JP6529451B2 - Sound source localization apparatus, method, and program - Google Patents

Description

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

  Source localization has a wide range of applications, such as radar and sonar. In particular, it is important to be able to localize and track moving wave sources instantaneously in small arrays. Conventional methods for source localization problems include Multiple Signal Classication (MUSIC) method, Generalized Cross-Correlation methods with Phase Transform (GCC-PHAT) method, and methods based on wave source constrained partial differential equations (Non-patent documents 1 to 3), etc. is there.

  Since the MUSIC method and the GCC-PHAT method assume a plane wave as a sound source and use the difference in arrival time between sensors of each sound source as a clue for localization, generally larger array sizes are advantageous. Also, since all of them are methods 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 always suitable for source localization with only a small array size and instantaneous observation. On the other hand, the method based on the source constrained partial differential equation performs sound source localization based on the spatiotemporal partial differential equation of the acoustic signal established at each time, and theoretically, the source localization is performed only by instantaneous small area observation. It is possible to do.

Atsushi Fujita, Junki Ono, Shigeru Ando, "A fast and accurate method of sound source localization enabling use of finite time window and discrete Fourier transform and its experiment" Proceedings of the Fall Meeting of the Acoustical Society of Japan, 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, "Immediate sound source localization by spatial load integration of partial differential equations," Proceedings of the Acoustical Society of Japan Annual Conference 2008 Fall Meeting, 2-8-20, pp. 679-682, Sep 2008.

  However, since the method based on the above-described source-constrained partial differential equation is based on the equation that holds for a single wave source, it is not possible to simultaneously localize a plurality of sound sources. It also has the disadvantage of being vulnerable if the observed acoustic signal deviates from the partial differential equation, such as in the presence of noise.

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

  In order to achieve the above object, a sound source localization apparatus according to the present invention estimates a position of each of a plurality of sound sources from an observation signal in which sound source signals from a plurality of sound sources input by a microphone array are mixed. A localization apparatus comprising: a spatial difference calculation unit that calculates a difference between the observation signals input by a pair of microphones arranged in the direction among the microphone arrays in each of a plurality of directions; Among them, the observation time frequency component of each frequency is output with the observation signal input by the reference microphone as an input, and the observation signal calculated for each of the plurality of directions by the spatial difference calculation unit A time frequency expansion unit which outputs an observation time frequency component of each frequency in each of the plurality of directions with a difference as an input; The frequency domain of the sound source restricted partial differential equation based on the observation time frequency component of each frequency of the reference microphone and the observation time frequency component of each frequency for each of the plurality of directions output by the time frequency expansion unit An observation time-frequency component of each frequency of the reference microphone, the position of each of the plurality of sound sources being determined in the presence of the plurality of sound sources and the additive noise, which are determined using a representation; And a sound source position estimation unit for estimating the position of each of the plurality of sound sources so as to increase the probability density value of the observation time frequency component of each frequency with respect to each direction of.

  A sound source localization method according to the present invention is a sound source localization method in a sound source localization apparatus for estimating the position of each of the plurality of sound sources from observation signals in which sound source signals from a plurality of sound sources input by a microphone array are mixed. The spatial difference calculation unit calculates, for each of a plurality of directions, a difference between the observation signals input by a pair of microphones aligned in the direction in the microphone array, and the time-frequency expansion unit The observation time frequency component of each frequency is output with the observation signal input by the reference microphone in the microphone array as an input, and the space difference calculation unit calculates the direction calculated for each of the plurality of directions. An observation time frequency component of each frequency is output in each of the plurality of directions with the difference of the observation signal as an input, and the sound source position is output. The estimation unit is a sound source constrained partial differential based on the observation time frequency component of each frequency of the reference microphone and the observation time frequency component of each frequency for each of the plurality of directions output by the time frequency expansion unit. An observation time frequency component of each frequency of the reference microphone based on the position of each of the plurality of sound sources in the presence of the plurality of sound sources and the additive noise, which is determined using a frequency domain expression of an equation The position of each of the plurality of sound sources is estimated so as to increase the probability density value of the observation time frequency component of each frequency for each of the plurality of directions.

