JP5583181B2 - Cascade connection type transmission system parameter estimation method, cascade connection type transmission system parameter estimation device, program - Google Patents

Description

  The present invention estimates an unknown parameter of a transmission system when a transmission system through which an electric signal, sound, vibration, etc. propagates can be regarded as a cascade connection between a system having nonlinear characteristics and a system having linear characteristics. Regarding technology.

  Estimating the characteristics of an unknown transmission system through which an electric signal, sound, vibration, or the like 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 a transmission system is often handled as a problem of preliminarily giving a model that can be expressed by 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. For example, when the relationship between input and output can be regarded as linear, a linear FIR (Finite Impulse Response) filter or IIR (Infinite Impulse Response) filter is selected as a model of the transmission system in the discrete time domain.

  The unknown transmission system is not always such a linear transmission system, and the relationship between input and output in the unknown transmission system may have nonlinear characteristics. For example, there may be a case where an unknown transmission system is expressed in a composite form of linear characteristics and nonlinear characteristics. Specifically, as shown in FIG. 1, the transmission system 1 to be estimated can be expressed by a cascade connection of a nonlinear system 2 and a linear system 3, and the input to the transmission system 1 is input to the nonlinear system 2. The output of the nonlinear system 2 is input to the linear system 3, and the output of the linear system 3 is the output of the transmission system 1.

  In such a transmission system 1, it can be given as a cascade-connected model by the independent nonlinear system 2 and linear system 3, and the characteristics of the nonlinear system 2 do not depend on past inputs (outputs). The technique disclosed in Non-Patent Document 1 deals with the problem of parameter estimation of the transmission system 1 when it can be regarded as a hard clip characteristic and the characteristic of the linear system 3 can be regarded as an impulse response of a finite length.

[Nonlinear system model]
When the nonlinear system 2 in FIG. 1 has a hard clip characteristic that does not depend on the past input (output), the relationship between the input signal x (n) and the output signal s (n) is expressed as a threshold a (> 0). The hard clip function f used is given by equation (1).

  Here, n is a discrete time, and the output signal s (n) is related to the input signal x (n) as being dependent only on the value at the same discrete time n. Here, the threshold value a is an unknown model parameter to be estimated.

[Linear model]
Assuming that an input signal to the linear system 3 in FIG. 1 is s (n) and its output signal y (n), y (n) can be expressed in the form of a convolution operation of equation (4). Here, finite impulse responses h ₀ , h ₁ , h ₂ ,..., H _L are unknown model parameters to be estimated. However, the order L is an integer of 0 or more, and s (n) is an internal signal that cannot actually be observed directly.

Thus, the parameters to be estimated are a in equation (1) and h ₀ , h ₁ , h ₂ ,..., H _L in equation (2).

  Non-Patent Document 1 shows an example of a parameter estimation method in such a framework. FIG. 5 is a configuration example for realizing a conventional parameter estimation method based on Non-Patent Document 1.

[Cascade estimation device / method for cascade connection type in the prior art]
At the discrete time n, the nonlinear parameter application / synthesis unit 601 uses the nonlinear system estimation parameter a ^ (n), which will be described later, to calculate an estimated value s ^ (n) corresponding to the output of the nonlinear system 2 using Equation (3). Calculate and output.

  The signal storage unit 602 receives the estimated value s ^ (n) of the output of the nonlinear system 2 and inputs L + 1 nonlinear system output estimated values s ^ (n), s ^ ( n-1), s ^ (n-2), ..., s ^ (nL) are accumulated.

The linear system parameter multiplication / synthesis unit 603 obtains L + 1 nonlinear system output estimated values s ^ (n), s ^ (n-1), s ^ (n-2),... Obtained from the signal storage unit 602. , S ^ (nL) and linear system estimation parameters h ^ ₀ (n), h ^ ₁ (n), h ^ ₂ (n), ..., h ^ _L (n) described later All are added, and the estimated value y ^ (n) of the output signal from the transmission system 1 to be estimated is output.

For convenience, H (n) = [h ^ ₀ (n), h ^ ₁ (n), h ^ ₂ (n), ..., h ^ _L (n)] ^T , S (n) = [s ^ (n), s ^ (n-1), s ^ (n-2), ..., s ^ (nL)] If expressed as ^T , equation (4) is an inner product operation of vectors as in equation (5) It corresponds to. Here, T represents transposition.

The error calculation unit 604 subtracts the estimated value y ^ (n) from the output signal y (n) from the transmission system 1 to be estimated, and outputs an error signal e (n) by Expression (6).

The differential signal generation unit 605 outputs a partial differential value s ^ '(n) for a ^ (n) of the estimated value s ^ (n) of the output of the nonlinear system 2 by Expression (7).

For the error signal e (n), the non-linear / linear system parameter update unit 606 calculates the gradient for the parameters a ^ (n) and H (n) with respect to the evaluation equation given by the equation (8) and the equation (9). Since it is obtained by equation (10), parameters a ^ (n) and H (n) are updated by equations (11) and (12), and a new updated value at time n is output. ‖ / ‖ Represents the norm

S '(n) = [s ^' (n), s ^ '(n-1), s ^' (n-2), ..., s ^ '(nL)] ^T This is a vector whose elements are values accumulated back to the past of L samples of partial differential values generated by the unit 605. The step sizes μ _a and μ _h are selected within the range of 0 to 1.

A. Stenger, W. Kellermann; “Nonlinear acoustic echo cancellation with fast converging memoryless preprocessor”, IEEE International Conference on Acoustics, Speech, and Signal Processing, 2000. (ICASSP '00), Vol. 2, II805-II808, 2000.

