JP2017150903A - Sound source localization device, method, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To enable a plurality of sound sources to be localized at the same time even when noise exists.SOLUTION: A spatial difference calculation unit 22 calculates a difference in observation signal for each of a plurality of directions. A sound source position estimation unit 25 estimates, on the basis of a difference between an observation signal inputted by a reference microphone and an observation signal calculated for each of a plurality of directions, the position of each of a plurality of sound sources so as to increase the probability density value of a difference between an observation signal at each time of a day of the reference microphone and an observation signal at each time of a day for each of the plurality of directions, with the position of each of a plurality of sound sources for the case where a plurality of sound sources and additive noise exist that is defined using a sound source constraint partial differential equation as being a condition.SELECTED DRAWING: Figure 3

Description

  The present invention relates to a sound source localization device, method, and program, and more particularly, to a sound source localization device, method, and program for estimating the position of a sound source from an acoustic signal.

  Wave source localization has a wide range of applications such as radar and sonar. In particular, it is important to be able to quickly locate and track a moving wave source with a small array. Conventional methods for the source localization problem include Multiple Signal Classication (MUSIC) method, Generalized Cross-Correlation methods with Phase Transform (GCC-PHAT) method, and methods based on source-constrained partial differential equations (Non-Patent Documents 1 to 3). is there.

  Since the MUSIC method and GCC-PHAT method assume a plane wave for the sound source and use the arrival time difference between the sensors of each sound source as a key for localization, in general, a larger array size is advantageous. In addition, since both methods are based on statistics such as autocorrelation function and cross-correlation function between received signals of the sensor array, it is necessary to take a sufficiently long observation time width in order to localize the sound source with high accuracy. For this reason, these methods are not necessarily suitable for wave source localization using only a small array size and instantaneous observation. On the other hand, the method based on the partial differential equation of the wave source performs sound source localization based on the spatio-temporal partial differential equation of the acoustic signal that is established at each time. Theoretically, the source localization is performed only by instantaneous small region observation. Is possible.

Junya Fujita, Junki Ono, Shigeru Ando, "Fast and accurate solution of sound source localization that enables the use of finite time windows and discrete Fourier transform" and Proceedings of the Autumn Meeting of the Acoustical Society of Japan 2006, 3-1 -3, pp. 483-484, Sep. 2006. S. Ando, N. Ono, T. Nara, "Direct algebraic method for sound source localization with nest resolution both in time and frequency," in Proc. ICSV14, Jul. 2007. Shoichi Koyama, Toru Kurihara, Shigeru Ando, "Instant sound source localization by spatial load integration of partial differential equations," Proceedings of the 2008 Annual Meeting of the Acoustical Society of Japan, 2-8-20, pp. 679-682, Sep . 2008.

  However, since the method based on the above-mentioned wave source-constrained partial differential equation is based on an equation that holds for a single wave source, a plurality of sound sources cannot be localized simultaneously. In addition, there is a drawback that it is fragile when the observed acoustic signal deviates from the partial differential equation, such as when noise is present.

  The present invention has been made in view of the above circumstances, and an object thereof is to provide a sound source localization apparatus, method, and program capable of simultaneously locating a plurality of sound sources even in the presence of noise. To do.

  In order to achieve the above object, a sound source localization apparatus according to the present invention is a sound source that estimates the position of each of a plurality of sound sources from an observation signal mixed with sound source signals from a plurality of sound sources input by a microphone array. A localization apparatus, for each of a plurality of directions, a spatial difference calculation unit that calculates a difference between the observation signals input by a pair of microphones arranged in the direction of the microphone array; Of these, the plurality of signals determined using a sound source constrained partial differential equation based on the observed signal input by a reference microphone and the difference between the observed signals calculated for each of the plurality of directions. When there is a sound source and additive noise, the observation signal at each time of the reference microphone on the condition of the position of each of the plurality of sound sources, So as to increase the probability density value of the difference of the observed signals at each time with respect to fine the plurality of directions each is configured to include a sound source position estimating section for estimating the position of each of the plurality of sound sources.

