JP6343585B2 - Unknown transmission system estimation device, unknown transmission system estimation method, and program - Google Patents

Description

  The present invention relates to a technique for estimating characteristics of a transmission system through which an electric signal, sound, and vibration propagate.

  Estimating the characteristics of an unknown transmission system through which an electric signal, sound, or vibration propagates is useful for predicting the output of the transmission system with respect to an arbitrary input to the transmission system. The problem of estimating the characteristics of a transmission system is often handled as a problem of preliminarily giving a model that can be expressed with a finite parameter and estimating the value of the parameter. The model given in advance is selected based on the physical features (relationship between input and output) of the transmission system to be estimated. The object of the present invention is that the input to an unknown transmission system and the output to it have a linear relationship, and the characteristics of the transmission system can be modeled by a FIR (Finite Impulse Response) filter. It is a problem of filter coefficient estimation.

  The observed output signal y (n) with respect to the input signal x (n) to the transmission system can be expressed by equation (1).

Here, h ₀ , h ₁ ,..., H _L are each element of an unknown finite-length impulse response to be estimated. However, L is an integer greater than or equal to 0, and n represents discrete time. Further, v (n) is a disturbance signal that can be mixed when the output signal is observed.

The filter coefficient W (n) is a vector having the estimated values of h ₀ , h ₁ ,..., H _L at time n as elements, and is represented by Expression (2).

  Then, the residual signal r (n) obtained at time n is expressed by Expression (3).

  At this time, it is known that the estimated value of the filter coefficient can be updated by Expression (4) (for example, see Non-Patent Document 1).

However,

And μ and ε are constants used for adjusting the convergence characteristics. μ is called a step size, and ε is called a regularization coefficient. Further, when each element of the filter coefficient W (n) is written down, the following equation (6) is obtained.

  The validity of the update formula of Formula (4) can be interpreted as follows. First, the posterior probability of the estimated value W (n + 1) of the filter coefficient to be updated under the condition where the output signal y (n) is observed is expressed by Equation (7) according to Bayes' theorem. It holds.

In formula (7), the notation of time n is omitted for simplicity. Here, p (y | W) represents the probability (likelihood for W) that the output signal y can take when the characteristic of the unknown transmission system is W, and p (W) This is the prior probability of the value that W can take. p (y | W) is the probability of the possible value of the disturbance signal v (n), which is the other signal component, assuming that the output of the unknown transmission system due to W is given among the output signals y. Equivalent to.

  If the disturbance signal v (n) and the filter coefficient W (n) both follow a Gaussian distribution, Expression (7) can be expressed by Expression (8).

Here, α and β are the reciprocals (accuracy) of the variances of the disturbance signal v (n) and the filter coefficient W (n), and _W represents the estimated value before the update (_ -Represents an underlined symbol). || · || ₂ represents the L2 norm of the vector. Regarding the equation (8), taking the logarithm of both sides,

Thus, W giving the maximum value of J gives the maximum value of the posterior probability of equation (8). there,

If W is satisfied,

Is obtained. Comparing equation (4) and equation (11), it can be seen that in equation (4), if μ = 1 and ε = β / α, they match.

As shown in FIG. 1, the unknown transmission system estimation apparatus 200 based on the above-described conventional technique includes a filter coefficient storage unit 201, an output signal estimation unit 202, a residual signal calculation unit 203, an input signal square value calculation unit 204, and a filter. An expected value calculation unit 205 is included. The filter coefficient storage unit 201 holds the estimated filter coefficient W (n). The output signal estimation unit 202 estimates the output signal of the unknown transmission system (contains no disturbance signal v (n)) by convolution of the sequence X (n) of the input signal x (n) and the filter coefficient W (n). W (n) ^T X (n) is calculated. The residual signal calculation unit 203 is a residual signal r (() of the observed output signal y (n) of the unknown transmission system (which may include the disturbance signal v (n)) and the estimated output signal W (n) ^T X (n). n) is calculated by equation (3). The input signal square value calculation unit 204 calculates a series of square values x (n) ² of the input signal. The expected filter value calculation unit 205 uses the input signal x (n) sequence, the input signal square value x (n) ² sequence, and the residual signal r (n) to calculate the filter coefficient W (n) and the disturbance. Assuming that the amplitude value of the signal v (n) follows a Gaussian distribution, the expected value W (n + 1) that the filter coefficient can take under the condition that the observed output signal y (n) is observed is given by The filter coefficient W (n) calculated and updated in the filter coefficient storage unit 201 is updated.

