CN104105049A - Room impulse response function measuring method allowing using quantity of microphones to be reduced - Google Patents

Abstract

The invention discloses a room impulse response function measuring method allowing the using quantity of microphones to be reduced. The room impulse response function measuring method allowing the using quantity of the microphones to be reduced comprises the following steps that a proper quantity of microphones are distributed and arranged in a space in an even and equal division mode, transfer functions are measured, and the obtained transfer functions serve as a training database; a GMM is established by using the obtained training database and corresponding position information, and model parameters are obtained; a GMR is established by using the model parameters, and an input and output formula is obtained; position coordinates are input to the input and output formula, and the transfer functions of corresponding positions are obtained. According to the room impulse response function measuring method allowing the using quantity of the microphones to be reduced, modeling is conducted on the position coordinates and the transfer functions corresponding to the positions by using the GMM, and then the input and output formula of the position coordinates and the transfer functions corresponding to the positions is obtained by using the GMR. The transfer function corresponding to the position can be obtained by inputting any position coordinate in an observation area. According to the room impulse response function measuring method, the quantity of the microphones used in the process of measuring the transfer functions can be effectively reduced, and the obtained data are more accurate.

Description

A kind of room impulse response function measurement method that reduces microphone usage quantity

Technical field

The present invention relates to sound synthetic treatment technology, particularly a kind of room impulse response function measurement method that reduces microphone usage quantity.

Background technology

Synthetic (WFS) technology of sound field is to take Huygen's principle as the basic three-dimensional sound field that synthesizes in a big way.It has extensive use in fields such as consumer electronics, communications.Audience can experience the azimuth information of sound source in synthetic sound field, thereby has the impression of a kind of " on the spot in person ".The synthetic application scenario of sound field mostly is indoor, and the wall in room can reduce the quality of synthetic sound field to sound wave reflection, so need to add room compensation in practical application.

Before carrying out room compensation, each loud speaker need to be measured acquisition to the transfer function of viewing area (in room synthetic sound field) interior part position.Yet when measuring position is more, use a large amount of microphones to affect greatly sound field, thereby make the data that measure inaccurate, and then reduced the effect of room compensation, even make the deterioration of synthetic sound field.

1, the technical scheme of prior art one

(the J.J.L ó pez such as Fuster, A.Gonz á lez, L.Fuster.Room compensation in wave field synthesis by means of multichannel inversion.IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, New Paltz, New York, 2005:146-149) designed a kind of transfer function measurement scheme, for measuring the transfer function of viewing area.This scheme is placed on a plurality of microphones on a straight-bar, and one end of straight-bar is fixed on a rotating shaft.Rotating shaft often turns a fixed angle, just measures the transfer function of this position.After rotating shaft rotating 360 degrees, the position measuring in space as shown in Figure 1.This method has reduced the impact of microphone on whole sound field, and the microphone using is less.

Because a small amount of microphone of this technology utilization takes multiple measurements, so Measuring Time is longer.And when space is large or space in while having barrier (as pillar), this method of measurement cannot be used.

2, the technical scheme of prior art two

The scheme of technology two is to transfer function modeling in whole space based on local Information Monitoring, scheme flow process as shown in Figure 2, in this scheme, D microphone uniform layout is in whole viewing area, first use space coordinates position as the importation of training dataset, loud speaker arrives the transfer function at each control point as the output of training dataset, and training dataset, by SVR, is obtained to the mapping model between locus and transfer function; On this basis, using position, whole observation area as this mode input, thereby obtain the transfer function of whole viewing area.When training pattern, also available ANN replaces SVR.

There is problem concerning study in ANN model, needs training data sample larger.SVR finds the optimization classification face between different classes of, reflection be the difference between heterogeneous data, but its training time is long, and can not reflect the characteristic of training data itself, the precision of the transfer function of reconstruct is not high.

In sum, when existing reduction transfer function gathers, microphone is used the technology of number to have following problem: (1) measures difficulty in compare great room, space, and is subject to the impact of barrier in space; (2) process time of training is long, and the number of samples needing is more.