  The sound source localization method according to the present invention is a sound source localization method in a sound source localization apparatus that estimates the position of each of the plurality of sound sources from an observation signal obtained by mixing sound source signals from a plurality of sound sources input by a microphone array. Then, for each of a plurality of directions, a spatial difference calculation unit calculates a difference between the observation signals input by a pair of microphones arranged in the direction in the microphone array, and a sound source position estimation unit, Based on the observation signal input from a reference microphone in the microphone array and the difference between the observation signals calculated for each of the plurality of directions, the sound source constraint partial differential equation is used. , Each time of the reference microphone on the condition of each position of the plurality of sound sources in the presence of the plurality of sound sources and additive noise Observed signal, and so as to increase the probability density value of the difference of the observed signals at each time for each of said plurality of directions, estimating the position of each of the plurality of sound sources.

  The program according to the present invention is a program for causing a computer to function as each part of the sound source localization apparatus.

  As described above, according to the sound source localization apparatus, method, and program of the present invention, the plurality of sound sources in the case where the plurality of sound sources and additive noise exist, which are determined using a sound source constrained partial differential equation. In order to increase the probability density value of the difference between the observation signal at each time of the reference microphone and the observation signal at each time with respect to each of the plurality of directions on the condition of each position of the plurality of sound sources, By estimating each position, it is possible to obtain an effect that a plurality of sound sources can be localized simultaneously even in the presence of noise.

It is a figure which shows the spherical wave which arrives at the observation point r from a point sound source. It is a figure which shows an example of arrangement | positioning of a microphone array. It is the schematic which shows the structure of the sound source localization apparatus which concerns on embodiment of this invention. It is a flowchart which shows the content of the sound source localization process routine in the sound source localization apparatus which concerns on embodiment of this invention. It is a figure which shows a microphone array reference point and a sound source position. It is a figure which shows the localization result in the case of one sound source, no noise, and a wall reflection coefficient of 0.01 It is a figure which shows the localization result in the case of one sound source, noise, and a wall reflection coefficient of 0.01. It is a figure which shows the localization result in the case of one sound source, noise, and a wall reflection coefficient of 0.25. It is a figure which shows the localization result in the case of one sound source, noise, and a wall reflection coefficient of 0.5. It is a figure which shows a microphone array reference point and a sound source position. It is a figure which shows the localization result in the case of two sound sources, noise, and a wall reflection coefficient of 0.01

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. The technique proposed in the present invention is a signal processing technique for the purpose of estimating a wave source position from an acoustic signal.

<Outline of Embodiment of the Present Invention>
The embodiment of the present invention is a technology that enables wave source localization of a plurality of sound sources by small region / instantaneous observation, which has the advantages of the conventional method described above.

  In the embodiment of the present invention, the probability distribution of the mixed signal in the case where there are a plurality of sound sources and additive noise is described by constructing the probability distribution of the acoustic signal based on the time domain representation of the sound source constrained partial differential equation. , Localization of multiple sound sources using the Expectation-Maximization (EM) algorithm.

<Principle of Embodiment of the Present Invention>
Next, the principle of estimating the position of the sound source will be described.

<Sound source constrained partial differential equation>
As shown in FIG. 1, the position vector that becomes the reference of the observation point is

And the position vector of a single source

And Assuming that the wave source signal is g (t), the sound velocity is c, and spherical wave propagation from a single point source is assumed, the observed value at the observation point is

It is expressed. here,

It is. If the unit vector going from the observation point toward the wave source is n,

Therefore, the spatial derivative of f (r, t) is

It becomes. The time derivative of f (r, t) is

Therefore, substituting Equation (1) and Equation (8) into Equation (7) eliminates g,

Thus, an equation including only the observed signal and its time / space derivative can be established. However, R = | r−r ₀ | is the distance from the observation point to the wave source. This equation is called a sound source constraint equation (Non-Patent Documents 1 to 3). As described above, the sound source constraint equation is a partial differential equation describing a unique relationship between the position of the sound source and the space field, which is formed by an arbitrary sound source signal waveform.

