Localization and Secure Localization The Problem The determination

Localization and Secure Localization

The Problem • The determination of the geographical locations of sensor nodes • Why do we need Localization? – Manual configurations of locations is not feasible for large-scale WSNs – Location information is necessary for some applications and services, e. g. geographical routing – Providing each sensor with localization hardware (e. g. , GPS) is expensive in terms of cost and energy consumption

Localization • In some applications, it is essential for each node to know its location • Global Positioning System (GPS) is not always possible – GPS cannot work indoors – GPS power consumption is very high

Solutions • Range-based – Use exact measurements (point-to-point distance estimate (range) or angle estimates) – More expensive – Ranging: the process of estimating the distance between the pair of nodes • Range-free – Only need the existences of beacon signals – Cost-effective alternative to range-based solutions

Localization Algorithms in WSNs • Beacon Nodes know their locations • Range-based Algorithms – Sensor nodes need to measure physical distance-related properties – How to measure distance • RSSI (Received Signal Strength Indication) • To. A (Time of Arrival) • TDOA (Time Difference of Arrival) – How to estimate location • MMSE (Minimum Mean Square Estimation) • Range Free Algorithms – Do Not involve distance estimation

Localization Algorithms in WSNs

Range-based Solutions - MMSE • MMSE: – Minimum Mean Square Estimation

Range-based Solutions - MMSE • Ideally, ei should be 0

Range-based Solutions - MMSE • Rearrange the previous equations, we have • We have N equations

Range-based Solutions - MMSE • Eliminate equations • Hx = z , we get the following N-1

Range-based Solutions - MMSE • H

Range-based Solutions - MMSE • z

Range-based Solutions - MMSE • x • Solution

Range-free Approach - Centroid • Ref[Loc_1], Section 2. 1

Security Concerns in WSNs • Secure Localization Problem • Secure Localization Solutions

Secure Localization • Attack-resistant Minimum Mean Square Estimation • Ref[Loc_2]

Attack-resistant Minimum Mean Square Estimation

Minimum Mean Square Estimation • The more inconsistent a set of location references is, the greater the corresponding mean square error should be • Ref[Loc_2], Section 2

Impact of Malicious Beacons

Impact of Malicious Beacons

Minimum Mean Square Estimation • τ is important: Depend on many factors

How to Decide the set of Consistent Location References? • Given a set L of n location references and a threshold τ – Optimal solution – Greedy solution

How to decide τ? • Measurement error model • How to obtain? – Study the distribution of the mean square error when there are no malicious attacks

Voting-based Location Estimation – Basic Ideas

Iterative Refinement • The larger the number of cells – More state variables need to be kept – The smaller each cell will be – precision • Iterative Refinement – Initially, the number of cells is chosen based on memory constraints – After the first round, the node may perform the voting process on the smallest rectangle that contains all the cells having the largest vote