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FIELD OF THE INVENTION The present invention relates to the art of adaptive identification. In
particular, but not exclusively, it is suitable for use with echo cancelers used for
BACKGROUND OF THE INVENTION The linear adaptive identification featured by impulse
response has been widely studied and many algorithmic solutions have been proposed in expert
The general problems that apply in many cases of practical application when identifying directly
by transversal adaptive filtering are considered.
FIG. 1 illustrates a system 10 to be identified, which is provided with a signal xt that changes
over time.
The response of system 10 to input signal xt is written as zt.
The measurement of the response zt is necessarily performed by adding an interference
component bt called observation noise. This observation noise bt, although it may contain noise
(for example, white noise or traffic noise) to be precise, also includes a useful signal. The
component bt interferes with the observation of the response zt and is called observation noise.
The adder 12 in the drawing represents that the component bt considered to be an additive is
overlapped with the component zt. The measured observation signal yt is thus the response of
the real system 14 with the system 10 to be identified and the adder 12.
The adaptive identification device 16 receives an input signal xt at a first input E1 and receives
an observation signal yt at a second input E2. The signals xt and yt are amplified, filtered and
digitized at the input of the device 16 by conventional elements not shown. The adaptive
identification unit 16 comprises an identification filter comprising a programmable filter having a
finite impulse response (FIR) expressed as Ht-1T = (ht-10, ht-11, ..., ht-1L-1). There are 18 and
here (. ) T represents a transposed matrix. (In the present specification, the above-described
formula represents, and the same applies hereinafter. The coefficients of the identification filter
18 are adapted such that this impulse response Ht-1T is representative of the impulse response
of the system 10 to be identified. The filter 18 receives the digitized input signal xt and estimates
the response zt of the system 10 * zt (herein the above expression represents and so on) give.
The subtractor 20 removes the estimate * zt from the digitized observation signal yt, which gives
an error signal et, which can be viewed as an estimate of the interference component bt.
The updating unit 22 of the identification filter adapts the coefficients of the filter 18 based on
the input signal xt and the error signal et, generally taking into account the adaptation phase μ.
A number of algorithms have been proposed to automatically determine the coefficients of
adaptive filter 18.
For practical use, the creators of these devices have often been forced to seek a compromise
between algorithmic speed, which is easy to control and implement, and mathematical
complexity and numerical stability. .
The LMS (least squares method) algorithm is the most widely used algorithm to adapt the
impulse response of the FIR identification filter continuously over time.
Such an algorithm efficiently implements a Wiener filter with L coefficients, which minimizes the
average value of the power of the filter error in the stochastic approximation. It is defined by the
following equation. et = yt−XtTHt−1 (1) Ht = Ht−1 + μetXt (2) where Xt = (xt, xt−1,..., xt−L +
1) T is the last L pieces of the input signal Represents a vector of samples of and μ represents
the adaptation phase of the algorithm. The main advantages of this algorithm are that it is
numerically less complex, easy to implement and robust against errors. Unfortunately, when
highly interrelated signals (such as speech signals) are used to excite unknown systems, this
algorithm rapidly degrades in convergence speed.
To avoid these problems, special ones of the LMS algorithm are often used, incorporating an
adaptive phase that can modify the parameters. This algorithm corresponds to LMS normalized
or NLMS (<< Least Normalized Least Squares>), where the coefficients of the adaptive filter are
updated according to the following equation.
The optimum filter H opt of the unknown system 10 is an FIR filter of an order lower than L but
equal, and equation (3) becomes the following equation. ΔHt = [I-μXt (XtTXt) -1XtT] ΔHt-1TμXt (XtTXt) -1 bt where Ht = Hopt-Ht represents an error in the estimated value of the filter
coefficient at repetition t . This equation corresponds to the geometrical interpretation of the
NLMS algorithm. In the case of μ 式, Eq. (4) spans the affine subspace, which is entirely
determined by the matrix between the brackets and knowing the first shift given by the last term
of Eq. (4) , Corresponding to the relaxed projection of the vector ΔHt−1.
