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# Error minimization with global optimization for difference of convex functions

• * Corresponding author: Enwen Hu

The first author is supported by The National Key Research and Development Program of China grant 2016YFB0502001

• In this paper, a hybrid positioning method based on global optimization for difference of convex functions (D.C.) with time of arrival (TOA) and angle of arrival (AOA) measurements are proposed. Traditional maximum likelihood (ML) formulation for indoor localization is a nonconvex optimization problem. The relaxation methods can?t provide a global solution. We establish a D.C. model for TOA/AOA fusion positioning model and give a solution with a global optimization. Simulations based on TC-OFDM signal system show that the proposed method is efficient and more robust as compared to the existing ML estimation and convex relaxation.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

 Citation: • • Figure 1.  Simulation scenario and sensor nodes distribution

Figure 2.  PDF of positioning error for different methods

Figure 3.  RMSE of target location estimate versus $\sigma_{\theta}$ and $\sigma_{t}$

Table 1.  Global optimization of error minimization

 INPUT: $t_1, \theta_1 \in IR$ For $k = 1, \cdots, N$ do Find $u_k$ approximately by solving the problem $\partial \left(F\left(u_{k}, \aleph \right)+\Lambda \left(u_{k}\right)\right)-\Lambda^{'}\left(u_{k}\right)+N\left(u_{k};S\right)=0$ Find $\Phi_{k+1} \in \Phi\left(u_{k}\right)$ by solving the problem minimize $F\left(u_{k}, \aleph\right)+\Lambda\left(u_k\right)-\Phi_{k+1}$ End for OUTPUT:$u_{N+1}$
•  Open Access Under a Creative Commons license

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