Cooperative Localization in Wireless Ad Hoc and Sensor Networks

EDITORIAL

Estimasi Lokasi Relatif Sensor pada Jaringan Sensor Nirkabel Menggunakan Metode Maximum Likelihood Estimation dan Cramer-Rao Bound

Pada Jaringan Sensor Nirkabel, lokasi sensor yang tidak diketahui keberadaanya dapat diestimasi dengan pengukuran jarak relatif terhadap sensor anchor-nya. Teknik lokalisasi sensor ini didasarkan pada perkiraan jarak berbasis kuat sinyal yang diterima (RSS) atau waktu kedatangan sinyal (TOA). Hasil perkiraan ini akan menghasilkan error yang tidak bisa dihindari. Untuk itu perlu dilakukan estimasi kesalahan posisi masing-masing sensor. Metode Maximum Likelihood Estimation (MLE) menyeleksi nilai-nilai dari parameter-parameter model, dan memaksimalkan fungsi likelihood-nya, sedangkan metode Cramer_Rao bound digunakan untuk mengestimasi lower bound dari sebuah obyek yang dicari. Dari implementasi algoritma penghitungan kesalahan posisi sensor untuk dua jenis perkiraan jarak dapat ditunjukkan bahwa semakin banyak sensor yang tidak dikenal disebar pada sebuah lokasi, semakin sempit jarak antar mereka, maka semakin mengecil lower bound yang dihasilkan dengan CRB, namun nilai estimasi kesalahan dengan MLE meningkat. Kenaikan koefisien path loss pada RSS menyebabkan penyempitan lower bound CRB sehingga mempersulit penentuan lokasi relatif

Estimation of Spatial Fields of Nlos/Los Conditions for Improved Localization in Indoor Environments

A major challenge in indoor localization is the presence or absence of line-of-sight (LOS). The absence of LOS, denoted as non-line-of-sight (NLOS), directly affects the accuracy of any localization algorithm because of the induced bias in ranging. The estimation of the spatial distribution of NLOS-induced ranging bias in indoor environments remains a major challenge. In this paper, we propose a novel crowd-based Bayesian learning approach to the estimation of bias fields caused by LOS/NLOS conditions. The proposed method is based on the concept of Gaussian processes and exploits numerous measurements. The performance of the method is demonstrated with extensive experiments

Graph invariants for unique localizability in cooperative localization of wireless sensor networks: rigidity index and redundancy index

Rigidity theory enables us to specify the conditions of unique localizability in the cooperative localization problem of wireless sensor networks. This paper presents a combinatorial rigidity approach to measure (i) generic rigidity and (ii) generalized redundant rigidity properties of graph structures through graph invariants for the localization problem in wireless sensor networks. We define the rigidity index as a graph invariant based on independent set of edges in the rigidity matroid. It has a value between 0 and 1, and it indicates how close we are to rigidity. Redundant rigidity is required for global rigidity, which is associated with unique realization of graphs. Moreover, redundant rigidity also provides rigidity robustness in networked systems against structural changes, such as link losses. Here, we give a broader definition of redundant edge that we call the "generalized redundant edge." This definition of redundancy is valid for both rigid and non-rigid graphs. Next, we define the redundancy index as a graph invariant based on generalized redundant edges in the rigidity matroid. It also has a value between 0 and 1, and it indicates the percentage of redundancy in a graph. These two indices allow us to explore the transition from non-rigidity to rigidity and the transition from rigidity to redundant rigidity. Examples on graphs are provided to demonstrate this approach. From a sensor network point of view, these two indices enable us to evaluate the effects of sensing radii of sensors on the rigidity properties of networks, which in turn, allow us to examine the localizability of sensor networks. We evaluate the required changes in sensing radii for localizability by means of the rigidity index and the redundancy index using random geometric graphs in simulations.Comment: 13 pages, 7 figures, to be submitted for possible journal publicatio

Assur decompositions of direction-length frameworks

A bar-joint framework is a realisation of a graph consisting of stiff bars linked by universal joints. The framework is rigid if the only bar-length preserving continuous motions of the joints arise from isometries. A rigid framework is isostatic if deleting any single edge results in a flexible framework. Generically, rigidity depends only on the graph and we say an Assur graph is a pinned isostatic graph with no proper pinned isostatic subgraphs. Any pinned isostatic graph can be decomposed into Assur components which may be of use for mechanical engineers in decomposing mechanisms for simpler analysis and synthesis. A direction-length framework is a generalisation of bar-joint framework where some distance constraints are replaced by direction constraints. We initiate a theory of Assur graphs and Assur decompositions for direction-length frameworks using graph orientations and spanning trees and then analyse choices of pinning set

Fundamentals of Large Sensor Networks: Connectivity, Capacity, Clocks and Computation

Sensor networks potentially feature large numbers of nodes that can sense their environment over time, communicate with each other over a wireless network, and process information. They differ from data networks in that the network as a whole may be designed for a specific application. We study the theoretical foundations of such large scale sensor networks, addressing four fundamental issues- connectivity, capacity, clocks and function computation. To begin with, a sensor network must be connected so that information can indeed be exchanged between nodes. The connectivity graph of an ad-hoc network is modeled as a random graph and the critical range for asymptotic connectivity is determined, as well as the critical number of neighbors that a node needs to connect to. Next, given connectivity, we address the issue of how much data can be transported over the sensor network. We present fundamental bounds on capacity under several models, as well as architectural implications for how wireless communication should be organized. Temporal information is important both for the applications of sensor networks as well as their operation.We present fundamental bounds on the synchronizability of clocks in networks, and also present and analyze algorithms for clock synchronization. Finally we turn to the issue of gathering relevant information, that sensor networks are designed to do. One needs to study optimal strategies for in-network aggregation of data, in order to reliably compute a composite function of sensor measurements, as well as the complexity of doing so. We address the issue of how such computation can be performed efficiently in a sensor network and the algorithms for doing so, for some classes of functions.Comment: 10 pages, 3 figures, Submitted to the Proceedings of the IEE

Range estimation in multicarrier systems in the presence of interference: Performance limits and optimal signal design

Cataloged from PDF version of article.Theoretical limits on time-of-arrival (equivalently, range) estimation are derived for multicarrier systems in the presence of interference. Specifically, closed-form expressions are obtained for Cramer-Rao bounds (CRBs) in various scenarios. In addition, based on CRB expressions, an optimal power allocation (or, spectrum shaping) strategy is proposed. This strategy considers the constraints not only from the sensed interference level but also from the regulatory emission mask. Numerical results are presented to illustrate the improvements achievable with the optimal power allocation scheme, and a maximum likelihood time-of-arrival estimation algorithm is studied to assess the effects of the proposed approach in practical estimators. © 2011 IEEE

Radio Frequency-Based Indoor Localization in Ad-Hoc Networks

The increasing importance of location‐aware computing and context‐dependent information has led to a growing interest in low‐cost indoor positioning with submeter accuracy. Localization algorithms can be classified into range‐based and range‐free techniques. Additionally, localization algorithms are heavily influenced by the technology and network architecture utilized. Availability, cost, reliability and accuracy of localization are the most important parameters when selecting a localization method. In this chapter, we introduce basic localization techniques, discuss how they are implemented with radio frequency devices and then characterize the localization techniques based on the network architecture, utilized technologies and application of localization. We then investigate and address localization in indoor environments where the absence of global positioning system (GPS) and the presence of unique radio propagation properties make this problem one of the most challenging topics of localization in wireless networks. In particular, we study and review the previous work for indoor localization based on radio frequency (RF) signaling (like Bluetooth‐based localization) to illustrate localization challenges and how some of them can be overcome