N. J. Bershad, “Behavior of the ε-normalized LMS algorithm with Gaussian inputs”, IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 35, No. 5, pp. 636-644, 1987.

  The update of the estimated value W (n) of the filter coefficient based on the expression (4) is obtained by considering the disturbance signal v (n) and the filter coefficient W (n) as random variables according to a Gaussian distribution. Similar to renewal formula. In other words, the update equation of Equation (4) is valid when the disturbance signal v (n) and the filter coefficient W (n) follow a Gaussian distribution, but there may be a more appropriate update equation otherwise. It can be said. For example, when the transfer characteristic to be estimated is an impulse response of an acoustic transfer system, it often has an exponential attenuation characteristic. In this case, it is assumed that the distribution of the amplitude values of the tap coefficients has a superior Gaussian property with a high degree of concentration near zero. Also, the assumption of the Gaussian distribution is not always appropriate when the disturbance signal is an unsteady signal such as sudden or intermittent noise or a voice signal.

  The object of the present invention is to estimate the characteristics of the unknown transmission system more appropriately when the amplitude value of the impulse response of the unknown transmission system and the amplitude value of the disturbance signal mixed during observation do not follow the assumption of the Gaussian distribution. It is to provide unknown transmission system estimation technology.

  In order to solve the above-described problems, an unknown transfer system estimation device according to the present invention includes a filter coefficient storage unit that stores a filter coefficient representing transfer characteristics of an unknown transfer system, and a series of absolute values of an input signal to the unknown transfer system. An input signal absolute value calculation unit for calculating the output signal, an output signal estimation unit for calculating an estimated output signal by convolution of the input signal sequence and the filter coefficient, and observing the output of the unknown transmission system using the input signal as an input A residual signal calculation unit for calculating a residual signal between the observed output signal and the estimated output signal obtained in step (a), a residual signal absolute value calculation unit for calculating an absolute value of the residual signal, a sequence of input signals, and an input signal Using the absolute value series, residual signal, and absolute value of the residual signal, the observed output signal is observed as if the amplitude value of the disturbance signal that can be included in the filter coefficient and the observed output signal follows a Gaussian distribution. Conditions Calculating an expected value of the filter coefficients can take the original, including a filter expected value calculation unit for updating the filter coefficients, the.

  According to the unknown transmission system estimation technique of the present invention, when the amplitude value of the impulse response of the unknown transmission system or the amplitude value of the disturbance signal mixed at the time of observation does not follow the assumption of the Gaussian distribution, the characteristics of the transmission system can be improved more appropriately. Can be estimated.

FIG. 1 is a diagram illustrating a functional configuration of a conventional unknown transmission system estimation apparatus. FIG. 2 is a diagram illustrating a functional configuration of the unknown transmission system estimation apparatus according to the embodiment. FIG. 3 is a diagram illustrating a processing flow of the unknown transmission system estimation method according to the embodiment.

  Prior to the description of the embodiments, the basic concept of the present invention will be described.

  In the present invention, in the conventional unknown transmission system estimation technique, a Laplace distribution, which is one of the probability distributions having a superior Gaussian property, is applied to the posterior probability defined by Expression (7), and is expressed by Expression (12). An updated value of the filter coefficient is obtained based on the posterior probability.

Where || · || ₁ is the L1 norm, ^T is the transpose of the matrix, _W is a vector having the value of the filter coefficient before the update as an element, α is the accuracy of the disturbance signal, B is a diagonal matrix of L + 1 rows and L + 1 columns having non-negative elements β ₀ , β ₁ ,..., Β _L as diagonal components. The matrix B can be expressed by Equation (13).

  When the diagonal components of the matrix B are equal and take a value of β, the equation (12) can also be expressed by the equation (14).

Since the distribution of posterior probabilities given by Equation (12) or Equation (14) does not have a symmetric shape around the maximum value, W giving the maximum value matches the expected value E (W | y) do not do. Therefore, an expected value is directly calculated for each element w _k (k = 0, 1,..., L) of W, and an updated value is given as Expression (15).

  Specifically, from Equation (12) and Equation (15),

And give. However,

It is. Here, Q is an arbitrary multiplier that can be canceled by the denominator and the numerator of Expression (16), and is not necessarily required.

The updated value of each filter coefficient w _k (n) is basically calculated based on Equation (16). D _v (n), D _i (n), G _{v, k} (n), The calculation method of G _{i, k} (n) does not necessarily need to match the forms of Expressions (17) to (20), and may be calculated based on an expression that is equivalent or approximately equivalent to these. . Alternatively, a stabilization term such as prevention of division by zero may be added, or another calculation formula or constant may be given depending on the case when the denominator takes a small value. Further, the present invention is not limited to the form of the expression (16), and the case of calculation based on an expression equivalent or approximately equivalent to this is also included in the technique of the present invention.