Several attempts have been presented with non-table materials (frequency domain and subband
filter implementations) to derive new algorithms that converge faster than the NLMS algorithm.
In the following, as in the case based on using a fluorescence filter, we will see the case based on
changing the direction of projection of the NLMS.
The convergence of the NLMS can be improved by changing the direction of projection, as
described above. This analysis is based on the affine projection algorithm (APA), which is based
on projections of many orders equal to P. As a result, the algorithm obtains better convergence
properties for interrelated signals compared to the NLMS algorithm (corresponding to the special
case of P = 1). P. Next APA algorithm (K. Oseki et al., Telecommunication Journal in Japan, 1984,
67-A, n. The characteristics are determined by updating the coefficients of the identification filter
18 according to the following equation: see p. 19-27 "Adaptive algorithm using orthogonal
projection to affine subspace and its characteristics". et, P = Yt, P-& Xt, PHt-1 (5) Ht = Ht-1 + μ &
Xt, P # et, P (6) where & Xt, P = (Xt, Xt-1, ..., Xt- P + 1) T (7) Yt, P = (yt, yt-1, ..., yt-P + 1) T (8) (In
the present specification, the above & X represents , And the same expression below. In the
above, et, P denotes a leading error vector, & Xt, P # = X X PT PT PT PT (& Xt, P & Xt, PT) -1 is
the inverse of the Moore-Penrose matrix of L × P in general. Represents With these equations
for updating the coefficients of the identification filter, the estimates of the subsequent error
vectors et, Ppost are then equal. et, Ppost = Yt, P- & Xt, PHt = (1-μ) et, P (9)
Assuming that the adaptation phase of the algorithm is single, the Pth-order affine projection
algorithm cancels out the P subsequent errors defined in equation (9). This latter property
explains whether the convergence behavior of the algorithm is very good. Unfortunately, in the
basic one described in equations (5), (6), the theoretical complexity of such an algorithm is of the
order of 2 LP + KinvP2, where Kinv is the equation (6) And the parameters L and P represent the
number of coefficients of the identification filter and the order of the projection, respectively.
In order to reduce this initial complexity, several fast versions of these algorithms are presented,
which deal with splitting up similar autocorrelation matrices in a manner similar to the fast
recursive least squares algorithm. Have. Such techniques can reduce the initial complexity to a
more reasonable value of 2L + 20P next (see below). Steven L. Gay 高速 Fast Convergence and
Low Complexity Adaptive Filter Algorithm Proc Proceedings of the 3rd International Workshop
on Acoustic and Noise Control, Plestin-Les-Greves, France 1993-223-226, Steven L. Gay G Speech
Projection Algorithm Applied to the Echo Cancellation of Speech》 Ph.D. Dissertion of the State
University of New Jersy 1994, Steven L. Gay et al. 高速 High-speed affine projection algorithm》
ICASSP '95 Proceedings, pp. 3023-3026, 1995 Year, by M. Montazeri, “Une Famille
d'algorithmes adaptatifs comprenant les algorithmes NLMS et RLS: application a l'annulation
d'echo acoustique”, These de Doctorat de l'Universite de Paris Sud, 1994, M. Tanaka et al.
Reduction of computation for high-order projection algorithm》 The Fall Seminar of the Institute
of Electronics, Information and Communication Engineers, Tokyo, 1993)
Numerous research papers have been submitted on how to improve the performance of adaptive
identification systems using predictive composition. (See below M. Mbup et al. “LMS coupled
adaptive prediction and system identification: statistical models and transition analysis” IEEE
Transactions on signal processing, 42 n. 10, October, 2607-2615, S. Benjebara, Caracteristiques
des signaux et capacite de poursuite des non-stationnarites aleatoires: apport des schemas
predictifs et multiresolutions TheThese de l'Ubiversite des Sciences, des Techniques et de
Medecines II, Tunis, 1997). Case studies have been able to illustrate two main configurations
(symmetrical or asymmetric) for prewhitening the filter's excitation signal using adaptive filter
techniques. The general principle as to whether an asymmetric configuration is processed is
illustrated in FIG.