The terminological interpretation the present invention relates to is as follows:

WFS:Wave Field Synthesis, sound field is synthetic;

GMR:Gaussian Mixture Regression, Gaussian Mixture returns;

GMM:Gaussian Mixture Model, gauss hybrid models;

ANN:Artificial Neural Networks, artificial neural net;

SVR:Support Vector Regression, support vector regression;

EM:Expectation Maximization, expectation-maximization algorithm.

Summary of the invention

The problems referred to above that exist for solving prior art, the present invention will design a kind of room impulse response function measurement method that is achieved as follows the minimizing microphone usage quantity of object.

(1) in compare great room, space, measure easily, and be not subject to the impact of barrier in space;

(2) process time of training is shorter, and the number of samples needing is less.

To achieve these goals, technical scheme of the present invention is as follows: a kind of room impulse response function measurement method that reduces microphone usage quantity, comprises the following steps:

A, in space, adopt even decile layout to place appropriate microphone, carry out the measurement of transfer function, and using the transfer function obtaining as tranining database;

If arbitrary position r _pand transfer function H (r when frequency is Ω in corresponding frequency domain _p, Ω) form a four-dimensional observation signal x=[x _p, y _p, H _r, H _i], x wherein _pand y _pbe respectively the coordinate figure in space, H _rand H _ibe respectively real part and the imaginary part of transfer function H in frequency domain.In a region to be collected, evenly choose D diverse location and carry out transfer function measurement, and obtain D four-dimensional observation signal.This D four-dimensional observation signal is configured to the training characteristics vector sequence X=[x of GMM model _n, n=1,2 ... D], this sequence is training storehouse.

Training storehouse and corresponding positional information that B, utilization obtain are set up GMM, draw model parameter;

X is set up to GMM.GMM is similar to the probability density distribution of arbitrary shape by the weighted sum of a plurality of single Gauss models, when used single Gauss model number is abundant, can reach good Approximation effect.GMM expression formula is

$\mathrm{pdf}\left(x\right)=\mathrm{pr}\left(x\right|\mathrm{\λ})=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{w}_i{f}_i\left(x\right)---\left(1\right)$

Wherein, f _i(x) be single Gauss model.

The modeling method of GMM model is as follows:

B1, according to sound absorbing object in room is how many etc., situation and experience determine that in GMM, Gaussian component number is M.

B2, gauss hybrid models parameter lambda can be described as

λ＝[w _i,u _i,Σ _i] (2)

Wherein, w _ibe mixed weighting value, it meets mean value vector u _i=[u (x _p), u (y _p), u (p _r), u (p _i)], covariance matrix Σ _i=E[(x-u _i) ^t(x-u _i)].

Use K-Mean Method to carry out cluster analysis to training dataset, obtain the initial parameter λ of GMM model ⁰.K-average concrete steps are as follows:

First using front M four-dimensional observation signal x in Dataset as initial cluster center cx ₁, cx ₂..., cx _m; And for other observation signal of be left, according to the Euclidean distance d of they and these cluster centres _j, respectively they are distributed to the cluster the most similar to it, shown in (3); Then the cluster centre mean using the average of all observation signals in cluster as new cluster _i, shown in (4); Constantly iterative (3) and (4), until the difference of the mean square deviation formula (5) of this M cluster centre before and after iteration is in threshold value 10 ^-10in; Finally with M the cluster data obtaining, calculate λ ⁰, shown in (6)～(8):

$d_j=\underset{i\∈\{\mathrm{1,2},...M\}}{\min }{\left|\right|x_j-{\mathrm{cx}}_i\left|\right|}_2---\left(3\right)$

${\mathrm{mean}}_i=\frac{1}{{\mathrm{num}}_i}{\mathrm{\Σ}}_{i}x---\left(4\right)$

$E_i=\underset{j=1}{\overset{{\mathrm{num}}_i}{\mathrm{\Σ}}}{|x_j-{\mathrm{mean}}_i|}^2---\left(5\right)$

$w_i^0=\frac{{\mathrm{num}}_i}{D}---\left(6\right)$

$u_i^0={\mathrm{mean}}_i---\left(7\right)$

${\mathrm{\Σ}}_i^0=E\left[{(x-u_i^0)}^T(x-u_i^0)\right]---\left(8\right)$

Wherein, num _ibe the number of the observation signal that contains in i cluster, meanwhile, in formula (4) and (8), x belongs to i cluster.