  A transmission system 1 in which a nonlinear system 2 and a linear system 3 are cascade-connected as shown in FIG. 1 is modeled by Equation (1) and Equation (2), and these parameters are sequentially determined according to Equation (11) and Equation (12). In the conventional technique for updating and estimating, in updating the nonlinear system estimation parameter a ^ (n), as can be seen from Equation (7), x having a small amplitude satisfying | x (n) | <a ^ (n) When (n) is input, since S ′ (n) = 0, the update expression of Expression (11) is a ^ (n + 1) = a regardless of the magnitude of the error signal e (n). ^ (n), and there is a problem that the update stops completely.

  This satisfies | x (n) | ≧ a for the true nonlinear system parameter a, and the observed error signal e (n) is not zero (that is, the true value a and the estimated value a ^ (n Even if there is a divergence with), S '(n) = 0 is satisfied when | x (n) | <a ^ (n) is satisfied in the update formula of formula (11) Therefore, the nonlinear system estimation parameter a ^ (n) cannot be updated.

  This problem seems to be solved by making the initial value of a ^ (n) sufficiently small. However, in practice, for example, when applied to an acoustic echo canceller, such countermeasures are sufficient. I can't say that. For example, consider a case where an amplifier 201 that outputs a signal to the speaker 202 is initially used with a small amplification amount as shown in FIG. 4 and the amplification amount is increased in the middle because the volume is not sufficient. At this time, when the amplification amount is small, clipping by the amplifier hardly occurs, and the true nonlinear system parameter a which is a clipping threshold tends to take a large value. On the other hand, when the amplification amount is increased, clipping by the amplifier tends to occur, and the true nonlinear system parameter a tends to take a small value. Therefore, for example, even if the initial value of a ^ (n) is set sufficiently small, if the amplifier is initially set to a small amplification amount and the nonlinear system estimation parameter update is activated, the value of a ^ (n) Is updated to a large value, and then the amplification amount is set to a large value, for example, because it is difficult to hear the voice, and when the true clipping threshold a decreases accordingly, a ^ (n) There are cases where updating is impossible.

  Therefore, the present invention provides a nonlinear system estimation parameter a ^ even if | x (n) | <a ^ (n) in a nonlinear system model modeled with a hard clip function, unless the error signal e (n) is zero. An object of the present invention is to provide a technique for estimating a parameter of a cascaded transmission system of a nonlinear system and a linear system that can update (n).

The present invention relates to a transmission system that can be regarded as a cascade connection of a nonlinear system that outputs a value corresponding to an input signal or model parameter by comparing the magnitude of the input signal with a model parameter and a linear system having a finite-length impulse response characteristic. This is a cascaded transmission system parameter estimation technology that estimates nonlinear system model parameters and linear system model parameters. The input signal x (n) is larger than the input signal x (n) to the transmission system at time n. Applying and synthesizing nonlinear parameters to output estimated value s ^ (n) corresponding to input signal x (n) or estimated model parameter a ^ (n) Processing, and the estimated values s ^ (n), s ^ (n-1), s ^ (n-2) for the nonlinear system corresponding to each time from time nL to time n, where L is an integer greater than or equal to zero …, S ^ (nL) and estimated model parameters of the linear system h ^ ₀ (n), h ^ ₁ (n), h ^ ₂ (n), ..., h ^ _L (n) and linear system parameter multiplication / synthesis processing that outputs the estimated value y ^ (n) by convolution, and the output signal y ( Error calculation process to obtain an error signal e (n) obtained by subtracting the estimated value y ^ (n) of the linear system from n) and the estimated model parameter a ^ (n of the nonlinear system estimated value s ^ (n) ) Pseudo-differential signal generation processing that outputs estimated partial differential value s ^ '(n) for), error signal e (n), and estimated partial differential value s ^' corresponding to each time from time nL to time n (n), s ^ '(n-1), s ^' (n-2), ..., s ^ '(nL) and nonlinear system estimates s ^ (n), s ^ (n-1), Using s ^ (n-2), ..., s ^ (nL), the estimated model parameter a ^ (n + 1) of the nonlinear system at time n + 1 and the estimated model parameter h ^ ₀ (n +1), h ^ ₁ (n + 1), h ^ ₂ (n + 1), ..., h ^ _L (n + 1) are estimated, and non-linear / linear system parameter update processing is performed. In the signal generation process, the magnitude of the input signal x (n) If the magnitude of the input signal x (n) is not larger than the estimated model parameter a ^ (n) of the nonlinear system by comparison with the estimated model parameter a ^ (n) of the linear system, the nonlinear system is estimated The non-zero value that decreases in size as the model parameter a ^ (n) increases is output as the estimated partial differential value s ^ '(n); otherwise, the estimated value s ^ ( The partial differential value of n) is output as an estimated partial differential value s ^ '(n).

