9). )
(k) Calculate the real part A and the imaginary part A, and send the calculation results to the imaginary component covariance matrix calculation unit 21. a, real component covariance matrix calculation unit 21b, and Gaussian transformation matrix calculation unit 2
Send to 4a and 24b.

In the imaginary component covariance matrix calculation unit 21a, (24) formula % formula %
( ) I AI is calculated, and the calculation result is provided to the real component covariance matrix calculation unit 22a. The real component covariance matrix calculation section 22a calculates the real component covariance matrix obtained by calculating the covariance matrix, and sends the calculation result to the eigenvalue decomposition section 23a.

The eigenvalue decomposition unit 23a decomposes the real component covariance matrix (k) into eigenvalues according to equation (19), and obtains the eigenRW value λ1. ..., λ, and the spectrum decomposition unit 26
Send to a.

On the other hand, multiplying equation (18) by A from the left, x of equation (17>)
By substituting =Af, the following equation is obtained.

Left side=A AA x=A AA Af=(A*A
>2f Two people on the right side A AA f Here, assuming that AA is a regular matrix and the existence of an inverse matrix, A Af2λf becomes, and the symmetric matrix B (mode matrix) is B = A * A ... (26) When defined, equation (26) becomes the following equation (27).

Bf - λf ...... (27) Therefore, the eigenvalues of the symmetric matrix B are expressed in descending order of the eigenvalues of the covariance matrix V as λ = λ 〉λ2〉...〉λD - λm1nI
max, and the orthonormal eigenhector of the symmetric matrix B corresponding to the eigenvalue λj is fj, then the eigenvalue decomposition Bf・2λ・f JJJ (j=1...,D)...(28) is can get.

The symmetric matrix defined by equation (26) is Gaussian (Ga, I
Jss) transformation matrix, as shown in the following equation (29>).

B=A A +J (ARAI AI 1AR) ・・・・・・(29) Therefore, the real Gaussian transformation matrix BR and the imaginary Gaussian transformation matrix B1 are converted to 1°C BI””ARAI −Ar AR・・・・・・(
31) Therefore, the crow transformation matrix calculation unit 24. In a, to the estimated mode matrix calculated by the mode matrix calculation unit 20 (k)
-(k) To t (k) Calculate the first term "DR" ARAR and give the calculation result to the eigenvalue decomposition unit 25a. (k) The value decomposition unit 25a converts the crow transformation matrices B and R into (28
), the eigenvalue R1λRD is calculated and sent to the ζ spectrum decomposition unit 26a.

The spectrum decomposition unit 26a generates a real component covariance matrix. r
The spectral decomposition of matrix A [CHXD that satisfies ank (A)=D can be expressed by the following equation (32).

A=μmX1 f I T...f, 1-J)
Of D* (3?) However, j AfJ Bf.

For D, * 1μJX J-A
j, λRj (j-1,..., D>, and the eigenvalue decomposition unit 2
Eigenvector T RJ (J-L
D), from equation (3?), the actual mode line (K=1
) Calculates the spectral decomposition of the column size and sends the calculation result to the noise matrix calculation unit 14 and the mode matrix update unit 27.

On the other hand, on the imaginary component covariance matrix side, the real component covariance matrix calculation unit 21b calculates (k) to the first term on the right side of equation (24).
(k) Calculate the real component covariance matrix ARAR corresponding to t. Similar to the real component covariance matrix calculation section 22a, the imaginary component covariance matrix calculation section 22b calculates the imaginary component covariance matrix V.
DI -~'I-person Fk) input R[k) rk) 1 is calculated and given to the eigenvalue decomposition unit 23b. Similarly to the eigenvalue decomposition unit 23a (k), the eigenvalue decomposition unit 23b calculates the eigenvector I mer 3 and the eigenvalue λ1j (j−1,..., D> by the eigenvalue decomposition of The spectrum decomposition unit 26b'\ is sent.

In addition, the Gaussian transformation matrix calculating unit 24b calculates the Gaussian transformability (k) to (k) t to (k) in the same manner as the Gaussian transformation matrix calculating unit 24a, and calculates the circumferential sequence BDI
-AI AI Give to value decomposition 25b. The eigenvalue decomposition unit 25b is
Similar to the eigenvalue decomposition unit 25a, from the eigenvalue decomposition of B, ■,
The eigenvector f and the eigenvalue λIJ (J-1J- . . . , D) are calculated, and the calculation results are sent to the spectrum decomposition unit 26b.

