Chair of
Multimedia Communications and Signal Processing
Prof. Dr.-Ing. André Kaup
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Self-Configuration of Evolutionary Models

Motivation

The identification of linear and nonlinear physical systems by discrete-time adaptive filters has received an increasing interest in recent years. Such processing is required for a large variety of applications in order to remove undesired signal components by subtraction of appropriate estimates, as for the compensation of linearly and/or nonlinearly distorted acoustic echos. Although the development of suitable adaptation algorithms with all different advantages and drawbacks has been constantly improved, most algorithms still employ adaptive filters of a fixed size. However, this approach will often lead to under- or overmodelling situations, thus implying either a reduced filter performance or unnecessarily great computational complexity, since the memory length of the unknown system is generally not known a-priori. In order to circumvent this problem, we have proposed novel evolutionary models, allowing for a dynamic size of the adaptive model that is automatically adjusted to the requirements of the underlying system.

Evolutionary Models Concept

As can be seen from Fig. 1a, such a mechanism for the automatic configuration of the optimum filter length can be realized by comparing the performance of two adaptive filter structures (A) and (B) that differ in memory by a certain (but constant) number of coefficients throughout the whole processing. Seeking a fairly simply and intuitive assessment, this is done by means of a convex combination between both filter outputs and residual errors, respectively. These are weighted time-variantly by the mixture factor (eta) that is chosen from within the unit interval so as to minimize the currently obtained global error.

[EVOLVE]

Fig. 1a: Memory control scheme for self-configuring adaptive filters.
[EVOLVE]

Fig. 1b: Evolution of the filter size depending on the mixing factor (eta).

 

Fig. 1b illustrates the temporal evolution of the optimum length estimate. By observing a smoothed version of the obtained mixing factor (eta), the currently better filter component can be inferred and the sizes of both adaptive structures can be adjusted accordingly. For instance, if the larger filter is preferred for the initial convergence (phase 1), both filters are enlarged until some equilibrium is reached (phase 2). The length of the smaller filter then corresponds to the optimum length (Nopt) as well. Vice versa, a shrinking of the filter may also take place, if the smaller component is preferred due to providing a smaller residual error (phase 3). The resulting operation of this control algorithm is mainly defined by the thresholds specifying the regions where increase/decrease events take place (inc/dec), the increment size in terms of filter coefficients (dN) and the settling time (K). The latter is necessary in order to guarantee for a proper reconvergence after each change in memory.

Since the estimation of the filter size is performend ''online'', i.e. in parallel to the also required coefficient adaptation, this technqiue therefore constitutes a doubly adaptive filter approach. In that sense, the underlying structure respresents an evolving adaptive filter that will always prefer the better-suited model out of two competing components and, hence, further develop the overall model accordingly. Moreover, following this idea, there could also be applications with more than two components.

[EVOLVE (virtual)]

Fig. 2: Virtual implementation of the memory control scheme.


In order to compensate for the increased algorithmic complexity that is given by the parallel operation of several filter components, the concept of virtual filters has been proposed recently. Here, the coefficients of the smaller components are jointly used for all filters and only the additional memory ranges of the competing larger filters are taken into account explicitly. Using this approach, significant savings in computational complexity are obtained, which is especially true considering the relatively large filter lengths in the context of acoustic systems. Fig. 2 depicts this concept for a linear adaptive filter which should be compared with the full implementation from Fig. 1a.

Generalized Nonlinear Filters

Besides the application to linear system identification, these techniques are particularly useful in connection with the modelling of nonlinear systems by adaptive Volterra filters. Evolutionary filters can be employed here so as to determine the optimum size of higher-order Volterra kernels (quadratic, cubic, etc.), thereby considerably minimizing the computational complexity. This is especially important, since the number of coefficients of these models grows exponentially with the order of nonlinearity and may be quite large in acoustic applications. The focus of our current research is furthermore put on deriving a more generalized treatment of nonlinear filter structures. This is done by regarding so-called diagonal-coordinate representations and suitable algorithms for truncating/growing the length and the number of kernel diagonals which also allows for a better physical interpretation of the Volterra coefficients.

Promotion

The LMS Chair gratefully acknowledges the funding for the research on a generalized modelling of nonlinear systems by the Deutsche Forschungsgemeinschaft (DFG) in project KE 890/5-1. In order to intensify European relations in research, a several-months cooperation with scientists from the Universidad Carlos III de Madrid (Spain) has also been supported by KE 890/6-1.


