JP2541040B2 - Coefficient updating method in adaptive filter device - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a coefficient updating method in an adaptive filter device which is one of digital filters used for noise canceling, system identification and the like.

[0002]

2. Description of the Related Art As an adaptive signal processing algorithm, L
MS (Least Mean Square) algorithm, self-orthogonalization algorithm, RLS (Recurs)
Known is an easteast square) algorithm, a transform domain LMS algorithm that performs an LMS algorithm after orthogonally transforming an input, a learning identification method, and the like.
Among them, the LMS algorithm is inferior to other algorithms in terms of convergence, but it is widely used because of its small calculation amount, simplicity of mechanism, and easy implementation.
Methods have been proposed to improve these characteristics of the algorithm to improve vitality such as convergence and convergence.

A conventional adaptive filter (adaptive digital filter) according to the LMS algorithm method is as shown in FIG.
Data (input signal) x (k) at a fixed sampling period
To the input terminal 1 for inputting the input signal x (k) with one sampling period as a unit delay time. The L delay elements M1 and M2 function as delay means 2 for sequentially delaying the input signal x (k).
ML, L + 1 lines C0, C1 ... CL connected to the input terminal 1 and the output stages of the delay elements M1 to ML, respectively.
To form a multiplier A0, A1 ... AL, an adder 3, a reference signal input terminal 4 as a means for inputting a request signal, that is, a reference signal d (k), and an error signal e (k). Error calculation circuit 5 of FIG. L + 1 (where L is 1
(Positive integers above) L + 1 input signals x at different sampling times obtained simultaneously on the lines C0 to CL
(K), x (k−1), x (k−2) ... x (k−L) are input to the multipliers A1 to AL, and the coefficients w ₀ (k),
w ₁ (k) ... W _L (k) are multiplied and output x (k) w
₀ (k), x (k−1) w ₁ (k) ... x (k−L) w _L
(K) is obtained, and these are added by the adder 3 to output y
(K). The output y (k) is input to the error calculation circuit 5, and the error output e corresponding to the difference from the reference signal d (k) is output.
(K) occurs. Note that y (k) and d (k) can be expressed by the following equations (1) and (2). _{y (k) = w 0 (} k) x (k) + w 1 (k) x (k-
1) ... + w _L (k) x (k−L) (1) e (k)
= D (k) -y (k) (2) The vector expression of the expression (1) representing y (k) is the following expression (3), and the vector expression of the signals on the lines C0 to CL is the following expression (4). The vector expression of the coefficient is expressed by the following expression (5), and the vector expression of the expression of the error signal e (k) is expressed by the following expression (6). Note that T in the expressions (3) to (6) represents the transposition of the vector.

[0004]

Although not shown in FIG. 1, in the conventional adaptive filter, the coefficient w is calculated based on the error signal e (k).
The updated values of ₀ (k), w ₁ (k) ... W _L (k) are calculated. The following equation (7) shows the coefficient update of the adaptive filter by the conventional LMS algorithm.

[0006]

The average value of the coefficients of the adaptive filter converges to the Wiener solution when the following conditions are satisfied. 0 <μ <1 / λmax (8) where λmax is the maximum eigenvalue of the correlation matrix of the input signal xk.

[0008]

In the LMS algorithm, the step size needs to be set large in order to speed up the convergence, but the step size must be set sufficiently small in order to ensure the convergence and the desired convergence is obtained. Getting sex is often difficult.

Therefore, an object of the present invention is to provide a method for accelerating convergence in an adaptive filter device.

[0010]

