Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 62, Issue 10, Pages 2580-2594Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2014.2314064
Keywords
Angle of arrival; auxiliary variables; bias compensated auxiliary variable based pseudo-linear estimator; closed-form pseudo-linear estimator; node self-localization; weighted instrumental variables; wireless sensor networks
Categories
Funding
- National Natural Science Foundation of China [NSFC61273079, NSFC11174316]
- Strategic Priority Research Program of the Chinese Academy of Sciences [XDA06020300, XDA06020201]
- Open Research Project of the State Key Lab. of Industrial Control Tech., Zhejiang University [ICT1423, ICT1430]
- Key Lab.of Wireless Sensor Network & Communication of Chinese Academy of Sciences [WSNC2011001]
- Natural Sciences and Engineering Research Council of Canada (NSERC) [RGPIN239031]
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Node self-localization is a key research topic for wireless sensor networks (WSNs). There are two main algorithms, the triangulation method and the maximum likelihood (ML) estimator, for angle of arrival (AOA) based self-localization. The ML estimator requires a good initialization close to the true location to avoid divergence, while the triangulation method cannot obtain the closed-form solution with high efficiency. In this paper, we develop a set of efficient closed-form AOA based self-localization algorithms using auxiliary variables based methods. First, we formulate the self-localization problem as a linear least squares problem using auxiliary variables. Based on its closed-form solution, a new auxiliary variables based pseudo-linear estimator (AVPLE) is developed. By analyzing its estimation error, we present a bias compensated AVPLE (BCAVPLE) to reduce the estimation error. Then we develop a novel BCAVPLE based weighted instrumental variable (BCAVPLE-WIV) estimator to achieve asymptotically unbiased estimation of locations and orientations of unknown nodes based on prior knowledge of the AOA noise variance. In the case that the AOA noise variance is unknown, a new AVPLE based WIV (AVPLE-WIV) estimator is developed to localize the unknown nodes. Also, we develop an autonomous coordinate rotation (ACR) method to overcome the tangent instability of the proposed algorithms when the orientation of the unknown node is near pi/2. We also derive the Cramer-Rao lower bound (CRLB) of the ML estimator. Extensive simulations demonstrate that the new algorithms achieve much higher localization accuracy than the triangulation method and avoid local minima and divergence in iterative ML estimators.
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