JP2002528778A - Method and apparatus for determining parameters of a technical system - Google Patents

Abstract

(57) [Summary] A method for determining parameters of a technical system is determined. In this way, the output signals are determined from a superimposed set of statistically independent input signals. The parameters are determined so that the statistical independence of the output signal is maximized.

Description

DETAILED DESCRIPTION OF THE INVENTION

The present invention relates to a method and a device for determining the parameters of a technical system.

In multi-channel transmission and multi-channel reception of signals, for example, signal / image interference frequently occurs. A typical example is a mixture of voice signals and noise in this case, which can be a major problem in telecommunications and video conferencing. Therefore,
The invention relates to the field of signal separation, for example to reproduce the original audio signal.

[0003] Typical known techniques for separating a source signal from a mixed signal are based on time averaging or filtering of the signal. However, this has disadvantages in terms of computational costs.

[0004] Methods based on so-called blind channel equalization (signal equalization without prior knowledge of the transmission channel) are also known. However, this method always requires certain knowledge about the source signal, for example knowledge about the statistical distribution of the source signal.

[0005] The problem of signal separation is, for example, when two speakers speak with two microphones remote from them, so that each microphone receives a mixed signal of the signals spoken by the two speakers. Also occurs. Therefore, there is a problem that the mixed signal, that is, the set of superimposed input signals is separated again. L. Molgedy, HG Sc
huster, "Separation of a Mixture of Independent Signals using Time-Delay
ed. Correlations ", Phys. Ref. Left. 72, 3634 (1994), in which case the following method is known: The n superimposed and correlated source signals (input signals) are separated and simultaneously sourced. The problem of determining the intensity mixing factor is reduced to an eigenvalue problem, in which two symmetric nxn matrices must be diagonalized at the same time, and the matrix elements have a measurable time-delayed correlation. The solution of this eigenvalue problem is performed by a neural network, the learning rule for lateral inhibiting interaction between neurons is determined by the Lyapunov function, and the minimum value of this Lyapunov function is Provide a (degenerate) solution.

[0006] This method has already been applied to acoustic input signals (F. Ehlers, HGSchuster, "Bl
ind Separation of convolutive mixtures and an application in automatic s
peech recognition "IEEE Trans. Signal Proc. (1997)).

[0007] From DE 195 31 388 C1, a signal separation method and a signal separation device for the non-linear mixing of unknown signals (blind channels) are known and are shown in FIG.

This German patent deals with the separation of a mixed signal consisting of a non-linear superposition of M unknown source signals X1, X2. N (N≥M) different mixtures of the M source signals X1, X2, possibly including interfering signals, are fed to a signal estimator, which is non-linear by statistical analysis of these signals. Transfer coefficient (nonlinea
r transmission factor) and cancels out this mixing by these calculated coefficients, so that the N outputs of the signal separation device contain the M source signals as close as possible without overlap. This allows processing of non-linear mixed signals. In this case, non-linear means that the source signals X1, X2 are mixed by the unknown non-linear system G. This unknown system G is a so-called Volterra (
Described by a Volterra series, the signal separation device G ^{- 1} determines the coefficients of this Volterra series. The knowledge of these coefficients allows the separation of the mixed signal. In addition, these coefficients can be used for subsequent analysis for signal source position or velocity detection.

The method known from this print consists in this case essentially of two steps: firstly, the nonlinear equation uniquely determined during mixing by the selectable grade of nonlinearity has a sliding time window And these solutions are averaged over time. This time averaging is a major drawback of this known technique. This is because this time average increases the calculation cost and at the same time the calculation time.

Second, the potential formed from a sufficiently large number of different cumulants of the estimated output signal is minimized, and the value required for the calculation of this potential is determined from a sliding time window of selectable length. Comes from. In this case, it is assumed that the mixing system changes very slowly and this change is negligible in the calculation of the required mixing coefficients. According to this German patent, a cost function is constructed and minimized for performing the second step. When a global minimum is reached, in this case an optimum value of the transfer coefficient has been found.

In terms of time costs as well as computational costs, the method described in DE 195 31 388 C1 is disadvantageous for performing a time averaging at the end of the first above-mentioned method step.

It is therefore an object of the present invention to provide a method and a device which enable the superimposed, statistically independent acoustic signals to be separated at a very low computational cost.

[0013] The object is achieved by a method and a device having the features of the independent claims.

In a method for determining the parameters of a technical system, the method determines the output signal from a superimposed statistically independent set of input signals and maximizes the statistical independence of the output signal. Parameters are determined as follows.

In an apparatus for determining parameters of a technical system, the apparatus determines an output signal from a superimposed set of statistically independent input signals, the apparatus comprising a processor, the processor comprising an output It is configured to determine parameters such that the statistical independence of the signal is maximized.