<Probability modeling of acoustic signals based on sound source constrained partial differential equations>
Consider a case in which the spatial differentiation of an observation signal is approximated by a spatial difference in a microphone array as shown in FIG. In the example of the array geometry for obtaining the spatial differential of the observation signal f shown in FIG. 2, for example, the spatial differential of f in the x direction can be approximated by (f _{1, t} −f _{2, t} ) / 2D.

However, the arrangement of the microphone array is not limited as long as the spatial differentiation of the observation signal can be approximated by a spatial difference, and the following theory is not limited to the arrangement shown in FIG. In the case of the microphone array of FIG. 2, the signal f _{0, l} at the reference point and the spatial difference in each direction at each time t ₁ using seven microphones.



Can be obtained. Here, l represents an index of discrete time.

If the time derivative of the observed signal at the reference point is approximated by the time difference, Equation (9) becomes

It can be expressed. Where n _x , n _y , and _nz are the components in the x, y, and z directions, respectively, and T is the sampling period.

If the left side of Equation (10) is moved to the right side and rearranged,

Is obtained. The right side of Equation (11) is not always exactly 0 due to the presence of noise and errors accompanying differential approximation. Therefore, the right side of equation (11)

_Are replaced with error variables ε _{x, l} , ε _{y, l} , ε _{z, l} , and these are normal random variables whose mean is 0 and independent of each other (random variables that follow a complex normal distribution)

Assume that The observation signal at the observation point is a normal random variable with an average of 0 and a variance of σ ² ₀ . this is,

Is equivalent to assuming.

Where f _{x, l} , f _{y, l} , f _{z, l} , f _{0, l} vector and ε _{x, l} , ε _{y, l} , ε _{z, l} , ε _{0, l} vector The

And a vector concatenated f _0,0 , f ₁ , ..., f _L and a vector concatenated ε _0,0 , ε ₁ , ..., ε _L

And (12) becomes

Can be written in the form of However, θ = {R, n} and A (θ) is

Given in. From Eqs. (13) and (15), ε is 0 on average and the variance-covariance matrix is

Complex normal distribution of

Follow.

(A (θ) is regular), so f is

From equation (27),

I can say. Therefore, the maximum likelihood sound source position ^ θ under the given observation signal and its spatial difference is


Is obtained.

<Multiple sound source localization algorithm>
By the probability modeling of f above, it is possible to derive the probability distribution of the observed signal when there are a plurality of sound sources and when there is noise. The sound source index is k, and the components of the observation signal derived from the sound source k and the sound source position parameters are f ^(k) and θ ^(k) , respectively. Further, the variance of f ^(k) is σ ^(k) ₀ ² . From equation (32)

It becomes. Also, the additive noise is v and the observed signal is

And If f ⁽¹⁾ , ..., f ^(K) , v are independent of each other, the observed signal y is

Follow. Where Γ is the variance covariance matrix of v. From the above, the maximum likelihood sound source position of each sound source when multiple sound sources and noise exist

Under the observation signal y

Is obtained by solving

y is incomplete data,

Can be applied to the above maximum likelihood estimation problem. The complete data log likelihood log p (x | θ) is

The conditional expectation value (Q function) of log p (x | θ) with respect to x under y is given by

Given in. However,

Means an equal sign only for terms related to x. The step of updating θ so that this function increases (M step), and the updated θ is substituted into θ ′,

When

By repeating the step of calculating (E step), θ that locally maximizes p (y | θ) can be obtained.

The relationship between complete data x and incomplete data y is

So you can write

Each

Given in. As described above, an algorithm including the following initial setting, E step, and M step is obtained.

(Initial step)
Initialize θ.

(E step)
Substituting θ into θ ′, and using equation (41)

Calculate

(M step)
Update θ using the following formula.

<M step update formula>
In M step,

To be as large as possible

Update.

