Location

Y. Richard Yang

4/6/2011

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Wireless Networking: Summary

send receive

status

info info/control

- The ability to communicate is a foundational support of wireless mobile networks- Unfortunately, the capacity of such networks using current techniques is limited- Much progress has been made, but still more are coming.

Outline

Admin. Localization

overview

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Motivations The ancient question:

Where am I?

Localization is the process of determining the positions of the network nodes

This is as fundamental a primitive as the ability to communicate

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Localization: Many Applications

Location aware information services e.g., E911, location-based search,

advertisement, inventory management, traffic monitoring, emergency crew coordination, intrusion detection, air/water quality monitoring, environmental studies, biodiversity, military applications, resource selection (server, printer, etc.)

“Sensing data without knowing the location is meaningless.” [IEEE Computer, Vol. 33, 2000]

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Measurements

The Localization Process

Localizability (opt)

Location Computation

Location Based Applications

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Classification of Localization based on Measurement Modality Coarse-grained measurements, e.g.,

signal signature • a database of signal signature (e.g. pattern of received

signal, visible set of APs (http://www.wigle.net/)) at different locations

• match to the signature connectivity

Usage e.g., Microsoft “Locate Me” Place lab: http://data.placelab.org/

Advantages low cost; measurements do not need line-of-sight

Disadvantages low precision

For a detailed study, see “Accuracy Characterization for Metropolitan-scale Wi-Fi Localization,” in Mobisys 2005.

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Classification of Localization based on Measurement Modality (cont’) Fine-grained localization

distance angle (esp. with MIMO)

Usage GPS, sensor networks

Advantages high precision

Disadvantages measurements need

line-of-sight for goodperformance

Cricket

Outline

Admin. Localization

Overview GPS

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Global Position Systems

US Department of Defense: need for very precise navigation

In 1973, the US Air Force proposed a new system for navigation using satellites

The system is known as: Navigation System with Timing and Ranging: Global Positioning System or NAVSTAR GPS

http://www.colorado.edu/geography/gcraft/notes/gps/gps_f.html

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GPS Operational Capabilities

Initial Operational Capability - December 8,

1993

Full Operational Capability declared by the

Secretary of Defense at 00:01 hours onJuly 17, 1995

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NAVSTAR GPS Goals

What time is it? What is my position (including attitude)? What is my velocity? Other Goals: - What is the local time? - When is sunrise and sunset? - What is the distance between two

points? - What is my estimated time arrival?

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GSP Basics

Simply stated: The GPS satellites are nothing more than a set of wireless base stations in

the sky

The satellites simultaneously broadcast beacon messages (called navigation messages)

A GPS receiver measures time of arrival to the satellites, and then uses “trilateration” to determine its position

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GPS Basics: Triangulation

Measurement:

Computes distance

c

pptt SR 11

)( 11

SR ttcpp

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GPS Basics: Triangulation

In reality, receiver clockis not sync’d with satellites

Thus need to estimate clock

driftclockSR

c

dtt 11 )( 1

1 driftclockSR ttcpp

driftclockSR cttc )( 1

called pseudo range

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GPS with Clock Synchronization?

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GPS Design/Operation

Segments (components)user segment: users with receivers

control segment: control the satellites

space segment: • the constellation of satellites• transmission scheme

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Control Segment

Master Control Station is located at the Consolidated Space Operations Center (CSOC) at Flacon Air Force Station nearColorado Springs

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CSOC

Track the satellites for orbit and clock determination

Time synchronization

Upload the Navigation Message

Manage Denial Of Availability (DOA)

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Space Segment: Constellation

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Space Segment: Constellation

System consists of 24 satellites in the operational mode: 21 in use and 3 spares

3 other satellites are used for testing Altitude: 20,200 Km with periods of 12 hr. Current Satellites: Block IIR- $25,000,000

2000 KG Hydrogen maser atomic clocks

these clocks lose one second every 2,739,000 million years

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GPS Orbits

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GPS Satellite Transmission Scheme: Navigation Message

To compute position one must know the positions of the satellites

Navigation message consists of: - satellite status to allow calculating pos - clock info

Navigation Message at 50 bps each frame is 1500 bits Q: how long for each message?