Alternatively, for a transmission system that can be regarded as a cascade connection of a nonlinear system that outputs a value according to the input signal or model parameter by comparing the magnitude of the input signal with the model parameter, and a linear system that has a finite-length impulse response characteristic, Is a cascade connection type transmission system parameter estimation technology that estimates model parameters of systems and linear system parameters, and the magnitude and nonlinearity of the input signal x (n) relative to the input signal x (n) to the transmission system at time n A nonlinear parameter application / synthesis process that outputs the estimated value s ^ (n) corresponding to the input signal x (n) or the estimated model parameter a ^ (n) by comparing with the estimated model parameter a ^ (n) of the system , L is an integer greater than or equal to zero, and nonlinear system estimates s ^ (n), s ^ (n-1), s ^ (n-2), ..., corresponding to each time from time nL to time n s ^ (nL) and the estimated model parameters of the linear system h ^ ₀ (n), h ^ ₁ (n), h ^ ₂ (n), ..., h ^ _L (n) and linear system parameter multiplication / synthesis processing that outputs the estimated value y ^ (n) by convolution, and the output signal y ( Error calculation process to obtain an error signal e (n) obtained by subtracting the estimated value y ^ (n) of the linear system from n) and the estimated model parameter a ^ (n of the nonlinear system estimated value s ^ (n) ) Pseudo-differential signal generation processing that outputs estimated partial differential value s ^ '(n) for), error signal e (n), and estimated partial differential value s ^' corresponding to each time from time nL to time n (n), s ^ '(n-1), s ^' (n-2), ..., s ^ '(nL) and nonlinear system estimates s ^ (n), s ^ (n-1), Using s ^ (n-2), ..., s ^ (nL), the estimated model parameter a ^ (n + 1) of the nonlinear system at time n + 1 and the estimated model parameter h ^ ₀ (n +1), h ^ ₁ (n + 1), h ^ ₂ (n + 1), ..., h ^ _L (n + 1) are estimated, and non-linear / linear system parameter update processing is performed. In the signal generation process, (1) periodically, (2) Randomly, (3) when the magnitude of the input signal x (n) takes the maximum value or the maximum value in the sample for a predetermined time, the magnitude of the input signal x (n) If the magnitude of the input signal x (n) is not larger than the estimated model parameter a ^ (n) of the nonlinear system by comparison with the estimated model parameter a ^ (n) of the nonlinear system, or The non-zero value that decreases as the estimated model parameter a ^ (n) of the nonlinear system increases is output as the estimated partial differential value s ^ '(n); otherwise, the nonlinear system is estimated If the partial differential value of the value s ^ (n) is output as the estimated partial differential value s ^ '(n) and none of the above (1), (2), or (3) applies, The partial differential value of the estimated value s ^ (n) is output as the estimated partial differential value s ^ '(n).

  According to the present invention, as will be described in detail later, when a partial differential value by a nonlinear system model parameter is zero for a hard clip function used as a nonlinear system model, a pseudo non-zero partial differentiation is performed. By replacing with a value, the parameter can be updated even in such a case.

The figure which shows the structure of a transmission system. The figure which shows the function structural example of the cascade connection type transmission system parameter estimation apparatus 100. FIG. The figure which shows the function structural example of the cascade connection type transmission system parameter estimation apparatus 101. FIG. The figure which shows the function structural example in the case of making the cascade connection type transmission system parameter estimation apparatus 100 function as an echo canceller. The figure which shows the function structural example of the cascade connection type transmission system parameter estimation apparatus by a prior art. The figure which showed the error curve and its gradient typically. (A) An error curve related to the nonlinear system estimation parameter a ^ (n). (B) The slope of the error curve for the nonlinear system estimation parameter a ^ (n). (C) The pseudo slope of the error curve for the nonlinear system estimation parameter a ^ (n).

[Unknown transmission system subject to the present invention]
An unknown transmission system (also referred to as an estimation target transmission system) as an object of the present invention is, as in the transmission system 1 shown in FIG. The system 1 is expressed, the input to the transmission system 1 is input to the nonlinear system 2, the output of the nonlinear system 2 is input to the linear system 3, and the output of the linear system 3 is the output of the transmission system 1. In addition, the characteristic of the nonlinear system 2 does not depend on past inputs (outputs), and the characteristic of the linear system 3 can be regarded as a finite-length impulse response. ”

[Nonlinear system model]
As described above, when the input signal to the nonlinear system 2 in FIG. 1 is x (n) and the output signal of the nonlinear system 2 is s (n), the relationship expressed by the above equation (1) is given. The symbols are also followed, n is discrete time, and f is a non-linear function (hard clip function). The threshold value a is 0 or more. The output signal s (n) is related to the input signal x (n) as being dependent only on the value at the same discrete time n.

[Linear model]
As described above, if the input signal to the linear system 3 in FIG. 1 is s (n) and its output signal y (n), y (n) is expressed in the form of the convolution operation of the above equation (2). be able to. The symbol follows, the order L is an integer greater than or equal to 0, and s (n) is treated as an internal signal that cannot actually be observed directly.

Thus, the model parameters to be estimated in the transmission system 1 are the threshold value a in the above equation (1) and the impulse responses h ₀ , h ₁ , h ₂ ,..., H _L in the above equation (2). is there.

[Outline of the present invention]
The present invention is characterized in that the nonlinear system estimation parameter a ^ (n) can be updated if the error signal e (n) is not zero even when | x (n) | <a ^ (n). The outline of the present invention will be described.

  First, when the evaluation formula of Formula (8) is schematically shown as a function of a ^ (n), an error curve as shown in FIG. 6A can be drawn. Here, for convenience, the linear system parameter is regarded as a scalar rather than a vector, and L = 0 is assumed. The error is minimized when a ^ (n) = a (true value), and if the value of a ^ (n) is increased from there, the error becomes 2 until a ^ (n) = x (n). It increases in the form of a quadratic curve, and takes a constant value beyond that. This is because the input signal is not hard clipped when a ^ (n)> x (n), and the estimated value of the nonlinear system output is s ^ (n) = x (n), so the magnitude of the error is a ^ This can be seen as being no longer dependent on (n).

  Looking at this state with the gradient shown in Fig. 6 (b), in the range of a ^ (n) ≤ | x (n) |, the gradient becomes zero only in a ^ (n) = a (true value). In the range ^ (n)> x (n), the gradient is zero in all of them. In the parameter estimation method based on the gradient, the gradient is assumed to be zero only when a ^ (n) = a (true value), and the update is advanced so that the gradient becomes zero. At this point, the update is automatically stopped. It is mathematically correct that the slope is zero in a ^ (n)> x (n), but if the true value a satisfies a <x (n), the nature of the error curve Is not correctly understood.

  Therefore, in the present invention, it is considered to give a pseudo nonzero gradient in the range of a ^ (n)> x (n). For example, it is a curve as shown in Fig. 6 (c), where the value of non-zero gradient of a ^ (n) = x (n) is gradually decreased, and the gradient becomes smaller at a ^ (n) → ∞. It has characteristics that approach 0. By giving a pseudo gradient in this way, updating of a ^ (n) does not stop even in the range of a ^ (n)> x (n).

