Localization

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.

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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 :

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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 :

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Mathematics of Lateration After subtracting the third equ. and

reordering them we have :

That can be expressed using a linear matrix.

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Mathematics of Lateration Which the Matrix on the left side

and right side are known constant.

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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

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Multilateration When order the so called Euclidian formula , we

have :

A solution can be computed that minimizes the mean square error. which is :

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Single Hop Localization This is about systems where a

node with unknown position can directly communicate with anchors.

Active Badge

IR sensor (receiver)

Central Server

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.

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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

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.

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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 :

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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.

Iterative Multilateration

Iterative Multilateration When more information becomes

available – more neighbors have estimated their own position – it is possible to use it to improve the position estimate and propagate an updated estimate to a node’s neighbors.

Collaborative Multilateration There can be nodes in the network that

can not estimate their position.

When this occurs a node can use location information over multiple Hubs to attempt to estimate its position.

Collaborative Multilateration Savvides : participating nodes can

be defined as nodes that have at least three anchors or other participating nodes as neighbours. Nodes 2 and 4 are participating nodes

and its position can be solved.

Collaborative Multilateration Savarese : a sound node has

independent references to at least 3(4) anchors. That is, the multi-hop routes to the anchors have no link (edge) in common. Node 2,4 are sounds.

Probabilistic Positioning As mentioned before an RSSI value,

gives rise to a probability density function, relating each distance to a certain probability with which it corresponds to the RSSI value.

Probabilistic Positioning Once information from a second

anchor becomes available, the two density functions can be convoluted and an improved description of the node’s position probabilities results.

Anchor Placement Properly placed anchor act an important role

in estimating the position. Accuracy improves if more anchors are

available. Several Articles expressing a preference for

anchors to be placed in perimeter of a given area.

Some adaptive placement algorithms are available for low density networks.

Global Positioning System

GPS Consists of 24 MEO satellites that

transmit precise microwave signals.

GPS Four satellites are placed in each of six

orbital planes with 55° tilt to the equator. Four to ten GPS satellites will be visible

anywhere in the world

GPS The satellite altitude is about

20,200km above the Earth’s surface.

GPS The satellite constellation is

managed by the United States Air Force 50th Space Wing in Colorado.

The cost of maintaining the system is approximately US$750 million per year.

GPS Navigation Signals GPS satellites broadcast three

different types of data in the primary navigation signal.

Almanac Ephemeris Clock information

Almanac and Ephemeris Ephemeris :

Contains orbital information that allows the receiver to calculate the position of the satellite, is transmitted every 30 sec.

Almanac: Information and status concerning all the

satellites; their locations and PRN numbers.

framed in Navigation Message of 37500 bit

Clock informations The coordinates (the location) of

the satellites as a function of time. The transmitted signals are

controlled by highly accurate atomic clocks.

Clock Information Coarse / Acquisition code

Is freely available Precise code, or P-code

Restricted to public users by encrypting it.

CA code The C/A code is a 1,023 bit long

PRN broadcast at 1.023 MHz, repeating every millisecond.

Each satellite sends a distinct C/A code, which allows it to be uniquely identified.

P-code The P-code is a stream of about

2.35 × 1014 chips!. It is also 10 times faster than the

C/A-code (10.23 Mbps). Segmented between satellites. P-code is encrypted to Y-Code.

Positioning Requirements Current time. The position of the satellite Measured delay of the received

signal. The position accuracy is primarily

dependent on the satellite position and signal delay.

Measuring Delay The receiver compares the bit

sequence received from the satellite with an internally generated version.

Measuring Delay Modern electronics can measure signal

offset to within about 1% of a bit time, or approximately 10 nanoseconds for the C/A code or about 3 meters.

Using the higher-speed P(Y) signal. Assuming the same 1% bit time accuracy, the high frequency P(Y) signal results in an accuracy of about 30 centimeters.

Calculating Position Knowing Satellite position and

calculating distance using delay One can use Lateration on at least

3 satellites to find out its position.

Calculating Positiong Due to receiver clock error (bias)

we need forth satellite to solve this problem using MMS.

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User Segment A typical GPS device contains a 12-

channel receiver and an antenna to capture satellite signals.

Most systems take around one to two minutes to acquire a 3D fix during a cold start, while some can take a few minutes.

User Segment BMW continues to offer onboard

navigation with voice recognition and voice guidance on most of its new vehicles, with prices starting at $1,800.

What Feature shoud I look for ?

Display Maps Form factor Navigation feature Accessories

Acknowledge Thanks to audiences