In the spectrum decomposition unit 26b, the spectrum decomposition unit 26a
Similarly, the smooth vector decomposition of the mode matrix person (K+1) is converted to
, eigenvalue λIj (j=1. . . , D) and eigenvector T IJ (, J−
1,...,D). The matrix update unit 27 to the mode 1 then spectra decomposition units 26a and 2 (to -1
) 1 to (K-1 6b's subectno [decomposition output person. AI), use the least squares method to update 6 people (K = 11
to (k) to (K+1) to (k)
1R- to R, β△I A1 This is updated 5, and the mode matrix of the moat matrix calculation unit 20 is changed to
to rk) ~, to (k) -11=AR・,JA
t-9ru.

The noise matrix calculation unit 14 includes a spectrum decomposition unit 2 (K=1
) and the spectral decomposition output large R(k) of 6a and 26b.

is calculated, and the output VDRW difference of the noise removal unit 13 is calculated as a noise estimation matrix. In the noise updating unit 15, the noise estimation matrix W
(K+1) is replaced with W(k) and input to the noise removal unit 13. The above noise removal calculation is repeated until trace (W(k)) becomes less than a certain value.

As described above, in this embodiment, h7'? is added to the sound source signal S1. When estimating and removing noise sequentially from a certain initial noise, update the noise matrix using spectral decomposition of the matrix into Mo1! , even if the factor matrix consisting of non-orthogonal column vector elements is the covariance matrix of the sound source signal S1 or the factorization jt, highly accurate noise removal can be achieved. Furthermore, if the noise matrix is updated using, for example, the least squares method, the updating process can be performed in a short time and accurately. Note that the present invention is not limited to the above embodiments, and can be applied to the real component covariance matrix side or the imaginary Even if the mode matrix and the noise matrix are updated using only the component covariance matrix side, substantially the same operation and effect as in the above embodiment can be obtained. In addition, each flock in Figure 1 is
It may be implemented by a processor (DSP), a microcomputer, etc. that performs program processing. Further, the present invention can be applied to noise removal in sound source signals from various sound sources existing underwater, in the air, etc.

(Effects of the Invention) As explained in detail above, according to the first invention, when noise added to an input signal is sequentially estimated and removed from a certain initial noise, spectral decomposition of a mode matrix is used. Since the noise matrix is updated using the factor matrix consisting of non-orthogonal column vector elements, highly accurate noise removal is possible even if the covariance matrix of the sound source signal is factorized. becomes.

In the second invention, by performing optimal updating using the square method, the updating process can be performed with high accuracy and in a short time.

[Brief explanation of the drawing]

FIG. 1 is a functional block diagram of a noise removal device using a noise removal method showing an embodiment of the present invention. DESCRIPTION OF SYMBOLS 1... Sound source, 2... Signal receiving part, 3... Covariance matrix calculation part, 10... Noise removal means, 11... Noise initial setting part, 12... Noise matrix setting part, 13... Noise defect section, 14... Noise matrix calculation section, 1-5... Noise update section, 20 mod matrix calculation section, 21a, , 21b...
Imaginary component covariance matrix calculation unit, 2]b column calculation pressure unit, 23a, 2 value decomposition unit, 24a pressure unit, 26a, 26b... mode matrix update unit. 22.3...Real component joint distribution Toshiyuki 3b, 2pa, 23b...Field 24b...Crow transformation matrix calculation spectrum decomposition unit, 27

Claims (1)

[Claims] 1. When noise added to an input signal is sequentially estimated and removed from a certain initial noise, eigenvalue decomposition of a covariance matrix in the input signal, eigenvalue decomposition of a reference signal, and eigenvalues and eigenvectors are performed. , updating a noise matrix using vector decomposition of a mode matrix using the eigenvalues and eigenvectors, and removing the noise based on the update result. 2. The noise removal method according to claim 1, wherein the noise matrix is optimally updated using a least squares method when updating the noise matrix.