  Hereinafter, embodiments of the present invention will be described in detail. In addition, the same number is attached | subjected to the component which has the same function in drawing, and duplication description is abbreviate | omitted.

[First embodiment]
As illustrated in FIG. 2, the unknown transmission system estimation apparatus 300 according to the first embodiment includes a filter coefficient storage unit 201, an output signal estimation unit 202, a residual signal calculation unit 203, an input signal absolute value calculation unit 301, a residual. A signal absolute value calculation unit 302 and a filter expected value calculation unit 303 are included. The unknown transmission system estimation apparatus 300 performs the process of each step illustrated in FIG. 3 to realize the unknown transmission system estimation method of the first embodiment.

  The unknown transmission system estimation apparatus 300 is configured, for example, by loading a special program into a known or dedicated computer having a central processing unit (CPU), a main storage (RAM), and the like. Special equipment. The unknown transmission system estimation apparatus 300 executes each process under the control of the central processing unit, for example. The data input to the unknown transmission system estimation device 300 and the data obtained in each process are stored in, for example, the main storage device, and the data stored in the main storage device is read to the central processing unit as necessary. And used for other processing. At least a part of each processing unit of the unknown transmission system estimation apparatus 300 may be configured by hardware such as an integrated circuit.

  The filter coefficient storage unit 201 included in the unknown transfer system estimation apparatus 300 is, for example, a main storage device such as a RAM (Random Access Memory), an auxiliary configured by a semiconductor memory element such as a hard disk, an optical disk, or a flash memory. It can be configured by a storage device or middleware such as a relational database or a key-value store.

The filter coefficient storage unit 201 of the unknown transfer system estimation apparatus 300 stores the filter coefficient W (n) before update. The filter coefficient W (n) is the same as in the prior art, and is a vector having estimated values of the transfer characteristics h ₀ , h ₁ ,..., H _L of the unknown transfer system 100 at time n as elements.

  As illustrated in FIG. 2, an input signal x (n) is input to the unknown transmission system estimation apparatus 300 and the unknown transmission system 100, and the unknown transmission system 100 outputs an output signal corresponding to the input signal x (n). An observed output signal y (n) obtained by observing the output signal is input to unknown transmission system estimation apparatus 300. The observation output signal y (n) is mixed with a disturbance signal v (n) at the time of observation. In unknown transmission system estimation apparatus 300, input signal x (n) is sent to input signal absolute value calculation section 301, output signal estimation section 202, and filter expected value calculation section 303. The observation output signal y (n) is input to the residual signal calculation unit 203.

  With reference to FIG. 3, the processing procedure of the unknown transmission system estimation method of the embodiment will be described.

  In step S301, the input signal absolute value calculation unit 301 calculates a series of absolute values | x (n) | of the input signals from the series of input signals x (n). A series of absolute values | x (n) | of the input signal is sent to the filter expected value calculation unit 303.

In step S202, the output signal estimation unit 202 reads the filter coefficient W (n) stored in the filter coefficient storage unit, and convolves the sequence X (n) of the input signal x (n) with the filter coefficient W (n). An estimated output signal W (n) ^T X (n) is calculated by calculation. The estimated output signal W (n) ^T X (n) is sent to the residual signal calculation unit 203.

In step S203, the residual signal calculation unit 203 subtracts the estimated output signal W (n) ^T X (n) from the observed output signal y (n) that may include the disturbance signal v (n). n) is calculated by equation (3). Residual signal r (n) is sent to residual signal absolute value calculation section 302 and filter expected value calculation section 303.

  In step S302, the residual signal absolute value calculator 302 calculates the absolute value | r (n) | of the residual signal from the residual signal r (n). The absolute value | r (n) | of the residual signal is sent to the filter expected value calculation unit 303.

  In step S303, the filter expectation value calculation unit 303 determines the sequence of the input signal x (n), the sequence of the input signal absolute value | x (n) |, the residual signal r (n), and the absolute value of the residual signal | r (n) | and the amplitude of the filter coefficient W (n) and disturbance signal v (n) follow the Gaussian distribution under the conditions under which the observed output signal y (n) was observed. To calculate the expected value W (n + 1) that the filter coefficient can take. Specifically, the filter expected value calculation unit 303 calculates the expected value of the filter coefficient that maximizes the posterior probability defined by the equation (12) or the equation (14). The expected value of each element of the filter coefficient can be calculated based on Equation (16). The calculated expected value W (n + 1) of the filter coefficient is stored in the filter coefficient storage unit 201 as an updated value of the filter coefficient.

