A Consensus-Based Diffusion Levenberg-Marquardt Method for Collaborative Localization With Extension to Distributed Optimization
Non-linear least squares problems arise from data fitting have received recently a lot of attention, particularly for the estimates of the model parameters over networked systems. Although the diffusion Gauss-Newton method offers many advantages for solving the non-linear least squares problem in wi...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9274340/ |
| _version_ | 1818876599114661888 |
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| author | Mou Wu Liangji Zhong Bin Xu Naixue Xiong |
| author_facet | Mou Wu Liangji Zhong Bin Xu Naixue Xiong |
| author_sort | Mou Wu |
| collection | DOAJ |
| description | Non-linear least squares problems arise from data fitting have received recently a lot of attention, particularly for the estimates of the model parameters over networked systems. Although the diffusion Gauss-Newton method offers many advantages for solving the non-linear least squares problem in wireless sensor network to estimate target position parameter, there are some key challenges when applying it to practice, including singularity of Gauss-Newton Hessian, selection to constant step sizes and steady state oscillation. These remaining issues lead to obvious performance degradation such as high computational cost, vulnerability to step size change and resulting instability on estimation.In this paper, to eliminate the singularity, we develop a diffusion Levenberg-Marquardt method such that the problem of constant step size is also addressed together. Then, to reach agreement on estimated vector, a consensus implementation is further proposed, thus eliminating the oscillation during steady state. Consequently, the proposed consensus-based diffusion Levenberg-Marquardt method provides a general solution for the non-linear least squares problems with an objective that takes the form of a sum of squared residual terms. By applying to collaborative localization and distributed optimization arise in large scale machine learning, simulation results confirm the effectiveness and wide applicability of proposed method in terms of convergence rate, accuracy and consistency of estimates. |
| first_indexed | 2024-12-19T13:44:57Z |
| format | Article |
| id | doaj.art-e27bb508517b490ab5b651bffd1cd07c |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-19T13:44:57Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-e27bb508517b490ab5b651bffd1cd07c2022-12-21T20:18:54ZengIEEEIEEE Access2169-35362020-01-01821564921566010.1109/ACCESS.2020.30414919274340A Consensus-Based Diffusion Levenberg-Marquardt Method for Collaborative Localization With Extension to Distributed OptimizationMou Wu0https://orcid.org/0000-0001-5742-6553Liangji Zhong1https://orcid.org/0000-0002-3354-3250Bin Xu2https://orcid.org/0000-0002-9612-1880Naixue Xiong3https://orcid.org/0000-0002-0394-4635College of Intelligence and Computing, Tianjin University, Tianjin, ChinaSchool of Computer Science and Technology, Hubei University of Science and Technology, Xianning, ChinaSchool of Computer Science and Technology, Hubei University of Science and Technology, Xianning, ChinaCollege of Intelligence and Computing, Tianjin University, Tianjin, ChinaNon-linear least squares problems arise from data fitting have received recently a lot of attention, particularly for the estimates of the model parameters over networked systems. Although the diffusion Gauss-Newton method offers many advantages for solving the non-linear least squares problem in wireless sensor network to estimate target position parameter, there are some key challenges when applying it to practice, including singularity of Gauss-Newton Hessian, selection to constant step sizes and steady state oscillation. These remaining issues lead to obvious performance degradation such as high computational cost, vulnerability to step size change and resulting instability on estimation.In this paper, to eliminate the singularity, we develop a diffusion Levenberg-Marquardt method such that the problem of constant step size is also addressed together. Then, to reach agreement on estimated vector, a consensus implementation is further proposed, thus eliminating the oscillation during steady state. Consequently, the proposed consensus-based diffusion Levenberg-Marquardt method provides a general solution for the non-linear least squares problems with an objective that takes the form of a sum of squared residual terms. By applying to collaborative localization and distributed optimization arise in large scale machine learning, simulation results confirm the effectiveness and wide applicability of proposed method in terms of convergence rate, accuracy and consistency of estimates.https://ieeexplore.ieee.org/document/9274340/Gauss-Newton methodcollaborative localizationLevenberg-Marquardtwireless sensor networksnonlinear least squares |
| spellingShingle | Mou Wu Liangji Zhong Bin Xu Naixue Xiong A Consensus-Based Diffusion Levenberg-Marquardt Method for Collaborative Localization With Extension to Distributed Optimization IEEE Access Gauss-Newton method collaborative localization Levenberg-Marquardt wireless sensor networks nonlinear least squares |
| title | A Consensus-Based Diffusion Levenberg-Marquardt Method for Collaborative Localization With Extension to Distributed Optimization |
| title_full | A Consensus-Based Diffusion Levenberg-Marquardt Method for Collaborative Localization With Extension to Distributed Optimization |
| title_fullStr | A Consensus-Based Diffusion Levenberg-Marquardt Method for Collaborative Localization With Extension to Distributed Optimization |
| title_full_unstemmed | A Consensus-Based Diffusion Levenberg-Marquardt Method for Collaborative Localization With Extension to Distributed Optimization |
| title_short | A Consensus-Based Diffusion Levenberg-Marquardt Method for Collaborative Localization With Extension to Distributed Optimization |
| title_sort | consensus based diffusion levenberg marquardt method for collaborative localization with extension to distributed optimization |
| topic | Gauss-Newton method collaborative localization Levenberg-Marquardt wireless sensor networks nonlinear least squares |
| url | https://ieeexplore.ieee.org/document/9274340/ |
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