Maximize

Although it is difficult to analytically find the simultaneous optimal solution of

By repeatedly updating so that becomes the maximum

(The EM algorithm guarantees convergence if the auxiliary function is guaranteed to increase monotonically in M steps). Two examples of M-step update methods are shown below.

<Example 1>
<Renewal formula of n ^(k) >
n ^(k) is a unit vector, so

Under

Update n ^(k) so that becomes as small as possible. This constrained optimization problem is, for example,

It can be solved by the Lagrange multiplier method using a Lagrangian such as A (θ ^(k) ) is


, The term that depends on n ^(k) and the term that does not depend on n ^(k) can be decomposed, and by setting the partial derivative of L (n ^(k) ) with respect to n ^(k) to 0,

Get. However, E _{i, j} is a 4 × 4 matrix in which only the element in the i-th row and j-th column is 1 and the rest is 0.

And the rest

Search for γ ^(k) by the bisection method or the like so that

<Renewal formula of sound source distance R ^(k) >

And As above, A (θ ^(k) ) is

As shown in Fig. 1, the term that depends on ρ ^(k) and the term that does not depend on ρ ^(k) can be decomposed, so by setting the partial derivative of Q (θ, θ ′ ^{) with} respect to ρ ^(k) to 0,

Get.

<Updating formula for σ ^(k) ₀ ² >
As above, Σ ^{(k) -1}

Thus, it can be decomposed into terms that depend on σ ^(k) _{0, m} ² and terms that do not, so by putting the partial derivative of Q (θ, θ ′) with respect to σ ^(k) ₀ ² as 0,

Get.

<Update formula of noise variance covariance matrix Γ>
Noise variance covariance matrix

As shown, the product of the normalized variance covariance matrix model W and the noise energy ν ² is used, and ν ² _m is a variable. W is a constant matrix derived from a spatial uncorrelated model or a diffuse sound field model. By setting the partial derivative of Q (θ, θ ′) with respect to ν ² to 0,

Get.

<Example 2>
<Update formula of sound source position vector r (k)>
This example differs from Example 1 only in the way of updating the arrival direction. In this example

Is a variable. In this case, no norm constraint is required, and r (k) that maximizes Q (θ, θ ′) may be obtained as an unconstrained optimization problem. A (θ (k)) is

As we can divide into terms that depend on r (k) and terms that do not, like this, by setting the partial derivative of Q (θ, θ ′) with respect to r (k) to 0,

Get. The update formula for the sound source distance R ^(k), the update formula for σ ^(k) ₀ ² , and the update formula for the noise variance covariance matrix Γ are the same as in Example 1.

<Inverse matrix calculation>
From Eq. (41)

Inverse matrix calculation is required. Here, it is shown that this inverse matrix calculation can be performed efficiently when there is one point sound source and one noise source and when there are two point sound sources.

<1 sound source and 1 noise source>
For one sound source and one noise source, (HΛH ^T ) ^-1 is

Can be written. Where Woodbury's official

(61) becomes

Can be written. Since Γ is a block diagonal matrix and V ₁ is a band matrix (block tridiagonal matrix), Γ ⁻¹ + V ₁ is a band matrix, and calculation of (Γ ⁻¹ + V ₁ ) V ₁ is efficient using Cholesky decomposition. Can be done.

<In the case of 2 sound sources>
In the case of two sound sources, (HΛH ^T ) ^-1 is

Can be written. As above, using Woodbury's formula, equation (65) becomes

Can be written. Since V ₁ and V ₂ are both band matrices, V ₂ + V ₁ is also a band matrix, and the calculation of (V ₂ + V ₁ ) −1V ₁ can be efficiently performed using Cholesky decomposition.

<System configuration>
Next, an embodiment of the present invention will be described by taking as an example a case where the present invention is applied to a sound source localization apparatus that estimates the positions of a plurality of sound sources from acoustic signals input from a microphone array.

  As shown in FIG. 3, the sound source localization apparatus 100 according to the first embodiment of the present invention is a computer including a CPU, a RAM, and a ROM that stores a program for executing a sound source localization processing routine. It is configured and functionally configured as follows.

