Lower bounds for Arrangement-based Range-Free Localization in Sensor Networks

Colander are location aware entities that collaborate to determine approximate location of mobile or static objects when beacons from an object are received by all colanders that are within its distance $R$. This model, referred to as arrangement-based localization, does not require distance estimation between entities, which has been shown to be highly erroneous in practice. Colander are applicable in localization in sensor networks and tracking of mobile objects. A set $S \subset {\mathbb R}^2$ is an $(R,\epsilon)$-colander if by placing receivers at the points of $S$, a wireless device with transmission radius $R$ can be localized to within a circle of radius $\epsilon$. We present tight upper and lower bounds on the size of $(R,\epsilon)$-colanders. We measure the expected size of colanders that will form $(R, \epsilon)$-colanders if they distributed uniformly over the plane

On the structural nature of cooperation in distributed network localization

We demonstrate analytically that the contribution of cooperation in improving the accuracy of distributed network localization has a fundamentally structural nature, rather then statistical as widely believed. To this end we first introduce a new approach to build Fisher Information Matrices (FIMs), in which the individual contribution of each cooperative pair of nodes is captured explicitly by a corresponding information vector. The approach offers new insight onto the structure of FIMs, enabling us to easily account for both anchor and node location uncertainties in assessing lower bounds on localization errors. Using this construction it is surprisingly found that in the presence of node location uncertainty and regardless of ranging error variances or network size, the Fisher information matrix (FIM) terms corresponding to the information added by node-to-node cooperation nearly vanish. In other words, the analysis reveals that the key contribution of cooperation in network localization is not to add statistical node-to-node information (in the Fisher sense), but rather to provide a structure over which information is better exploited

Power Optimization for Network Localization

Reliable and accurate localization of mobile objects is essential for many applications in wireless networks. In range-based localization, the position of the object can be inferred using the distance measurements from wireless signals exchanged with active objects or reflected by passive ones. Power allocation for ranging signals is important since it affects not only network lifetime and throughput but also localization accuracy. In this paper, we establish a unifying optimization framework for power allocation in both active and passive localization networks. In particular, we first determine the functional properties of the localization accuracy metric, which enable us to transform the power allocation problems into second-order cone programs (SOCPs). We then propose the robust counterparts of the problems in the presence of parameter uncertainty and develop asymptotically optimal and efficient near-optimal SOCP-based algorithms. Our simulation results validate the efficiency and robustness of the proposed algorithms.Comment: 15 pages, 7 figure

Non-line-of-sight Node Localization based on Semi-Definite Programming in Wireless Sensor Networks

An unknown-position sensor can be localized if there are three or more anchors making time-of-arrival (TOA) measurements of a signal from it. However, the location errors can be very large due to the fact that some of the measurements are from non-line-of-sight (NLOS) paths. In this paper, we propose a semi-definite programming (SDP) based node localization algorithm in NLOS environment for ultra-wideband (UWB) wireless sensor networks. The positions of sensors can be estimated using the distance estimates from location-aware anchors as well as other sensors. However, in the absence of LOS paths, e.g., in indoor networks, the NLOS range estimates can be significantly biased. As a result, the NLOS error can remarkably decrease the location accuracy. And it is not easy to efficiently distinguish LOS from NLOS measurements. In this paper, an algorithm is proposed that achieves high location accuracy without the need of identifying NLOS and LOS measurement.Comment: submitted to IEEE ICC'1

Low cost underwater acoustic localization

Over the course of the last decade, the cost of marine robotic platforms has significantly decreased. In part this has lowered the barriers to entry of exploring and monitoring larger areas of the earth's oceans. However, these advances have been mostly focused on autonomous surface vehicles (ASVs) or shallow water autonomous underwater vehicles (AUVs). One of the main drivers for high cost in the deep water domain is the challenge of localizing such vehicles using acoustics. A low cost one-way travel time underwater ranging system is proposed to assist in localizing deep water submersibles. The system consists of location aware anchor buoys at the surface and underwater nodes. This paper presents a comparison of methods together with details on the physical implementation to allow its integration into a deep sea micro AUV currently in development. Additional simulation results show error reductions by a factor of three.Comment: 73rd Meeting of the Acoustical Society of Americ

Bayesian CRLB for hybrid ToA and DoA based wireless localization with anchor uncertainty

In this paper, we derive the Bayesian Cramér-Rao lower bound for three dimensional hybrid localization using time-of-arrival (ToA) and direction-of-arrival (DoA) types of measurements. Unlike previous works, we include the practical constraint that the anchor position is not known exactly but rather up to some error. The resulting bound can be used for error analysis of such a localization system or as an optimality criterion for the selection of suitable anchors

Geometric Interpretation of Theoretical Bounds for RSS-based Source Localization with Uncertain Anchor Positions

The Received Signal Strength based source localization can encounter severe problems originating from uncertain information about the anchor positions in practice. The anchor positions, although commonly assumed to be precisely known prior to the source localization, are usually obtained using previous estimation algorithm such as GPS. This previous estimation procedure produces anchor positions with limited accuracy that result in degradations of the source localization algorithm and topology uncertainty. We have recently addressed the problem with a joint estimation framework that jointly estimates the unknown source and uncertain anchors positions and derived the theoretical limits of the framework. This paper extends the authors previous work on the theoretical performance bounds of the joint localization framework with appropriate geometric interpretation of the overall problem exploiting the properties of semi-definiteness and symmetry of the Fisher Information Matrix and the Cram{\`e}r-Rao Lower Bound and using Information and Error Ellipses, respectively. The numerical results aim to illustrate and discuss the usefulness of the geometric interpretation. They provide in-depth insight into the geometrical properties of the joint localization problem underlining the various possibilities for practical design of efficient localization algorithms.Comment: 30 pages, 15 figure