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

  As described above, according to the sound source localization apparatus, method, and program of the present invention, in the case where the plurality of sound sources and the additive noise are determined using the frequency domain representation of the sound source constrained partial differential equation, In order to increase the probability density value of the observation time-frequency component of each frequency for each frequency of the reference microphone and the direction of each of the plurality of microphones, the position of each of the plurality of sound sources being conditions By estimating the position of each of the plurality of sound sources, it is possible to simultaneously localize a plurality of sound sources 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 based on embodiment of this invention. It is a figure which shows the experimental result in the case of frame width L = 16. It is a figure which shows the experimental result in the case of frame width L = 32. It is a figure which shows the experimental result in the case of frame width L = 64.

  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 aiming to estimate a wave source position from an acoustic signal.

<Overview of the embodiment of the present invention>
The embodiment of the present invention is a technology that enables source localization of a plurality of sound sources by small-area / instant observation, which has the advantage of the above-described conventional method.

  In the embodiment of the present invention, a mixed signal in the case where a plurality of sound sources and additive noise exist by constructing an acoustic signal based on a frequency domain representation of a sound source constrained partial differential equation and a probability distribution of its spatial difference Describe probability distribution of spatial difference, and perform source localization of multiple sound sources by Expectation-Maximization (EM) algorithm.

<Principle of the embodiment of the present invention>
Next, the principle of estimating the position of the sound source will be described.

<Source-constrained partial differential equation>
As shown in Figure 1, the position vector that is the reference of the observation point

And the position vector of the single wave source

I assume. Assuming that the signal of the wave source is g (t), the sound speed is c, and the spherical wave propagation from the single point wave source is assumed, the observed value at the observation point is

It is expressed as here,

It is. Assuming that the unit vector from the observation point to the source direction is n,

So that the spatial derivative of f (r, t) is

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

Therefore, g is eliminated by substituting equation (1) and equation (8) into equation (7),

, An equation including only the observed signal and its time-space derivative can be established. Where R = | r-r ₀ | is the distance from the observation point to the wave source. This equation is called a sound source constraint equation (the above non-patent documents 1 to 3). As described above, the sound source constraint equation is a partial differential equation which is established by an arbitrary sound source signal waveform and describes a unique relationship between the position of the sound source and the spatial field.

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

However, the arrangement of the microphone array may be any arrangement as long as the spatial differentiation of the observation signal can be approximated by the spatial difference, and the following theory is not limited to the arrangement of 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 thereof at each time t _l using seven microphones



You can get Where l represents the index of discrete time.

When the time derivative of the observation signal at the reference point is approximated by the time difference, equation (9) is

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

Transposing the left side of equation (10) to the right side

Is obtained. Here, let f _{0, l} , f _{x, l} , f _{y, l} , f _{z, l} be signals obtained by windowing with a window function. Assuming that the influence of both end points of the clipping interval can be ignored, equation (11) is

It is expressed as Where F _{0, m} , F _{x, m} , F _{y, m} , F _{z, m} are discrete Fourier transforms of f _{0, m} , f _{x, m} , f _{y, m} , f _{z, m} and m is It is a discrete frequency index.

  The right side of the equation (12) is not necessarily exactly zero in practice due to the presence of noise and an error caused by the difference approximation.

Therefore, the right side of equation (11)

Replace the error variables ε _{x, m} , ε _{y, m} , ε _{z, m} with 0 mean and independent from each other normal random variables (random variables according to complex normal distribution)

Suppose. Also, let each frequency component of the observation signal at the observation point be a normal random variable with an average of 0 and a variance of σ ² _{0, m} . this is,

It corresponds to assuming.

Here, a vector in which F _{x, m} , F _{y, m} , F _{z, m} , F _{0, m} are arranged and a vector in which ε _{x, m} , ε _{y, m} , ε _{z, m} , ε _{0, m} are arranged The


Let f ₀ , ..., f _{L / 2} be a connected vector and ε ₀ , ..., ε _{L / 2} be a connected vector

If it is written that, equation (13) is

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

Given by From Eqs. (14) and (16), ε has a mean of 0 and a variance-covariance matrix

Complex normal distribution of

Obey.

