scholarly journals A Novel Method for Asynchronous Time-of-Arrival-Based Source Localization: Algorithms, Performance and Complexity

Sensors ◽  
2020 ◽  
Vol 20 (12) ◽  
pp. 3466
Author(s):  
Yuanpeng Chen ◽  
Zhiqiang Yao ◽  
Zheng Peng
Keyword(s):  
Source Localization ◽  
Signal Propagation ◽  
Least Square ◽  
Time Of Arrival ◽  
Propagation Time ◽  
Performance Loss ◽  
Localization Algorithms ◽  
Least Square Problem ◽  
Localization Performance ◽  
Asynchronous State

In time-of-arrival (TOA)-based source localization, accurate positioning can be achieved only when the correct signal propagation time between the source and the sensors is obtained. In practice, a clock error usually exists between the nodes causing the source and sensors to often be in an asynchronous state. This leads to the asynchronous source localization problem which is then formulated to a least square problem with nonconvex and nonsmooth objective function. The state-of-the-art algorithms need to relax the original problem to convex programming, such as semidefinite programming (SDP), which results in performance loss. In this paper, unlike the existing approaches, we propose a proximal alternating minimization positioning (PAMP) method, which minimizes the original function without relaxation. Utilizing the biconvex property of original asynchronous problem, the method divides it into two subproblems: the clock offset subproblem and the synchronous source localization subproblem. For the former we derive a global solution, whereas the later is solved by a proposed efficient subgradient algorithm extended from the simulated annealing-based Barzilai–Borwein algorithm. The proposed method obtains preferable localization performance with lower computational complexity. The convergence of our method in Lyapunov framework is also established. Simulation results demonstrate that the performance of PAMP method can be close to the optimality benchmark of Cramér–Rao Lower Bound.

A Least Square Solution for Energy-Based Source Localization in Sensor Networks

2012 ◽  
Vol 605-607 ◽  
pp. 1094-1098
Author(s):  
Na Jiang ◽  
Wen Bao Ai
Keyword(s):  
Sensor Networks ◽  
Computational Complexity ◽  
Maximum Likelihood ◽  
Source Localization ◽  
Relaxation Method ◽  
Least Square ◽  
Initial Estimate ◽  
Least Square Problem ◽  
Simulation Results ◽  
High Degree

In this paper, we consider the energy-based source localization in sensor networks. A least square solution to the maximum likelihood (ML) formulation of energy-based source localization is proposed. Since the ML-formulation is nonlinear and non-convex, we approximate it to a convex least square problem which can be solved directly. Simulation results show that with a rough initial estimate range of the acoustic source’s location, the proposed method can achieve a high degree of accuracy. Moreover, with thousands of times lower computational complexity than the semi-definite relaxation method, the proposed method can be effectively used in real time location systems (RTLS).

scholarly journals LSRR-LA: An Anisotropy-Tolerant Localization Algorithm Based on Least Square Regularized Regression for Multi-Hop Wireless Sensor Networks

Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 3974 ◽  
Author(s):  
Wei Zhao ◽  
Fei Shao ◽  
Song Ye ◽  
and Wei Zheng
Keyword(s):  
Least Square ◽  
Sensor Nodes ◽  
Localization Algorithm ◽  
Regularized Regression ◽  
Positioning Accuracy ◽  
Localization Algorithms ◽  
Geographical Distances ◽  
Localization Performance ◽  
The Given ◽  
Range Free

As is well known, multi-hop range-free localization algorithms demonstrate pretty good performance in isotropic networks in which sensor nodes distribute evenly and densely. However, these algorithms are easily affected by network topology, causing a significant decrease in positioning accuracy. To improve the localization performance in anisotropic networks, this paper presents a multi-hop range-free localization algorithm based on Least Square Regularized Regression (LSRR). By building a mapping relationship between hop counts and real distances, we can regard the process of localization as a regularized regression. Firstly, the proximity information of the given network is measured. Then, a mapping model between the geographical distances and the hop distances is constructed by LSRR. Finally, each sensor node finds its own position via this mapping. The Average Localization Error (ALE) metric is used to evaluate the proposed method in our experiments, and results show that, compared with similar methods, our approach can effectively decrease the effect of anisotropy, thus considerably improving the positioning accuracy.