B3, by expectation-maximization algorithm, determine the parameter lambda of gauss hybrid models.The target function Q of expectation-maximization algorithm:

$Q(\mathrm{\λ},{\mathrm{\λ}}^{\′})=\frac{1}{D}\underset{n=1}{\overset{D}{\mathrm{\Σ}}}\log \left(\underset{k=0}{\overset{M}{\mathrm{\Σ}}}{w}_k{f}_k\left(x_n\right)\right)---\left(9\right)$

Wherein, the model parameter that λ ' goes out for last iterative estimate, and for the target function computational process of this expectation-maximization algorithm iteration; The model estimated parameter of λ for obtaining after an expectation-maximization algorithm iteration; f _i(x) be four-dimensional Gaussian probability-density function

$f_i\left(\stackrel{\→}{x}\right)=\frac{1}{{\left(2\mathrm{\π}\right)}^2{\left|{\mathrm{\Σ}}_i\right|}^{1/2}}\exp \{-\frac{1}{2}{(x-u_i)}^T{\mathrm{\Σ}}_i^{-1}(x-u_i)\}---\left(10\right)$

E process---asking for the posterior probability of training data under i Gaussian component is:

$p(i_n=i|x_n,\mathrm{\λ})=\frac{w_i{f}_i\left(x_n\right)}{\underset{k=1}{\overset{M}{\mathrm{\Σ}}}{w}_k{f}_k\left(x_n\right)}---\left(11\right)$

Wherein, λ is λ when iteration for the first time ⁰, the model parameter producing for M process afterwards.M process---calculate the various estimates of parameters of Q:

${\stackrel{\‾}{w}}_i=\frac{1}{D}\underset{n=1}{\overset{D}{\mathrm{\Σ}}}\mathrm{pr}(i_n=i|x_n,\mathrm{\λ})---\left(12\right)$

${\stackrel{\‾}{u}}_i=\frac{\underset{n=1}{\overset{D}{\mathrm{\Σ}}}\mathrm{pr}(i_n=i|x_n,\mathrm{\λ})x_n}{\underset{n=1}{\overset{D}{\mathrm{\Σ}}}\mathrm{pr}(i_n=i|x_n,\mathrm{\λ})}---\left(13\right)$

${\stackrel{\‾}{\mathrm{\Σ}}}_i^2=\frac{\underset{n=1}{\overset{D}{\mathrm{\Σ}}}\mathrm{pr}(i_n=i|x_n,\mathrm{\λ})x_n^2}{\underset{n=1}{\overset{D}{\mathrm{\Σ}}}\mathrm{pr}(i_n=i|x_n,\mathrm{\λ})}-{\stackrel{\‾}{u}}_i^2---\left(14\right)$

Wherein, with be respectively the estimation of weighted value, mean value and the covariance matrix of i component.After M process finishes, will with upgrade.Consider the stability of numerical computations, in M process, after estimate covariance matrix, the diagonal element of covariance matrix is increased to a very little constant 10 ^-5.

Then, according to formula (12)～(14) calculating formula (9), if the difference between the Q calculating and last iteration result surpasses threshold value 10 ^-10, repeat E process and M process, until formula (9) result of calculation is less than threshold value 10 ^-10.Set up out like this gauss hybrid models λ.