This type of configuration essentially changes the signal used to update the coefficients of the
adaptive filter and adjusts the autocorrelation matrix (the maximum and minimum of the
eigenvalues of the autocorrelation matrix of this signal). Based on empirical methods aimed at
converting to reduce the ratio). As a result, the coefficients are updated by the adaptation module
22 with the signal available at the output of the linear prediction circuit 24, where a prediction is
performed from the M coefficients. The algorithm provided by the module 22 to update the L
coefficient of the identification filter 18 corresponds to LMS (eq. 2) or NLMS (eq. 3). Similarly,
the prediction circuit 24 is implemented as an adaptive filter with M coefficients obtained and
updated with the LMS algorithm.
Studies to analyze the performance obtained from this type of configuration particularly
emphasize that there is a very strong correlation between the prediction module and the
adaptation module of the system. In particular, this leads to an adaptation of the coefficient
adaptive formula of the adaptive predictor 24 and that of the identification filter 18. This strong
link also appears in the choice between the two adaptation stages, μP and μH, which creates
regions of very low stability of the overall configuration.
As a result, the author mentions the instability of the overall predictive configuration
identification system, but it limits the prediction order used when always using values less than 4
to ensure relative stability. In addition, therefore, identification performance is limited. It is
necessary to choose low adaptation stages μP and μ which are not compatible with the purpose
of improving the convergence speed.
The following conclusions can be drawn when looking at the solutions presented in the literature
for improving the convergence speed of adaptive identification algorithms. One is that the
algorithm based on updating the projection direction is still complicated, in that many
mathematical processes are needed to update the filter coefficients when the projection order P
is high The other is in terms of controlling and providing a reduced gain in convergence since the
prediction order M actually used is low to ensure that the overall configuration remains relatively
stable. Predictive configuration identification is still very cumbersome.
The object of the present invention is to provide a method of adaptive identification which has
good convergence properties and which is relatively easy to realize, but of limited mathematical
SUMMARY OF THE INVENTION Accordingly, the present invention provides an adaptive
identification method for estimating the response of a system to an input signal, comprising the
steps of:
Receiving, on the one hand, the input signal and, on the other hand, the observation signal which
is partly a response to the input signal, and, at the time t, determining the error signal et
according to the equation et = yt-XtTHt-1; Adapting the L coefficient of the discrimination filter
taking into account the input signal and the error signal, where yt represents the value of the
observed signal at time t, and Ht-1 is the value of the system A column vector consisting of L
coefficients of an identification filter (18) having a typical finite impulse response of an impulse
response, and XtT = (xt, xt-1,..., Xt-L + 1) represents time t and It is a row vector consisting of
values xt, xt-1,..., Xt-L + 1 of input signals at preceding time L-1. By means of the invention, the
prediction parameters of the input signal are observed, where the energy of the prediction
residue on successive frames of the input signal is minimized and the L coefficient of the
discrimination filter is {et / (XtTUt + λ)} Ut. Is adapted to be applied by adding it to a column
vector Ht-1 proportional to where Ut is a column vector consisting of the L values of the
predicted residual of the input signal at time t and the time L-1 preceding it, Is a positive or zero
In the preferred embodiment that provides this method,-the frame of the input signal has a
duration of at least 5 ms. The frames of the input signal have mutual overlap. The input signal is
analyzed by P-1 linear prediction, preferably equal to 5 or more orders, and the column vector U
t is given by: where the term aq is the linear of the above analysis It represents the prediction
factor. The order P-1 of linear prediction is also a function of the constancy of the input signal by
guessing. The input signal is a speech signal reconstructed by the decoder from the input binary
sequence, the prediction parameters of the input signal being extracted by the decoder from the
input binary sequence, and the identification filter It is also possible to provide a prediction
residue to adapt the L factor of.