[0016] Advantageous embodiments of the invention result from the dependent claims.

The parameters are advantageously determined in an iterative manner.

In another embodiment, the parameters are elements of a separation matrix, which is multiplied or convolved with the set of superimposed input signals, thereby forming an output signal.

The optimization of the parameters of the separation matrix is advantageously obtained by the following steps:
In other words, a time-delayed inverse correlation calculation (time-delayed
repeat the decorrelation calculation), find the eigenvalues of the separation matrix, take the minimum cross-correlation for these eigenvalues, implement cumulant minimization, and use the eigenvalues found in the previous step as the start value for this cumulant minimization Is used.

[0020] Cumulant minimization is performed, for example, by training a neural network, but by any other minimization technique, such as, for example, steepest descent or Monte Carlo simulation.

In one embodiment, in optimizing the parameters of the separation matrix, at least one diagonal parameter of the separation matrix is set to a preset value, thereby stabilizing the minimization process to a global minimum. Is guaranteed.

The separation matrix is advantageously limited to a finite impulse response. That is, an FIR filter (Finite Impulse Response) is used to form the individual elements of the separation matrix.
Is used. The FIR filter can be a causal FIR filter or an acausal FIR filter.
An R filter.

Furthermore, the separation matrix is stabilized during cumulant minimization, advantageously by projection onto the unit circle.

These embodiments apply to the method and the device. In the device, a processor is respectively operable or configured to perform the corresponding method steps.

The invention as well as embodiments of the invention are advantageously used for the separation of superimposed, statistically independent input signals, in particular acoustic input signals.

The method and apparatus of the present invention are applicable to any number of input signals.

Further advantages, configurations and characteristics of the present invention will now be described in detail based on embodiments with reference to any of the drawings.

FIG. 1 shows an application example of a system for separating superimposed statistically independent sound signals according to an embodiment of the present invention.

FIG. 2 shows a symbolic schematic of the system of FIG.

FIG. 3 shows a prior art (DE19531388C1) for nonlinear mixing of unknown signals.
) Shows a known signal separation device.

In order to reproduce the original audio signal, from the signal mixture, a dynamic in which the signal mixture is generated by utilizing the statistical independence between the source signals (the original audio signal and noise), hereinafter referred to as an input signal, is used. The inverse process of the system is substantially trained. Two different mixtures of audio or noise signals are obtained, for example, by two microphones 1, 2 (see FIG. 1). These two microphones 1, 2 are spaced from each other and / or oriented in diametrically opposite directions. In the method of the present invention, to start the learning phase,
That is, a so-called time-delayed decorrelation (TDD) is used to obtain and set the start value for the learning phase. This reduces the computational cost for cumulant minimization, described later, and reduces the risk of local minima.

FIG. 1 shows two microphones 1, 2 and these two microphones 1
, 2 receive a first input signal Z1 (t) and a second input signal Z2 (t). These input signals Z1 (t) and Z2 (t) are each mixed with noise. This is symbolically illustrated in FIG. 1 by the mixing matrix S (reference 3). After reception or transmission, a set X1 (t) and X2 (t) of superimposed statistically independent input signals Z1 (t) and Z2 (t) is obtained. These signals are input to a calculation unit 4 where substantially two
Two steps are performed. These two steps are symbolically illustrated by a calculation unit B (reference numeral 6) for the first step and a neural network 5 for the second step.

The calculation unit 4 determines two output signals Y 1 (t) to Y 2 (t). These two output signals Y1 (t) or Y2 (t) are calculated by the calculation unit 4
Input signals Z1 (t) through Z
2 (t). In other words, in the optimal adjustment of the parameters of the matrix used in the calculation unit 4, the calculation unit 4 performs the inverse process of the dynamic mixing process, which is substantially symbolically indicated by the matrix S (reference numeral 3). This embodiment relates to an optimization process for adjusting the parameters of the separation matrix.

The parameters of the matrix in the calculation unit 4 are optimized by maximizing the statistical independence between the output signals Y 1 (t), Y 2 (t) obtained by the matrix process in the calculation unit 4. For this purpose, the output signal Y1 (t)
Alternatively, Y2 (t) is fed back to the calculation unit 4 (see feedback loops 7 and 8). By an iterative method, the output signals Y1 (t) or Y2 (t)
Has increased statistical independence compared to the previous step of this iteration (and thus this iteration takes the "right" direction in the direction of the global minimum of the cost function described later) I can ask for it.

FIG. 2 shows a mathematical illustration of the scheme of FIG. 1, where the mixing process 3 comprises a matrix S (q)
And the separation process to be performed by the calculation unit 4 is indicated by the separation matrix M (q).

