Self-regularized nonlinear diffusion algorithm based on levenberg gradient descent

Lu, Lu; Zheng, Zongsheng; Champagne, Benoı̂t; Yang, Xiaobo; Wu, Wei

doi:10.1016/j.sigpro.2019.05.018

Signal Processing

2019

DOI: 10.1016/j.sigpro.2019.05.018

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Self-regularized nonlinear diffusion algorithm based on levenberg gradient descent

Lu Lu

Zongsheng Zheng

Benoı̂t Champagne

et al.

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Cited by 10 publications

(1 citation statement)

References 23 publications

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“…There is no doubt that this complex Hessian places a great computation burden on the iteration because it needs to be calculated repeatedly. Moreover, LM generally has a poor convergence performance [23] [24], especially when the cost function is significantly not zero at the solution we are looking for [25]. This slow and poor convergence may lead to more iteration counts and poor precision of the solution.…”

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confidence: 99%

A Novel Carrier Loop Based on Adaptive LM-QN Method in GNSS Receivers

Yan

Chen

Tang

et al. 2022

IEEE Trans. Veh. Technol.

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A well-designed carrier tracking loop in a receiver of the Global Navigation Satellite System (GNSS) is the premise of accurate positioning and navigation in an aircraft-based surveying and mapping system. To deal with the problems of Doppler estimation in high-dynamic maneuvers, the interest on maximumlikelihood estimation (MLE) is increasing among the academic community. Levenberg-Marquardt (LM) method is usually regarded as an effective and promising approach to obtain the solution of MLE, but the computation of Hessian matrix loads a great burden on the algorithm. Besides, a poor performance on convergency in final iterations is the common failing of LM implementations. To solve these problems, an LM method based on Gauss-Newton and a Quasi-Newton (QN) method based on Hessian approximation are derived, making the computation cost of Hessian decline from O(N) to O(1). Then, on the basis of these two methods, a closed carrier loop with adaptive LM-QN algorithm is further proposed which can switch between LM and QN adaptively according to a damping parameter. Besides, an ideal LM with super-linear convergence (SLM) is constructed and proved as a reference of the convergence analysis. Finally, through the analyses and experiments using aircraft data, the improvements on computation cost and convergence are verified. Compared with scalar tracking and vector tracking, results indicate a magnitude increase in the precision of LM-QN loop, even though more computation counts are needed by LM-QN.

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confidence: 99%

A Novel Carrier Loop Based on Adaptive LM-QN Method in GNSS Receivers

Yan

Chen

Tang

et al. 2022

IEEE Trans. Veh. Technol.

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Correction-Based Diffusion LMS Algorithms for Distributed Estimation

Chang

2020

Circuits Syst Signal Process

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Recursive second-order Volterra filter based on Dawson function for chaotic memristor system identification

Yang

Wang

et al. 2020

Nonlinear Dyn

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Self-regularized nonlinear diffusion algorithm based on levenberg gradient descent

Cited by 10 publications

References 23 publications

A Novel Carrier Loop Based on Adaptive LM-QN Method in GNSS Receivers

A Novel Carrier Loop Based on Adaptive LM-QN Method in GNSS Receivers

Correction-Based Diffusion LMS Algorithms for Distributed Estimation

Recursive second-order Volterra filter based on Dawson function for chaotic memristor system identification

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