Another aspect of the invention relates to an adaptive identification device for a system, to which
the input signal is provided, the first input receiving the input signal, and one of the elements
therein being the input signal A second input receiving the observed signal, the identification
filter having a finite impulse response of the system, and a subtractor producing the error signal
et represented by equation (1) above; , Where the energy of the predicted residual on successive
frames of the input signal is minimized, means for obtaining the prediction parameters from the
input signal, and the column vector Ht-1 proportional to {et / (XtTUt + λ)} Ut And adaptation
means for updating the L coefficient of the identification filter.
Another aspect of the invention relates to an adaptive echo canceler for removing the echo
component of a direct signal from a return signal, the first input receiving the direct signal as an
input signal, and the observation signal as a return signal. , And a second input, the error signal
being characterized in that it constitutes the output signal of the echo canceler.
Other features and advantages of the present invention will become apparent from the following
example of embodiment.
The features are given by way of example and are not limiting in any respect, and reference is
made to the accompanying drawings in which:
-Figures 1 and 2 described above are block diagrams of adaptive identification devices known
from the prior art. -Figure 3 is a block diagram of an echo canceler which can be combined with
the adaptive identification device presented by the present invention. -Figure 4 is a block
diagram of another embodiment of the echo canceller presented by the present invention.
In the case of a stationary signal, the P-1 linear prediction coefficients a 1,. The following
equation can be defined among (the matrix & Xt, P is defined by equation (7)).
Assuming that an APA algorithm of order P, defined above, has an adaptation stage μ = 1, by
canceling the following error (equation (9)) the leading vector (5): et, P = (et, 0, ..., 0) Simplify T,
and the adaptive formula (6) of the identification filter is as follows, considering equation (10).
Ht = Ht-1 + (et / XtTUt) Ut (12)
Based on this, a variant of the APA algorithm of order P can be defined, hereinafter called
“provisional APA algorithm of order P”, where the adaptation stage μ is selectively positive
normalization constant λ Will be reintroduced. The error signal in the tentative APA algorithm is
defined by equation (1), and the identification filter is updated according to: Ht = Ht-1 + {μet /
(XtTUt + λ)} Ut (13)
The adaptation phase μ is usually between 0.1 and 1 and λ ≧ 0. There are two differences in
the provisional APA algorithm of order P compared to the linear reference identification scheme
described above. The prediction factor aq is not evaluated at the speed of the sample but at the
speed of the block. They correspond to minimizing linear prediction energy on a frame with N
sample sizes. Predictor filter coefficient set {aq; q = 1,. . . , P-1}, effective implementation
techniques can be used. The equation (13) used to update the coefficients of the identification
filter Ht-1 does not correspond to that used in the studies already performed. In fact, it relies on
an empirical approach aimed at whitening the excitation signal to improve the rate of mode
convergence, which corresponds to the adjustment of the autocorrelation matrix of the excitation
signal. As a result, the LMS or NLMS algorithm presented by the author as a means of updating
the coefficients of the identification filter (and also of the predictor) does not correspond to that
of equation (13). These algorithms depend on the normalization period included in the equation
used to update the filter coefficients, and the term expressed as (UtTUt) -1 in LMS is decoded in
equation (13) It is replaced by the term (XtTUt) -1 or (XtTUt + λ) -1.
The method presented by the present invention solves the problems often caused by the strong
correlation of the signals to be processed. In fact, in the latter case, conventional algorithms tend
to lose good convergence properties. By means of the method presented by the present
invention, these good convergence properties can be uniquely preserved and occur in fact
frequently, even with very highly correlated signals. Limited arithmetic complexity to be stored is
also possible, and implementing these identification algorithms in real time by a digital signal
processor is a great advantage.
