CN103716013B - Variable element ratio sef-adapting filter - Google Patents

Abstract

The invention discloses a kind of variable element ratio sef-adapting filter, belong to digital filter design field. Variable element ratio sef-adapting filter is adjusted the value of the coefficient gain of sef-adapting filter with a time-varying parameter. This time-varying parameter can be expressed as the monotonically increasing function of error signal power and system noise power ratio. In the starting stage of adaptive-filtering, error signal power and system noise power ratio are larger, thereby the large coefficient of sef-adapting filter has larger yield value; In the converged state of adaptive-filtering, error signal power and system noise power ratio are less, thereby the large coefficient of sef-adapting filter has less yield value. Therefore, this variable element method can keep the fast convergence rate of ratio sef-adapting filter, can obtain again the stable state imbalance fluctuation that ratio sef-adapting filter is low.

Description

Variable Parameter Scale Adaptive Filter

technical field

The invention belongs to the field of digital filter design, and relates to a coefficient update method of an adaptive filter, in particular to a proportional adaptive filter whose parameters are automatically adjusted.

Background technique

The coefficient vector of traditional digital filter is fixed. The main task of the traditional digital filter is to filter out the useless spectral components in the input signal, while retaining the required spectral components, so its operation mode is to obtain the output signal according to the input signal and the coefficient vector of the filter. Different from traditional filters with fixed coefficient vectors, adaptive filters can approach the unknown system according to the input and output signals of the unknown system. Since the essence of solving problems such as system identification, echo cancellation, active noise control, channel equalization, and interference cancellation is to obtain the unknown system based on the input and output signals of the unknown system, adaptive filters are used in hands-free telephones, video conferencing, etc. , hearing aids, channel equalizers, electronic scalpels and other equipment have been widely used.

The main indicators to measure the performance of adaptive filter are convergence speed and steady-state misadjustment. The convergence speed determines the time required for the adaptive filter to approximate the unknown system, and the steady-state misadjustment determines the accuracy that the unknown system can achieve. A major factor affecting the convergence speed of the adaptive filter is the sparsity of the unknown system. For an unknown system, the more coefficients close to or equal to 0, the higher the sparsity; otherwise, the lower the coefficient. Traditional LMS and NLMS adaptive filters converge very slowly when the sparsity of the unknown system is high. The unknown systems that need to be approximated in hands-free phones, video conferencing, and hearing aids have a high degree of sparsity. In order to obtain faster convergence speed, more effective adaptive filters need to be designed.

DonaldL.Duttweiler proposed a proportional adaptive filter in 2000, namely the famous PNLMS adaptive filter. Different from the traditional NLMS adaptive filter, the PNLMS adaptive filter assigns a different gain to each coefficient, and the gain is proportional to its corresponding adaptive filter coefficient. The adaptive filter converges quickly when approaching the unknown system with high sparsity, but the convergence performance will decrease as the coefficient degree of the system decreases. In order to improve the performance of estimating sparse unknown systems, Jacob Benesty and Steven L. Gay proposed an improved scale adaptive filter, namely IPNLMS adaptive filter. Due to its superior performance and simple structure, the proportional adaptive filter has been widely used.

Two important performance indicators of adaptive filters are convergence speed and steady-state misadjustment. Although the IPNLMS adaptive filter is used to estimate the sparse unknown system, its convergence speed is very fast, but the performance of its steady-state misadjustment is weakened, that is, the steady-state misadjustment has great volatility. The large fluctuation of the steady-state dissonance indicates that the steady-state dissonance is very large at many time points and very small at many other time points. Points in time where the steady-state misalignment is very large have very poor accuracy. Therefore, in order to obtain high precision, it is necessary to find an effective solution.

Contents of the invention

The purpose of the present invention is to provide a variable parameter proportional adaptive filter, which solves the problem that the IPNLMS adaptive filter has very large fluctuations in steady-state imbalance at many time points due to its fast convergence speed.