[Second Embodiment]
In the first embodiment, Expression (12) or Expression (14) is given on the assumption that the disturbance signal v (n) has a superior Gaussian property. However, in a real environment, a highly stationary noise having Gaussian characteristics is often mixed. In the second embodiment, as in the case of an acoustic echo canceller, by assuming that the input signal is mainly a strong Gaussian voice signal, it is possible to cope with a case where the disturbance signal is Gaussian noise. Show. Specifically, equation (12) is modified as equation (21), and equation (14) is modified as equation (22).

Here, f (X) is a function that takes a non-negative value depending on the magnitude of the input signal, such as the L1 norm or L2 norm of X, for example. f (X) does not necessarily have to be calculated based on the values of all elements of the input signal X. It is also possible to use a value of the input signal X that is past the time n, or to calculate a value by using the current and past values together.

  In order to implement this correction, α is replaced with α / f (X) in the calculations of Expressions (17) to (20) when obtaining the updated value of Expression (16). In this way, by controlling the magnitude of the disturbance signal according to the change in the magnitude of the input signal X, when the input signal has a dominant Gaussian property, the original disturbance signal has a Gaussian or dominant Gaussian property. In any case, the nature of the disturbance signal divided by f (x) has a strong Gaussian property. Thereby, the unknown transmission system estimation technique of the second embodiment can expand the applicable range.

[Other variations]
In Equation (12) or Equation (14), coefficients such as α and β that indicate the degree of concentration (accuracy) at the center of the distribution assume the amplitude value of the impulse response of the unknown transmission system and the magnitude of the disturbance signal. Alternatively, it may be given as a fixed value in advance. Further, the correction may be made sequentially with time based on the estimated value of the filter coefficient and the magnitude of the observed output signal. Alternatively, values obtained by iterative learning based on the EM algorithm or the like may be given sequentially.

  The input signal and the output signal are divided into a plurality of frequency component signals, and any of the above-described embodiments is applied to the divided frequency component signals to estimate the transfer characteristics for each divided frequency component. May be.

  According to the unknown transmission system estimation technique of the present invention, an unknown transmission system having a strong Gaussian transmission characteristic (impulse response) can be estimated at higher speed. Actually, since the impulse response is a response waveform of the impulse signal, it often has a characteristic of gradually decaying while taking a large amplitude immediately after the impulse is input, and such a response is dominant Gaussian. In many cases, it can be considered. In addition, since disturbance signals are also derived with a presumption of superior Gaussianity, unknown transmission with high accuracy is possible even when the disturbance signal is a superior Gaussian audio signal, such as double talk in an acoustic echo canceller. The characteristics can be estimated. As a result, it is possible to suppress the occurrence of echoes and howling, and to provide a comfortable hands-free call.

  The conventional unknown transfer system estimation technology is appropriate when the amplitude value of the impulse response of the unknown transfer system and the amplitude value of the disturbance signal mixed when observing the output signal from the unknown transfer system are distributed based on the Gaussian distribution. Although it can be interpreted, an actual impulse response or disturbance signal is not necessarily generated based on a Gaussian distribution. The unknown transmission system estimation technique of the present invention is particularly suitable for estimating the impulse response and the estimation of the Gaussian property that takes a value near zero or suddenly takes a larger value than the Gaussian distribution. Assuming both disturbance signals to be disturbed, by determining the posterior probability that the amplitude value of the impulse response under the condition where the output signal was observed, and deriving a new estimated update formula different from the conventional technology, Highly accurate estimation is possible even in a real environment.

  The present invention is not limited to the above-described embodiment, and it goes without saying that modifications can be made as appropriate without departing from the spirit of the present invention. The various processes described in the above embodiment may be executed not only in time series according to the order of description, but also in parallel or individually as required by the processing capability of the apparatus that executes the processes or as necessary.

[Program, recording medium]
When various processing functions in each device described in the above embodiment are realized by a computer, the processing contents of the functions that each device should have are described by a program. Then, by executing this program on a computer, various processing functions in each of the above devices are realized on the computer.

  The program describing the processing contents can be recorded on a computer-readable recording medium. As the computer-readable recording medium, for example, any recording medium such as a magnetic recording device, an optical disk, a magneto-optical recording medium, and a semiconductor memory may be used.

  This program is distributed by selling, transferring, or lending a portable recording medium such as a DVD or CD-ROM in which the program is recorded. Furthermore, the program may be distributed by storing the program in a storage device of the server computer and transferring the program from the server computer to another computer via a network.

