Abstract
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.
Highlights
Target localization and tracking have found wide applications with location awareness in wireless sensor networks (WSNs) [1], where accurate position information plays a critical role, such as position-based routing protocol [2], environmental monitoring [3], anomaly detection including fire or poisonous gas [4], disaster relief [5], industrial detection [6] and so on
Range free localization techniques are easy to implement with low hardware cost, which are mainly depend on the coarse position estimation by exchanging them among neighboring nodes including connectivity and hop counts, etc
PERFORMANCE EVALUATION we present the numerical results to confirm the performance of proposed consensus-based diffusion LM method for collaborative localization in WSNs
Summary
Target localization and tracking have found wide applications with location awareness in wireless sensor networks (WSNs) [1], where accurate position information plays a critical role, such as position-based routing protocol [2], environmental monitoring [3], anomaly detection including fire or poisonous gas [4], disaster relief [5], industrial detection [6] and so on. M. Wu et al.: Consensus-Based Diffusion Levenberg-Marquardt Method for Collaborative Localization the higher accuracy of target position is better, regardless of cost in computaion/communication or inconvenience in deployment. Wu et al.: Consensus-Based Diffusion Levenberg-Marquardt Method for Collaborative Localization the higher accuracy of target position is better, regardless of cost in computaion/communication or inconvenience in deployment In this situation, the range-based localization receives more and more attentions because of its good estimation performance. The node localization is formulated as a NLLS problem, where each anchor node estimates cooperatively the coordinate of unknown target based on their available noisy range measurements. A distributed GN method based on diffusion learning is proposed to solve such a NLLS localization problem. The main difficulties in applying LM method to localization problem are its distributed implementation and maintenance of consensus To this end, a consensus-based LM algorithm with diffusion strategy is developed to achieve the network-wide. We will use subscripts k and l to denote node, and superscript i to denote time
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