This book, written by two major figures in adaptive control, provides a wealth of material for researchers, practitioners, and students. While some researchers in adaptive control may note the absence of a particular topic, the book‘s scope represents a high-gain instrument. It can be used by designers of control systems to enhance their work through the information on many new theoretical developments, and can be used by mathematical control theory specialists to adapt their research to practical needs. The book is strongly recommended to anyone interested in adaptive control.

Adaptive Control

Digital processing of speech signals

We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skew-Hermitian) and the spectral properties of the problem. We classify numerical methods and catalogue available software.

/pdf/the-quadratic-eigenvalue-problem-4ozf2mxadi.pdf

The Quadratic Eigenvalue Problem

Digital Coding of Waveforms

Steady-state visually evoked potentials: focus on essential paradigms and future perspectives.

An algorithm for recursively computing the total least squares (TLS) solution to the adaptive filtering problem is described. This algorithm requires O(N) multiplications per iteration to effectively track the N-dimensional eigenvector associated with the minimum eigenvalue of an augmented sample covariance matrix. It is shown that the recursive least squares (RLS) algorithm generates biased adaptive filter coefficients when the filter input vector contains additive noise. The TLS solution on the other hand, is seen to produce unbiased solutions. Examples of standard adaptive filtering applications that result in noise being added to the adaptive filter input vector are cited. Computer simulations comparing the relative performance of RLS and recursive TLS are described. >

An efficient recursive total least squares algorithm for FIR adaptive filtering

Weighted averages of brain evoked potentials (EPs) are obtained by weighting each single EP sweep prior to averaging. These weights are shown to maximize the signal-to-noise ratio (SNR) of the resulting average if they satisfy a generalized eigenvalue problem involving the correlation matrices of the underlying signal and noise components. The signal and noise correlation matrices are difficult to estimate and the solution of the generalized eigenvalue problem is often computationally impractical for real-time processing. Correspondingly, a number of simplifying assumptions about the signal and noise correlation matrices are made which allow an efficient method of approximating the maximum SNR weights. Experimental results are given using actual auditory EP data which demonstrate that the resulting weighted average has estimated SNRs that are up to 21% greater than the conventional ensemble average SNR. >

Weighted averaging of evoked potentials

This correspondence describes a method for estimating the parameters of an autoregressive (AR) process from a finite number of noisy measurements The method uses a modified set of Yule-Walker (YW) equations that lead to a quadratic eigenvalue problem that, when solved, gives estimates of the AR parameters and the measurement noise variance

A subspace approach to estimation of autoregressive parameters from noisy measurements

This paper describes two new algorithms for tracking the subspace spanned by the principal eigenvectors of the correlation matrix associated with time-domain (i.e., time series) data. The algorithms track the d principal N-dimensional eigenvectors of the data covariance matrix with a complexity of O(Nd/sup 2/), yet they have performance comparable with algorithms having O(N/sup 2/d) complexity. The computation reduction is achieved by exploiting the shift-invariance property of temporal data covariance matrices. Experiments are used to compare our algorithms with other well-known approaches of similar and/or lower complexity. Our new algorithms are shown to outperform the subset of the general approaches having the same complexity. The new algorithms are useful for applications such as subspace-based speech enhancement and low-rank adaptive filtering.

http://lyle.smu.edu/~cd/papers/ef_rev.pdf

Efficient, high performance, subspace tracking for time-domain data

A new algorithm for doing signal averaging of steady-state visual evoked potentials (VEPs) is described. The subspace average is obtained by finding the orthogonal projection of the VEP measurement vector onto the signal subspace, which is based on a sinusoidal VEP signal model. The subspace average is seen to out-perform the conventional average using a new signal-to-noise-ratio-based performance measure on simulated and actual VEP data.

C.E. Davila

Papers

An efficient recursive total least squares algorithm for FIR adaptive filtering

Weighted averaging of evoked potentials

A subspace approach to estimation of autoregressive parameters from noisy measurements

Efficient, high performance, subspace tracking for time-domain data

Subspace averaging of steady-state visual evoked potentials