(A (θ) is regular), so f is

It can be expressed as equation (24),

Can be said. Therefore, the maximum likelihood source position ^ θ given the observed signal and its spatial difference is

Obtained by

<Localization algorithm of multiple sound sources>
The above probability modeling of f 1 can lead to the probability distribution of the observed signal when there are a plurality of sound sources and when there are noises. The sound source index is k, and the component of the observed signal derived from the sound source k and the sound source position parameter are f ^(k) and θ ^(k) , respectively. Also, let the component energy of the frequency m of f ^{(k) be} σ ^(k) _{0, m} ² . From equation (29),

It becomes. Also, let the additive noise be v and the observation signal be

I assume. If f ⁽¹⁾ , ..., f ^(K) , v are independent of each other, the observation signal y is

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

Is the observation signal

Under the given

It is obtained by solving

y is incomplete data,

By considering as a complete data, the Expectation-Maximization (EM) algorithm 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) for x of log p (x | θ) given y is given by

Given by However,

Means the equal sign only for the term related to x. Updating θ to increase this function (M step), substituting the updated θ into θ ′,

When

By repeating the step of calculating (E step), it is possible to obtain θ which maximizes p (y | θ) locally.

The relationship between complete data x and incomplete data y is

I can write

Are each

Given by From the above, an algorithm consisting of the following initial setting, E step and M step is obtained.

(Initial step)
Initialize θ.

(E step)
Substituting θ into θ ′, equation (39)

Calculate

(M step)
Update θ by the following equation.

<M step update formula>
Since A (θ ^(k) ) is a block diagonal matrix in which C ₁ (θ ^(k) ), ..., _CL (θ ^(k) ) are arranged diagonally,

It is written. However,

It is. Also, ^((k) _m is a 4 × 4 block diagonal component of ^((k) .

In the M step, n ^(k) , R ^(k) , σ ^(k) _{0, m} ² and Γ are updated so that Q (θ, θ ′) becomes as large as possible.

It is difficult to analytically find simultaneous optimal solutions of n ^(k) , R ^(k) , σ ^(k) _{0, m} ² and す る that maximize Q (θ, θ ' ⁾ , but it is difficult It is possible to locally maximize p (y | θ) by iteratively updating Q (θ, θ ') with respect to variables of the maximum (in EM algorithm, the auxiliary function monotonously increases in M steps) Convergence is guaranteed if it is guaranteed). Below is an example of how to update M step.

<N ^(k) update formula>
Since n ^(k) is a unit vector,

Under

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

It can be solved by Lagrange undetermined multiplier method using Lagrangian like. Let E _{i, j} be a 4 × 4 matrix in which only the i th row and j th column elements are 1 and the remainder is 0. Then C _m (θ ^(k) ) is

Partial derivatives of L (n ^(k) ) with respect to n ^(k) because it can be decomposed into terms that depend on n ^(k) and terms that do not.

By putting 0 as

Get Here, [·] _{i, j} represents the component of the i-th row and j-th column of the matrix.

After that, γ ^(k) is searched by the dichotomy so that n ^(k) _x ² + n ^(k) _y ² + n ^(k) _z ² = 1 and substituted into equations (52) to (54). Just do it.

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

I assume. As above, C _m (θ ^(k) ) is

Since it can be decomposed into terms dependent on ^((k) and terms not depending on よ う^{(k) as in,} partial derivatives of Q (θ, θ ' ^{) with} respect to ^((k)

By putting 0 as

Get In the case of notation for each matrix element

It becomes. However,

It is. In the molecule of formula (60)

Can be efficiently calculated using Fast Fourier Transform (FFT).

<Update formula for σ ^(k) _{0, m} ² >
As above, Σ ^{(k) -1} _m

Since it can be decomposed into terms that depend on σ ^(k) _{0, m} ² and terms that do not, like this, by setting the partial derivative of Q (θ, θ ') with respect to σ ^(k) _{0, m} ² to 0,

Get

<Update formula of noise variance covariance matrix >>
The variance-covariance matrix of the noise

As shown, the product of the normalized variance-covariance matrix W _m and the component energy ^{2 2} _m of the frequency m is represented, and ν ² _m is a variable to be estimated. As described later, W _m is a constant matrix derived from a spatial decorrelation model, a diffuse sound field model, and the like. By setting the partial derivative of Q (θ, θ ') with respect to ^{2 2} as 0,

Get

<Setting method of normalized variance-covariance matrix model W>
Here, a setting example of the normalized variance-covariance matrix model W _m will be described from the spatial correlation matrix of noise. The arrangement of seven microphones as shown in Fig. 2 is assumed. _{Here, f i, 0, ...,} f i, L-1 of the Fourier transform of _{F i, 0, ..., F} i, and _L-1. ~ f _m = (F _{0, m} , ..., F _{6, m} ) ^T and f _m = (F _{x, m} , F _{y, m} , F _{z, m} , F _{0, m} ) ^T is

From the fact that it is written that the dispersion covariance matrix of ~ f _m = (F _{0, m} , ..., F _{6, m} ) ^T is Ψ _m , the dispersion covariance matrix of f _m is BΨ _m B ^T Become. Thus, for example, assuming the noise equal power in a spatially uncorrelated, since the [psi _m identity matrix, the variance-covariance matrix W _m of f _m

Just put it.

