3,217 research outputs found
Stability analysis of adaptive filters with regression vector nonlinearities
We present a unified framework to analyze the mean and mean-square stability of a large class of adaptive filters. We do this without obtaining a full transient model, allowing us to acquire sufficient conditions on the stability without assuming a given statistical distribution for the input regressors. We also apply the proposed framework to some popular adaptive filtering schemes, showing that in some cases the sufficient conditions derived are very tight and even necessary too.Fil: Rey Vega, Leonardo Javier. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; Argentina. Universidad de Buenos Aires; ArgentinaFil: Rey, Hernan. Universidad de Buenos Aires; ArgentinaFil: Benesty, Jacob. Centre Armand-frappier SantĂ© Biotechnologie ; Institut National de Recherche Scientifique; . UniversitĂ© du QuĂ©bec a Montreal; Canad
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
Challenges with bearings only tracking for missile guidance systems and how to cope with them.
This paper addresses the problem of closed loop missile guidance using bearings and target angular extent information. Comparison is performed between particle filtering methods and derivative free methods. The extent information characterizes target size and we show how this can help compensate for observability problems. We demonstrate that exploiting angular extent information improves filter estimation accuracy. The performance of the filters has been studied over a testing scenario with a static target, with respect to accuracy, sensitivity to perturbations in initial conditions and in different seeker modes (active, passive and semi-active)
Performance Analysis of l_0 Norm Constraint Least Mean Square Algorithm
As one of the recently proposed algorithms for sparse system identification,
norm constraint Least Mean Square (-LMS) algorithm modifies the cost
function of the traditional method with a penalty of tap-weight sparsity. The
performance of -LMS is quite attractive compared with its various
precursors. However, there has been no detailed study of its performance. This
paper presents all-around and throughout theoretical performance analysis of
-LMS for white Gaussian input data based on some reasonable assumptions.
Expressions for steady-state mean square deviation (MSD) are derived and
discussed with respect to algorithm parameters and system sparsity. The
parameter selection rule is established for achieving the best performance.
Approximated with Taylor series, the instantaneous behavior is also derived. In
addition, the relationship between -LMS and some previous arts and the
sufficient conditions for -LMS to accelerate convergence are set up.
Finally, all of the theoretical results are compared with simulations and are
shown to agree well in a large range of parameter setting.Comment: 31 pages, 8 figure
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