Publications:

2013-60
CRIS
L.A. Azpicueta-Ruiz, M. Zeller, A.R. Figueiras-Vidal, W. Kellermann, J. Arenas-Garcia
   [link]   [doi]   [bib]

Enhanced adaptive volterra filtering by automatic attenuation of memory regions and its application to acoustic echo cancellation
IEEE Transactions on Signal Processing (IEEE TSP) Vol. 61, Online Publication, Num. 11, Pages: 2745--2750, 2013
2013-58
CRIS
M. Zeller
   [bib]

Generalized Nonlinear System Identification using Adaptive Volterra Filters with Evolutionary Kernels
Dr. Hut Verlag, München, 2013
2011-42
CRIS
M. Zeller, W. Kellermann
   [link]   [bib]

Evolutionary Adaptive Filtering Based on Competing Filter Structures
European Signal Processing Conf. (EUSIPCO), Pages: 1264--1268, Barcelona, Spain, Aug. 2011
2011-7
CRIS
M. Zeller, Azpicueta-Ruiz, Luis A., Arenas-Garcia, Jeronimo, W. Kellermann
   [doi]   [bib]

Adaptive Volterra Filters with Evolutionary Quadratic Kernels using a Combination Scheme for Memory Control
IEEE Transactions on Signal Processing (IEEE TSP) Vol. 59, Num. 4, Pages: 1449--1464, Apr. 2011
2011-2
CRIS
L.A. Azpicueta Ruiz, M. Zeller, A. Figueiras-Vidal, J. Arenas-Garcia, W. Kellermann
   [doi]   [bib]

Adaptive Combination of Volterra Kernels and its Application to Nonlinear Acoustic Echo Cancellation
IEEE Transactions on Audio, Speech and Language Processing (IEEE TASLP) Vol. 19, Num. 1, Pages: 97--110, Jan. 2011
2010-79
CRIS
L.A. Azpicueta Ruiz, M. Zeller, A.R. Figueiras-Vidal, J. Arenas-Garcia, W. Kellermann
   [link]   [bib]

Improved Acoustic Echo Cancellation for low SNR based on blockwise combination of filters
Proc. 20th International Congress on Acoustics (ICA), Sydney, Australia, Aug. 2010
2010-57
CRIS
M. Zeller, W. Kellermann
   [doi]   [bib]

Advances in Identification and Compensation of Nonlinear Systems by Adaptive Volterra Models
Proc. 44th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove (CA), USA, Nov. 2010
2010-43
CRIS
M. Zeller, W. Kellermann
   [link]   [bib]

Self-Configuring System Identification via Evolutionary Frequency-Domain Adaptive Filters
Int. Workshop on Acoustic Echo and Noise Control (IWAENC), Tel Aviv, Israel, Aug. 2010
2010-10
CRIS
M. Zeller, W. Kellermann
   [doi]   [bib]

Fast and Robust Adaptation of DFT-Domain Volterra Filters in Diagonal Coordinates Using Iterated Coefficient Updates
IEEE Transactions on Signal Processing (IEEE TSP) Vol. 58, Num. 3, Pages: 1589 - 1604, Mar. 2010
2010-5
CRIS
M. Zeller, L.A. Azpicueta Ruiz, Jeronimo Arenas-Garcia, W. Kellermann
   [doi]   [bib]

Efficient Adaptive DFT-Domain Volterra Filters Using an Automatically Controlled Number of Quadratic Kernel Diagonals
IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP), Pages: 4062-4065, Dallas (TX), USA, Mar. 2010
2009-4
CRIS
M. Zeller, L.A. Azpicueta Ruiz, W. Kellermann
   [doi]   [bib]

Online Estimation of the Optimum Quadratic Kernel Size of Second-Order Volterra Filters Using a Convex Combination Scheme
IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP), Pages: 2965-2968, Taipei, Taiwan, Apr. 2009
2009-3
CRIS
L.A. Azpicueta Ruiz, M. Zeller, J. Arenas-Garcia, W. Kellermann
   [doi]   [bib]

Novel Schemes for Nonlinear Acoustic Echo Cancellation Based on Filter Combinations
IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP), Pages: 193-196, Taipei, Taiwan, Apr. 2009
2008-21
CRIS
M. Zeller, W. Kellermann
   [link]   [bib]

Coefficient Pruning for Higher-Order Diagonals of Volterra Filters Representing Wiener-Hammerstein Models
Proc. Int. Workshop on Acoustic Echo and Noise Control (IWAENC), Seattle (WA), USA, Sep. 2008
2008-5
CRIS
M. Zeller, W. Kellermann
   [doi]   [bib]

Framewise Repeated Coefficient Updates for Enhanced Nonlinear AEC by Diagonal Coordinate Volterra Filters
Proc. Joint Workshop on Hands-free Speech Communication and Microphone Arrays (HSCMA), Pages: 196-199, Trento, Italy, May 2008
2007-32
CRIS
M. Zeller, W. Kellermann
   [link]   [bib]

Fast Adaptation of Frequency-Domain Volterra Filters Using Inherent Recursions of Iterated Coefficient Updates
European Signal Processing Conf. (EUSIPCO), Pages: 1605-1609, Poznan, Poland, Sep. 2007