C, utilize model parameter to set up GMR, draw input and output formula;

Using the spatial position data that need to rebuild arbitrarily acoustic pressure on viewing area as input data characteristics vector X _in={ x _inn, n=1 ..., L}, using the transfer function of rebuilding as output data characteristics vector X _out={ x _outn, n=1 ..., L}, it is to be input as X that Gaussian Mixture returns _in=x _inncondition under, X _outexpectation as output x _outn:

$x_{\mathrm{outn}}=E\left[X_{\mathrm{out}}\right|X_{\mathrm{in}}=x_{\mathrm{inn}},\mathrm{\λ}]=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{m}_i\left(x_{\mathrm{inn}}\right)\mathrm{pr}\left(i\right|x_{\mathrm{inn}},\mathrm{\λ})---\left(15\right)$

In formula, $m_i=\left(x_{\mathrm{inn}}\right)={u_{\mathrm{iX}}}_{\mathrm{out}}+{\mathrm{\Σ}}_{{\mathrm{iX}}_{\mathrm{out}}{X}_{\mathrm{in}}}{\mathrm{\Σ}}_{{\mathrm{iX}}_{\mathrm{in}}}^{-1}(x_{\mathrm{inn}}-u_{i{X}_{\mathrm{in}}})$ To be input as x _inncondition under x _outnexpectation, and p (i|x _inn, λ) be input data x _innposterior probability under i Gaussian component.

D, position coordinates is inputted to formula, obtain the transfer function of relevant position.

Utilize formula (15), the observation signal that can form any point in viewing area, input data x _in, return output x _out, x here _outfor the transfer function of reconstruct.

In GMM of the present invention, Gaussian component number M span is 20～110.

Compared with prior art, the present invention has following beneficial effect:

1, the present invention adopts even decile layout, at x axle or y axle up-sampling points N, directly affects the quantity of microphone used.The transfer function that the present invention's gauss hybrid models used can approach viewing area well distributes, thereby has significantly reduced microphone number used.

2, the present invention is iteration that EM algorithm carries out GMM optimized parameter λ while obtaining by expectation-maximization algorithm, first by K average, carries out cluster analysis, then using its result as EM algorithm initial model parameter value, thereby has improved iterative convergence speed.

3, the present invention, in the M of EM algorithm process, after estimate covariance matrix, increases a very little constant to its each diagonal element, can improve the stability of numerical computations.

4, the method for repeatedly measuring with respect to a small amount of microphone, the present invention is not subject to the restriction of barrier in space, can in larger space, use simultaneously.

5, the present invention uses Gaussian Mixture recurrence to carry out transfer function interpolation, train the time used few, and required sample is less.

6, the inventive method adopts GMR to carry out interpolation to the transfer function in room, makes the transfer function that obtains more accurate.The room backoff algorithm of transfer function after reconstruct in can be synthetic for sound field.At large space with have barrier in the situation that, the present invention stands good.And the present invention uses the less time just can obtain good effect.

7, in order effectively to obtain the transfer function in viewing area, the present invention has used GMM to carry out modeling to position coordinates and transfer function corresponding to this position, then utilizes the input and output formula of transfer function corresponding to GMR acquisition position coordinates and this position.By optional position coordinate in input viewing area, just can obtain transfer function corresponding to this position.It is the microphone quantity of use that the present invention can effectively reduce in measurement transfer function process, makes the data of acquisition more accurate.Meanwhile, the present invention can obtain for the transfer function in large space, and is not subject to the impact of barrier in space (such as pillar).

Accompanying drawing explanation

13, the total accompanying drawing of the present invention, wherein:

Fig. 1 is measuring position distribution map in viewing area.

Fig. 2 is the transfer function reconstruct flow chart based on SVR (ANN).

Fig. 3 is the room impulse response interpolation flow chart based on GMR.

Fig. 4 is microphone distribution map in the viewing area returning based on Gaussian Mixture.

Fig. 5 is the modeling flow chart of gauss hybrid models.

Fig. 6 is microphone distribution map in viewing area A.

Fig. 7 is the error mean square value of frequency transfer function real part and imaginary part while being 350Hz, M=40.

Fig. 8 is the error mean square value of frequency transfer function real part and imaginary part while being 350Hz, N=27.

Fig. 9 is the acoustic pressure distribution map (real part) of frequency simulated environment while being 350Hz, N=27, M=45.

