Optimal sensor placement for source localization based on RSSD
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Optimal sensor placement for source localization based on RSSD Ali Heydari1 • MasoudReza Aghabozorgi1
•
Mehrzad Biguesh2
Ó Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Source localization based on the received signal strength (RSS) has received great interest due to its low cost and simple implementation. In this paper we consider the source localization problem based on the received signal strength difference (RSSD) with unknown transmitted power of the source using spatially separated sensors. It is well- known that the relative sensor-source geometry (SSG) plays a significant role in localization performance. For this issue, the fisher information matrix (FIM) which inherently is a function of relative SSG is derived. Then for different scenarios the SSG based on the maximization of determinant of FIM is investigated to obtain the optimal sensor placement. Finally, computer simulations are used to study the performance of various sensor placements. Both theoretical analysis and simulation results reveal the ability of the proposed sensor- source geometries. Keywords Source localization Optimal sensor placement Fisher information matrix (FIM) Cramer Rao bound (CRB) Sensor-source geometry (SSG) Received signal strength difference (RSSD)
1 Introduction Source localization, has been attractive in many research fields such as wireless sensor networks (WSNs), mobile communication, microphone array, radio astronomy [1–13]. Several techniques are available for source localization, including time of arrival (TOA) [14, 15], time difference of arrival (TDOA) [10, 13], angle of arrival (AOA) [16, 17], received signal strength (RSS) [16, 18], frequency doppler, and combination of these techniques [7–9, 19, 20]. Among these methods, the TOA and TDOA based methods usually provide better results but they are expensive to implement [9]. On the other hand, the AOA based method, requires sensors with multiple antennas or
& MasoudReza Aghabozorgi [email protected] Ali Heydari [email protected] Mehrzad Biguesh [email protected] 1
Department of Electrical Engineering, Yazd University, Yazd, Iran
2
Department of Electrical Engineering, Shiraz University, Shiraz, Iran
rotating directional antenna to obtain the AOA of source [21]. In contrast, the energy based methods using the received signal strength (RSS) or the received signal strength differences (RSSD) are attractive due to their low cost and simple implementation [22–25]. Unlike the RSSbased localization, the RSSD based localization has not been adequately investigated. In RSSD method the difference of the powers measured by a pair of sensors, in a homogenous environment defines a circle where the source could lay on it. As a result, the source location is obtained using the intersection of at least two of such circles [25]. Since the signal power measurements are noisy, therefore instead of the single cross-point, we encounter with ambiguous areas. The source location esti
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