  A computer that executes such a program first stores, for example, a program recorded on a portable recording medium or a program transferred from a server computer in its own storage device. When executing the process, the computer reads a program stored in its own recording medium and executes a process according to the read program. As another execution form of the program, the computer may directly read the program from a portable recording medium and execute processing according to the program, and the program is transferred from the server computer to the computer. Each time, the processing according to the received program may be executed sequentially. A configuration in which the above-described processing is executed by a so-called ASP (Application Service Provider) type service that realizes a processing function only by an execution instruction and result acquisition without transferring a program from the server computer to the computer. It is good. Note that the program in this embodiment includes information that is used for processing by an electronic computer and that conforms to the program (data that is not a direct command to the computer but has a property that defines the processing of the computer).

  In this embodiment, the present apparatus is configured by executing a predetermined program on a computer. However, at least a part of these processing contents may be realized by hardware.

100 unknown transmission system 200, 300 unknown transmission system estimation device 201 filter coefficient storage unit 202 output signal estimation unit 203 residual signal calculation unit 204 input signal square value calculation unit 205, 303 filter expected value calculation unit 301 input signal absolute value calculation unit 302 Residual signal absolute value calculator

Claims (5)

A filter coefficient storage unit that stores a filter coefficient representing a transfer characteristic of an unknown transfer system;
An input signal absolute value calculation unit for calculating a series of absolute values of the input signal to the unknown transmission system;
An output signal estimator that calculates an estimated output signal by convolution of the input signal sequence and the filter coefficient;
A residual signal calculator for calculating a residual signal between the observed output signal obtained by observing the output of the unknown transmission system having the input signal as an input and the estimated output signal;
A residual signal absolute value calculator for calculating an absolute value of the residual signal;
Using the input signal series, the absolute value series of the input signal, the residual signal, and the absolute value of the residual signal, the amplitude value of the disturbance signal that can be included in the filter coefficient and the observed output signal is A filter expectation value calculation unit that calculates an expected value that the filter coefficient can take under the condition where the observed output signal is observed as being obeying a Gaussian distribution, and updates the filter coefficient;
An unknown transmission system estimation device including: The unknown transmission system estimation apparatus according to claim 1,
|| ・ || ₁ is the L1 norm, ^T is the transpose of the matrix, _W is a vector with the values before the filter coefficients updated, and W is the value that the filter coefficients can take after updating And y is the observed output signal, X is a vector having the input signal sequence as an element, α is the accuracy of the disturbance signal, and B is a diagonal having the accuracy of the filter coefficient as a diagonal component. A matrix,
The filter expected value calculation unit calculates an expected value when the filter coefficient is based on a posterior probability defined by the following equation:

Unknown transmission system estimation device. The unknown transmission system estimation apparatus according to claim 1,
|| ・ || ₁ is the L1 norm, ^T is the transpose of the matrix, _W is a vector with the values before the filter coefficients updated, and W is the value that the filter coefficients can take after updating And y is the observed output signal, X is a vector having the input signal sequence as an element, α is the accuracy of the disturbance signal, and B is a diagonal having the accuracy of the filter coefficient as a diagonal component. A matrix, and f (X) is a function that takes a non-negative value depending on the magnitude of the input signal,
The filter expected value calculation unit calculates an expected value when the filter coefficient is based on a posterior probability defined by the following equation:

Unknown transmission system estimation device. The filter coefficient storage unit stores the filter coefficient representing the transfer characteristic of the unknown transfer system,
An input signal absolute value calculation unit calculates an input signal absolute value calculation step for calculating a series of absolute values of the input signal to the unknown transmission system;
An output signal estimating unit that calculates an estimated output signal by convolution of the input signal sequence and the filter coefficient;
A residual signal calculating unit that calculates a residual signal between the observed output signal obtained by observing the output of the unknown transmission system having the input signal as an input and the estimated output signal;
A residual signal absolute value calculating step, wherein the residual signal absolute value calculating unit calculates an absolute value of the residual signal;
A filter expected value calculation unit is included in the filter coefficient and the observed output signal using the input signal series, the absolute value series of the input signal, the residual signal, and the absolute value of the residual signal. A filter expectation value calculating step for calculating an expected value that the filter coefficient can take under the condition that the observed output signal is observed, assuming that the amplitude value of the disturbance signal follows a Gaussian distribution, and updating the filter coefficient; ,
An unknown transmission system estimation method including:   The program for functioning a computer as an unknown transmission system estimation apparatus in any one of Claim 1 to 3.

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