Accordingly, FIG. 2 shows a so-called multi-channel blind source in two dimensions (
The problem of separation of multi-channel sources without a priori knowledge is illustrated. In this case, it is assumed that the mixing system S (q), where q is a unit delay, is stable and at the same time has a stable inversion, ie this system is a minimal phase system. . Further, the input signal Z
Assume that 1 (t) and Z2 (t) (eg, speech or noise signals) are statistically independent of each other and do not have a Gaussian distribution. The superimposed input signals Z1 (t) to Z1
The sets X1 (t) and X2 (t) of 2 (t) are input signals to a separation system having a separation matrix M (q), and the parameters (matrix elements) of the separation matrix M (q) are output signals. Trained to maximize statistical independence between Y1 (t) and Y2 (t). "Training" is in this case known, for example, as the well-known learning process of neural networks, which is mentioned as an example of a technique for maximizing statistical independence. This is done by minimizing a cost function J (M) described later.

A cumulant cost function is formed. This cumulant cost function minimizes the diagonal cumulant elements of cumulant order 2-4:

[0038]

(Equation 1)

In this case, the following aspects of the dynamic mixing with the mixing matrix S (q) are considered: Stability of the separation system: M (q) is limited to a finite impulse response (FIR filter) If achieved. The stability of the FIR system M (q) is also obtained by projecting onto the unit circle during the learning phase. The acausality of the inversion of S (q) that may be present can be compensated by a suitable time shift (delay) of the input signal X (t).

Uniqueness of the separated signal Y (t): In the case of stationary mixing, the original source signal is reproduced by scaling. In the case of dynamic separation, the risk of non-uniqueness of the separated signal Y (t) is even greater. If Y1 (t) and Y2 (t) are statistically independent of each other, it is clear that any linearly filtered modification of these signals is always statistically independent. Therefore, additional information is essential to reduce the inherent non-uniqueness of this problem.

Gaussian Transformation of Data: A cumulant-based algorithm for stationary blind source separation effectively minimizes or eliminates diagonal cumulants of relatively high order corresponding to the output signal Y (t). . On the other hand, linear filtering causes a Gaussian deformation of the data, in which the higher order cumulants go in direction 0. Thus, this leads to a boundary solution (Randloesung) where the cost function reaches a local minimum and the desired actual separation (global minimum) is not performed. To avoid this undesirable case, the separation transfer function (separation matrix)
The structure of M (q) is subject to some limitations. To avoid the above problem, choose an approach where at least one (or all) of the diagonal elements is set to unit value: M11 (q) = 1 and M22 (q) = 1 Similarly, if the mixing element S11 (q) and / or S22 (q)
1 "is true. Otherwise, S11 (q) and / or S11 (q)
Assume that 22 (q) has a stable inversion. This allows the diagonal elements of M (q) to be scaled to unit values. This approach essentially reduces the non-uniqueness of the solution and avoids the risk of excessive Gaussian deformation of the output signal in a more efficient manner. Even though at first glance the diagonal element limitation of M (q) as described above works very restrictively, this assumption is usually satisfied in practical applications. A typical example is denoising from a speech signal based on recording with two microphones, where these microphones are spatially separated from each other or one microphone is oriented towards the speaker. , While the other microphone is pointed in the opposite direction,
Thus, the second signal in the opposite direction to the speaker contains substantially only the noise signal.

[0042] The cumulant approach is described in the paper F. Ehlers, HGSchuster, "B
lind Separation of convolutive mixtures and an application in automatic
speech recognition "based on the direct calculation of diagonal cumulants as done in IEEE Trans. Signal Proc. (1997). However, this has the disadvantage that the numerical solution is inherently very cumbersome. In order to determine a starting value for the minimization method, the technique of time-delay inverse correlation (TDD) uses the technique of time-delay inverse correlation (TDD) for the simultaneous inverse correlation of two different time delays. The TDD technique is reduced to a suitable matrix eigenvalue problem, which, as already mentioned, is used in the present invention to start the diagonal (cross-correlation) cumulant minimization problem.

In summary, the method can be divided into two steps: 1. Iteration of the TDD method based on eigenvalue problems in the frequency domain for different delay pairs and calculation of the solution whose cross-correlation term has a minimum.

2. Start of diagonal cumulant minimization (start) based on the start value (FIR parameter) calculated in the above steps.

Next, some more main features and advantages are summarized again.

No a priori knowledge of signal characteristics is required except that statistical independence is required.

The stability of the dynamic separation system is ensured by adjusting the components of this dynamic separation system as FIR filters.

Excessive Gaussian deformation is avoided by the following approach. That is, this is avoided by the approach that at least one of the elements of the mixed transfer function matrix (separation matrix) can be set to unit values or scaled to unit values.