  As shown in FIG. 3, the sound source localization apparatus 100 includes an input unit 10, a calculation unit 20, and an output unit 90.

  The input unit 10 receives time-series data of an acoustic signal (hereinafter referred to as an observation signal) output from each microphone of the microphone array as shown in FIG. 2 and mixed with sound source signals from a plurality of sound sources.

  The calculation unit 20 includes a spatial difference calculation unit 22 and a sound source position estimation unit 25.

The spatial difference calculation unit 22 acquires the observation signal f _{0, l} at the microphone at the reference point from each observation signal output from each microphone of the microphone array at each time t ₁ , and each direction x , Y, z spatial differences f _{x, l} , f _{y, l} , f _{z, l} are calculated.

Sound source position estimation unit 25 was obtained by the spatial difference calculating unit 22, the observed signal f ₀ of the time t _l of the microphone of the reference _{point, l} and, spatial difference in each direction x, y, z at each time t _l f _{x, l,} f _{y, l,} f _z, based on the observed signal y consisting of _l, using the EM algorithm, defined by using the sound source restraining partial differential equations, there is a plurality of sound sources and additive noise In this case, the position of each of the plurality of sound sources is estimated so as to increase the probability distribution P (y | θ) of the observation signal y on the condition of each position of the plurality of sound sources.

  The sound source position estimation unit 25 includes an expected value calculation unit 26, a variable update unit 28, and a convergence determination unit 30.

Expected value calculation unit 26 was obtained by the spatial difference calculating section 22, and the observed signal f _{0, l} at each time t _l at the microphone of the reference point, the spatial difference of the directions x, y, z at each time t _l an observation signal y consisting of f _{x, l} , f _{y, l} , f _{z, l,} and a sound source position θ ^{(k) of} each sound source k that has been initialized or updated last time, Based on the variance σ ^(k) ₀ ² of the sound source signal of each sound source k updated last time,

Calculate

The variable update unit 28 is calculated by the expected value calculation unit 26.

, The direction vector n ^{(k) of} each sound source k according to the above formula (52), formula (54), and formula (56) to formula (58) so that Q (θ, θ ′) becomes as large as possible. Then, the sound source distance R ^(k) , variance σ ^(k) ₀ ² , and noise covariance matrix Γ are updated. Note that, as in Example 2 described above, the position vector r ^(k) , the sound source distance R ^(k) , and the sound source distance k of each sound source k according to the above formulas (60), (54), and (56) to (58 ⁾ . Update the variance σ ^(k) ₀ ² and the noise covariance matrix Γ.

  The convergence determination unit 30 repeats each process performed by the expected value calculation unit 26 and the variable update unit 28 until a predetermined convergence determination condition is satisfied. The convergence determination condition is, for example, reaching a predetermined number of repetitions.

When the convergence determination condition is satisfied, the output unit 90 outputs the direction vector n ^(k) and the sound source distance R ^(k) of each sound source k finally obtained as the estimation result of the position of each sound source k. .

<Operation of sound source localization device>
Next, the operation of the sound source localization apparatus 100 according to the present embodiment will be described.

  When the input unit 10 receives time-series data of observation signals output from each microphone of the microphone array, the sound source localization apparatus 100 executes a sound source localization processing routine shown in FIG.

First, in step S120, the observation signal f _{0, l} at the reference point microphone is obtained at each time t ₁ from the time series data of the observation signal input from each microphone of the microphone array, and each direction x, y , Z spatial differences f _{x, l} , f _{y, l} , f _{z, l} are calculated.

In step S122, initial values are set for the sound source position θ ^(k) of each sound source k and the sound source signal variance σ ^(k) ₀ ^{2 of} each sound source k.

In step S123, the observation signal f _{0, l at} each time t _l acquired in step S120 and the spatial differences f _{x, l} , f _{y, l} , in each direction x, y, z at each time t _l are obtained. The observation signal y composed of f _{z, l} and the sound source position θ ^(k) and variance σ ^(k) ₀ ^{2 of} each sound source k that is initially set in step S122 or updated last time in step S124 described later. Based on the above equation (41)

Calculate

In step S124, the value calculated in step S123 is calculated.