  In other words, in the cascade connection type transmission system parameter estimation technique according to the present invention, the partial differential value based on the nonlinear system model parameter of the hard clip function used as the nonlinear system model has a larger estimated value of the nonlinear system model parameter than the input signal. In this case, in order to solve the problem that the parameter cannot be updated because it becomes zero, in the case where the original partial differential value becomes zero, this is replaced by a pseudo non-zero partial differential value. Even in such a case, the parameter can be updated.

[Example of how to give a pseudo gradient]
Now, an example of how to give a pseudo gradient schematically shown in FIG. 6C will be described below.

Here, in Equation (9), the element of S ′ (n) is either 1,0, −1. Therefore, consider replacing an element that becomes 0 in Equation (7) with a non-zero value in the range of greater than 0 and less than or equal to 1. For example, if the element that becomes 0 in equation (7) is | x (n) | <a ^ (n), the output of the function that decreases in output as a ^ (n) increases is expressed as s ^ ' Give as (n). As a specific example, the value of s ^ '(n) is given by equation (13) instead of equation (7).

Here, the signal s ^ '(n) given by the equation (13) is called a pseudo differential signal. γ is a positive real number, and when applying the cascaded transmission system parameter estimation according to the present invention to an acoustic echo canceller described later, γ may be a value of about 1 to 4, for example, γ = 1 or 2 may be selected. it can. At this time, the value of (x (n) / a ^ (n)) ^γ approaches 1 as a ^ (n) approaches x (n), and approaches 0 when a ^ (n) → ∞.

[Cascade estimation device / method for cascade connection type]
FIG. 2 shows an embodiment of a cascade connection type transmission system parameter estimation apparatus 100 according to the present invention in which the differential signal generation unit 605 included in the configuration shown in FIG. 5 of the prior art is replaced with a pseudo differential signal generation unit 505. Since the differential signal generation unit 605 is the same as the conventional configuration shown in FIG. The pseudo differential signal generation unit 505 generates s ^ '(n) as a pseudo differential signal according to the equation (13).

In equation (13), the continuity of the gradient is given by giving (x (n) / a ^ (n)) ^γ so that a ^ (n) approaches 1 as x (n) approaches. Although it can be maintained, gradient continuity is not necessarily a requirement of the present invention. For example, (x (n) / a ^ (n)) ^γ / β, β> 1, and as a ^ (n) approaches x (n), it takes a value less than 1 and close to 1, and a ^ (n ) → ∞, a value approaching 0 may be taken (see equation (13a)). The function that takes a value less than 1 and close to 1 as a ^ (n) approaches x (n) and takes a value that approaches 0 when a ^ (n) → ∞ is not a monotonically decreasing function. Good. Also, the function that gives s ^ '(n) when | x (n) | <a ^ (n) is discontinuous or stepped as a ^ (n) becomes larger, such as a step reduction function. Alternatively, a value that decreases automatically may be output. In addition, in the equation (13a), when the cascade connection type transmission system parameter estimation according to the present invention is applied to the acoustic echo canceller described later, γ is in the range of about 1 to 4, and β is about 1 to 100. You can choose from a range.

  In the present invention, when the state where | x (n) | <a ^ (n) is satisfied for a long time, the partial differential value is always s ^ '(n) during the duration. One of the features is that the update of the nonlinear system model parameter a ^ (n) is not stagnated by avoiding = 0. This means that for all discrete times n, s ^ '(n) ≠ 0 (provided that | x (n) | <a ^ (n)) based on equation (13) or equation (13a). This can be achieved without outputting a pseudo differential signal. That is, output a pseudo differential signal in which s ^ '(n) ≠ 0 instead of the original partial differential value s ^' (n) = 0, that is, from the output based on the expression (7), the expression (13) or the expression Change to the output based on (13a) is performed only when pattern [a] is performed at regular intervals, pattern [b] is performed randomly, or pattern [c] | x (n) | Or you may. Specifically, for the discrete time n, the above change is performed once for each pattern [a] N samples, or the above change is performed once randomly selected in the pattern [b] N samples. The above change may be performed when | x (n) | has the maximum value (or maximum value) in the pattern [c] N samples. For example, as a specific value of N, a linear system The order L for the parameters can be given. Thus, appropriately adopting the original partial differential value s ^ '(n) = 0 leads to a reduction in the amount of calculation. In addition, the present invention is not limited to the configuration in which only one of the patterns [a], [b], and [c] is employed, and a configuration in which a plurality of patterns among these patterns are combined may be employed. For example, when pattern [a] and pattern [c] are combined, the above change is performed when the logical sum of pattern [a] and pattern [c] is true.

[Example of normalization integration]
Update of the parameters a ^ (n) and H (n) in the configuration of FIG. 5 which is the prior art is executed by the nonlinear / linear system parameter update unit 606 according to the equations (11) and (12). Here, since normalization of the equations (11) and (12) is performed independently for each of the parameters a ^ (n) and H (n), there is a problem that mutual influence is not taken into consideration.

In order to solve this problem, as shown in the functional configuration example of the cascade connection type transmission system parameter estimation apparatus 101 in FIG. 3, nonlinearity instead of the nonlinear / linear system parameter update unit 606 of the cascade connection type transmission system parameter estimation apparatus 100 is used. The linear system parameter integration normalization update unit 507 may be used. In the nonlinear / linear system parameter integration normalization updating unit 507, for parameters a ^ (n) and H (n), a ^ (n) is one scalar quantity, whereas H (n) is L Since it is a + 1-dimensional vector, an update formula subjected to the following normalization considering the influence of the difference in the number of parameters is applied.

Here, the weight function w ₁ (L) is a function of the order L of the linear system parameter, and has a property of increasing monotonously with respect to L. For example, w ₁ (L) = L + 1 or w ₁ (L) = L can be given. δ _a and δ _H are positive real numbers given to prevent zero subtraction.

