Diffusion LMS With Correlated Regressors I: Realization-Wise Stability

Piggott, Marc J.; Solo, Victor

doi:10.1109/tsp.2016.2576426

Cited by 24 publications

(8 citation statements)

References 35 publications

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“…The LMS algorithm replaces the mean squared error (MSE) E[e 2 (n)] with the instantaneous squared value of output error |e(n)| 2 [23]. In each iteration, the gradient estimation takes the following form: On this basis, the iterative formula of the LMS algorithm can be derived as:…”

Section: Lms Algorithmmentioning

confidence: 99%

An Adaptive Filtering Algorithm for Non-Gaussian Signals in Alpha-Stable Distribution

Yang¹

2020

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Currently, many adaptive filtering algorithms are available for the non-Gaussian environment, namely, least mean square (LMS) algorithm, recursive least square (RLS) algorithm, least mean fourth (LMF) algorithm, and subspace minimum norm (SMN) algorithm. Most of them can converge to the steady-state, but face various constraints in the presence of alpha (α)-stable noises. To solve the problem, this paper aims to develop an adaptive filtering algorithm for non-Gaussian signals in α-stable distribution, drawing on the merits of existing adaptive filtering algorithms. Firstly, the authors introduced the theory of α-stable distribution, the central limit theorem and fractional lower-order statistics (FLOS). Next, two classic adaptive filtering algorithms, RLS and LMS, were summarized, and compared through tests. On this basis, the FLOS-SMN algorithm was designed in the light of the features of the LMS and the SMN, which applies to the filtering of non-Gaussian signals in αstable distribution. Finally, the proposed algorithm was proved as faster, more stable and more adaptable than the traditional method.

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Section: Lms Algorithmmentioning

confidence: 99%

An Adaptive Filtering Algorithm for Non-Gaussian Signals in Alpha-Stable Distribution

Yang¹

2020

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“…Under Assumption A1-A3, ρ(F ) < 1 gives the sufficient condition for the convergence of the proposed algorithm. Moreover, in practical diffusion adaptation, the step size of all nodes are always set to the same value, and S is always set to doubly stochastic matrix [26]- [30], [46]. Therefore, in the following analysis we set D = µI where µ is the identical step size for all nodes.…”

Section: Further Analysis Under General Parameter Settingsmentioning

confidence: 99%

Maximum correntropy adaptation approach for robust compressive sensing reconstruction

Wang

et al. 2019

Information Sciences

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“…Piggott & Solo [19]- [20] studied distributed estimation with temporally correlated observation matrices and a fixed communication graph. Ishihara & Alghunaim [21] studied distributed estimation with spatially independent observation matrices.…”

Section: Introductionmentioning

confidence: 99%

Decentralized Cooperative Online Estimation With Random Observation Matrices, Communication Graphs and Time Delays

Wang

Zhang

2019

Preprint

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We analyze convergence of distributed cooperative online estimation algorithms by a network of multiple nodes via information exchanging in an uncertain environment. Each node has a linear observation of an unknown parameter with randomly time-varying observation matrices. The underlying communication network is modeled by a sequence of random digraphs and is subjected to nonuniform random time-varying delays in channels. Each node runs an online estimation algorithm consisting of a consensus term taking a weighted sum of its own estimate and neighbours' delayed estimates, and an innovation term processing its own new measurement at each time step. By stochastic time-varying system, martingale convergence theories and the binomial expansion of random matrix products, we transform the convergence analysis of the algorithm into that of the mathematical expectation of random matrix products. Firstly, for the delay-free case, we show that the algorithm gains can be designed properly such that all nodes' estimates converge to the real parameter in mean square and almost surely if the observation matrices and communication graphs satisfy the stochastic spatialtemporal persistence of excitation condition. Especially, this condition holds for Markovian switching communication graphs and observation matrices, if the stationary graph is balanced with a spanning tree and the measurement model is spatially-temporally jointly observable. Secondly, for the case with time-delays, we introduce delay matrices to model the random time-varying communication delays between nodes, and propose a mean square convergence condition, which quantitatively shows the intensity of spatial-temporal persistence of excitation to overcome time-delays.

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Diffusion LMS With Correlated Regressors I: Realization-Wise Stability

Cited by 24 publications

References 35 publications

An Adaptive Filtering Algorithm for Non-Gaussian Signals in Alpha-Stable Distribution

An Adaptive Filtering Algorithm for Non-Gaussian Signals in Alpha-Stable Distribution

Maximum correntropy adaptation approach for robust compressive sensing reconstruction

Decentralized Cooperative Online Estimation With Random Observation Matrices, Communication Graphs and Time Delays

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