The tentative APA algorithm forms the basis of a new set of adaptive identification devices that
can be used in various fields (echo canceller, propagation channel equalizer automatic processing
control, etc). In the case of automatic echo cancellation, this will be discussed below using a nonlimiting example.
canceler in combination with the adaptive identification device 16 proposed by the present
invention. The echo canceler is combined with a hands-free telephone system. The input signal xt
received at the input E1 of the device is a direct signal aimed at the loudspeaker 11 of the handfree system. The observation signal yt received at the input E2 of the device is a return signal
picked up by the microphone 13 of the hand-free system. The observed signal yt contains the
reverberation component from the direct signal and the disturbance component bt which may
contain noise and speech emitted by the loudspeaker. This is the case if the system to be
identified consists of an echo path or a path between the loudspeaker 11 and the microphone 13.
The output signal from the echo canceler is the error signal et provided by the subtractor 20
from the observed signal yt and the echo estimate * zt produced by the discrimination filter 18.
The time window of the input signal xt is at least the last L samples xt, xt-1,. . . , Xt−L + 1 are
managed by the module 30.
These L samples forming the vector Xt are (i) an identification filter 18 which filters according to
the last term of equation (1), and (ii) an adaptation which updates the coefficients of filter 18
according to equation (13) The module 22 and (iii) the last L values of the prediction residual are
provided to the prediction filter 32 which provides the adaptation module 22 with the vector Ut
defined by equation (11).
At each time t, the filter 32 only has to produce the first component of the vector Ut, i.e. the
current value of the residue is and the other components have received the preceding samples
Sometimes it was calculated and stored.
In the example illustrated in FIG. 3, the prediction filter 32 is a conventional trellis configuration,
and the prediction coefficients aq (1 ≦ q ≦ P) have reflection coefficients r1,. . . , RP-1 is
represented by P-1.
The reflection coefficient ri follows, for example, the well-known Levinson-Durbin algorithm
based on the autocorrelation φ (i) of the input signal obtained by the module 34 and calculated
by the module 36. The Levinson-Durbin algorithm implemented by module 34 can be expressed
The reflection coefficient r i given to the filter 32 is obtained after the repetition P-1 in the same
manner as the coefficient aq (aq = aqP-) of the equation (11). The quantity E (P-1) is the energy
of the remaining misprediction.
The correlation coefficient φ (i) is calculated by module 36 as follows. Represents an input signal
multiplied by a conventional window function, such as a rectangle, Hamming, or other function.
The calculation of the coefficients φ (i) and Levinson-Durbin's algorithm, equivalent to
minimizing the prediction energy E (P−1), is performed on a frame of N samples of the input
signal, where N is The number of the same order as the length L of the impulse response of the
identification filter 18.
As an example, if the signal is sampled at frequency Fe = 8 kHz, then filter 18 will have L = 256
coefficients and the frame size will be N = 160, ie the frame is 20 ms. It is a length.
In the field of telephony, over such a period, the speech signal is almost fixed, demonstrating the
justification of one of the assumptions in deriving the tentative APA algorithm from the APA
algorithm. Generally, this frame period will be longer than 5 ms.
The frames of the input signal processed by the predictive analysis module 34, 36 preferably
overlap and allow non-stationary features of the signal to be considered. The prediction analysis
is then performed every K samples of the input signal while K <N. As an example, the overlapping
period between two consecutive frames would be on the order of 15 ms. In the case of the
numerical example above, this corresponds to K = 40, and each frame constitutes four
consecutive blocks.
If N is a multiple of K, this will further simplify the calculation of the correlation coefficient by
module 36. After receiving each block of K values of the input signal xt, calculating the partial
correlation of each i corresponding to the recent K terms of equation (14), and the calculation
has just been taken from It is sufficient to update the correlation φ (i) by adding a partial
correlation such that the partial correlation previously calculated N / K blocks is removed.