Here, Expression (16) obtained by modifying Expression (14) and Expression (17) obtained by modifying Expression (15) may be used.

Furthermore, paying attention to the fact that the relationship expressed by equation (17a) is approximately established with E as the expected value, updating may be performed according to equations (18) and (19) instead of equations (14) and (15). it can.

At this time, the weighting function w ₂ (a ^ (n) ² ) is given as w ₂ (a ^ (n) ² ) = κa ^ (n) ² + ε, for example. One representative example is that κ = 1 and ε = 0. Further, in consideration of the influence of both L and a ^ (n) ² , it can be updated according to the equations (18b) and (19b) instead of the equations (18) and (19).

At this time, as a representative example of the weight function w ₃ (L, a ^ (n) ² ), w ₃ (L, a ^ (n) ² ) = a ^ (n) ² (L + 1) and w ₃ ( L, a ^ (n) ² ) = a ^ (n) ² √L, and more generally w ₃ (L, a ^ (n) ² ) = κa ^ (n) ² ( L + 1) + ε or w ₃ (L, a ^ (n) ² ) = κa ^ (n) ² √ (L) + ε may be given. Where κ is a real number greater than 0 and never greater than 1, ε is greater than 0, and the average value of ‖S (n) ‖ ² / ‖H (n) ^T S '(n) ‖ ² It is a real number that does not greatly exceed. In other words, κ and ε do not necessarily have to be determined by the respective denominators of Equation (18), Equation (18b), Equation (19), and Equation (19b). This parameter indicates that the effect of the invention can be obtained.

  As described above, according to the cascade connection type transmission system parameter estimation technique according to the present invention, modeling is performed by using a nonlinear system parameter modeled by a hard clip function such as Equation (1) and an FIR filter such as Equation (2). When trying to estimate the parameters of the linear system at the same time, the estimated value of the nonlinear system model parameter of the hard clip function is the value given as the initial value in advance or the value taken during the update is the magnitude of the input signal. The following problems that occur when the value becomes larger than the above can be solved. In other words, the nonlinearity model parameter is smaller than the input signal, the clipping phenomenon due to the nonlinear system actually occurs, and the non-zero value of the error signal to be minimized can be observed. When the estimated value of the system model parameter is larger than the input signal, the prior art cannot update the nonlinear system model parameter of the nonlinear system. According to the present invention, even in such a situation, the nonlinear system model parameter of the nonlinear system can be updated, and can be applied to, for example, an acoustic echo canceller. In an acoustic echo canceller, when reproducing an acoustic signal from a speaker, the nonlinear distortion tends to be smaller as the volume of the amplifier is smaller, and the nonlinear distortion tends to be larger as the volume of the amplifier is increased. That is, the nonlinear system model parameter of the hard clip function becomes a larger value as the volume is smaller (a linear region is wider), and becomes a smaller value as the volume is larger (a linear region is narrower). For this reason, for example, when the sound is initially reproduced with a small volume and the nonlinear system model parameter of the nonlinear system is once updated to a large value, if the user subsequently increases the volume, the conventional technique is used. Even when the nonlinear system model parameters of the nonlinear system cannot be updated and the echo cancellation becomes insufficient, the echo cancellation is possible according to the technique of the present invention.

[Application to acoustic echo canceller]
The cascade connection type transmission system parameter estimation technique of the present invention can be diverted to, for example, an acoustic echo canceller. The acoustic echo canceller cancels the echo by subtracting the pseudo echo signal obtained by estimating the echo that echoes into the microphone in the same room and the acoustic signal reproduced from the speaker is echoed in the room, from the collected sound signal of the microphone. The output signal is output. As shown in FIG. 4, when a reproduction signal x (n) to be reproduced by a speaker is gained by an amplifier 201 and reproduced from the speaker 202, the amplifier 201 or the speaker 202 may distort the signal. In other words, the transfer characteristic until the reproduced signal x (n) to be reproduced by the speaker passes through the amplifier 201 and the speaker 202 that generate distortion and a signal emitted from the speaker is obtained is regarded as nonlinear. 2 can be assumed. Further, the acoustic signal emitted from the speaker 202 passes through the indoor reverberation path 301 to the microphone 302, and the transfer characteristic until the sound pickup signal y (n) is obtained is regarded as linear. It can be assumed that it is composed.

  In this case, the cascade connection type transmission system parameter estimation apparatus 100 or the cascade connection type transmission system parameter estimation apparatus 101 can operate as the acoustic echo canceller 100a (in FIG. 4, the cascade connection type transmission system parameter estimation apparatus 100 is acoustically connected. An example in the case of use as the echo canceller 100a is shown), and in the above description, the input signal x (n) is reproduced to the reproduction signal x (n) for reproducing by the speaker, and the output signal y (n) is converted to the speaker Since it is only necessary to read the sound collected signal y (n) collected in the same space as in FIG. The acoustic echo canceller 100a outputs the error signal e (n) as a transmission signal, instead of outputting the nonlinear system estimation parameter and the linear system estimation parameter to the outside.

  The collected sound signal y (n) includes the utterance voice of the near-end speaker in addition to the echo originating from the transmission system. When the near-end speaker's voice and echo are mixed, it is obtained by subtracting the estimated value y ^ (n) of the output signal from the target transmission system 1, which is a pseudo echo signal, from y (n). The error signal e (n) to be transmitted is mainly the voice of the near-end speaker and becomes a transmission signal to the communication partner. At the same time, however, the near-end speaker's voice present in the error signal e (n) also becomes a factor that disturbs the estimation results of the nonlinear system parameters and linear system parameters. Therefore, when the value of step size μ is fixed, if the value is given sufficiently small, or the presence of the near-end speaker's voice can be detected, the near-end speaker's voice is detected. However, it is necessary to take another measure to control the step size μ to be small.