In accordance with the above equation, the direction vector n ⁽ ) of each sound source k is obtained according to the above equations (52), (54), and (56) to (58) so that Q (θ, θ ′) becomes as large as possible. ^k) , the sound source distance R ^(k) , the variance σ ^(k) ₀ ² , and the noise covariance matrix Γ are updated.

  In step S125, it is determined whether or not a predetermined convergence determination condition is satisfied. If the convergence determination condition is not satisfied, the process returns to step S123. On the other hand, if the convergence determination condition is satisfied, the process proceeds to step S126.

In step S126, the output unit 90 outputs the direction vector n ^(k) and the sound source distance R ^(k) of each sound source k finally obtained in step S124 as the estimation result of the position of each sound source k. Then, the sound source localization processing routine ends.

<Experiment>
As shown in Fig. 5, a single sound source and a microphone array were arranged, and a sound source localization experiment was performed under a noise / reverberation environment under the following conditions.

(Experimental conditions)
Number of Sound Sources: 1
Reflection coefficient considering room reflection: 0.01, 0.5, 0.8
Observation time length: 64 points (4 ms)
Microphone interval: 1cm

  6-9 show the localization results for each condition.

  FIG. 6 shows a localization result in the case of one sound source, no noise, and a wall reflection coefficient of 0.01. Each point represents an estimated sound source direction obtained for each different initial value. Since the difference of 180 degrees may be regarded as a correct answer, it can be seen that the true sound source direction can be correctly estimated from any initial value.

  FIG. 7 shows a localization result in the case of one sound source, noise, and a wall reflection coefficient of 0.01. Each point represents an estimated sound source direction obtained for each different initial value.

  FIG. 8 shows a localization result in the case of one sound source, noise, and a wall reflection coefficient of 0.25. Each point represents an estimated sound source direction obtained for each different initial value.

  FIG. 9 shows a localization result in the case of one sound source, noise, and a wall reflection coefficient of 0.5. Each point represents an estimated sound source direction obtained for each different initial value.

  In addition, as shown in FIG. 10, two sound sources and a microphone array were arranged, and a sound source localization experiment under a noise / reverberation environment was performed under the following conditions.

(Experimental conditions)
Number of Sound Sources: 2
Reflection coefficient considering room reflection: 0.01
Observation time length: 64 points (4 ms)
Microphone interval: 1cm

  FIG. 11 shows the localization result. FIG. 11 shows a localization result in the case of two sound sources, noise, and a wall reflection coefficient of 0.01. Each point represents an estimated sound source direction obtained for each different initial value. Since the difference of 180 degrees may be regarded as a correct answer, it can be seen that the true sound source direction can be correctly estimated from any initial value.

  As described above, according to the sound source localization apparatus according to the present embodiment, each position of a plurality of sound sources when there are a plurality of sound sources and additive noises determined using a sound source constrained partial differential equation. By estimating the position of each of a plurality of sound sources so as to increase the probability distribution of the observation signal at each time of the reference microphone and the observation signal at each time in each of a plurality of directions under the condition of Even if there is a sound, a plurality of sound sources can be localized simultaneously.

  Note that the present invention is not limited to the above-described embodiment, and various modifications and applications are possible without departing from the gist of the present invention.

  For example, the sound source localization apparatus described above has a computer system inside, but the “computer system” includes a homepage providing environment (or display environment) if a WWW system is used.

  In the present specification, the embodiment has been described in which the program is installed in advance. However, the program can be provided by being stored in a computer-readable recording medium.

