11,975 research outputs found
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
Improved convergence performance of adaptive algorithms through logarithmic cost
We present 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 the least mean logarithmic square (LMLS) algorithm that achieves comparable convergence performance with the least mean fourth (LMF) algorithm and overcomes the stability issues of the LMF algorithm. In addition, we introduce the least logarithmic absolute difference (LLAD) algorithm. 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 interference and outperforms the sign algorithm (SA). © 2014 IEEE
Universal MMSE Filtering With Logarithmic Adaptive Regret
We consider the problem of online estimation of a real-valued signal
corrupted by oblivious zero-mean noise using linear estimators. The estimator
is required to iteratively predict the underlying signal based on the current
and several last noisy observations, and its performance is measured by the
mean-square-error. We describe and analyze an algorithm for this task which: 1.
Achieves logarithmic adaptive regret against the best linear filter in
hindsight. This bound is assyptotically tight, and resolves the question of
Moon and Weissman [1]. 2. Runs in linear time in terms of the number of filter
coefficients. Previous constructions required at least quadratic time.Comment: 14 page
Nonlinear Attitude Filtering: A Comparison Study
This paper contains a concise comparison of a number of nonlinear attitude
filtering methods that have attracted attention in the robotics and aviation
literature. With the help of previously published surveys and comparison
studies, the vast literature on the subject is narrowed down to a small pool of
competitive attitude filters. Amongst these filters is a second-order optimal
minimum-energy filter recently proposed by the authors. Easily comparable
discretized unit quaternion implementations of the selected filters are
provided. We conduct a simulation study and compare the transient behaviour and
asymptotic convergence of these filters in two scenarios with different
initialization and measurement errors inspired by applications in unmanned
aerial robotics and space flight. The second-order optimal minimum-energy
filter is shown to have the best performance of all filters, including the
industry standard multiplicative extended Kalman filter (MEKF)
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