Efficient Closed-Form Algorithms for AOA Based Self-Localization of Sensor Nodes Using Auxiliary Variables

• Published in: IEEE transactions on signal processing Vol. 62; no. 10; pp. 2580 - 2594
• Main Authors: SHAO, Hua-Jie, ZHANG, Xiao-Ping, ZHI WANG
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-05-2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Angle of arrival; Applied sciences; auxiliary variables; bias compensated auxiliary variable based pseudo-linear estimator; closed-form pseudo-linear estimator; Closed-form solutions; Detection, estimation, filtering, equalization, prediction; Estimators; Exact sciences and technology; Exact solutions; Information, signal and communications theory; Mathematical analysis; Mathematical models; Maximum likelihood estimation; node self-localization; Noise; Remote sensors; Signal and communications theory; Signal processing algorithms; Signal, noise; Telecommunications and information theory; Triangulation; Variance; Vectors; weighted instrumental variables; Wireless sensor networks; Performance evaluation; Autonomous system; Angle of arrival; wireless sensor networks; Wireless telecommunication; Signal estimation; auxiliary variables; Iterative method; Closed form equation; Remote sensing; Accuracy; Linear estimation; Localization; Signal detection; bias compensated auxiliary variable based pseudo-linear estimator; Cramer Rao inequality; Estimation error; weighted instrumental variables; Triangulation; Least squares problem; Measurement sensor; Algorithm; Unbiased estimation; Algorithm performance; Simulation; closed-form pseudo-linear estimator; Arrival angle; Signal processing; Wireless network; Maximum likelihood; Sensor array; node self-localization
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2014.2314064

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 π/2. We also derive the Cramér-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.