According to the present invention for achieving the above object, a reference signal d is provided at a predetermined sampling period.
(K) reference signal supply means for supplying (where k is time) , and an input signal x related to the reference signal
An input signal supply means for supplying (k) at a predetermined sampling cycle, the reference signal supply means and the input signal supply means are connected, and the input signal is sequentially delayed with one sampling cycle as a unit delay time. Therefore, L + 1 from 0th to Lth at different sampling points
(Where L is a positive integer of 1 or more ) input signals are obtained at the same time, and 0th to Lth coefficients {w ₀ (k), w ₁ (k) ... Are added to the 0th to Lth input signals. w _L (k)}, and a digital filter signal processing circuit for obtaining an output signal y (k) obtained by adding L + 1 multiplication outputs obtained by the multiplication, thereby updating the coefficients. A method of performing, based on the reference signal d (k) and the L + 1 input signals at time k, T _ij (k) = − 2x (k−i) x (k−j) I _i (k ) = 2d (k) x (k-i) {where i and j are L + 1 variables for distinguishing 0 to L, respectively, and k is a symbol indicating sampling time. , T ij _(k) is a first value for use in updating calculation of each coefficient , Including the same value (L +
1) ^Two values are shown, I _i (k) is a second value used in the update operation of each coefficient, and shows L + 1 values, x
(K-i) indicates L + 1 first input signals sequentially selected from the L + 1 input signals obtained at the same time,
x (k-j) indicates L + 1 second input signals sequentially selected from the L + 1 input signals obtained at the same time}, and T _ij (k), I _i (k) and the plurality of coefficients w _{0 at} time k
(K), w ₁ (k) ... W _L (k) {Where i is L + 1 variables from 0 to L, j is L + 1 variables from 0 to L, and n is one sampling period from the sampling time k to the next sampling time k + 1. Is a variable indicating the number of internal update operations in, and w _in−1 (k) indicates the coefficient value before each update in the n + 1 internal update operations of L + 1 coefficients from the 0th to the Lth, respectively, and w in _in (k) indicates the coefficient value after each update in the n-th internal updating operation of L + 1 coefficients from the 0th to the Lth, μ indicates the step size, and w _jn-1 (k) indicates the update In the period from the time k to the next sampling time k + 1, n internal updating operations (where n is a positive integer of 2 or more) are performed according to the arithmetic expression represented by the preceding L + 1 coefficient} The internal update coefficient value of Those relating to the coefficient updating method in the adaptive filter apparatus characterized by a second step of a coefficient value at sampling time k + 1.

In the coefficient updating method according to the present invention, attention is paid to the similarity between the Hopfield model, which is one of neural networks, and the LMS method, and the coefficient is independent of the error signal e (k). Update. FIG. 2 shows the Hopfield model. The Hopfield model is a neural network formed by mutual coupling of non-linear units called neurons that output "0" or "1". The operation of the units in the Hopfield model is discrete or continuous, and the strength of mutual coupling between the units is symmetric. The input Ui to the unit i is expressed by the following equation (9).

[0012]

Here, N is the number of units in the Hopfield model, T _ij is the strength of coupling between units, and I _i is the bias value of unit i.
In the model in which the operation of the unit is discrete, the output V _{i of the} unit i is updated as in the following Expression (10). V _i (k + 1) = 1, (U _i (k)> 0 or U _i (k) = 0) V _i (k + 1) = 0, (U _i (k) <0) (10) Strength of mutual coupling It has been shown that if T _ij has symmetry (T _ij = T _ji ), the energy of the network expressed by the following equation decreases with the movement of the network and reaches the minimum point.

[0014]

As a numerical expression method by a unit when applying the Hopfield model to a numerical problem, a numerical value is expressed by a sum of units, and several groups representing one numerical value are provided to make the sum within each group. A method of expressing by weighting each group has been proposed. Here, a new unit i at time k is newly added.
Consider a model in which the output of is the sum of the function g [U _i (k)] at time k and the output V _i (k−1) of unit i at time (k−1).

[0016]

Considering the correspondence with the LMS algorithm, g (x) = 1, (x> 0 or x = 0) g (x) = − 1, (x <0) (13) is used as the function g. I will. The energy of the network defined in this way is represented by the following equation, as in the Hopfield model.

[0018]

At the energy shown in the equation (14), the output of the unit i is V-1 from k-1 to time k.
_The amount of change in energy when changing from _i (k-1) to V _i (k) is given by the following equation.

[0020]

From the relation of the equation (13), it can be seen that the amount of change in energy is always negative and the energy of the network decreases with the operation of the network. Expression (1
The model shown in 2) is used for the adaptive filter shown in FIG. Strength of network mutual connection T _ij and bias I
To obtain _i , the energy equation (14) of the network
The square of the error signal e (k) shown in Expression (6) is used as the energy of the adaptive filter corresponding to.

[0022]

The energy E in equation (16) is the time k.
It is a quadratic function of the coefficient of the adaptive filter in and has a single minimum value. By comparing the equations (14) and (16), the strength T _ij of the mutual coupling of the network and the bias I _i
Is given by T _ij (k) = − 2x (k−1) x (k−j) I _i (k) = 2d (k) x (k−1) (17) The term of d ² (k) in the equation (16). Is a constant term and can be ignored. Using equation (17), repeating V according to equation (12)
By calculating _i , it can be seen that the coefficient W _i of the adaptive filter corresponding to V _i changes in the direction of decreasing the energy defined in equation (16). However, in this model, the amount of change in the coefficient is limited to +1 and -1, so sufficient convergence cannot be obtained.

