105 research outputs found
Robust Adaptive Generalized Correntropy-based Smoothed Graph Signal Recovery with a Kernel Width Learning
This paper proposes a robust adaptive algorithm for smooth graph signal
recovery which is based on generalized correntropy. A proper cost function is
defined for this purpose. The proposed algorithm is derived and a kernel width
learning-based version of the algorithm is suggested which the simulation
results show the superiority of it to the fixed correntropy kernel version of
the algorithm. Moreover, some theoretical analysis of the proposed algorithm
are provided. In this regard, firstly, the convexity analysis of the cost
function is discussed. Secondly, the uniform stability of the algorithm is
investigated. Thirdly, the mean convergence analysis is also added. Finally,
the complexity analysis of the algorithm is incorporated. In addition, some
synthetic and real-world experiments show the advantage of the proposed
algorithm in comparison to some other adaptive algorithms in the literature of
adaptive graph signal recovery
Multi-kernel Correntropy-based Orientation Estimation of IMUs: Gradient Descent Methods
This paper presents two computationally efficient algorithms for the
orientation estimation of inertial measurement units (IMUs): the
correntropy-based gradient descent (CGD) and the correntropy-based decoupled
orientation estimation (CDOE). Traditional methods, such as gradient descent
(GD) and decoupled orientation estimation (DOE), rely on the mean squared error
(MSE) criterion, making them vulnerable to external acceleration and magnetic
interference. To address this issue, we demonstrate that the multi-kernel
correntropy loss (MKCL) is an optimal objective function for maximum likelihood
estimation (MLE) when the noise follows a type of heavy-tailed distribution. In
certain situations, the estimation error of the MKCL is bounded even in the
presence of arbitrarily large outliers. By replacing the standard MSE cost
function with MKCL, we develop the CGD and CDOE algorithms. We evaluate the
effectiveness of our proposed methods by comparing them with existing
algorithms in various situations. Experimental results indicate that our
proposed methods (CGD and CDOE) outperform their conventional counterparts (GD
and DOE), especially when faced with external acceleration and magnetic
disturbances. Furthermore, the new algorithms demonstrate significantly lower
computational complexity than Kalman filter-based approaches, making them
suitable for applications with low-cost microprocessors
An Examination of Some Signi cant Approaches to Statistical Deconvolution
We examine statistical approaches to two significant areas of deconvolution - Blind
Deconvolution (BD) and Robust Deconvolution (RD) for stochastic stationary signals.
For BD, we review some major classical and new methods in a unified framework of
nonGaussian signals. The first class of algorithms we look at falls into the class
of Minimum Entropy Deconvolution (MED) algorithms. We discuss the similarities
between them despite differences in origins and motivations. We give new theoretical
results concerning the behaviour and generality of these algorithms and give evidence
of scenarios where they may fail. In some cases, we present new modifications to the
algorithms to overcome these shortfalls.
Following our discussion on the MED algorithms, we next look at a recently
proposed BD algorithm based on the correntropy function, a function defined as a
combination of the autocorrelation and the entropy functiosn. We examine its BD
performance when compared with MED algorithms. We find that the BD carried
out via correntropy-matching cannot be straightforwardly interpreted as simultaneous
moment-matching due to the breakdown of the correntropy expansion in terms
of moments. Other issues such as maximum/minimum phase ambiguity and computational
complexity suggest that careful attention is required before establishing the
correntropy algorithm as a superior alternative to the existing BD techniques.
For the problem of RD, we give a categorisation of different kinds of uncertainties
encountered in estimation and discuss techniques required to solve each individual
case. Primarily, we tackle the overlooked cases of robustification of deconvolution
filters based on estimated blurring response or estimated signal spectrum. We do
this by utilising existing methods derived from criteria such as minimax MSE with imposed uncertainty bands and penalised MSE. In particular, we revisit the Modified
Wiener Filter (MWF) which offers simplicity and flexibility in giving improved RDs
to the standard plug-in Wiener Filter (WF)
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