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## Localization

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**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.