From the similarity between the model shown in equation (12) and the LMS algorithm, it is shown that the LMS algorithm can be expressed using the mutual coupling strength T _ij and the bias I _i shown in equation (17). We propose a new LMS algorithm that updates the coefficients of the adaptive filter multiple times using the strength T _ij and the bias I _i . The LMS algorithm is given by the following equation by substituting equation (6) into equation (7) and rearranging.

[0025]

The second term on the right side of the equation (18) corresponds to the mutual coupling strength T _ij and the bias I _i shown in the equation (17). A new LMS that adds the operation in the Hopfield model to the conventional LMS algorithm shown in equation (18)
Propose an algorithm. That is, (1) The mutual coupling strength T _ij (k) and the bias I _i (k) shown in the equation (17) are calculated based on the data at the time k.
(2) Similar to the operation of the Hopfield model, T _ij
The coefficient is updated n times using (k) and I _i (k). The last updated coefficient is the coefficient at time k + 1. In the table, it is assumed that the coefficient is updated 10 times (n = 10), and the coefficient w _im (k) is m as the i-th coefficient at time k.
The coefficient is obtained by repeating the operation of the time Hopfield model.

[0027]

In the new LMS algorithm, the value of the coefficient corresponding to the unit of the Hopfield model is given by the equation (1
It does not perform the discrete operation as shown in 3), but takes a continuous value. That is, a linear function that monotonically increases is used as the function g shown in Expression (13). At this time, the output of the unit i represented by the equation (15) is time k−
It can be seen that the change in energy when changing from 1 to time k is always negative or zero because the function g is monotonically increasing.

[0029]

The new LMS algorithm is compared with the conventional LMS algorithm, and its convergence and the range of the converged step size μ are examined. The proposed algorithm is based on real-time processing, the processing time is limited, and the number of times the coefficient wk is updated by the operation of the Hopfield model is limited. The algorithm shown in the table, the following relationship holds between the coefficient W _{k + 1} is determined by the update of coefficients W _k and n times.

[0030]

Here, "I" represents an identity matrix. When the value of the step size μ is small, the following approximation holds.

[0032] From this, the equation (19) is given by the following equation.

It can be seen that in the equation (22), the step size μ is several times (n times) the number of repetitions as compared with the equation (18), and the convergence is improved. When the step size μ is sufficiently small, the coefficient estimated by the proposed algorithm has a step size of “nμ” in the equation (18).
It can be seen that the coefficient is equivalent to As the range of the step size μ in which the adaptive filter converges, the absolute value of the first term on the right side of Expression (19) may be smaller than 1. That is,

[0034]

From this, the range of the step size μ to which the new LMS algorithm converges is 0 <μ <1 / λmax (24) as in the conventional LMS algorithm.

Regarding the time constant, the conventional LMS and the L of the present invention are used.
Comparing MS, the time constant of conventional LMS is 1/4 μλ
In contrast, the time constant of the LMS of the present invention is 1/4 μn
λ, which is 1 / n.

[0037]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Next, an adaptive filter device according to an embodiment of the present invention will be described with reference to FIG. However, in FIG. 3, the same parts as those in FIG. 1 are designated by the same reference numerals and the description thereof will be omitted. The noise canceling circuit of FIG. 3 comprises a transversal type adaptive filter 10 and a comparison circuit, that is, an error calculation circuit 5. In reality, all or part of them is configured by a computer or a digital signal processing device, but is shown as a tapped delay line filter or transversal filter for easy understanding. In FIG. 3, using the error signal e (k), the coefficients w ₀ (k), w ₁
(K) ... Instead of updating w _L (k), the input signal x
Each coefficient is updated using (k) and the reference signal (request signal) d (k). Therefore, the signal input terminal 1 and the reference signal input terminal 4 are connected to the data processing circuit 11, and the output lines from 0 to L of the data processing circuit 11 are connected to the multipliers (coefficient multipliers) A0 to AL. There is. The data processing circuit 11 outputs 1 every 1 sampling cycle of the input signal x (k).
Output the coefficient updated at the rate of times. However, the data processing circuit 11 performs calculation for internal update n times during one sampling period, and the last internal update value is multiplied by the multipliers A0 to AL.
Give to. The method of updating the coefficient is as described in the section of the means for solving the invention.

