We study the application of matrix completion in the process of calibrating physical devices. In particular we propose an algorithm together with reconstruction bounds for calibrating circular ultrasound tomography devices. We use the time-of-flight (ToF) measurements between sensor pairs in a homogeneous medium to calibrate the system. The calibration process consists of a low-rank matrix completion algorithm to de-noise and estimate random and structured missing ToFs, and the classic multi-dimensional scaling method to estimate the sensor positions from the ToF measurements. We provide theoretical bounds on the calibration error. Several simulations are conducted to evaluate the theoretical results presented in this paper.
@cite_7: The recent advances in radio and em beddedsystem technologies have enabled the proliferation of wireless microsensor networks. Such wirelessly connected sensors are released in many diverse environments to perform various monitoring tasks. In many such tasks, location awareness is inherently one of the most essential system parameters. It is not only needed to report the origins of events, but also to assist group querying of sensors, routing, and to answer questions on the network coverage. In this paper we present a novel approach to the localization of sensors in an ad-hoc network. We describe a system called AHLoS (Ad-Hoc Localization System) that enables sensor nodes to discover their locations using a set distributed iterative algorithms. The operation of AHLoS is demonstrated with an accuracy of a few centimeters using our prototype testbed while scalability and performance are studied through simulation.
@cite_21: Position information of individual nodes is useful in implementing functions such as routing and querying in ad-hoc networks. Deriving position information by using the capability of the nodes to measure time of arrival (TOA), time difference of arrival (TDOA), angle of arrival (AOA) and signal strength have been used to localize nodes relative to a frame of reference. The nodes in an ad-hoc network can have multiple capabilities and exploiting one or more of the capabilities can improve the quality of positioning. In this paper, we show how AOA capability of the nodes can be used to derive position information. We propose a method for all nodes to determine their orientation and position in an ad-hoc network where only a fraction of the nodes have positioning capabilities, under the assumption that each node has the AOA capability.
@cite_1: Sensor localization has become an essential requirement for realistic applications over wireless sensor networks (WSN). Radio propagation irregularity and the stringent constraint on hardware cost, however, make localization in WSN very challenging. Range-free localizations are more appealing than range-based ones, since they do not depend on received signal strength to estimate distance and thus need simple and cheap hardware only. In this paper, we propose a ring-overlapping, range-free approach using the Ring Overlapping based on Comparison of Received Signal Strength Indicator (ROCRSSI). Simulation results have verified the high estimation accuracy achieved with ROCRSSI.
@cite_15: Wireless Sensor Networks have been proposed for a multitude of location-dependent applications. For such systems, the cost and limitations of the hardware on sensing nodes prevent the use of range-based localization schemes that depend on absolute point-to-point distance estimates. Because coarse accuracy is sufficient for most sensor network applications, solutions in range-free localization are being pursued as a cost-effective alternative to more expensive range-based approaches. In this paper, we present APIT, a novel localization algorithm that is range-free. We show that our APIT scheme performs best when an irregular radio pattern and random node placement are considered, and low communication overhead is desired. We compare our work via extensive simulation, with three state-of-the-art range-free localization schemes to identify the preferable system configurations of each. In addition, we study the effect of location error on routing and tracking performance. We show that routing performance and tracking accuracy are not significantly affected by localization error when the error is less than 0.4 times the communication radio radius.
@cite_20: 
Calibration for circular tomography devises is a variant of sensor localization, a problem that has been extensively studied for the past decade @cite_15 @cite_20 . In sensor localization, given the (i.e., which sensors are in the communication range of which others), the objective is to devise an algorithm that can infer the global position of the sensors. In practice, several methods are deployed as a means of obtaining this local information: the Signal Strength @cite_1 , the Angle of Arrival (AOA) @cite_21 , and the Time Difference of Arrival (TDOA) @cite_7 . Our problem is naturally related to sensor localization when estimated TDOAs are used to measure the pairwise distances between nearby nodes. One should note that due to energy constraints, each node has a small communication range compared to the field size they are installed. As a result, only nodes within the communication range of each other can communicate and hence estimate their pairwise TDOA's. This situation is depicted in Fig. .