Location Discovery Based on Fuzzy Geometry in Passive Sensor Networks

Location discovery with uncertainty using passive sensor networks in the nation's power grid is known to be challenging, due to the massive scale and inherent complexity. For bearings-only target localization in passive sensor networks, the approach of fuzzy geometry is introduced to investigate the fuzzy measurability for a moving target in space. The fuzzy analytical bias expressions and the geometrical constraints are derived for bearings-only target localization. The interplay between fuzzy geometry of target localization and the fuzzy estimation bias for the case of fuzzy linear observer trajectory is analyzed in detail in sensor networks, which can realize the 3-dimensional localization including fuzzy estimate position and velocity of the target by measuring the fuzzy azimuth angles at intervals of fixed time. Simulation results show that the resulting estimate position outperforms the traditional least squares approach for localization with uncertainty. 1. Introduction Wireless sensor network localization in smart grid is an important area that attracted significant research interest. As a national smart grid constructed, it is important for developers to consider target localization problems to ensure both the smart grid operation efficiently. The objective of location discovery in sensor networks for smart grid is to estimate the location of a target from measurements collected by a single moving sensor or several fixed sensors at distinct and known locations. For passive bearings-only localization, the sensor node detects the signals transmitted by a target to generate directional information in the form of bearing measurements. These measurements are triangulated to estimate the target location. While triangulation yields a unique intersection point for bearing lines in the absence of measurement errors, the noise present in bearing and observer measurements requires an optimal solution to be formulated based on noisy measurements; hence, statistical techniques for bearings-only target localization is introduced. The pioneering work of Stansfield [1] provided a closed-form small error approximation of the maximum likelihood estimator in 1947. It is shown in [2] that the Stansfield estimator is asymptotically biased, where the traditional maximum likelihood (TML) formulation is examined in detail including a bias and variance analysis. A linearized least squares approach to bearings-based localization is given in [3]. The linearized and iterative algorithms typically require an initial estimate of the target location [2–5]. Liu et al. [6]