<Hardware configuration example of cascade connection type transmission system parameter estimation device>
The cascade connection type transmission system parameter estimation apparatus according to the above-described embodiment includes an input unit to which a keyboard or the like can be connected, an output unit to which a liquid crystal display or the like can be connected, a CPU (Central Processing Unit) Good. ] RAM (Random Access Memory) or ROM (Read Only Memory) and external storage device as a hard disk, and data exchange between these input unit, output unit, CPU, RAM, ROM, and external storage device It has a bus that can be connected. If necessary, the cascade connection type transmission system parameter estimation device may be provided with a device (drive) capable of reading and writing a storage medium such as a CD-ROM. A physical entity having such hardware resources includes a general-purpose computer.

  The external storage device of the cascade connection type transmission system parameter estimation device stores a program for estimating a parameter and data necessary for processing of this program [not limited to the external storage device, for example, reading a program. It may be stored in a ROM which is a dedicated storage device. ]. Data obtained by the processing of these programs is appropriately stored in a RAM or an external storage device. Hereinafter, a storage device that stores data, addresses of storage areas, and the like is simply referred to as a “storage unit”.

The storage unit of the cascaded transmission system parameter estimation device stores the input signal x (n) or the estimated model parameter a ^ by comparing the magnitude of the input signal x (n) with the nonlinear system estimation model parameter a ^ (n). A program for outputting the estimated value s ^ (n) according to (n) and the estimated values s ^ (n) and s ^ (n-1 of the nonlinear system corresponding to each time from time nL to time n ), S ^ (n-2), ..., s ^ (nL), and estimated model parameters of the linear system h ^ ₀ (n), h ^ ₁ (n), h ^ ₂ (n), ..., h ^ A program for outputting the estimated value y ^ (n) by convolution with _L (n) and the error signal e () obtained by subtracting the linear system estimated value y ^ (n) from the output signal y (n) of the transmission system n) and the magnitude of the input signal x (n) is compared with the estimated model parameter a ^ (n) of the nonlinear system. Zero or non-linear if not greater than parameter a ^ (n) A non-zero value that decreases in size as the estimated model parameter a ^ (n) of the non-linear system is assumed to be an estimated bias for the estimated model parameter a ^ (n) of the nonlinear system. Output as differential value s ^ '(n). Otherwise, estimate partial differential value obtained by partial differentiation of estimated value s ^ (n) of nonlinear system with estimated model parameter a ^ (n) of nonlinear system A program to output as value s ^ '(n), error signal e (n), and estimated partial differential values s ^' (n), s ^ '(n- 1), s ^ '(n-2), ..., s ^' (nL) and nonlinear system estimates s ^ (n), s ^ (n-1), s ^ (n-2), ..., s ^ (nL) and the estimated model parameter a ^ (n + 1) of the nonlinear system at time n + 1 and the estimated model parameters h ^ ₀ (n + 1) and h ^ ₁ (n + Programs for estimating 1), h ^ ₂ (n + 1), ..., h ^ _L (n + 1) are stored.

  In the cascade connection type transmission system parameter estimation device, each program stored in the storage unit and data necessary for the processing of each program are read into the RAM as necessary, and interpreted and executed by the CPU. As a result, the CPU has predetermined functions (nonlinear system parameter application / synthesis unit, linear system parameter application / synthesis unit, nonlinear / linear parameter update unit [or nonlinear / linear parameter integrated normalization update unit], pseudo differential signal generation unit) By realizing the above, parameter estimation is realized.

<Supplementary note>
The present invention is not limited to the above-described embodiment, and can be appropriately changed without departing from the spirit of the present invention. In addition, the processing 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 processing. .

  Further, when the processing functions in the hardware entity (cascade connection type transmission system parameter estimation device) described in the above embodiment are realized by a computer, the processing contents of the functions that the hardware entity should have are described by a program. Then, by executing this program on a computer, the processing functions in the hardware entity 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. Specifically, for example, as a magnetic recording device, a hard disk device, a flexible disk, a magnetic tape or the like, and as an optical disk, a DVD (Digital Versatile Disc), a DVD-RAM (Random Access Memory), a CD-ROM (Compact Disc Read Only). Memory), CD-R (Recordable) / RW (ReWritable), etc., magneto-optical recording medium, MO (Magneto-Optical disc), etc., semiconductor memory, EEP-ROM (Electronically Erasable and Programmable-Read Only Memory), etc. Can be used.

  The 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. Also, the program is not transferred from the server computer to the computer, and the above-described processing is executed by a so-called ASP (Application Service Provider) type service that realizes the processing function only by the execution instruction and result acquisition. 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, a hardware entity is configured by executing a predetermined program on a computer. However, at least a part of these processing contents may be realized by hardware.

Claims (8)