In order to solve these problems in the prior art, the technical scheme provided by the invention is as follows:

A variable parameter proportional adaptive filter is characterized in that the filter comprises:

A noise power estimation module, used to estimate the power of the system noise when the adaptive filter is static;

An error power estimation module is used to perform time smoothing on the output error signal of the adaptive filter to estimate the power of the error signal;

The intermediate variable generating module is used to generate an intermediate variable by the power of the error signal and the power of the system noise, and the intermediate variable is obtained by calculating the logarithm of the power ratio of the power of the error signal to the system noise;

A time-varying parameter generation module is used to convert the intermediate variable through a Sigmoid function to obtain a time-varying parameter for the proportional adaptive filter;

A proportional matrix construction module is used to obtain the gain of each coefficient from the obtained time-varying parameters, and then construct a proportional matrix by the coefficient gain;

The filter coefficient update module is configured to update the coefficients of the adaptive filter according to the constructed scale matrix, and calculate a new error signal value.

The preferred technical solution is: the noise power estimation module estimates the power of the system noise Shilling the input signal u(n)=0, then the output error e(n) is the system noise v(n); through the method of time averaging, the power of the system noise is obtained

The preferred technical solution is: the error power estimation module performs error power estimation according to the following steps:

1) Calculate the value of the error signal through the input signal u(n) and the expected signal d(n) according to e(n)=d(n)-w ^T (n)u(n), where w(n)=[w ₁ (n),w ₂ (n),...,w _M (n)] is the coefficient vector of the adaptive filter at time n; u(n)=[u(n),u(n-1),... ,u(n-M+1)] ^T is the input signal vector of the adaptive filter at time n, which is composed of the current sample value of the input signal and its previous M-1 sample values;

2) According to Estimate the power of the output error signal where λ is the smoothing factor.

The preferred technical solution is: the intermediate variable generating module according to the system noise power and the error signal power according to Get the intermediate variable x(n).

The preferred technical solution is: the time-varying parameter generating module according to the intermediate variable x(n) according to α(n)=(2α+2)/{1+exp[-βx(n)]}-(α+2) Obtain the value of the time-varying parameter α(n), where α is the compromise parameter; β is the shape parameter of the Sigmoid function.

The preferred technical solution is: the proportional matrix construction module first according to the time-varying parameters according to g _m (n)=[1-α(n)]/2M+[1+α(n)]|w _m (n)|/ [2||w(n)|| ₁ +ε]Get the elements of the scale matrix, where m=1,2,..., M-1, w _m (n) is the mth coefficient of the adaptive filter at n The value at the moment, ||·|| ₁ represents the L ₁ norm, and ε is the small positive number introduced; then the elements of the obtained M proportional matrices form a diagonal matrix G(n)=diag[g ₁ (n) ,g ₂ (n),...,g _M (n)], where each diagonal element in G(n) corresponds to the gain g _m (n) of each filter coefficient.

The preferred technical solution is: the filter coefficient updating module according to the generated proportional matrix according to the updating formula w(n+1)=w(n)+μG(n)u(n)e(n)/[u ^T ( n) G(n)u(n)+δ] to update the coefficient vector of the adaptive filter, where δ is a regularization parameter used to solve numerical calculation difficulties.

Another object of the present invention is to provide a method for updating coefficient vectors of adaptive filter with variable parameter scale, characterized in that said method comprises the following steps:

(1) Estimate the power of the system noise when the adaptive filter is static;

(2) Perform time smoothing on the output error signal of the adaptive filter to estimate the power of the error signal;

(3) An intermediate variable is generated from the power of the error signal and the power of the system noise, and the intermediate variable is obtained by calculating the logarithm of the ratio of the power of the error signal to the power of the system noise;

(4) Convert the intermediate variable through the Sigmoid function to obtain the time-varying parameters for the proportional adaptive filter;

(5) Calculate the gain of each coefficient from the obtained time-varying parameters, and then construct a proportional matrix from the coefficient gain;

(6) Update the coefficients of the adaptive filter according to the constructed scale matrix, and calculate a new error signal value.