More detail: see http://home.tiscali.nl/~samsvl/nav2eu.htm

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GPS Satellite Transmission Scheme: Requirements

All 24 GPS satellites transmit Navigation Messages on the same frequencies

Resistant to jamming

Resistant to spoofing

Allows military control of access (selected availability)

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GPS As a Communication Infrastructure

All 24 GPS satellites transmit on the same frequencies BUT use different codes i.e., Direct Sequence Spread Spectrum

(DSSS), and Code Division Multiple Access (CDMA) Using BPSK to encode bits

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Basic Scheme

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GPS Control

Controlling precision Lower chipping rate, lower precision

Control access/anti-spoofing Control chipping sequence

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GPS Chipping Seq. and Codes

Two types of codes C/A Code - Coarse/Acquisition Code

available for civilian use on L1• Chipping rate: 1.023 M• 1023 bits pseudorandom numbers (PRN)

P Code - Precise Code on L1 and L2 used by the military

• Chipping rate: 10.23 M• PRN code is 6.1871 × 1012 (repeat about one

week)• P code is encrypted called P(Y) codehttp://www.navcen.uscg.gov/gps/geninfo/IS-GPS-200D.pdf

http://www.gmat.unsw.edu.au/snap/gps/gps_survey/chap3/chap3.htm

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GPS PHY and MAC Layers

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Typical GPS Receiver: C/A code on L1

During the “acquisition” time you are receiving the navigation message also on L1

The receiver then reads the timing information and computes “pseudo-ranges”

Military Receiver

Decodes both L1 and L2 L2 is more precise L1 and L2

difference allows computing ionospheric delay

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Denial of Accuracy (DOA)

The US military uses two approaches to prohibit use of the full resolution of the system

Selective availability (SA) noise is added to the clock signal and the navigation message has “lies” in it SA is turned off permanently in 2000

Anti-Spoofing (AS) - P-code is encrypted

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Extensions to GPS Differential GPS

ground stations with known positions calculate positions using GPS

the difference (fix) transmitted using FM radio used to improve accuracy

Assisted GPS put a server on the ground to help a GPS receiver reduces GPS search time from minutes to seconds E.g., iPhone GPS:

http://www.broadcom.com/products/GPS/GPS-Silicon-Solutions/BCM4750

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GPS: Summary

GPS is among the “simplest” localization technique (in terms topology): one-step trilateration

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GPS Limitations

Hardware requirements vs. small devices

GPS jammed by sophisticated adversaries

Obstructions to GPS satellites common• each node needs LOS to 4 satellites • GPS satellites not necessarily overhead, e.g., urban

canyon, indoors, and underground

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Percentage of localizable nodes localized by Trilateration.

Uniformly random 250 node network.

Limitation of TrilaterationR

atio

Average Degree

Outline

Admin. GPS General localization

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Extending GPS: Multilateration A subset of nodes (called anchors) know their

positions through GPS, e.g., nodes close to windows, at the

entrance of a cave, at an open field inside a forest, etc manual configuration

Nodes measure relative distance among each other

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General Localization

node with known position (anchor)

node with unknown position

distance measurement

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Localization Service Definition

Given: set of n nodes positions of k of them known distances between m pairs of nodesFind: positions of nodes

node with known position (anchor)

node with unknown position

distance measurement

Outline

Admin. GPS General localization

Overview Foundation

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Measurement Graph

Consider network nodes as vertices in a graph

There is an edge between two vertices if the distance between the corresponding nodes are known

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Grounded Graph The measurement graph structure needs to

distinguish between anchor nodes and non-anchor nodes

Solution: add an edge between every pair of anchor nodes, since the distance between them is implicitly known!

The resulting graph is called grounded graph, whose graphical properties determine localizability with probability 1

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Grounded Graphs

The grounded graph captures all distance constraintswe no longer need to distinguish between

anchor nodes and non-anchor nodesuse anchor only at the last to pinpoint all

nodes

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In case you were wondering: Why “with probability 1”?

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probability 1 case

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probability 0 case

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{x1, x2, x3}

{d14, d24, d34}

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?

?

In general, this graph is uniquely realizable.

In degenerate case, it is not:The constraints are redundant.

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Summary of Problem: General Localization using Grounded Graphs

Determine if the positions of all nodes are fixed relative to each other due to the known distance measurements, then all nodes have unique positions (the network is thus localizable) Then the only deformation allowed is

translation or rotation of the complete network

This is called trivial continuous transformation

Use anchors can remove trivial transformation

Example

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Question: any continuous transformation to move points from one configuration to another one while respecting all distance constraints?

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Non-Uniqueness Due to Continuous Deformation

Continuous non-uniqueness: -Non-trivial continuous transformation to move points from one configuration to another one while respecting all distance constraints

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Graph Rigidity

A localization network is flexible if it admits a non-trivial continuous deformation

A localization network with a unique realization cannot be flexible

A localization network that is not flexible is called rigid

Rigidity is a necessary condition for network localizability

Rigidity in Other Contexts

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Intuition:

Total degrees of freedom: 2n

How many distance constraints are necessary to limit a graph toonly trivial continuous deformations?