Next, for ease of understanding, a method for updating the two coefficients w ₀ (k) and w ₁ (k) as shown in FIG. 4 will be described. In FIG. 4, an input signal (digital data) x (k) is input from the input terminal 1 at a constant sampling cycle. The signal x (k-1) input earlier by one sampling period is output to the output line C1 of the unit delay element M1. Therefore, at a certain time k, the first and second input signals x (k) and x (k-1) are simultaneously obtained on the lines C0 and C1. Multiplier A
0, A1 is the first for the first and second input signals x (k), x (k-1) having different sampling times.
And the second coefficients w ₀ (k) and w ₁ (k) are multiplied to obtain outputs x (k) w ₀ (k) and x (k−1) w ₁ (k), which are added together. Output signal y (k)
become. The first and second coefficients w ₀ (k) and w ₁ (k) are updated once in one sampling cycle. The coefficient to be updated is not determined in one update operation but is determined after performing the internal update operation a plurality of times (n times). Now, in order to facilitate understanding, the number of internal updates in one sampling period is set to 2
I will explain as times.

First, in the first step, the reference signal d (k) at time k and the first and second input signals x
Based on (k) and x (k-1), -2x (k) x (k) (hereinafter referred to as T00 (k))
-2x (k-1) x (k) (hereinafter referred to as T01 (k)), -2x (k) x (k-1) (hereinafter referred to as T10 (k)), and -2x (K-1) x (k-1) (hereinafter referred to as T11 (k)), 2d (k) x (k) (hereinafter referred to as I0 (k)), and 2d (k) x (k -1) (hereinafter referred to as I1 (k)).

In the second step, T00 (k), T01 (k), T10 determined in the first step
(K), T11 (k), I0 (k), I1 (k), and the first and second coefficients w at the first sampling time k.
₀ (k), w ₁ (k) and the step size μ to determine a new first coefficient w ₀ (k + 1) for use at the next sampling time k + 1, the first internal The updated value w ₀₁ (k) is replaced with w ₀₁ (k) = w ₀₀
(K) + μ {T00 (k) w ₀₀ (k) + T01 (k)
w ₁₀ (k) + I0 (k)}.
Further, in order to determine the second coefficient w ₁ (k + 1) at the next sampling time k + 1, the first internal update value w ₁₁ (k) is calculated as w ₁₁ (k) = w ₁ (k) + μ.
{T10 (k) w ₀₀ (k) + T11 (k) w
₁₀ (k) + I1 (k)} is calculated. Next, the second internal update value w ₀₂ (k) of the first coefficient is
w ₀₂ (k) = w ₀₁ (k) + μ {T00 (k) w ₀₁
(K) + T01 (k) w ₁₁ (k) + I0 (k)}. In addition, the second internally updated value w ₁₂ (k) of the second coefficient is calculated as w ₁₂ (k) = w
₁₁ (k) + μ {T10 (k) w ₀₁ (k) + T11
(K) w ₁₁ (k) + I1 (k)} is calculated. After the second internal update is completed, the second coefficient is set as the first and second coefficients at the next sampling time k + 1.
The second internally updated values w ₀₂ (k) and w ₁₂ (k) are sent to the multipliers A0 and A1, and the first sampling value at the next sampling time k + 1
And the second input terminals x (k + 1) and x (k).

Now, the first and second coefficients at the next sampling time k + 1 are determined by the two internal updates, but in reality, n internal update operations more than two times are performed in the first and second internal update operations. It is desirable to perform the determination in the same manner as the internal update calculation of the number of times. If the internal update is performed twice, the time constant will be
2, the convergence is improved. When the internal updating is performed n times, the time constant becomes 1 / n of that of the conventional method, and the convergence is similarly improved.

The convergence of the adaptive filter device of this embodiment was confirmed by the method shown in FIG. In FIG. 5, first and second input terminals 1a and 1b and an adder 1c are provided in front of the input terminal 1, and a sin (2πk / N) sinusoidal signal is input from the first input terminal 1a. Random noise (white noise) r (k) having an average of 0 and a variance of 0.01 is input from two input terminals 1b, and these are added to form an input signal x (k). As the request signal, that is, the reference signal d (k), 2cos (2πk)
/ N) is input from the terminal 4.

FIGS. 6 and 7 show changes in the coefficients w ₀ and w _{1 in} an analog manner in the system according to the present invention in FIG. 5, and FIG.
Is 1 in one sampling period based on the error signal e (k).
The change in the coefficient of the conventional method that updates only once is shown. The sample numbers on the horizontal axis in FIGS. 6, 7, and 8 are sample numbers after 0 when the sample number at time k is 0. Therefore, the horizontal axis indicates time. FIG. 6 shows coefficient changes when the step size μ is 0.01 and the number of internal updates n is 10, and FIG. 7 shows coefficient changes when the step size μ is 0.1 and the number of internal updates n is 10, FIG. 8 shows a conventional coefficient change when the step size μ is 0.1, which is the same as in FIG. As is clear from the comparison between FIG. 6 and FIG. 7, in the adaptive filter according to the present invention, the step size .mu.
Even with / 10, the convergence does not decrease. Further, as is clear from the comparison between FIG. 7 and FIG. 8, when the step size μ is the same as the conventional one, the convergence is greatly improved. That is, FIG.
In the conventional method, the sample number converges at about sample number 500, whereas in FIG. 7 according to the present invention, the sample number converges at about sample number 50. Therefore, the time constant becomes 1/10, and the convergence is significantly improved. In FIG. 7, the convergence (convergence) is improved, but the coefficient variation (error) increases. Therefore, the present invention exerts a great effect in a system in which convergence must be prioritized over this coefficient error. Further, in order to reduce the influence of the coefficient error shown in FIG. 7, the number of internal updates n of the coefficient can be increased or decreased according to the degree of convergence of the adaptive filter. That is, the number of internal updates n of the coefficient is greatly increased during the adaptation process (at the time of rising), and n is decreased after the convergence.