Figure 10 is the acoustic pressure distribution map (imaginary part) of frequency simulated environment while being 350Hz, N=27, M=45.

Figure 11 is the acoustic pressure distribution map (real part) of frequency corresponding sound field of reconstruct transfer function while being 350Hz, N=27, M=45.

Figure 12 is the acoustic pressure distribution map (imaginary part) of frequency corresponding sound field of reconstruct transfer function while being 350Hz, N=27, M=45.

Figure 13 is frequency while being 350Hz, the acoustic pressure real part error mean square value of three kinds of method reconstruct sound fields.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described further.

For verifying feasibility of the present invention, by the flow process shown in Fig. 3, carried out emulation experiment.Testing virtual room length and width used is all 5 meters, ignores roof and the impact of ground in the face of sound field, and only considers that a sound field on fixed horizontal plane distributes.A loudspeaker position is (0.4,2.4).Viewing area A is the square area of length of side 2.6m, and the control point coordinate in its lower left corner is (1.3,1).Control point is uniformly distributed in viewing area, as shown in Figure 4.

Set up GMM model process as shown in Figure 5, the threshold value that K-averaging method and EM iterative method are used is 10-10.

First need to determine the number of microphone.As shown in Figure 6, the square area that listening zone is 2.6m * 2.6m, the spacing of horizontal and vertical two adjacent microphones is all identical.By adjusting the size of N, can change the distribution density of microphone.

Make single Gauss model number M=40 in gauss hybrid models, and calculate when N value is different, the mean square of error value of the transfer function of reconstruct and actual transfer function (the room reflections model of setting up before utilizing obtains).Error mean square value itself and N value relation curve are as shown in Figure 7.

In Fig. 7, when N=25, error tends to be steady.For the ease of calculating, N=27 in experiment below, every two adjacent microphone distances are 0.1m.

Fig. 8 is when N=27, when in gauss hybrid models, single Gauss model quantity M value is different, and the real part of transfer function and the mean square deviation of imaginary part.When M=45, error tends towards stability.So N=27 in experiment below, M=45

Fig. 9-12 are in the situation that frequency is 350Hz and N=27, M=45, speaker output signal amplitude is 1 o'clock, the sound field (amplitude has been carried out normalized) that the transfer function of the sound field of the transfer function in actual environment and the reconstruct of use Gaussian Mixture homing method calculates.

The performance that the method that the present invention is proposed and ANN and SVR method are carried out the reconstruct of sound field acoustic pressure compares analysis, and they are under same sample size, and its reconstruct sound pressure amplitude relative error as shown in figure 13.

The RBF neural net target error of selecting in Figure 13 is 0.001.That SVMs homing method is used is ε-SVR, and by Gaussian kernel as kernel function, γ=0.05 wherein, v=0.5, tolerable deviation is 0.001, penalty coefficient is 2.2.Can find out, along with N value increases, the error of three kinds of method reconstruct transfer functions reduces gradually.When N is larger, ε-SVR method has more advantage.In N value hour, Gaussian Mixture homing method is better than another two kinds of methods.

More than experiment shows, compares with ANN, SVR method, and when using microphone negligible amounts, the transfer function that the present invention reconstructs is more accurate, has clear superiority.And use of the present invention is not subject to the restriction of barrier in space, can in larger space, use simultaneously.

Claims (2)

1. a room impulse response function measurement method that reduces microphone usage quantity, is characterized in that: comprise the following steps:

A, in space, adopt even decile layout to place appropriate microphone, carry out the measurement of transfer function, and using the transfer function obtaining as tranining database;

If arbitrary position r _pand transfer function H (r when frequency is Ω in corresponding frequency domain _p, Ω) form a four-dimensional observation signal x=[x _p, y _p, H _r, H _i], x wherein _pand y _pbe respectively the coordinate figure in space, H _rand H _ibe respectively real part and the imaginary part of transfer function H in frequency domain; In a region to be collected, evenly choose D diverse location and carry out transfer function measurement, and obtain D four-dimensional observation signal; This D four-dimensional observation signal is configured to the training characteristics vector sequence X=[x of GMM model _n, n=1,2 ... D], this sequence is training storehouse; Described GMM model is gauss hybrid models and abbreviation;