==How many edges are necessary for a graph to be rigid?

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Each edge can remove a single degree of freedom

How Many Constrains are Necessary to Make a Localization Network of n Nodes Rigid?

Rotations and translations will always be possible, so at least 2n-3edges are necessary for a graph to be rigid.

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Are 2n-3 Edges Sufficient?

n = 3, 2n-3 = 3

yes yes

n = 4, 2n-3 = 5 n = 5, 2n-3 = 7

no

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Further Intuition

Need at least 2n-3 “well-distributed” edges

If not well-distributed, a subgraph has more edges than necessary: some edges are redundant

Non-redundant edgesare called independent

n = 5, 2n-3 = 7

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Determining Edge Independence

This means that a graph with 2n-3 edges is rigid if and only if no subgraph has more than 2n’-3 edges.

* n’ is the number of nodes |V’| in the subgraph (V’,E’).

The edges of a graph are independent if and only if no subgraph has more than 2n’-3 edges*.

Laman’s Condition:

n = 5, 2n-3 = 7

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Algorithm to Test Laman’s Condition

Laman’s condition taken literally leads to poor algorithm, as it involves checking all subgraphs

Efficient and intuitive algorithm exists, based on counting degrees of freedom to check and identify rigid components

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Alternate Laman’s condition

For a graph G=(V,E) with m edges and nvertices, the following are equivalent:

A. The edges of G are independent in 2-D.B. For each edge (a,b) in G, the graph formed

by adding 3 additional copies of (a,b) has no subgraph G’ with more than 2n’ edges.

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Illustration

no subgraph with >2n’ edges

“quadruple an edge”

G

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Basic idea

Grow a maximal set of independent edges one at a time

Each candidate edge quadrupled and the resulting graph tested using Laman’s revised condition

If 2n’-3 independent edges found for n’ nodes, the subgraph is rigid

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“The Pebble Game”

Each node assigned 2 pebbles

An edge is covered by having one pebble placed on either of its ends

Pebble covering is assignment of pebbles so that all edges in graph are covered

Existence of pebble covering of graph implies balanced edges implies all edges independent

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initialtesting e1 for independence

e1

4 co

pies

of e

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Pebble Covering

e2

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Assume we have a set of independent edges covered with pebbles and we want to add a new edge

First, look at vertices incident to new edge if either has a free pebble, use it to cover the edge

and done. otherwise, their pebbles are covering existing edges.

• if vertex at other end of one of these edges has free

pebble, then use that pebble to cover existing edge, freeing up pebble to cover new edge

• Search for free pebbles in a directed graph.– if edge ea,b is covered by pebble from vertex a, the edge if

directed from a to b

• Search until pebble is found, then swap pebbles until new edge covered, else fail

Pebble Game Algorithm

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unassigned pebble Assume node 0 gets a new edge to cover.

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initial state

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(a,b) independent

testing (a,b)

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after (a,b) included

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cba

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input to next step

a d

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after (b,c) included

testing (b,c)

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a

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input to next step c

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testing (a,c)

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after (a,c) included

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d

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input to next step

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testing (a,d)

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after (a,d) included

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b

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input to next step

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after (b,d) included

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testing (b,d)

G=({a,b,c,d}, {ab,ac,ad,bc,bd})is rigid

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a

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input to next step

a

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testing (c,d) fails!

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Pebble Game Properties

Testing edge for independence takes O(n) time. At worst, all m edges will be tested for a running time of O(nm)

If entire graph not rigid, pebble game discovers rigid subgraphs

Algorithm is amenable to distributed implementation

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Continuous Deformation Solved

Continuous non-uniqueness: -Can move points from one configuration to the other while respecting constraints

Backup Slides

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GPS PHY and MAC Layers

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GPS Chipping Seq. and Codes

Two types of codes C/A Code - Coarse/Acquisition Code

available for civilian use on L1• 1023 bits pseudorandom numbers (PRN)

P Code - Precise Code on L1 and L2 used by the military

• PRN code is 6.1871 × 1012 (repeat about one week)

• P code is encrypted called P(Y) code

http://www.navcen.uscg.gov/gps/geninfo/IS-GPS-200D.pdf

http://www.gmat.unsw.edu.au/snap/gps/gps_survey/chap3/chap3.htm