The preferred technical solution is: the method is specifically carried out according to the following steps:

(1) Let the input signal u(n)=0, then the output error e(n) is the system noise v(n); through the method of time averaging, the power of the system noise is obtained

(2) The error power estimation is carried out according to the following steps:

1) Calculate the value of the error signal through the input signal u(n) and the expected signal d(n) according to e(n)=d(n)-w ^T (n)u(n), where w(n)=[w ₁ (n),w ₂ (n),...,w _M (n)] is the coefficient vector of the adaptive filter at time n; u(n)=[u(n),u(n-1),... ,u(n-M+1)] ^T is the input signal vector of the adaptive filter at time n, which is composed of the current sample value of the input signal and its previous M-1 sample values;

2) According to Estimate the power of the output error signal where λ is the smoothing factor;

(3) According to the system noise power and error signal power according to Get the intermediate variable x(n);

(4) Obtain the value of the time-varying parameter α(n) according to the intermediate variable x(n) according to α(n)=(2α+2)/{1+exp[-βx(n)]}-(α+2) , where α is a compromise parameter; β is the shape parameter of the Sigmoid function;

(5) First according to the time-varying parameters according to g _m (n)=[1-α(n)]/2M+[1+α(n)]|w _m (n)|/[2||w(n)| | ₁ +ε] to obtain the elements of the scale matrix, where m=1,2,...,M-1, w _m (n) is the value of the mth coefficient of the adaptive filter at time n, ||·|| ₁ represents the L ₁ norm, and ε is a small positive number introduced; then the elements of the obtained M proportional matrices form a diagonal matrix G(n)=diag[g ₁ (n),g ₂ (n),…, g _M (n)], where each diagonal element in G(n) corresponds to the gain g _m (n) of each filter coefficient;

(6) According to the generated proportional matrix, follow the update formula w(n+1)=w(n)+μG(n)u(n)e(n)/[u ^T (n)G(n)u(n) +δ] to update the coefficient vector of the adaptive filter, where δ is a regularization parameter used to solve numerical calculation difficulties.

The principle of technical solution of the present invention is:

The present invention adopts the variable parameter ratio method to adjust the coefficient vector of the adaptive filter, that is, a time-varying parameter is used to adjust the value of the coefficient gain of the adaptive filter, and the time-varying parameter can be expressed as the ratio of error signal power to system noise power A monotonically increasing function of .

In the initial stage of the adaptive filter operation, due to the large ratio of the error signal power to the system noise power, the adaptive filter automatically assigns a larger gain value to the large coefficient, so as to maintain a fast convergence speed; in the adaptive filter In the convergence stage of the filter, since the ratio of the error signal power to the system noise power is small, the adaptive filter automatically assigns a small gain value to the large coefficient, thereby reducing the fluctuation of the steady-state imbalance.

Compared with the scheme in the prior art, the advantages of the present invention are:

The technical solution of the present invention is a variable parameter proportional adaptive filter, which belongs to the field of digital filter design. The variable parameter method is used to adjust the value of the coefficient gain of the adaptive filter by using a time-varying parameter, which can keep the proportional adaptive filter fast. The convergence speed of the proportional adaptive filter can be obtained, and the low steady-state misalignment volatility of the proportional adaptive filter can be obtained. The invention can be applied in equipments such as hands-free telephone, video conferencing, hearing aid, channel equalizer, electronic scalpel and the like.

Description of drawings

Fig. 1 is the schematic diagram of the variable parameter proportional adaptive filter structure;

Figure 2 is the impulse response of an unknown system containing 100 coefficients;

Figure 3 is the impulse response of an unknown system containing 512 coefficients;

Fig. 4 is a comparison of normalized offset curves when the adaptive filter estimates the unknown system shown in Fig. 2 under the condition of 20dB SNR, and the values of its parameters are μ = 0.3, β = 3;

Figure 5 is a comparison of the normalized offset curves when the adaptive filter estimates the unknown system shown in Figure 2 under the condition of 30dB SNR, and the values of its parameters are μ=0.5, β=1.5;

Figure 6 is a comparison of the normalized offset curves when the adaptive filter estimates the unknown system shown in Figure 2 under the condition of 40dB SNR, and the values of its parameters are μ=0.7, β=1;

Figure 7 is a comparison of the normalized offset curves when the adaptive filter estimates the unknown system shown in Figure 3 under the condition of 20dB SNR, and the values of its parameters are μ=0.3, β=7;

Figure 8 is a comparison of the normalized offset curves when the adaptive filter estimates the unknown system shown in Figure 3 under the condition of 30dB SNR, and the values of its parameters are μ=0.5, β=5;

Fig. 9 is a comparison of normalized offset curves when the adaptive filter estimates the unknown system shown in Fig. 3 under the condition of 40dB SNR, and the values of its parameters are μ=0.7, β=3.

detailed description

The above solution will be further described below in conjunction with specific embodiments. It should be understood that these examples are used to illustrate the present invention and not to limit the scope of the present invention. The implementation conditions used in the examples can be further adjusted according to the conditions of the specific system, and the unspecified implementation conditions are usually the conditions in routine experiments.