It should be pointed out that other techniques can be used to implement the prediction filter. For
example, methods other than Levinson-Durbin's algorithm can be used to calculate different
configurations for prediction filters based on reflection coefficient ri or reflection coefficient ri.
Directly based on the prediction coefficient aq or LAR coefficient ("Log-Area-Ratio", LARi = log 10
[(1-ri) / (1 + ri)]) or alternatively LSP coefficient ("Line Spectrum Pair"), ... It is also possible to use
other known configurations of the prediction filter.
The device presented by the present invention shows the possibility to change the P-1 order of
the prediction as a function of the simultaneous characteristics of the input signal. In particular,
the stationarity of the signal xt is calculated by the module 36 to take a relatively high prediction
order P-1 when the input signal is stationary and a lower prediction order when there is nonstationarity Correlation or partial correlation coefficients can be assessed by analysis.
It is possible to evaluate the computational complexity of the tentative APA algorithm. The
relevant features are illustrated in Table 1, where the features are compared to the exact
algorithm of the N LMS or APA of order P, the configuration of which is typical of echo cancelers.
In this table, P indicates the maximum order of the tentative APA algorithm that the circuit 16
can execute and the order of P that is effectively used in the comparative example.
The computational complexity of the tentative APA algorithm is essentially that the
discrimination filter has L = 256 coefficients, and every 5 ms of a 20 ms frame (K = 40, N = 160).
) Equal to the complexity of the coefficients to be evaluated with the prediction filter. Thus, the
present invention presents an algorithm that determines the performance of the high-order affine
control algorithm (generally 5 or more) at lower complexity than the order 2 exact affine
projection algorithm.
In terms of hardware, the identification unit 16 is configured from a commercially available
circuit, in particular from a real time digital signal processor (DSP) with commonly used floating
point arithmetic (eg sold by Texas Instruments, Inc. TMS320C3X or TMS320C4X, or AD21061
sold by Analog Devices. Fixed point arithmetic processors may also be used, at which time care
should be taken regarding proper framing of the data being processed.
In another embodiment illustrated in FIG. 4, the input signal xt is an audio signal reconstructed
by the decoder 40 from the input binary stream Φ. This binary stream Φ is made in two towards
the decoder 40 by the encoder and placed at the terminal used by the communication network or
by remote speakers.
As an example, the encoder / decoder corresponds to the RPE-LTP encoder used in the GSM
cellular radiotelephone system (European Telecommunications Standards Institute = specification
GSM 06.01 published by <European Telecommunications Standards Institute> reference). As
used by most digital speech coders, this coder operates on the basis of linear prediction on the
frame of the speech signal corresponding to the almost stationary area of the signal, and the
requirements of the present invention Will meet. In the case of GSM, the frame is 20 ms. In the
binary stream 中 among these, the encoder incorporates, on the one hand, the quantization
parameters for the LAR coefficients described above which characterize the 10th-order linear
prediction filter of the speech signal, and on the other hand the linear prediction residuals.
Incorporate the quantization parameter of the excitation signal corresponding to.
The decoder 40 has a circuit for recovering the excitation signal from the quantization parameter
read from the stream Φ, and a synthesis filter which is the inverse of the 10th-order prediction
filter to which the coefficient extracted by the quantized LAR is given. have. The synthesis filter
receives the excitation signal and emits a composite audio signal xt. Thus, the decoder 40 can
obtain linear prediction parameters from the stream Φ instead of the modules 34, 36 of the
device illustrated in FIG. The prediction module (corresponding to the excitation signal of the
synthesis filter) can also be provided to make the adaptation module 22 produce the components
of the vector Ut required.
It will be appreciated that in a device combined with a speech decoder and an adaptive echo
canceler, using the tentative APA algorithm as illustrated in FIG. 4 does not add complexity
compared to the NLMS regardless of the order P. I will.
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