A transmission system that can be regarded as a cascade connection between a nonlinear system that outputs a value corresponding to the input signal or the model parameter and a linear system having a finite impulse response characteristic by comparing the magnitude of the input signal with the model parameter. A cascade connection type transmission system parameter estimation method for estimating a model parameter of a nonlinear system and a model parameter of the linear system,
For the input signal x (n) to the transmission system at time n, the input signal x (n) is compared by comparing the magnitude of the input signal x (n) with the estimated model parameter a ^ (n) of the nonlinear system. n) or nonlinear parameter application / synthesis step for outputting an estimated value s ^ (n) corresponding to the estimated model parameter a ^ (n),
Estimated values s ^ (n), s ^ (n-1), s ^ (n-2), ..., corresponding to each time from time nL to time n, where L is an integer greater than or equal to zero Estimated value by convolution of s ^ (nL) and estimated model parameters h ^ ₀ (n), h ^ ₁ (n), h ^ ₂ (n), ..., h ^ _L (n) of the above linear system Linear system parameter multiplication / synthesis step that outputs y ^ (n),
An error calculating step for obtaining an error signal e (n) obtained by subtracting the estimated value y ^ (n) of the linear system from the output signal y (n) of the transmission system;
A pseudo differential signal generation step for outputting an estimated partial differential value s ^ '(n) of the estimated value s ^ (n) of the nonlinear system with respect to the estimated model parameter a ^ (n) of the nonlinear system;
The error signal e (n) and the estimated partial differential values s ^ '(n), s ^' (n-1), s ^ '(n-2) corresponding to each time from time nL to time n , ..., s ^ '(nL) and the estimated values s ^ (n), s ^ (n-1), s ^ (n-2), ..., s ^ (nL) for the above nonlinear system, Estimated model parameters a ^ (n + 1) of the nonlinear system at time n + 1 and estimated model parameters h ^ ₀ (n + 1), h ^ ₁ (n + 1), h ^ ₂ (n +1),..., H ^ _L (n + 1), and a nonlinear / linear system parameter updating step,
In the pseudo differential signal generation step,
By comparing the magnitude of the input signal x (n) with the estimated model parameter a ^ (n) of the nonlinear system, the magnitude of the input signal x (n) becomes the estimated model parameter a ^ (n If the estimated model parameter a ^ (n) of the nonlinear system increases, a non-zero value that decreases in size as the estimated partial differential value s ^ '(n) is output. In other cases, the partial differential value of the estimated value s ^ (n) of the nonlinear system is output as the estimated partial differential value s ^ '(n). . A transmission system that can be regarded as a cascade connection between a nonlinear system that outputs a value corresponding to the input signal or the model parameter and a linear system having a finite impulse response characteristic by comparing the magnitude of the input signal with the model parameter. A cascade connection type transmission system parameter estimation method for estimating a model parameter of a nonlinear system and a model parameter of the linear system,
For the input signal x (n) to the transmission system at time n, the input signal x (n) is compared by comparing the magnitude of the input signal x (n) with the estimated model parameter a ^ (n) of the nonlinear system. n) or nonlinear parameter application / synthesis step for outputting an estimated value s ^ (n) corresponding to the estimated model parameter a ^ (n),
Estimated values s ^ (n), s ^ (n-1), s ^ (n-2), ..., corresponding to each time from time nL to time n, where L is an integer greater than or equal to zero Estimated value by convolution of s ^ (nL) and estimated model parameters h ^ ₀ (n), h ^ ₁ (n), h ^ ₂ (n), ..., h ^ _L (n) of the above linear system Linear system parameter multiplication / synthesis step that outputs y ^ (n),
An error calculating step for obtaining an error signal e (n) obtained by subtracting the estimated value y ^ (n) of the linear system from the output signal y (n) of the transmission system;
A pseudo differential signal generation step for outputting an estimated partial differential value s ^ '(n) of the estimated value s ^ (n) of the nonlinear system with respect to the estimated model parameter a ^ (n) of the nonlinear system;
The error signal e (n) and the estimated partial differential values s ^ '(n), s ^' (n-1), s ^ '(n-2) corresponding to each time from time nL to time n , ..., s ^ '(nL) and the estimated values s ^ (n), s ^ (n-1), s ^ (n-2), ..., s ^ (nL) for the above nonlinear system, Estimated model parameters a ^ (n + 1) of the nonlinear system at time n + 1 and estimated model parameters h ^ ₀ (n + 1), h ^ ₁ (n + 1), h ^ ₂ (n +1),..., H ^ _L (n + 1), and a nonlinear / linear system parameter updating step,
In the pseudo differential signal generation step,
(1) Periodically, (2) Randomly, (3) When the magnitude of the input signal x (n) takes a maximum value or a maximum value in a sample of a predetermined time, at least one of By comparing the magnitude of the input signal x (n) with the estimated model parameter a ^ (n) of the nonlinear system, the magnitude of the input signal x (n) is determined as the estimated model parameter a ^ ( If it is not greater than n), zero or a non-zero value that decreases in size as the estimated model parameter a ^ (n) of the nonlinear system increases becomes the estimated partial differential value s ^ '(n Otherwise, the partial differential value of the estimated value s ^ (n) of the nonlinear system is output as the estimated partial differential value s ^ '(n),
If none of the above (1), (2), or (3) applies, the partial differential value of the estimated value s ^ (n) of the nonlinear system is set as the estimated partial differential value s ^ '(n). A cascade connection type transmission system parameter estimation method characterized by outputting. A cascade connection type transmission system parameter estimation method according to claim 1 or 2,
In the above nonlinear / linear parameter update step,
A cascade connection type characterized in that the estimated model parameter of the nonlinear system and the estimated model parameter of the linear system are updated by normalizing with the value of the L that is the order of the model parameter of the linear system. Transmission system parameter estimation method. A cascade connection type transmission system parameter estimation method according to any one of claims 1 to 3,
In the above nonlinear / linear parameter update step,
Let T denote transpose, 転 and ‖ denote norms, and H (n) = [h ^ ₀ (n), h ^ ₁ (n), h ^ ₂ (n),…, h ^ _L (n )] ^T , S (n) = [s ^ (n), s ^ (n-1), s ^ (n-2), ..., s ^ (nL)] ^T , S '(n) = [s ^ '(n), s ^ ' (n-1), s ^ '(n-2), ..., s ^' (nL)] T, μ a, the step of adjusting the updating amount of the mu _h respectively parameter Size, δ _a , δ _H are given positive real numbers to prevent zero grading, w ₃ (L, a ^ (n) ² ) is the value of L and estimated model parameter a ^ ( n) as input functions, the estimated model parameter a ^ (n + 1) of the nonlinear system and the estimated model parameter H (n + 1) = [h ^ ₀ (n + 1), h ^ ₁ (n + 1), h ^ ₂ (n + 1), ..., h ^ _L (n + 1)] ^T