Example of Variable Parameter Scale Adaptive Filter

As shown in Figure 1, the variable parameter proportional adaptive filter includes:

Noise power estimation module: the function of this module is to estimate the power of system noise when the adaptive filter is static;

Error power estimation module: the function of this module is to estimate the power of the error signal by time smoothing the output error signal of the adaptive filter;

Intermediate variable generation module: the function of this module is to generate an intermediate variable, which is obtained by calculating the logarithm of the power ratio of the error power to the system noise;

Time-varying parameter generation module: the function of this module is to convert the intermediate variable through the Sigmoid function to obtain the variable parameter required by the proportional adaptive filter with good filtering effect;

Proportional matrix construction module: the function of this module is to first obtain the gain of each coefficient from the obtained variable parameters, and then construct a proportional matrix from the gains of all coefficients;

Filter coefficient update module: the function of this module is to update the coefficient of the adaptive filter according to the divided ratio matrix, and calculate the new error signal value.

The specific operation of each module of the variable parameter proportional adaptive filter is as follows:

Step 1. The "Noise Power Estimation Module" estimates the variance of the system noise before the adaptive filter is iteratively updated. When estimating the variance, let the input signal u(n)=0, then the output error e(n) is the system noise v(n). The power of the system noise is obtained by the method of time averaging Then enter the adaptive filter adaptation stage.

Step 2. "Adaptive filter" calculates the value of the error signal through the input signal u(n) and the desired signal d(n), and its calculation formula is e(n)=d(n)-w ^T (n)u( n), where w(n)=[w ₁ (n), w ₂ (n),..., w _M (n)] is the coefficient vector of the adaptive filter at time n; u(n)=[u( n),u(n-1),...,u(n-M+1)] ^T is the input signal vector of the adaptive filter at time n, which is composed of the current sample value of the input signal and its previous M-1 composed of sampled values.

Step 3. The "Error Power Estimation Module" estimates the power of the output error signal It is estimated by using the following calculation formula: Among them, λ is a smoothing factor, which generally takes a value between 0.9 and 0.999. The longer the length of the unknown system, the larger the value of λ; otherwise, the smaller the value of λ.

Step 4. "Intermediate variable generation module", calculate the intermediate variable through the system noise power and error signal power obtained in step 1 and step 2, and its calculation formula is

Step 5. "Time-varying parameter generation module" uses the intermediate variable obtained in step 3 to calculate the value of the time-varying parameter α(n). The module chooses a monotonically increasing Sigmoid function, and performs translation and scaling. The function expression after translation and scaling is: α(n)=(2α+2)/{1+exp[-βx(n)]}-(α+2), where α is a compromise parameter, which is relatively A good value is 0 or -0.5; β is a shape parameter of the Sigmoid function, which determines the slope of the Sigmoid function waveform, and a good value range is between 1 and 10. When the signal-to-noise ratio is low, or the coefficient vector of the unknown system is long, or the signal correlation is high, β should take a larger value; otherwise, β should take a smaller value.

Step 6. The "scale matrix building block" first calculates the elements of the scale matrix using the time-varying parameters obtained in step 4, namely g _m (n) = [1-α(n)]/2M+[1+α(n)] |w _m (n)|/[2||w(n)|| ₁ +ε], m=1, 2,..., M-1, where w _m (n) is the mth adaptive filter The value of the coefficient at time n, ||·|| ₁ represents the L1 norm, and ε is a small positive number introduced to overcome the difficulty of numerical calculation. Then, the module forms a diagonal matrix G(n)=diag[g ₁ (n),g ₂ (n),…,g _M (n)] with the M elements calculated by the above calculation formula, where G(n Each diagonal element in ) corresponds to a scaling step g _m (n) for each filter coefficient.

Step 7. "filter coefficient update module" updates the coefficient vector of the adaptive filter by the scale matrix generated in step 6, and its updating formula is w(n+1)=w(n)+μG(n)u( n)e(n)/[u ^T (n)G(n)u(n)+δ], where δ is a regularization parameter used to solve numerical calculation difficulties.