The present invention can be applied to various application fields of adaptive filters such as modeling (system identification) other than noise canceling and adaptive prediction.

[0045]

As is apparent from the above, according to the present invention, the convergence of the adaptive filter can be improved.

[Brief description of drawings]

FIG. 1 is a block diagram showing a conventional adaptive filter.

FIG. 2 is a block diagram showing a Hopfield model.

FIG. 3 is a block diagram illustrating an adaptive filter according to an exemplary embodiment of the present invention.

FIG. 4 is a block diagram showing the simplest adaptive filter according to the present invention.

FIG. 5 shows a circuit for checking the convergence of an adaptive filter according to the present invention.

FIG. 6 is a diagram showing in analog form the coefficient change when the step size is 0.01 and the number of internal updates is 10 in the circuit of FIG. 5;

FIG. 7 is a diagram showing in analog form the coefficient change when the step size is 0.1 and the number of internal updates is 10 in the circuit of FIG. 5;

FIG. 8 is a diagram analogically showing the coefficient change when the circuit of FIG. 5 has a step size of 0.1 and coefficient update is performed only once based on the error signal e (k).

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 signal input terminal 2 delay means 3 adder 4 reference signal input terminal 11 coefficient update data processing circuit A0 to AL multiplier

(Equation 3)

[Equation 11]

Claims (1)

(57) [Claims] 1. A reference signal d at a predetermined sampling period.
(K) reference signal supply means for supplying (where k is time) , input signal supply means for supplying an input signal x (k) related to the reference signal at a predetermined sampling period, The input signal is connected to the reference signal supply means and the input signal supply means, and the input signal is sequentially delayed with one sampling period as a unit delay time, so that 0 + 1 to L + 1 different sampling points are provided (however, L + 1). Is 1
The above-mentioned positive integer) input signals are simultaneously obtained, and the 0th to Lth input coefficients {w are added to the 0th to Lth input signals.
Outputs obtained by multiplying ₀ (k), w ₁ (k) ... W _L (k)}, respectively, and adding L + 1 multiplication outputs obtained thereby.
A method for updating the coefficients in an adaptive filter device having a digital filter signal processing circuit for obtaining a signal y (k), the method being based on the reference signal d (k) and the L + 1 input signals at time k. , T _ij (k) = − 2x (k−
i) x (k−j) I _i (k) = 2d (k) x (k−i) {where i and j are L + 1 variables for distinguishing 0 to L, respectively. Where k is a symbol indicating the sampling time, T _ij (k) is the first value used in the update calculation of each coefficient, and includes the same value (L +
1) ^Two values are shown, I _i (k) is a second value used in the update operation of each coefficient, and shows L + 1 values, x
(K-i) indicates L + 1 first input signals sequentially selected from the L + 1 input signals obtained at the same time,
x (k-j) indicates L + 1 second input signals sequentially selected from the L + 1 input signals obtained at the same time}, and T _ij (k), I _i (k) and the plurality of coefficients w ₀ (k), w ₁ (k) ... W at time k
Based on _L (k), {Where i is L + 1 variables from 0 to L, j is L + 1 variables from 0 to L, and n is one sampling period from the sampling time k to the next sampling time k + 1. Is a variable indicating the number of internal update operations in, and w _in−1 (k) indicates the coefficient value before each update in the n + 1 internal update operations of L + 1 coefficients from the 0th to the Lth, respectively, and w in _in (k) indicates the coefficient value after each update in the n-th internal updating operation of L + 1 coefficients from the 0th to the Lth, μ indicates the step size, and w _jn-1 (k) indicates the update In the period from the time k to the next sampling time k + 1, n times (where n is 2
A second step of performing an internal update operation of the above positive integer) and setting the n-th internal update coefficient value to the coefficient value at the next sampling time k + 1. .