A sound field having a distribution in which the energy density is uniform and the energy flow in all directions can be regarded as equal probability in a certain area is called a diffuse sound field, and the sound field of the reverberant environment is well approximated. It is known to represent. In the diffuse sound field, the spatial correlation coefficient between two points depends only on the distance d,

Given by Therefore, assuming diffusive noise, in the example of array geometry as shown in FIG. 2, the variance-covariance matrix Ψ _m of ~ f _m = (F _{0, m} , ..., F _{6, m} ) ^T is

It becomes. Using this, the variance-covariance matrix W _m of f _m may be put and BΨ _m B ^T.

<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 by a microphone array.

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

  As shown in FIG. 3, the sound source localization apparatus 100 includes an input unit 10, an arithmetic 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) in which sound source signals from a plurality of sound sources are mixed, which are output from the microphones of the microphone array as shown in FIG.

  The calculation unit 20 includes a spatial difference calculation unit 22, a time frequency expansion unit 24, and a sound source position estimation unit 25.

The spatial difference calculation unit 22 acquires the observation signal f _{0, l} at the microphone of the reference point at each time t _l from the observation signals output from the microphones of the microphone array, and also according to the following equation: , Y, z spatial differences f _{x, l} , f _{y, l} , f _{z, l} are calculated.

Time-frequency expansion unit 24 were obtained by the spatial difference calculating unit 22, from the observed signal f _{0, l} at each time t _l at the microphone of the reference point, to calculate the observation time-frequency component F _{0, m} of each frequency m . Further, the time-frequency expansion unit 24 obtains each space difference f _{x, l} , f _{y, l} , f _{z, l} in each direction x, y, z at each time tl obtained by the space difference calculation unit 22. The observation time frequency components F _{x, m} , F _{y, m} , F _{z, m} of frequency _m are calculated. In the present embodiment, time-frequency expansion such as short-time Fourier transform or wavelet transform is performed.

The sound source position estimation unit 25 is based on the observation frequency component y consisting of the observation time frequency components F _{x, m} , F _{y, m} , F _{z, m} , F _{0, m of} each frequency m acquired in the time frequency expansion unit 24. Observation frequency determined on the basis of the position of each of a plurality of sound sources in the presence of a plurality of sound sources and additive noise determined using a frequency domain representation of a sound source constrained partial differential equation using an EM algorithm The position of each of the plurality of sound sources is estimated so as to increase the probability distribution P (y | θ) of the component y.

  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.

The expected value calculation unit 26 is an observation frequency component y consisting of observation time frequency components F _{x, m} , F _{y, m} , F _{z, m} , F _{0, m of} each frequency m acquired in the time frequency expansion unit 24; The sound source position θ ^{(k) of} each sound source k initialized or previously updated and the component energy σ ^(k) _{0, m} ² of the sound source signal of each sound source k initialized or previously updated Based on the above equation (39)

Calculate

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

Based on equation (52) to equation (54), equation (60), equation (64), equation (66), and equation (67) so that Q (θ, θ ′) becomes as large as possible. The direction vector n ^{(k) of} each sound source k, the sound source distance R ^(k) , the component energy σ ^(k) _{0, m} ² , and the noise covariance matrix Γ are updated.

  The convergence determination unit 30 repeats each processing by the expectation value calculation unit 26 and the variable update unit 28 until the 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) of} each sound source k finally obtained and the sound source distance R ^(k) 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 the microphones of the microphone array, the sound source localization apparatus 100 executes a sound source localization processing routine shown in FIG. 4.

First, in step S120, the time-series data of observation signals input from each microphone of the microphone array, at each time t _l, acquires the observation signal f _{0, l} at the microphone of the reference points, each direction x, y , Z spatial differences f _{x, l} , f _{y, l} , f _{z, l} are calculated.