A cascade connection type transmission system parameter estimation method characterized by: A cascade connection type transmission system parameter estimation method according to any one of claims 1 to 4,
The input signal is a reproduction signal for reproduction by a speaker,
The output signal is a sound collection signal collected in the same space as the speaker,
The cascade connection type transmission system parameter estimation method, wherein the error signal is a transmission signal from which echo is removed from the collected sound signal. A transmission system that can be regarded as a cascade connection between a nonlinear system that outputs a value corresponding to the input signal or the model parameter and a linear system having a finite impulse response characteristic by comparing the magnitude of the input signal with the model parameter. A cascade connection type transmission system parameter estimation device that estimates model parameters of a nonlinear system and model parameters of the linear system,
For the input signal x (n) to the transmission system at time n, the input signal x (n) is compared by comparing the magnitude of the input signal x (n) with the estimated model parameter a ^ (n) of the nonlinear system. n) or a nonlinear parameter application / synthesis unit that outputs an estimated value s ^ (n) corresponding to the estimated model parameter a ^ (n);
Estimated values s ^ (n), s ^ (n-1), s ^ (n-2), ..., corresponding to each time from time nL to time n, where L is an integer greater than or equal to zero Estimated value by convolution of s ^ (nL) and estimated model parameters h ^ ₀ (n), h ^ ₁ (n), h ^ ₂ (n), ..., h ^ _L (n) of the above linear system a linear parameter multiplication / synthesis unit that outputs y ^ (n);
An error calculation unit for obtaining an error signal e (n) obtained by subtracting the estimated value y ^ (n) of the linear system from the output signal y (n) of the transmission system;
A pseudo-differential signal generator that outputs an estimated partial differential value s ^ '(n) of the estimated value s ^ (n) of the nonlinear system with respect to the estimated model parameter a ^ (n) of the nonlinear system;
The error signal e (n) and the estimated partial differential values s ^ '(n), s ^' (n-1), s ^ '(n-2) corresponding to each time from time nL to time n , ..., s ^ '(nL) and the estimated values s ^ (n), s ^ (n-1), s ^ (n-2), ..., s ^ (nL) for the above nonlinear system, Estimated model parameters a ^ (n + 1) of the nonlinear system at time n + 1 and estimated model parameters h ^ ₀ (n + 1), h ^ ₁ (n + 1), h ^ ₂ (n +1),..., H ^ _L (n + 1), and a nonlinear / linear system parameter updating unit,
The pseudo differential signal generator is
By comparing the magnitude of the input signal x (n) with the estimated model parameter a ^ (n) of the nonlinear system, the magnitude of the input signal x (n) becomes the estimated model parameter a ^ (n If the estimated model parameter a ^ (n) of the nonlinear system increases, a non-zero value that decreases in size as the estimated partial differential value s ^ '(n) is output. In other cases, a cascade connection type transmission system parameter estimation device is characterized in that the partial differential value of the estimated value s ^ (n) of the nonlinear system is output as the estimated partial differential value s ^ '(n). . A transmission system that can be regarded as a cascade connection between a nonlinear system that outputs a value corresponding to the input signal or the model parameter and a linear system having a finite impulse response characteristic by comparing the magnitude of the input signal with the model parameter. A cascade connection type transmission system parameter estimation device that estimates model parameters of a nonlinear system and model parameters of the linear system,
For the input signal x (n) to the transmission system at time n, the input signal x (n) is compared by comparing the magnitude of the input signal x (n) with the estimated model parameter a ^ (n) of the nonlinear system. n) or a nonlinear parameter application / synthesis unit that outputs an estimated value s ^ (n) corresponding to the estimated model parameter a ^ (n);
Estimated values s ^ (n), s ^ (n-1), s ^ (n-2), ..., corresponding to each time from time nL to time n, where L is an integer greater than or equal to zero Estimated value by convolution of s ^ (nL) and estimated model parameters h ^ ₀ (n), h ^ ₁ (n), h ^ ₂ (n), ..., h ^ _L (n) of the above linear system a linear parameter multiplication / synthesis unit that outputs y ^ (n);
An error calculation unit for obtaining an error signal e (n) obtained by subtracting the estimated value y ^ (n) of the linear system from the output signal y (n) of the transmission system;
A pseudo-differential signal generator that outputs an estimated partial differential value s ^ '(n) of the estimated value s ^ (n) of the nonlinear system with respect to the estimated model parameter a ^ (n) of the nonlinear system;
The error signal e (n) and the estimated partial differential values s ^ '(n), s ^' (n-1), s ^ '(n-2) corresponding to each time from time nL to time n , ..., s ^ '(nL) and the estimated values s ^ (n), s ^ (n-1), s ^ (n-2), ..., s ^ (nL) for the above nonlinear system, Estimated model parameters a ^ (n + 1) of the nonlinear system at time n + 1 and estimated model parameters h ^ ₀ (n + 1), h ^ ₁ (n + 1), h ^ ₂ (n +1),..., H ^ _L (n + 1), and a nonlinear / linear system parameter updating unit,
The pseudo differential signal generator is
(1) Periodically, (2) Randomly, (3) When the magnitude of the input signal x (n) takes a maximum value or a maximum value in a sample of a predetermined time, at least one of By comparing the magnitude of the input signal x (n) with the estimated model parameter a ^ (n) of the nonlinear system, the magnitude of the input signal x (n) is determined as the estimated model parameter a ^ ( If it is not greater than n), zero or a non-zero value that decreases in size as the estimated model parameter a ^ (n) of the nonlinear system increases becomes the estimated partial differential value s ^ '(n Otherwise, the partial differential value of the estimated value s ^ (n) of the nonlinear system is output as the estimated partial differential value s ^ '(n),
If none of the above (1), (2), or (3) applies, the partial differential value of the estimated value s ^ (n) of the nonlinear system is set as the estimated partial differential value s ^ '(n). A cascade connection type transmission system parameter estimation device characterized by outputting.       A program for causing a computer to execute each process of the cascade connection type transmission system parameter estimation method according to any one of claims 1 to 5.

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