Frame theory and optimal anchor geometries in wireless localization

We revisit the problem of describing optimal anchor geometries that result in the minimum achievable MSE by employing the Cramer Rao Lower bound. Our main contribution is to show that this problem can be cast onto the whelm of modern Frame Theory, which not only provides new insights, but also allows the straightforward generalization of various classical results for the anchor placement problem. For example, by employing the frame potential for single-target localization, we see that the directions of the anchors, as seen from the target, should optimally be as orthogonal as possible, and that the existence of an optimal geometry for an arbitrary number of anchors is governed by the fundamental inequality in frame theory. Furthermore, the frame-theoretic approach allows for the simple derivation of some properties on optimal anchor placement that prove to be useful in a tractable approach for the more complex, multi-target anchor placement problem. In a more general sense, the paper builds a refreshing bridge between the classical problem of wireless localization and the powerful domain of Frame Theory, with far-reaching potential

Indoor Localization Simulation Framework for Optimized Sensor Placement to Increase the Position Estimation Accuracy

Indoor position estimation is an important part of any indoor application which contains object tracking or environment mapping. Many indoor localization techniques (Angle of Arrival – AoA, Time of Flight – ToF, Return Time of Flight – RToF, Received Signal Strength Indicator – RSSI) and technologies (WiFi, Ultra Wideband – UWB, Bluetooth, Radio Frequency Identification Device – RFID) exist which can be applied to the indoor localization problem. Based on the measured distances (with a chosen technique), the position of the object can be estimated using several mathematical methods. The precision of the estimated position crucially depends on the placement of the anchors, which makes the position estimate less reliable. In this paper a simulation framework is presented, which uses genetic algorithm and the multilateral method to determine an optimal anchor placement for a given pathway in an indoor environment. In order to make the simulation more realistic, the error characteristics of the DWM1001 UWB ranging module were measured and implemented in the simulation framework. Using the proposed framework, various measurements with an optimal and with a reference anchor placement were carried out. The results show that using an optimal anchor placement, a higher position estimation accuracy can be achieved

HyBloc: Localization in Sensor Networks with Adverse Anchor Placement

To determine the geographical positions of sensors, numerous localization algorithms have been proposed in recent years. The positions of sensors are inferred from the connectivity between sensors and a set of nodes called anchors which know their precise locations. We investigate the effect of adverse placement and density of anchors on the accuracies of different algorithms. We develop an algorithm called HyBrid Localization (HyBloc) to provide reliable localization service with a limited number of clustered anchors. HyBloc is distributed in nature with reasonable message overhead. Through simulations, we demonstrate that HyBloc provides more accurate location estimates than some existing distributed algorithms when there are only a few anchors. HyBloc also performs well when anchors are clustered together