In step S121, the observed signal f _{0, l} at each time t _l at the microphone of the resulting reference point in step S120, it calculates the observation time-frequency component F _{0, m} of each frequency m. Also, from the spatial differences f _{x, l} , f _{y, l} , f _{z, l} in each direction x, y, z at each time t _l , the observation time frequency components F _{x, m} , F _{y, m of} each frequency _m , F _{z, m} .

In step S122, initial values are set to the sound source position θ ^(k) of each sound source k and the component energy σ ^(k) _{0, m} ² of the sound source signal of each sound source k.

And in step S123, the observation frequency component y which consists of observation time frequency component _{Fx, m} , _{Fy, m} , _{Fz, m} , F _{0, m of} each frequency m acquired in the said step S121, and the said step S122 (39) based on the sound source position θ ^{(k) of} each sound source k initialized in step S124 or previously updated in step S124 described later and the component energy σ ^(k) _{0, m} ^{2 of the} sound source signal By

Calculate

In step S124, it is calculated in step S123.

Based on equation (52) to equation (54), equation (60), equation (64), equation (66), and equation (67) so that Q (θ, θ ′) becomes as large as possible. The direction vector n ^{(k) of} each sound source k, the sound source distance R ^(k) , the component energy σ ^(k) _{0, m} 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 above as the estimation result of the position of each sound source k. , End the sound source localization processing routine.

<Experiment>
We performed sound source localization experiments under reverberant environment under the following conditions.

(Experimental conditions)
Number of sound sources: 1 (+ diffuse noise)
Sound source position: microphone center + [-1. 73; 1.0; 0.0], microphone center + [2.0; 2.0; 0.0], microphone center + [0.0; -2.0; 0.0]
Room size: [6.0; 10.0; 8.0] (Mike placed at the center)
Wall reflection coefficient: 0.01, 0.5, 0.8 (equivalent to the magnitude of the reverberation effect)
Microphone interval: 0.01, 0.1 [m]
Frame width: 16, 32, 64 [points]
Experiment frame number: 2 x 10 (file) (silence section is not included)

  Because there are three microphone positions, there are practically 60 data per condition.

  The square root of error (rad) was used as an evaluation index.

  The experimental results are shown in FIGS. A method of maximizing the likelihood function (equation (28)) assuming the presence of only a single sound source (corresponding to the conventional method, and “OneSrc” in the figure means this method), the accuracy is high. It turned out that localization was done.

  As described above, according to the sound source localization apparatus according to the present embodiment, the plurality of sound sources determined in the frequency domain representation of the sound source restricted partial differential equation when there are a plurality of sound sources and additive noise The observation time-frequency component of each frequency of the reference microphone and the probability distribution of the observation time-frequency component of each frequency for each of a plurality of directions, each condition of each of the plurality of sound sources being conditional on each position of By estimating the position, multiple sound sources can be localized simultaneously, even in the presence of noise.

  The present invention is not limited to the above-described embodiment, and various modifications and applications can be made without departing from the scope of the present invention.

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

  Furthermore, although the present invention has been described as an embodiment in which the program is installed in advance, it is also possible to provide the program by storing the program in a computer readable recording medium.

DESCRIPTION OF SYMBOLS 10 input part 20 arithmetic part 22 space difference calculation part 24 time frequency expansion 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 apparatus for estimating the position of each of a plurality of sound sources from an observation signal in which sound source signals from a plurality of sound sources input by a microphone array are mixed,
A spatial difference calculation unit that calculates a difference between the observation signals input by a pair of microphones arranged in the direction among the microphone arrays for each of a plurality of directions;
An observation time frequency component of each frequency is output with the observation signal input by the reference microphone in the microphone array as an input, and calculated by the spatial difference calculation unit in each of the plurality of directions. A time-frequency expansion unit which outputs an observation time frequency component of each frequency in each of the plurality of directions with the difference of the observation signal as an input;
Based on the observation time frequency component of each frequency of the reference microphone and the observation time frequency component of each frequency for each of the plurality of directions output from the time frequency expansion unit, the frequency domain of the sound source restricted partial differential equation An observation time-frequency component of each frequency of the reference microphone, the position of each of the plurality of sound sources being determined in the presence of the plurality of sound sources and the additive noise, which are determined using a representation; A sound source position estimation unit for estimating the position of each of the plurality of sound sources so as to increase the probability density value of the observation time frequency component of each frequency for each of the directions of
Sound source localization device including: The sound source localization apparatus according to claim 1, wherein the probability density value is expressed by the following equation.






