7,942 research outputs found
An affine combination of two LMS adaptive filters - Transient mean-square analysis
This paper studies the statistical behavior of an affine combination of the outputs of two LMS adaptive filters that simultaneously adapt using the same white Gaussian inputs. The purpose of the combination is to obtain an LMS adaptive filter with fast convergence and small steady-state mean-square deviation (MSD). The linear combination studied is a generalization of the convex combination, in which the combination factor is restricted to the interval . The viewpoint is taken that each of the two filters produces dependent estimates of the unknown channel. Thus, there exists a sequence of optimal affine combining coefficients which minimizes the MSE. First, the optimal unrealizable affine combiner is studied and provides the best possible performance for this class. Then two new schemes are proposed for practical applications. The mean-square performances are analyzed and validated by Monte Carlo simulations. With proper design, the two practical schemes yield an overall MSD that is usually less than the MSD's of either filter
Projection methods in conic optimization
There exist efficient algorithms to project a point onto the intersection of
a convex cone and an affine subspace. Those conic projections are in turn the
work-horse of a range of algorithms in conic optimization, having a variety of
applications in science, finance and engineering. This chapter reviews some of
these algorithms, emphasizing the so-called regularization algorithms for
linear conic optimization, and applications in polynomial optimization. This is
a presentation of the material of several recent research articles; we aim here
at clarifying the ideas, presenting them in a general framework, and pointing
out important techniques
Stochastic analysis of an error power ratio scheme applied to the affine combination of two LMS adaptive filters
The affine combination of two adaptive filters that simultaneously adapt on the same inputs has been actively investigated. In these structures, the filter outputs are linearly combined to yield a performance that is better than that of either filter. Various decision rules can be used to determine the time-varying parameter for combining the filter outputs. A recently proposed scheme based on the ratio of error powers of the two filters has been shown by simulation to achieve nearly optimum performance. The purpose of this paper is to present a first analysis of the statistical behavior of this error power scheme for white Gaussian inputs. Expressions are derived for the mean behavior of the combination parameter and for the adaptive weight mean-square deviation. Monte Carlo simulations show good to excellent agreement with the theoretical predictions
A new projection method for finding the closest point in the intersection of convex sets
In this paper we present a new iterative projection method for finding the
closest point in the intersection of convex sets to any arbitrary point in a
Hilbert space. This method, termed AAMR for averaged alternating modified
reflections, can be viewed as an adequate modification of the Douglas--Rachford
method that yields a solution to the best approximation problem. Under a
constraint qualification at the point of interest, we show strong convergence
of the method. In fact, the so-called strong CHIP fully characterizes the
convergence of the AAMR method for every point in the space. We report some
promising numerical experiments where we compare the performance of AAMR
against other projection methods for finding the closest point in the
intersection of pairs of finite dimensional subspaces
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