Application example Using variable parameter proportional adaptive filter for system identification application

Use the variable parameter proportional adaptive filter disclosed in the embodiment (the variable parameter proportional adaptive filter of the present invention is referred to as VIPNLMS for short) adaptive filter to distinguish two sparse unknown systems respectively, and compare its performance with NLMS and IPNLMS adaptive filter performance for comparison.

The first unknown system is shown in Figure 2, and its coefficient vector length is 100; the second unknown system is shown in Figure 3, and its coefficient vector length is 512. When identifying the unknown system shown in Figure 2, this embodiment uses a 2-order autoregressive model as input, that is, the input is determined by u(n)=0.40u(n-1)-0.40u(n-2)+θ (n) obtain, wherein θ (n) is Gaussian white noise sequence;

When identifying the unknown system shown in Figure 3, the first-order autoregressive model is used as input, that is, the input is obtained by u(n)=0.9u(n-1)+η(n), where η(n) is Gaussian white noise sequence. A Gaussian white noise uncorrelated with the input signal is added to the input of the adaptive filter system as system noise, thereby forming a signal-to-noise ratio of 20dB, 30dB or 40dB. The regularization parameter of the NLMS adaptive filter is taken as And the regularization parameters of IPNLMS and VIPNLMS adaptive filters are taken as Use the normalized misalignment (NormalizedMisalignment) relative to the iteration number (IterationNumber) function to compare the performance of the three adaptive filters, which is defined as 20log ₁₀ ||w ₀ -w(n)||/||w ₀ ||, the unit is decibel (dB).

The experimental results are shown in Fig. 4 to Fig. 9, and Fig. 4 to Fig. 6 are comparisons of offset curves when the adaptive filter estimates the unknown system shown in Fig. 2 under the conditions of 20dB, 30dB, and 40dB SNR respectively; Figure 9 is a comparison of the offset curves when the adaptive filter estimates the unknown system shown in Figure 3 under the conditions of 20dB, 30dB, and 40dB SNR respectively.

It can be seen from the experimental results that:

1) The convergence speed of the variable parameter proportional adaptive filter disclosed in the present invention is faster than that of the NLMS adaptive filter, and the fluctuation of steady-state misalignment is comparable to that of the NLMS adaptive filter.

2) The convergence speed of the variable parameter proportional adaptive filter disclosed in the present invention is equivalent to that of the IPNLMS adaptive filter, while the fluctuation of steady-state imbalance is much lower than that of the IPNLMS adaptive filter. Therefore, the performance of variable parameter proportional adaptive filter is better than that of NLMS and IPNLMS adaptive filter.

The above-mentioned embodiments are only to illustrate the technical conception and characteristics of the present invention. The purpose is to enable those familiar with this technology to understand the content of the present invention and implement it accordingly, and cannot limit the protection scope of the present invention. All equivalent changes or modifications made according to the spirit of the present invention shall fall within the protection scope of the present invention.

Claims (3)

