5 research outputs found
A Robust Variable Step Size Fractional Least Mean Square (RVSS-FLMS) Algorithm
In this paper, we propose an adaptive framework for the variable step size of
the fractional least mean square (FLMS) algorithm. The proposed algorithm named
the robust variable step size-FLMS (RVSS-FLMS), dynamically updates the step
size of the FLMS to achieve high convergence rate with low steady state error.
For the evaluation purpose, the problem of system identification is considered.
The experiments clearly show that the proposed approach achieves better
convergence rate compared to the FLMS and adaptive step-size modified FLMS
(AMFLMS).Comment: 15 pages, 3 figures, 13th IEEE Colloquium on Signal Processing & its
Applications (CSPA 2017
Design of generalized fractional order gradient descent method
This paper focuses on the convergence problem of the emerging fractional
order gradient descent method, and proposes three solutions to overcome the
problem. In fact, the general fractional gradient method cannot converge to the
real extreme point of the target function, which critically hampers the
application of this method. Because of the long memory characteristics of
fractional derivative, fixed memory principle is a prior choice. Apart from the
truncation of memory length, two new methods are developed to reach the
convergence. The one is the truncation of the infinite series, and the other is
the modification of the constant fractional order. Finally, six illustrative
examples are performed to illustrate the effectiveness and practicability of
proposed methods.Comment: 8 pages, 16 figure
Time-domain response of nabla discrete fractional order systems
This paper investigates the time--domain response of nabla discrete
fractional order systems by exploring several useful properties of the nabla
discrete Laplace transform and the discrete Mittag--Leffler function. In
particular, we establish two fundamental properties of a nabla discrete
fractional order system with nonzero initial instant: i) the existence and
uniqueness of the system time--domain response; and ii) the dynamic behavior of
the zero input response. Finally, one numerical example is provided to show the
validity of the theoretical results.Comment: 13 pages, 6 figure
Enhanced Fractional Adaptive Processing Paradigm for Power Signal Estimation
Fractional calculus tools have been exploited to effectively model variety of engineering, physics and applied sciences problems. The concept of fractional derivative has been incorporated in the optimization process of least mean square (LMS) iterative adaptive method. This study exploits the recently introduced enhanced fractional derivative based LMS (EFDLMS) for parameter estimation of power signal formed by the combination of different sinusoids. The EFDLMS addresses the issue of fractional extreme points and provides faster convergence speed. The performance of EFDLMS is evaluated in detail by taking different levels of noise in the composite sinusoidal signal as well as considering various fractional orders in the EFDLMS. Simulation results reveal that the EDFLMS is faster in convergence speed than the conventional LMS (i.e., EFDLMS for unity fractional order)
Fractional gradient methods via ψ-Hilfer derivative
Motivated by the increasing of practical applications in fractional calculus, we study the classical gradient method under the perspective of the -Hilfer derivative. This allows us to cover in our study several definitions of fractional derivatives that are found in the literature. The convergence of the -Hilfer continuous fractional gradient method is studied both for strongly and non-strongly convex cases. Using a series representation of the target function, we develop an algorithm for the -Hilfer fractional order gradient method. The numerical method obtained by truncating higher-order terms was tested and analyzed using benchmark functions. Considering variable order differentiation and optimizing the step size, the -Hilfer fractional gradient method shows better results in terms of speed and accuracy. Our results generalize previous works in the literature.publishe