Training storehouse and corresponding positional information that B, utilization obtain are set up GMM, draw model parameter;

X is set up to GMM; GMM is similar to the probability density distribution of arbitrary shape by the weighted sum of a plurality of single Gauss models, when used single Gauss model number is abundant, can reach good Approximation effect; GMM expression formula is

$\mathrm{pdf}\left(x\right)=\mathrm{pr}\left(x\right|\mathrm{\λ})=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{w}_i{f}_i\left(x\right)---\left(1\right)$

Wherein, f _i(x) be single Gauss model;

The modeling method of GMM model is as follows:

B1, according to sound absorbing object in room is how many etc., situation and experience determine in GMM that Gaussian component number is M;

B2, gauss hybrid models parameter lambda can be described as

λ＝[w _i,u _i,Σ _i] (2)

Wherein, w _ibe mixed weighting value, it meets mean value vector u _i=[u (x _p), u (y _p), u (p _r), u (p _i)], covariance matrix Σ _i=E[(x-u _i) ^t(x-u _i)];

Use K-Mean Method to carry out cluster analysis to training dataset, obtain the initial parameter λ of GMM model ⁰; K-average concrete steps are as follows:

First using front M four-dimensional observation signal x in Dataset as initial cluster center cx ₁, cx ₂..., cx _m; And for other observation signal of be left, according to the Euclidean distance d of they and these cluster centres _j, respectively they are distributed to the cluster the most similar to it, shown in (3); Then the cluster centre mean using the average of all observation signals in cluster as new cluster _i, shown in (4); Constantly iterative (3) and (4), until the difference of the mean square deviation formula (5) of this M cluster centre before and after iteration is in threshold value 10 ^-10in; Finally with M the cluster data obtaining, calculate λ ⁰, shown in (6)～(8):

$d_j=\underset{i\∈\{\mathrm{1,2},...M\}}{\min }{\left|\right|x_j-{\mathrm{cx}}_i\left|\right|}_2---\left(3\right)$

${\mathrm{mean}}_i=\frac{1}{{\mathrm{num}}_i}{\mathrm{\Σ}}_{i}x---\left(4\right)$

$E_i=\underset{j=1}{\overset{{\mathrm{num}}_i}{\mathrm{\Σ}}}{|x_j-{\mathrm{mean}}_i|}^2---\left(5\right)$

$w_i^0=\frac{{\mathrm{num}}_i}{D}---\left(6\right)$

$u_i^0={\mathrm{mean}}_i---\left(7\right)$

${\mathrm{\Σ}}_i^0=E\left[{(x-u_i^0)}^T(x-u_i^0)\right]---\left(8\right)$

Wherein, num _ibe the number of the observation signal that contains in i cluster, meanwhile, in formula (4) and (8), x belongs to i cluster;

B3, by expectation-maximization algorithm, determine the parameter lambda of gauss hybrid models; The target function Q of expectation-maximization algorithm:

$Q(\mathrm{\λ},{\mathrm{\λ}}^{\′})=\frac{1}{D}\underset{n=1}{\overset{D}{\mathrm{\Σ}}}\log \left(\underset{k=0}{\overset{M}{\mathrm{\Σ}}}{w}_k{f}_k\left(x_n\right)\right)---\left(9\right)$

Wherein, the model parameter that λ ' goes out for last iterative estimate, and for the target function computational process of this expectation-maximization algorithm iteration; The model estimated parameter of λ for obtaining after an expectation-maximization algorithm iteration; f _i(x) be four-dimensional Gaussian probability-density function

$f_i\left(\stackrel{\→}{x}\right)=\frac{1}{{\left(2\mathrm{\π}\right)}^2{\left|{\mathrm{\Σ}}_i\right|}^{1/2}}\exp \{-\frac{1}{2}{(x-u_i)}^T{\mathrm{\Σ}}_i^{-1}(x-u_i)\}---\left(10\right)$

