Majid Nayeri

Least-square identification with error bounds for real-time signal processing and control

Set-membership (SM) identification, which refers to a class of algorithms using certain a priori knowledge about a parametric model to constrain the solutions to certain sets, is considered. The focus is on a class of SM-based techniques that are of particular interest in applications requiring real-time processing. The optimal bounding ellipsoid (OBE) algorithms are interpreted as a blending of the classical least-square error minimization approach with knowledge of bounds on model errors arising from SM considerations. Using this interpretation, a general framework embracing all currently used OBE algorithms is developed, and strategies for adaptation and for implementation on parallel machines are discussed. Computational complexity benefits are considered for the various algorithms. The treatment is tutorial, leaving many of the formal details to an appendix that presents an archival theoretical treatment of the key results. A second appendix gives an overview of current research in the general SM identification field. >

Uniqueness of MSOE estimates in IIR adaptive filtering; a search for necessary conditions

In adaptive IIR (infinite impulse response) filtering, gradient search techniques minimize the mean-square output error (MSOE). The uniqueness of the minimum MSOE estimate for exactly matching adaptive filters is a necessary condition for global convergence of these algorithms. Although the existence of stable degenerated solutions is sufficient for the existence of local minima, it is shown by an example not to be a necessary condition, this uniqueness is also guaranteed if T. Soderstroms (1985) condition, n/sub b/-n/sub e/+1>or=0, is met when the input is white. It is proved that n/sub b/-n/sub c/+2>or=0 is a weaker sufficient condition for exactly matching models. In fact, this serves as the weakest sufficient condition.<<ETX>>

Multiweight optimization in OBE algorithms for improved tracking and adaptive identification

Optimal bounding ellipsoid (OBE) algorithms offer an attractive alternative to traditional least squares methods for identifying linear-in-parameters signal and system models due to their low computational efficiency, superior tracking ability, and selective updating that permits processor sharing among tasks. These benefits are further enhanced by multiweight optimization (MWO) which yields improved per-point parameter convergence. This paper introduces the MWO process and describes advances in its implementation including the incorporation of a forgetting factor for improved tracking, a new method for efficient weight computation, and extensions to volume-minimizing OBE algorithms. Simulation studies illustrate the results.

Polyphase based adaptive structure for adaptive filtering and tracking

An asymptotically alias-free parallel structure for adaptive filtering applications is considered. The structure promotes the polyphase implementation of a sampling frequency filter bank. Using accumulators in each band as post-filters, the scheme forms a zooming mechanism on alias-free points in the frequency domain. This implies that the bands would become asymptotically uncorrelated which allows independent adaptations in each subband. If sufficient number of bands are used and the input is rich enough, perfect identification of unknown FIR systems is achieved, both analytically and experimentally. The effectiveness of this method in identifying long impulse responses, especially under adverse input coloring and changing environment, makes this structure a viable alternative to available methods. With theoretically proven convergence behavior, this method outperforms the LMS and RLS type algorithms in many cases, some of which are presented in the paper.

Practical considerations in the use of a new OBE algorithm that blindly estimates error bounds

Optimal bounding ellipsoid (OBE) identification algorithms require precise knowledge of bounds on model disturbance sequences, and such bounds are often difficult to ascertain in practice. The OBE algorithm with automatic bound estimation (OBE-ABE) theoretically obviates the need for precise a priori bound estimates, thereby removing the major obstacle to practical application of these powerful and interesting methods. Performance assessment of OBE-ABE, particularly with regard to its favorable convergence behavior, has involved asymptotic analysis over infinite frames of data. This paper discusses application of OBE-ABE to short-time frames of data, suggesting that the favorable asymptotic results apply to finite processing if care is taken in the choice of certain parameters. Example case studies, one using real speech data, illustrate the theoretical discussions.

On the performance surfaces of a frequency domain adaptive IIR filter

The performance surface of a recently proposed frequency-domain adaptive IIR (infinite-impulse response) filter are analyzed. It is shown that for the sufficient-order case the surfaces are unimodal up to an equivalence class of N-factorial members where N is the number of adaptive poles. It is also shown that there exist manifolds separating the N-factorial members in the equivalence class from each other. On these manifolds lie saddle points. These saddle points cause slow convergence which appears to be shoulders on the MSE (mean-squared error) convergence curves. This can be avoided by initializing adaption away from the manifolds. Methods of finding saddle points are given. A second-order example confirms the above results.<<ETX>>

A Weaker Sufficient Condition For The Unimodality Of Error Surfaces Associated With Exactly Matching Adaptive IIR Filters

In adaptive IIR filtering, the gradient search techniques such as LMS, SER, etc., minimize the mean square output error (MSOE). The uniqueness of the minimum MSOE estimate for exactly matching adaptive filters is a necessary condition for possible global convergence of these algorithms. This uniqueness is guaranteed if Soderstroms condition, n/sub b/-n/sub c/+1/spl ges/0, is met when the input is white. Here, we introduce a weaker sufficient condition for uninmodality of MSOE surfaces associated with exactly matching adaptive IIR filter. This is accomplished by manipulation of certain cross-correlation matrix of low order systems, and by generalization of the result to higher order systems, The result is then applied to some existing examples in the literature.

A mildly weaker sufficient condition in IIR adaptive filtering

The cross-covariance matrix of two stable autoregressive (AR) sequences is considered. A mildly weaker condition is identified that ensures the nonsingularity of this matrix. As one consequence of this result, a weaker sufficient condition is obtained that would guarantee the unimodality of the mean-square output error surface of an IIR adaptive filter with white noise excitation. >

Automatic bound estimation: a practical development in optimal bounding ellipsoid processing

Practical application of optimal bounding ellipsoid identification is made possible by the optimal bounding ellipsoid algorithm with automatic bound estimation (OBE-ABE), which automatically estimates model error bounds. Lack of tenable bounds in many real problems has rendered these interesting new methods impractical. OBE-ABE is consistently convergent under proven conditions, and offers significant computational advantages.

IIR sub-band adaptive filtering

Infinite impulse response (IIR) filter banks for multirate subband adaptive filtering are proposed. An allpass based realization of IIR filter banks is developed. It is shown that power symmetric filter banks form a wavelet basis for the signal space. An adaptive scheme incorporating the IIR filter banks is presented and an example follows.<<ETX>>