DESCRIPTION OF SYMBOLS 10 Input part 20 Calculation part 22 Spatial difference calculation part 25 Sound source position estimation part 26 Expected value calculation part 28 Variable update part 30 Convergence determination part 90 Output part 100 Sound source localization apparatus

Claims (7)

A sound source localization device that estimates the position of each of the plurality of sound sources from an observation signal mixed with sound source signals from a plurality of sound sources input by a microphone array,
For each of a plurality of directions, a spatial difference calculation unit that calculates a difference between the observation signals input by a pair of microphones arranged in the direction in the microphone array;
Based on the observation signal input from a reference microphone in the microphone array and the difference between the observation signals calculated for each of the plurality of directions, the sound source constraint partial differential equation is used. In addition, in the case where additive noise is present with the plurality of sound sources, the observation signal at each time of the reference microphone on the condition of the position of each of the plurality of sound sources, and each time for each of the plurality of directions A sound source position estimation unit that estimates the position of each of the plurality of sound sources so as to increase the probability density value of the difference between the observation signals;
Sound source localization device including The sound source localization apparatus according to claim 1, wherein the probability density value is represented by the following expression.



Where f (k) represents the observed sound source signal from the sound source k, Γ is the variance-covariance matrix of the additive noise, θ ^(k) represents the position of the sound source k, and σ _x ^{( k) 2} , σ _y ^{(k) 2} , σ _z ^{(k) 2} represent the variance in the difference between the observed sound source signal directions x, y, z from the sound source k, and σ ₀ ^{(k) 2} is represents the variance in the microphone of the reference sound source signals observed from the sound source k, R represents the distance to the sound source, c is, represents the sound velocity, T is, represents the sampling period, n _x, n _y, n _z represents the component of the direction x, y, z of the unit vector toward the sound source. The sound source position estimator uses a EM (Expectation-Maximization) algorithm so that the probability density value increases, the distance R ^(k) to each of the plurality of sound sources k, and the unit toward each of the plurality of sound sources k. By repeatedly updating the vector n ^(k) , the variance ₀ ^{(k) 2} in the reference microphone of each of the plurality of sound sources k, and the variance-covariance matrix Γ of the additive noise, each of the plurality of sound sources The sound source localization apparatus according to claim 2, wherein the position is estimated. A sound source localization method in a sound source localization device that estimates the position of each of the plurality of sound sources from an observation signal mixed with sound source signals from a plurality of sound sources input by a microphone array,
A spatial difference calculation unit calculates, for each of a plurality of directions, a difference between the observation signals input by a pair of microphones arranged in the direction in the microphone array,
A sound source position estimation unit is configured to generate a sound source constrained partial differential based on the observation signal input from a reference microphone in the microphone array and the difference between the observation signals calculated for each of the plurality of directions. An observation signal at each time of the reference microphone and a plurality of directions, which are defined using an equation, on the condition of each position of the plurality of sound sources in the presence of the plurality of sound sources and additive noise. A sound source localization method for estimating a position of each of the plurality of sound sources so as to increase a probability density value of a difference between observation signals at each time with respect to each of the sound sources. The sound source localization method according to claim 4, wherein the probability density value is represented by the following expression.



Where f (k) represents the observed sound source signal from the sound source k, Γ is the variance-covariance matrix of the additive noise, θ ^(k) represents the position of the sound source k, and σ _x ^{( k) 2} , σ _y ^{(k) 2} , σ _z ^{(k) 2} represent the variance in the difference between the observed sound source signal directions x, y, z from the sound source k, and σ ₀ ^{(k) 2} is represents the variance in the microphone of the reference sound source signals observed from the sound source k, R represents the distance to the sound source, c is, represents the sound velocity, T is, represents the sampling period, n _x, n _y, n _z represents the component of the direction x, y, z of the unit vector toward the sound source. When the sound source position estimation unit estimates, the distance R ^{(k) to} each of the plurality of sound sources k, the plurality of sound sources k, and the number of the sound sources k are increased so that the probability density value is increased by an EM (Expectation-Maximization) algorithm. By repeatedly updating the unit vector n ^(k) toward each, the variance ₀ ^{(k) 2} in the reference microphone of each of the plurality of sound sources k, and the variance covariance matrix Γ of the additive noise, The sound source localization method according to claim 5, wherein the position of each sound source is estimated.   The program for functioning a computer as each part of the sound source localization apparatus of any one of Claims 1-3.