JPH03154512A - Adaptive digital filter - Google Patents

Abstract

PURPOSE:To improve the tracking performance by updating a filter coefficient according to a specific update algorithm and applying positive uniform random number to a weight coefficient from a fixed value. CONSTITUTION:An input signal x[K] inputted to a main FIR(Finite Impulses Response) filter 13 is subjected to FIR filtering depending on a filter coefficient ai[K] stored in a filter coefficient storage register 15 and the resultant signal is outputted. Moreover, a square calculation part 14 squares the input signal x[K] to calculate x<2>[K] and a sub FIR filter 16 outputs a weighted square calculation result SIGMAalphaix<2>[K-i]. A weight coefficient alphai[K] stored in a weight coefficient storage register 17 is decided based on a positive uniform random number generated from a uniform random number generating section 18. A division section 21 divides a difference between a filter output of the main FIR filter 13 and an output of an unknown system 12 by a value being a sum of a weighted square sum and an offset, a filter coefficient revision section 23 updates the filter coefficient ai[K] and the result is transferred to the main FIR filter 13. Thus, the tracking performance is improved.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to an adaptive digital filter that is applied to an unknown system by varying filter coefficients.

[Conventional technology]

Conventionally, this type of adaptive digital filter uses a third filter.
As shown in the figure, the variable fill coefficient a+ (K
F I R (Finite Impulse Re5p) with "l (1=0.1.2.-・", L)
once) Te”Ijita/l.

Using the filter 11, the filling coefficient a, , (:
K E is the coefficient of unknown system 12, [K)(i
=0°1.2. ......, there is one that converges to L). This assumes that the unknown system 12 is an FIR type digital filter, and the filter coefficient at [K
] is estimated. In this case, the fill coefficient a,
As an algorithm to converge [K] to the coefficient h1 [K] of the unknown system, L shown in the following equation (1) is used.
M S (Least!, (ean 5square
) There is alcoholism.

at [K+l]=a, LK]-2a ゛
ε [Kko ° x[K−iko... (1) Here, α is called the step size, and is a weighting coefficient determined by the trade-off between system stability and convergence speed. be. Further, the limit on the weighting coefficient α for ensuring stability is shown in the following equation 2).

] [Problem to be solved by the invention] However, in the conventional adaptive digital filter, (2)
The weighting coefficient α is determined by satisfying the conditions of the equation and taking into account the stability and convergence speed of the system. However, since the weighting coefficient ′α is fixed, in the case of a tracking adaptive digital filter, the unknown system The disadvantage is that the 12 rose makeup cannot follow sudden changes.

Hereinafter, the drawbacks of the conventional adaptive dicicle filter will be explained with reference to the simulation results shown in FIGS. 4 to 13. In the following description, the order of the filter is assumed to be second order. Therefore, the coefficient ht of the unknown system 12
[:K) Hari. [K], h[K,], h, ['K], and the filter coefficient arc of the adaptive digital filter 11 is
K] is a.

[K], ae [K], a2 [K].

Figures 4 to 8 show the coefficient h+ of the unknown system 12.
Filter coefficient ai (K)(
This shows how the coefficients h and [K] of i=o, l, 2) converge. Figure 4 is α0.11 Figure 5 is α-0.5
, FIG. 6 shows the characteristics when α=140, FIG. 7 shows the characteristics when α-2,0, and FIG. 8 shows the characteristics when α-3,0. As is clear from these, when the weighting coefficient (step size) α is small, the convergence time is long, and when α is large, there is a period of severe oscillation before reaching the steady state as seen in Figure 8, and a, [ An undesirable problem arises in terms of the adaptive operation of [K].

Also, the coefficient hl (K) (i
9 to 13 show the behavior of at (K) and [K] heno tracking in the case where 0.1.2) changes. In FIG. 9, α=0.1, and in FIG. 10, α=0. 5
, α=1.0 in FIG. 11, α=2.0 in FIG.
Figure 3 shows the characteristics when α=3.0.

That is, when α is small, ao [:K) beam. [
K] cannot be followed at all, and even hz [K), which has the slowest temporal change, cannot be satisfactorily followed. When α is large (α = 30), ho (K) can be tracked, but conversely, when the time change is slow (a2 [K1)], h2 [K] cannot be qualitatively tracked. However,
The vertical variation of h2 [K] is increasing.

As described above, in the conventional adaptive digital filter, the weighting coefficient (step size) α is fixed, and in the case of the tracking type adaptive filter, there is a drawback that it cannot follow sudden changes in the parameters of the unknown system.

[Indispensable means to solve problems]

The adaptive digital filter of the present invention includes a main FIR filter that calculates a predetermined filter output based on an input signal, a filter coefficient storage register for storing filter coefficients of the main FIR filter, and a filter coefficient storage register that stores filter coefficients of the main FIR filter.
A square calculation unit that calculates a multiplicative value, a weighting coefficient storage register that stores a weighting coefficient determined by a positive uniform random number, and a weighted sum of squares that is calculated based on the weighting coefficient and the squared value of the input signal. a sub-FIR filter for dividing the error between the filter output of the main FIR filter and the output of the unknown system by a value obtained by adding an offset to the weighted sum of squares; and a filter coefficient updating unit for determining and updating the filter coefficients at the next time point based on the current weighting coefficients and manual values.

