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)• ToA (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

Beacon Nodes

Sensor Node Which need to estimate its location

d0

d1

d2

(x0, y0)

(x1, y1)

(x2, y2)Trilateration

Range-based Solutions - MMSE

• MMSE:– Minimum Mean Square

Estimation

Beacon Nodes

Sensor Node Which need to estimate its location

dN

d1

d2

How to estimate (x0, y0)?

(x1, y1)

(x2, y2)

(xN, yN)

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 , we get the following N-1 equations

• Hx = z

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

Beacon Nodes

Sensor Node Which need to estimate its location

Compromised Beacon Signals

• Secure Localization Solutions

Secure Localization

• Attack-resistant Minimum Mean Square Estimation

• Ref[Loc_2]

Attack-resistant Minimum Mean Square Estimation

Minimum Mean Square Estimation

• Ref[Loc_2], Section 2

• The more inconsistent a set of location references is, the greater the corresponding mean square error should be

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