E process---asking for the posterior probability of training data under i Gaussian component is:

$p(i_n=i|x_n,\mathrm{\λ})=\frac{w_i{f}_i\left(x_n\right)}{\underset{k=1}{\overset{M}{\mathrm{\Σ}}}{w}_k{f}_k\left(x_n\right)}---\left(11\right)$

Wherein, λ is λ when iteration for the first time ⁰, the model parameter producing for M process afterwards; M process---calculate the various estimates of parameters of Q:

${\stackrel{\‾}{w}}_i=\frac{1}{D}\underset{n=1}{\overset{D}{\mathrm{\Σ}}}\mathrm{pr}(i_n=i|x_n,\mathrm{\λ})---\left(12\right)$

${\stackrel{\‾}{u}}_i=\frac{\underset{n=1}{\overset{D}{\mathrm{\Σ}}}\mathrm{pr}(i_n=i|x_n,\mathrm{\λ})x_n}{\underset{n=1}{\overset{D}{\mathrm{\Σ}}}\mathrm{pr}(i_n=i|x_n,\mathrm{\λ})}---\left(13\right)$

${\stackrel{\‾}{\mathrm{\Σ}}}_i^2=\frac{\underset{n=1}{\overset{D}{\mathrm{\Σ}}}\mathrm{pr}(i_n=i|x_n,\mathrm{\λ})x_n^2}{\underset{n=1}{\overset{D}{\mathrm{\Σ}}}\mathrm{pr}(i_n=i|x_n,\mathrm{\λ})}-{\stackrel{\‾}{u}}_i^2---\left(14\right)$

Wherein, with be respectively the estimation of weighted value, mean value and the covariance matrix of i component; After M process finishes, will with upgrade; Consider the stability of numerical computations, in M process, after estimate covariance matrix, the diagonal element of covariance matrix is increased to a very little constant 10 ^-5;

Then, according to formula (12)～(14) calculating formula (9), if the difference between the Q calculating and last iteration result surpasses threshold value 10 ^-10, repeat E process and M process, until formula (9) result of calculation is less than threshold value 10 ^-10; Set up out like this gauss hybrid models λ;

C, utilize model parameter to set up GMR, draw input and output formula;

Using the spatial position data that need to rebuild arbitrarily acoustic pressure on viewing area as input data characteristics vector X _in={ x _inn, n=1 ..., L}, using the transfer function of rebuilding as output data characteristics vector X _out={ x _outn, n=1 ..., L}, it is to be input as X that Gaussian Mixture returns _in=x _inncondition under, X _outexpectation as output x _outn:

$x_{\mathrm{outn}}=E\left[X_{\mathrm{out}}\right|X_{\mathrm{in}}=x_{\mathrm{inn}},\mathrm{\λ}]=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{m}_i\left(x_{\mathrm{inn}}\right)\mathrm{pr}\left(i\right|x_{\mathrm{inn}},\mathrm{\λ})---\left(15\right)$

In formula, $m_i=\left(x_{\mathrm{inn}}\right)={u_{\mathrm{iX}}}_{\mathrm{out}}+{\mathrm{\Σ}}_{{\mathrm{iX}}_{\mathrm{out}}{X}_{\mathrm{in}}}{\mathrm{\Σ}}_{{\mathrm{iX}}_{\mathrm{in}}}^{-1}(x_{\mathrm{inn}}-u_{i{X}_{\mathrm{in}}})$ To be input as x _inncondition under x _outnexpectation, and p (i|x _inn, λ) be input data x _innposterior probability under i Gaussian component; Described GMR is the abbreviation that Gaussian Mixture returns;

D, position coordinates is inputted to formula, obtain the transfer function of relevant position;

Utilize formula (15), the observation signal that can form any point in viewing area, input data x _in, return output x _out, x here _outfor the transfer function of reconstruct.

2. a kind of room impulse response function measurement method that reduces microphone usage quantity according to claim 1, is characterized in that: in described GMM, Gaussian component number M span is 20～110.