Since the cumulant minimization step (step 2) requires a large calculation cost, for example, the learning algorithm of the neural network is initialized by the TDD method.

Matlab, Vers for implementing the above-described embodiment by a computer will be described below.
Submit the ion4 or Version program:

[0051]

[Outside 1]

[0052]

[Outside 2]

[Brief description of the drawings]

FIG. 1 shows an application example of a system for separating superimposed statistically independent sound signals according to an embodiment of the present invention.

FIG. 2 shows a symbolic schematic of the system of FIG.

FIG. 3 shows a signal separation device known from the prior art (DE19531388C1) for nonlinear mixing of unknown signals.

[Description of Signs] 1 microphone 2 microphone 3 mixing matrix 4 calculation unit 5 neural network 6 calculation unit 7 and 8 feedback loop

[Procedural Amendment] Submission of translation of Article 34 Amendment of the Patent Cooperation Treaty

[Submission Date] December 22, 2000 (2000.12.22)

[Procedure amendment 1]

[Document name to be amended] Statement

[Correction target item name] Claims

[Correction method] Change

[Correction contents]

[Claims]

──────────────────────────────────────────────────続 き Continued on the front page (51) Int.Cl. ⁷ Identification symbol FI Theme coat ゛ (Reference) G10L 15/16 G10L 9/00 F 21/02 301A H04L 25/03 3/00 539

Claims (20)

[Claims] 1. A method for determining a parameter of a technical system, comprising:
A parameter of a technical system, wherein the parameter is determined from a set of statistically independent input signals on which the output signal is superimposed by the method, and wherein the method is such that the statistical independence of the output signal is maximized. Way to find out. 2. The method of claim 1, wherein the parameters are determined in an iterative manner. 3. The method of claim 1, wherein the parameters are elements of a separation matrix, and the set of input signals superimposed by the separation matrix is multiplied to form an output signal. 4. The optimization of the parameters of the separation matrix is obtained by the following steps: a time-delayed inverse correlation calculation (dec is used to determine the eigenvalues of the separation matrix; 4. The method according to claim 3, wherein the cross-correlation takes the minimum value for the eigenvalue, performs cumulant minimization (5), and uses the eigenvalue determined in the previous step as a start value for the cumulant minimization. the method of. 5. The method according to claim 4, wherein the cumulant minimization is performed by training a neural network. 6. The method of claim 3, wherein at least one diagonal parameter of the separation matrix is set to a preset value in the optimization of the parameters of the separation matrix.
6. The method according to one of the five aspects. 7. The separation matrix according to claim 3, wherein the separation matrix is limited to a finite impulse response.
The method of claim 1. 8. The method according to claim 3, wherein the separation matrix is stabilized during cumulant minimization by projection onto a unit circle. 9. The method according to claim 1, which is used for separating superimposed, statistically independent input signals. 10. The method according to claim 1, which is used for separating superimposed, statistically independent audio input signals. 11. An apparatus for determining parameters of a technical system, comprising: determining an output signal from a set of statistically independent input signals superimposed by the apparatus; the apparatus comprising a processor, the processor comprising: An apparatus for determining a parameter of a technical system, wherein the apparatus is configured to determine the parameter such that statistical independence of an output signal is maximized. 12. The apparatus of claim 11, wherein the processor is configured to determine the parameters in an iterative manner. 13. The processor is configured as follows: the parameters are elements of a separation matrix, and the set of superimposed input signals is multiplied by the separation matrix, thereby forming an output signal. An apparatus according to claim 11 or claim 12. 14. The processor is constructed as follows: the optimization of the parameters of the separation matrix is obtained by the following steps: the inverse correlation time-delayed to determine the eigenvalues of said separation matrix. Calculation (time-del
ayed decorrelation calculation) (6) is repeated, the eigenvalue of the separation matrix is obtained, the cross-correlation takes the minimum value for the eigenvalue, cumulant minimization (5) is performed, and the start value for the cumulant minimization is obtained. 14. The apparatus according to claim 13, wherein eigenvalues determined in a previous step are used. 15. Apparatus according to claim 14, wherein the processor is configured as follows: cumulant minimization is performed by training a neural network (5). 16. The processor is configured as follows: at least one diagonal parameter of the separation matrix is set to a preset value in optimizing the parameters of the separation matrix. 1 out of 15
Item. 17. The apparatus according to claim 13, wherein the processor is configured as follows: the separation matrix is limited to a finite impulse response. 18. The processor according to claim 13, wherein the processor is configured as follows: the separation matrix is stabilized by projection onto the unit circle during cumulant minimization (5). Item. 19. The apparatus according to claim 11, which is used for separating superimposed statistically independent input signals. 20. Apparatus according to claim 11, which is used for separating superimposed, statistically independent audio input signals.