scholarly journals Towards Robust Multiple Blind Source Localization Using Source Separation and Beamforming

Sensors ◽  
2021 ◽  
Vol 21 (2) ◽  
pp. 532
Author(s):  
Henglin Pu ◽  
Chao Cai ◽  
Menglan Hu ◽  
Tianping Deng ◽  
Rong Zheng ◽  
...  
Keyword(s):  
Source Localization ◽  
Sound Source ◽  
Indoor Localization ◽  
Weighting Function ◽  
Signal To Noise Ratio ◽  
Source Separation ◽  
Sound Source Localization ◽  
Angle Of Arrival ◽  
Sound Sources ◽  
Localization Algorithms

Multiple blind sound source localization is the key technology for a myriad of applications such as robotic navigation and indoor localization. However, existing solutions can only locate a few sound sources simultaneously due to the limitation imposed by the number of microphones in an array. To this end, this paper proposes a novel multiple blind sound source localization algorithms using Source seParation and BeamForming (SPBF). Our algorithm overcomes the limitations of existing solutions and can locate more blind sources than the number of microphones in an array. Specifically, we propose a novel microphone layout, enabling salient multiple source separation while still preserving their arrival time information. After then, we perform source localization via beamforming using each demixed source. Such a design allows minimizing mutual interference from different sound sources, thereby enabling finer AoA estimation. To further enhance localization performance, we design a new spectral weighting function that can enhance the signal-to-noise-ratio, allowing a relatively narrow beam and thus finer angle of arrival estimation. Simulation experiments under typical indoor situations demonstrate a maximum of only 4∘ even under up to 14 sources.

scholarly journals Joint clock synchronization and position estimation in time of arrival–based passive positioning systems

2018 ◽  
Vol 14 (11) ◽  
pp. 155014771878689 ◽  
Author(s):  
Shenghong Li ◽  
Lingyun Lu ◽  
Mark Hedley ◽  
David Humphrey ◽  
Iain B Collings
Keyword(s):  
Clock Synchronization ◽  
Likelihood Estimation ◽  
Least Square Method ◽  
Position Estimation ◽  
Least Square ◽  
Time Of Arrival ◽  
Positioning Systems ◽  
Reference Node ◽  
Localization Scheme ◽  
Wireless Signal

A widely used scheme for target localization is to measure the time of arrival of a wireless signal emitted by a tag, which requires the clocks of the anchors (receivers at known locations) to be accurately synchronized. Conventional systems rely on transmissions from a timing reference node at a known location for clock synchronization and therefore are susceptible to reference node failure. In this article, we propose a novel localization scheme which jointly estimates anchor clock offsets and target positions. The system does not require timing reference nodes and is completely passive (non-intrusive). The positioning algorithm is formulated as a maximum likelihood estimation problem, which is solved efficiently using an iterative linear least square method. The Cramér–Rao lower bound of positioning error is also analyzed. It is shown that the performance of the proposed scheme improves with the number of targets in the system and approaches that of a system with perfectly synchronized anchors.

scholarly journals Numerical method to a class of boundary value problems

2018 ◽  
Vol 22 (4) ◽  
pp. 1877-1883 ◽  
Author(s):  
Yu-Yang Qiu
Keyword(s):  
Boundary Value Problems ◽  
Numerical Method ◽  
Conjugate Gradient ◽  
Iteration Method ◽  
Boundary Value ◽  
Solution Process ◽  
Least Square ◽  
Least Square Problem ◽  
Matrix Iteration

A class of boundary value problems can be transformed uniformly to a least square problem with Toeplitz constraint. Conjugate gradient least square, a matrix iteration method, is adopted to solve this problem, and the solution process is elucidated step by step so that the example can be used as a paradigm for other applications.

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