56,304 research outputs found
Stochastic Behavior of the Nonnegative Least Mean Fourth Algorithm for Stationary Gaussian Inputs and Slow Learning
Some system identification problems impose nonnegativity constraints on the
parameters to estimate due to inherent physical characteristics of the unknown
system. The nonnegative least-mean-square (NNLMS) algorithm and its variants
allow to address this problem in an online manner. A nonnegative least mean
fourth (NNLMF) algorithm has been recently proposed to improve the performance
of these algorithms in cases where the measurement noise is not Gaussian. This
paper provides a first theoretical analysis of the stochastic behavior of the
NNLMF algorithm for stationary Gaussian inputs and slow learning. Simulation
results illustrate the accuracy of the proposed analysis.Comment: 11 pages, 8 figures, submitted for publicatio
A Novel Family of Adaptive Filtering Algorithms Based on The Logarithmic Cost
We introduce a novel family of adaptive filtering algorithms based on a
relative logarithmic cost. The new family intrinsically combines the higher and
lower order measures of the error into a single continuous update based on the
error amount. We introduce important members of this family of algorithms such
as the least mean logarithmic square (LMLS) and least logarithmic absolute
difference (LLAD) algorithms that improve the convergence performance of the
conventional algorithms. However, our approach and analysis are generic such
that they cover other well-known cost functions as described in the paper. The
LMLS algorithm achieves comparable convergence performance with the least mean
fourth (LMF) algorithm and extends the stability bound on the step size. The
LLAD and least mean square (LMS) algorithms demonstrate similar convergence
performance in impulse-free noise environments while the LLAD algorithm is
robust against impulsive interferences and outperforms the sign algorithm (SA).
We analyze the transient, steady state and tracking performance of the
introduced algorithms and demonstrate the match of the theoretical analyzes and
simulation results. We show the extended stability bound of the LMLS algorithm
and analyze the robustness of the LLAD algorithm against impulsive
interferences. Finally, we demonstrate the performance of our algorithms in
different scenarios through numerical examples.Comment: Submitted to IEEE Transactions on Signal Processin
Discrete-time variance tracking with application to speech processing
Two new discrete-time algorithms are presented for tracking variance and reciprocal variance. The closed
loop nature of the solutions to these problems makes this approach highly accurate and can be used
recursively in real time. Since the Least-Mean Squares (LMS) method of parameter estimation requires an
estimate of variance to compute the step size, this technique is well suited to applications such as speech
processing and adaptive filtering
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