[Effect]

As a result, the adaptive digital filter of the present invention changes the weighting coefficient from a fixed value α to a variable value α1, and also determines the filter coefficient using the updating algorithm shown in equation (3) below, so that the followability of the adaptive digital filter is improved. can be improved.

ai [K+1] al [Kl-α, [K1 "ε' [K+1] -x[K+1-il [Example] Hereinafter, an example of the present invention will be described with reference to FIGS. 1 and 2. .

FIG. 1 is a block diagram in which an adaptive digital filter 11 of the present invention is applied to an unknown system 12.

The input signal X[K) to the adaptive digital filter 11 is
The main FIR filter 13 is inputted to the square calculation section 14 and the unknown system 12. Main FIR filter 13
The input signal X[K) input to the filter coefficient a+[K
), and the result is 9 [
Output as Kl. In addition, the square calculation unit 14 squares the input signal x (K) to calculate x' (Kl, and outputs it to the sub-FIR filter 16.
6 is the weighting coefficient α1 stored in the weighting coefficient storage register 17 [Kl] It performs the same operation as the main FIR filter 13, and outputs the result as the weighted sum of squares calculation result Eα,x2 (K-i). Here, the weighting coefficient α1 [Kl
is determined based on positive uniform random numbers generated by the −-like random number generating section 18.

Next, the weighted 2
The multiplicative sum calculation result Σα[K2 (K l:l is obtained by adding the offset value 1.0 from the offset 19 in the adder 20 and manually inputting it to the division unit 21. The calculated output V of the main FIR filter 13 (Kl and the difference between the output y of the unknown system 12 [K:I? [Kl - y CK] is also manually calculated, and the value obtained by adding the offset to the weighted sum of squares ( l+ΣαIx” (
K i]) is the difference between the filter output of the main FIR filter 13 and the output of the unknown system 12 (9[K) −y
Divide f:K) ).

This division result <9 (K)-y [K))/ (1+Σ
αLX2 [K−i)) is input to the filter coefficient updating unit 23. When the filter coefficient updating unit 23 has the manual power of this division result, it loads the value of the current filter coefficient a+ [K) from the filter coefficient storage register 15, and also loads the value of the current weighting coefficient α1 [K] from the weighting coefficient storage register 17.
While loading the value of Kl, the main FIR filter 1
From 3, the human power value X1:K], x CK -1],
Load -LE into -------, x [:. Then, the filter coefficient a+[K
l is updated and transferred to the main FrR filter 13 via the filter coefficient storage register 15.

By performing such an operation every time a new input signal is manually input, the following operation to the unknown system 12 is realized.

FIG. 2 shows the adaptive digital filter 11 shown in FIG.
This is the result of a computer simulation.

As can be seen from this figure, the adaptive filter's tracking of the unknown system 12 is sufficiently improved compared to that of the prior art.

〔Effect of the invention〕

As explained above, according to the present invention, the filter coefficients are updated using the update algorithm shown in equation (3), and the weighting coefficients α and [K] are changed from fixed values to positive uniform random numbers. This has the effect of improving the followability of the adaptive filter.

[Brief explanation of the drawing]

Fig. 1 is a block diagram showing an embodiment of the present invention, Fig. 2 is a characteristic diagram showing the characteristics of the present invention, Fig. 3 is a block diagram showing a conventional example, and Figs. 4 to 13 are characteristic diagrams of the conventional example. FIG. 11...Adaptive digital filter, 12...
...Unknown system, 13...Main FIR filter, 14...
... Square calculation unit, 15 ... Filter coefficient storage register, 6 ...
...Sub FIR system, 7...Register for storing weighting coefficients, 8...
--like random number generator, 9...offset, 20...adder,
1...Division section, 22...Subtractor, 3.
...Filter coefficient update section.

Claims (1)

[Claims] 1. A main FIR filter that calculates a predetermined filter output based on an input signal; a filter coefficient storage register for storing filter coefficients of the main FIR filter; and 2.
a square calculation unit for calculating a multiplication value; a weighting coefficient storage register for storing a weighting coefficient determined by a positive uniform random number; and a weighted sum of squares based on the weighting coefficient and the square value of the input signal. a sub-FIR filter for calculating the weighted sum of squares; a division unit that divides the error between the filter output of the main FIR filter and the output of the unknown system by a value obtained by adding an offset to the weighted sum of squares; An adaptive digital filter characterized by comprising a filter coefficient updating unit for determining and updating the filter coefficient at the next time based on the current filter coefficient, the current weighting coefficient, and the input value. . 2. The adaptive digital filter according to claim 1, wherein the filter coefficient updating section calculates the filter coefficients using the following arithmetic expression. a_i[K+1] = a_i[K]−α_i[K]・ε′[K+1]・x[K
+1-i] {However, ε′ [K+1] = ▲ There are mathematical formulas, chemical formulas, tables, etc. ▼ α_i [K]: Positive uniform random number