Joint RSSD/AOA Source Localization: Bias Analysis and Asymptotically Efficient Estimator
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Joint RSSD/AOA Source Localization: Bias Analysis and Asymptotically Efficient Estimator Ali Heydari1 · Masoudreza Aghabozorgi1
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper we study blind source localization problem based on the joint received signal strength difference (RSSD) and angle of arrival (AOA) measurements with unknown transmit power of source. Since RSSD and AOA measurements are uncorrelated, combining two methods leads to a better performance for source localization. This paper focus on the pseudo linear estimator (PLE) with a closed-form and low complexity solution. One of the main limitations in this estimator is the bias created from the correlation between system matrix and error vector, which is not vanished by increasing the number of measurements. To overcome this problem first, we present a bias compensated PLE using the closed instrumental variable (IV). Then, for improving the localization performance a weighting IV estimator (WIV) is presented. Finally, for achieving the Cramer–Rao lower bound (CRLB) an improved WIV (IWIV) estimator is used based on the known relation between the estimated parameters of WIV estimator. The proposed IWIV estimator is proved to be asymptotically efficient (i.e., obtaining zero bias and the Cramer–Rao lower bound). Numerical simulations also verify the theoretical development and show source localization using hybrid information RSSD/AOA has a superior performance than RSSD and AOA solely. Keywords Source localization · Received signal strength difference · Angle of arrival · Crammer–Rao lower bound
1 Introduction Source localization has received much attention over the past two decades and has wide applications in many fields such as wireless sensor networks (WSNs), surveillance, mobile communication, microphone array, radio astronomy, radar and navigation [1–10]. The main purpose of source localization problem is to determine the location of a signal emitted from an unknown location source based on received noisy measurements using sensors * Masoudreza Aghabozorgi [email protected] Ali Heydari [email protected] 1
Department of Electrical Engineering, Yazd University, Yazd, Iran
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that are distributed over a geographic area. Based on the received noisy measurements, source localization can be categorized in to time of arrival (TOA) [11], time difference of arrival (TDOA) [12, 13], angle of arrival (AOA) [14–16], received signal strength (RSS) measurements [15–18] and combination of these techniques [14–16, 19, 20]. Among these methods, TOA and TDOA, usually provide better results for precision source localization, but they are often difficult to implement since they require high precision hardware and perfect synchronization among sensors [21], AOA-based methods, need sensors equipped with either multiple antenna arrays or directional antennas to obtain the AOA of source. On the other hand, implementation of energy based approaches such as received
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