Introduction We are here !
Applications • Wildlife Tracking • Weather Monitoring • Location-based Authentication • Routing in ad-hoc networks • Surveillances
Properties of Localization • Physical position versus symbolic location • Absolute versus relative coordinates • Localized versus centralized computation • Percision • Cost • Scale • Limitations
Possible Approaches • Triangulation, Trilateration • Location determined using geometry. • Scene Analysis • Observed features used to infer location. • Proximity • Detection of change near known location.
Scene Analysis • Features of an observed scene from a particular vantage point used to infer location. • Not applicable in WSNs.
Proximity • Can be used for positioning when several overlapping anchors are avialalbe. • Centronoid localization • It can be used to decide whether a node is in the proximity of an anchor. • E.g. Active Badge
Triangulation Vs. Lateration • The proximity helps to determine geometric relationship between nodes. • The distance between them or angle of a singular triangle can be easily estimated.
Lateration vs. Angulation • When distances between entities are used, the approach is called lateration. • when angles between nodes are used, one talks about angulation.
Trilateration • Using distances and anchor positions, the node’s position has to be at the intersection of three circles around the anchors. d d d
Distance measure Approaches • RSSI • ToA • TDoA • Determining Angles
RSSI • Known : • Transmission power Ptx • The path loss model • Path lost coefficient α • Receiver can determine the distance d to the transmitter :
RSSI • Challenges: • Signal propagation issues, especially indoors: • Shadowing, Scattering, Multipath propagation. • It’s usually a random process.
Time of Arrival • Conditions : • The speed of propagation is known. • Sound speed depends on environmental factors. • Receiver and sender are synchronized.(drawback) • The distance can be estimated, using the transmission time.
TDoA • TDoA use two transmissions mediums of different propagation speeds to generate an implicit synchronization. • First signal is used to measure ToA of the second one.
Triangulation • Angulation: using angles to determine distance with directional, or phased-array antennas. • 2D position requires two angle + one distance measurement. • 3D position requires two angle + one length + one azimuth measurement. • d is known d
Mathematics of Lateration • there are three anchors with known positions. • For the unknown position of (xu,yu) and those anchors we have :
Mathematics of Lateration • After subtracting the third equ. and reordering them we have : • That can be expressed using a linear matrix.
Mathematics of Lateration • Which the Matrix on the left side and right side are known constant.
Solving the Distance Errors. • Distance measurements are not perfect but only estimates with an unknown error ε are known. • How to Solve this ? • More than three anchors are needed. • Use Multilateration Problem
Multilateration • When order the so called Euclidian formula , we have : • A solution can be computed that minimizes the mean square error. which is :
Single Hop Localization • This is about systems where a node with unknown position can directly communicate with anchors.
Central Server Badge IR sensor (receiver) Active Badge • Every badge periodically, sends unique identifier, via infrared, to the receivers. receivers, receive this identifiers and store it on a central server.
Active office • The devices which its position is to be determinate act as ultrasound senders • Receivers are placed at well-known position, mounted in array at the ceiling of a room. • controller sends a radio message which contains the address of this specific device. • The device sends out an ultrasound pulse, which is received by the array of receivers.
Active office • This array computes the difference between the arrival of the ultrasound pulse and the time when the radio signal was sent. (TDoA)
Cricket • In both recent cases, infrastructure determines device position. • Here the devices themselves can compute their own positions or locations.
Cricket • Anchors spread in a building send ultrasound pulses that combined with radio pulses, which allow the receiver to employ the TDoA to extract symbolic location information of its position.
Overlapping Connectivity • Try to use only the observation of connectivity to a set of anchors to determine a node’s position.
APIT • Decide whether a node is within or outside of a triangle formed by any three anchors.
APIT • Nodes cannot move always ! • how to decide ?
APIT • Approximate P.I.T Test: If no neighbor of M is further from/closer to all three anchors A, B and C simultaneously, M assumes that it is inside triangle ΔABC. Otherwise, M assumes it resides outside this triangle.
Two possible Errors • the percentage of APIT tests exhibiting such an error is relatively small (14% in the worst case).
APIT Aggregation • APIT aggregates the results (inside/outside decisions among which some may be incorrect) through a grid SCAN algorithm.
Using Angle of Arrival • use anchors nodes that use narrow, rotating beams where the rotation speed is constant and known to all nodes.
Positioning in MultiHop • Recent approaches was based on connectivity of nodes to anchors. • This assumption is not always true in a WSN – not every node is in direct contact with at least three anchors.
SDP • Geometric constraints between nodes are represented as linear matrix inequalities (LMIs). • The LMIs can be combined to form a single semidefinite program. • only constraints that form convex regions are amenable to representation as an LMI.
SDP • Angle of arrival data can be represented as a triangle and hop count data can be represented as a circle, but precise range data cannot be conveniently represented.
SDP • Given a set of convex constraints on a node’s position, SDP simply finds the intersection of the constraints.
MDS • MDS-MAP is a centralized algorithm. • Suppose there are n points, suspended in a volume. We don’t know the positions of the points, but we do know the distance between each pair of points. Find the relative positions of the points based on the pairwise distances.
MDS • Estimates shortest path between any pair of nodes , then applies a MDS , and at the end Transform the estimates into global coordinates using some number of fixed anchor nodes using a CSR routine.
MDS • It is fairly stable with respect to anchor placement, achieving good results even if only few anchors are available or placed.
Multihop Range Estimation • Niculescu described three different approach. • DV-Hop • DV-Distance • Euclidean Distance
DV-Hop • Count Shortest hop numbers between all two nodes. • Each anchors estimate hop length and propagates to the network. • Node calculates its position based on average hop length and shortest path to each anchor.
DV Hop • L1 calculates average hope length : • So do L2 and L3 :
DV-Hop • Node A uses trilateration to estimate it’s position by multiplying the average hope length of every received anchor to shortest path length it assumed.
DV-Distance • Distance between neighboring nodes is measured using radio signal strength and is propagated in meters rather than in hops. • Range estimation is more precise. • The algorithm uses the same method to estimate but shortest distance length are assumed.
Euclidean Distance • Assuming that the distances AB, AC, BC, XB, XC are all known, it is possible to compute the unknown distance XA.
Iterative Multilateration • When a node is not located within a range of three anchors, multilateration can not be implemented. • use normal nodes, once they have estimated their positions, just like anchor nodes in a multilateration algorithm.