Where y _m represents the observed time frequency component of the frequency m of the reference microphone and the observed time frequency component of the frequency m for each of the plurality of directions, and Γ _m represents the variance covariance of the frequency m of the additive noise The variance matrix, θ ^(k) represents the position of the sound source k, σ _{x, m} ^{(k) 2} , σ _{y, m} ^{(k) 2} , σ _{z, m} ^{(k) 2} is from the sound source k Represents the component energy of frequency m in the direction x, y, z difference of the source signal, σ _{0, m} ^{(k) 2} represents the component energy of frequency m of the reference microphone of the source signal from the source k, R represents the distance to the sound source, c represents the speed of sound, L is a constant for defining the index of the frequency, T represents the sampling period, n _x , n _y , n _z is Represents components in the directions x, y, z of the unit vector toward the sound source. The sound source position estimation unit is a unit for each of the distance R ^{(k) to} each of the plurality of sound sources k and each of the plurality of sound sources k such that the probability density value is increased by an EM (Expectation-Maximization) algorithm. vector n ^(k), pre-Symbol repetition plurality of sound sources component energy sigma ₀ frequency m at the reference microphone for each _{^k, m} ^{(k) _2,} and a variance-covariance matrix gamma _m frequency m of the additive noise The sound source localization apparatus according to claim 2, wherein the position of each of the plurality of sound sources is estimated by updating. A sound source localization method in a sound source localization apparatus for estimating the position of each of a plurality of sound sources from an observation signal in which sound source signals from a plurality of sound sources input by a microphone array are mixed,
The spatial difference calculation unit calculates, for each of a plurality of directions, a difference between the observation signals input by a pair of microphones aligned in the direction in the microphone array;
The time-frequency expansion unit outputs the observation time-frequency component of each frequency with the observation signal input by the reference microphone in the microphone array as an input, and the space difference calculation unit calculates each of the plurality of directions. The observation time frequency component of each frequency is output for each of the plurality of directions, using the difference of the observation signal calculated for
The sound source position estimation unit is based on the observation time frequency component of each frequency of the reference microphone and the observation time frequency component of each frequency for each of the plurality of directions output by the time frequency expansion unit. Observation time of each frequency of the reference microphone based on the position of each of the plurality of sound sources in the presence of the plurality of sound sources and the additive noise, which is determined using a frequency domain representation of a partial differential equation A sound source localization method for estimating the position of each of the plurality of sound sources so as to increase the probability density value of the frequency component and the observation time frequency component of each frequency in each of the plurality of directions. The sound source localization method according to claim 4, wherein the probability density value is expressed by the following equation.






Where y _m represents the observed time frequency component of the frequency m of the reference microphone and the observed time frequency component of the frequency m for each of the plurality of directions, and Γ _m represents the variance covariance of the frequency m of the additive noise The variance matrix, θ ^(k) represents the position of the sound source k, σ _{x, m} ^{(k) 2} , σ _{y, m} ^{(k) 2} , σ _{z, m} ^{(k) 2} is from the sound source k Represents the component energy of frequency m in the direction x, y, z difference of the source signal, σ _{0, m} ^{(k) 2} represents the component energy of frequency m of the reference microphone of the source signal from the source k, R represents the distance to the sound source, c represents the speed of sound, L is a constant for defining the index of the frequency, T represents the sampling period, n _x , n _y , n _z is Represents components in the directions x, y, z of the unit vector toward the sound source. In the estimation performed by the sound source position estimation unit, a distance R ^{(k) to} each of the plurality of sound sources k is set according to an EM (Expectation-Maximization) algorithm so that the probability density value becomes large. unit towards each vector n ^(k), the variance-covariance matrix of the frequency m of the previous SL plurality of component energy sigma ₀ frequency m at the reference microphone for each sound source _{^k, m} ^{(k) _2,} and the additive noise The sound source localization method according to claim 5, wherein the position of each of the plurality of sound sources is estimated by repeatedly updating Γ _m .   The program for functioning a computer as each part of the sound source localization apparatus in any one of Claims 1-3.