1. A variable parameter proportional adaptive filter, characterized in that said filter comprises: A noise power estimation module, used to estimate the power of the system noise when the adaptive filter is static; An error power estimation module is used to perform time smoothing on the output error signal of the adaptive filter to estimate the power of the error signal; The intermediate variable generating module is used to generate an intermediate variable by the power of the error signal and the power of the system noise, and the intermediate variable is obtained by calculating the logarithm of the power ratio of the power of the error signal to the system noise; A time-varying parameter generation module is used to convert the intermediate variable through a Sigmoid function to obtain a time-varying parameter for the proportional adaptive filter; A proportional matrix construction module is used to obtain the gain of each coefficient from the obtained time-varying parameters, and then construct a proportional matrix by the coefficient gain; A filter coefficient update module, configured to update the coefficients of the adaptive filter according to the constructed scale matrix, and calculate a new error signal value; The noise power estimation module estimates the power of the system noise Shilling the input signal u(n)=0, then the output error e(n) is the system noise v(n); through the method of time averaging, the power of the system noise is obtained The error power estimation module performs error power estimation according to the following steps: 1) Calculate the value of the error signal according to e(n)=d(n)-w ^T (n)u(n) through the input signal u(n) and the expected signal d(n), where w(n)=[w ₁ (n),w ₂ (n),...,w _M (n)] is the coefficient vector of the adaptive filter at time n; u(n)=[u(n),u(n-1),... ,u(n-M+1)] ^T is the input signal vector of the adaptive filter at time n, which is composed of the current sample value of the input signal and its previous M-1 sample values; 2) According to Estimate the power of the output error signal where λ is the smoothing factor; The intermediate variable generation module according to the system noise power and the error signal power according to Get the intermediate variable x(n); The time-varying parameter generation module obtains the time-varying parameter α( n), where α is a compromise parameter; β is the shape parameter of the Sigmoid function; The proportional matrix construction module first follows the time-varying parameters according to g _m (n)=[1-α(n)]/2M+[1+α(n)]|w _m (n)|/[2||w( n)|| ₁ +ε] to obtain the elements of the scale matrix, where m=1,2,...,M-1, w _m (n) is the value of the mth coefficient of the adaptive filter at time n, || ·|| ₁ represents the L ₁ norm, ε is the small positive number introduced; then the elements of the obtained M proportional matrices form a diagonal matrix G(n)=diag[g ₁ (n),g ₂ (n) ,...,g _M (n)], where each diagonal element in G(n) corresponds to the gain g _m (n) of each filter coefficient. 2. variable parameter ratio adaptive filter according to claim 1, is characterized in that described filter coefficient update module according to the ratio matrix that generates according to update formula w(n+1)=w(n)+μG(n)u(n)e(n)/[u ^T (n)G(n)u(n)+δ] to update the coefficient vector of the adaptive filter , where δ is a regularization parameter used to solve numerical difficulties. 3. A variable parameter scale adaptive filter coefficient vector update method, characterized in that said method comprises the following steps: (1) Estimate the power of the system noise when the adaptive filter is static; (2) Carry out the power of time smoothing estimation error signal to the output error signal of adaptive filter; (3) produce an intermediate variable by the power of the error signal and the power of the system noise, and the power ratio of the power of the error signal and the system noise is obtained by calculating the logarithm of the intermediate variable; (4) Convert the intermediate variable through the Sigmoid function to obtain time-varying parameters for the proportional adaptive filter; (5) Calculate the gain of each coefficient from the obtained time-varying parameters, and construct a proportional matrix by the coefficient gain; (6) Update the coefficients of the adaptive filter according to the constructed scale matrix, and calculate a new error signal value; Described method is specifically carried out according to the following steps: (1) Let the input signal u(n)=0, then the output error e(n) is the system noise v(n); through the method of time averaging, the power of the system noise is obtained (2) Perform error power estimation according to the following steps: 1) Calculate the value of the error signal according to e(n)=d(n)-w ^T (n)u(n) through the input signal u(n) and the expected signal d(n), where w(n)=[w ₁ (n),w ₂ (n),...,w _M (n)] is the coefficient vector of the adaptive filter at time n; u(n)=[u(n),u(n-1),... ,u(n-M+1)] ^T is the input signal vector of the adaptive filter at time n, which is composed of the current sample value of the input signal and its previous M-1 sample values; 2) According to Estimate the power of the output error signal where λ is the smoothing factor; (3) According to the system noise power and error signal power according to Get the intermediate variable x(n); (4) Obtain the value of the time-varying parameter α(n) according to α(n)=(2α+2)/{1+exp[-βx(n)]}-(α+2) according to the intermediate variable x(n) , where α is a compromise parameter, and β is the shape parameter of the Sigmoid function; (5) According to the time-varying parameters, g _m (n)=[1-α(n)]/2M+[1+α(n)]|w _m (n)|/[2||w(n)| | ₁ +ε] to obtain the elements of the scale matrix, where m=1,2,...,M-1, w _m (n) is the value of the mth coefficient of the adaptive filter at time n, ||·|| ₁ represents the L ₁ norm, and ε is a small positive number introduced; then the elements of the obtained M proportional matrices form a diagonal matrix G(n)=diag[g ₁ (n),g ₂ (n),…, g _M (n)], where each diagonal element in G(n) corresponds to the gain g _m (n) of each filter coefficient; (6) According to the generated ratio matrix according to the update formula w(n+1)=w(n)+μG(n)u(n)e(n)/[u ^T (n)G(n)u(n)+δ] to update the coefficient vector of the adaptive filter , where δ is a regularization parameter used to solve numerical difficulties.