1. Location
Y. Richard Yang
4/6/2011

2. 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.

3. Outline
Admin.
Localization
overview

4. 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

5. 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]

6. The Localization Process
Location Based Applications
Location Computation
Localizability (opt)
Measurements

7. 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 ( at different locations
match to the signature
connectivity
Usage
e.g., Microsoft “Locate Me”
Place lab:
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.

8. 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 good performance
Cricket

9. Outline
Admin.
Localization
Overview
GPS

10. 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

11. GPS Operational Capabilities
Initial Operational Capability - December 8,
1993
Full Operational Capability declared by the
Secretary of Defense at 00:01 hours on
July 17, 1995

12. 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?

13. 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

14. GPS Basics: Triangulation
Measurement:
Computes distance

15. GPS Basics: Triangulation
In reality, receiver clock is not sync’d with satellites
Thus need to estimate clock
called pseudo range

16. GPS with Clock Synchronization?

17. GPS Design/Operation Segments (components)
user segment: users with receivers
control segment: control the satellites
space segment:
the constellation of satellites
transmission scheme

18. Control Segment Master Control Station is located at the
Consolidated Space Operations Center
(CSOC) at Flacon Air Force Station near
Colorado Springs

19. CSOC Track the satellites for orbit and clock determination
Time synchronization
Upload the Navigation Message
Manage Denial Of Availability (DOA)

20. Space Segment: Constellation

21. 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, KG
Hydrogen maser atomic clocks
these clocks lose one second every 2,739,000 million years

22. GPS Orbits

23. 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

24. 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)

25. 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

26. Basic Scheme

27. GPS Control Controlling precision Control access/anti-spoofing
Lower chipping rate, lower precision
Control access/anti-spoofing
Control chipping sequence

28. GPS Chipping Seq. and Codes
Two types of codes
C/A Code - Coarse/Acquisition Code available for civilian use on L1
Chipping rate: M
1023 bits pseudorandom numbers (PRN)
P Code - Precise Code on L1 and L2 used by the military
Chipping rate: M
PRN code is × 1012 (repeat about one week)
P code is encrypted called P(Y) code

29. GPS PHY and MAC Layers

30. 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”

31. Military Receiver Decodes both L1 and L2 L2 is more precise
L1 and L2 difference allows computing ionospheric delay

32. 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

33. Extensions to GPS Differential GPS Assisted 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:

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

35. 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

36. Limitation of Trilateration
Percentage of localizable nodes localized by Trilateration.
Ratio
Average Degree
Uniformly random 250 node network.

37. Outline
Admin.
GPS
General localization

38. 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 3 5 2 4 1

39. General Localization node with known position (anchor)
node with unknown position
distance measurement

40. Localization Service Definition
Given:
set of n nodes
positions of k of them known
distances between m pairs of nodes
Find:
positions of nodes
node with known position (anchor)
node with unknown position
distance measurement

41. Outline
Admin.
GPS
General localization
Overview
Foundation

42. Measurement Graph Consider network nodes as vertices in a graph3
Consider network nodes as vertices in a graph
There is an edge between two vertices if the distance between the corresponding nodes are known 5 2 4 1 5 4 1 2 3

43. 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 5 4 1 2 3 5 4 1 2 3

44. Grounded Graphs The grounded graph captures all distance constraints
we no longer need to distinguish between anchor nodes and non-anchor nodes
use anchor only at the last to pinpoint all nodes

45. In case you were wondering: Why “with probability 1”?4 2 1 3
{x1, x2, x3}
{d14, d24, d34} ?
In general, this graph is
uniquely realizable.
In degenerate case, it is not:
The constraints are redundant. 2 1 3 4
probability 1 case 2 1 3 4
probability 0 case

46. 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

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

48. 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

49. 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

50. Rigidity in Other Contexts

52. Intuition:
How many distance constraints are necessary to limit a graph to
only trivial continuous deformations? ==
How many edges are necessary for a graph to be rigid?
Total degrees of freedom: 2n

53. How Many Constrains are Necessary to Make a Localization Network of n Nodes Rigid?
Each edge can remove a single degree of freedom
Rotations and translations will always be possible, so at least 2n-3
edges are necessary for a graph to be rigid.

54. Are 2n-3 Edges Sufficient?
n = 5, 2n-3 = 7
n = 4, 2n-3 = 5
n = 3, 2n-3 = 3
yes
yes no

55. 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 edges are called independent
n = 5, 2n-3 = 7

56. Determining Edge Independence
The edges of a graph are independent if and only if no subgraph
has more than 2n’-3 edges*.
Laman’s Condition:
* n’ is the number of nodes |V’| in the subgraph (V’,E’).
n = 5, 2n-3 = 7
This means that a graph with 2n-3 edges is rigid if and only if no subgraph has more than 2n’-3 edges.

57. 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

58. Alternate Laman’s condition
For a graph G=(V,E) with m edges and n
vertices, the following are equivalent:
The edges of G are independent in 2-D.
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.

59. Illustration
no subgraph with >2n’ edges
“quadruple an edge” G

60. 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

61. “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

62. Pebble Covering 4 copies of e2 e2 e1 initial testing e1 for
independence

63. Pebble Game Algorithm
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

64. unassigned pebble
Assume node 0 gets a new edge to cover. 4 5 4 3 1 2 3 4 3 2 2 1 1 3 2 3

65. b c d a
initial state b c
(a,b) independent d a b c
testing (a,b) d a
after (a,b) included

66. b c d a b c
input to next step d a b c
testing (b,c) d a
after (b,c) included

67. b c d a
input to next step b c ? a c d b
after (a,c) included d a
testing (a,c)

68. b c d a b c
input to next step d a a c d b
after (a,d) included
testing (a,d)

69. G=({a,b,c,d}, {ab,ac,ad,bc,bd}) is rigid
input to next step d a a c d b
after (b,d) included
testing (b,d)
G=({a,b,c,d}, {ab,ac,ad,bc,bd})
is rigid

70. b c d b a c
input to next step d a
testing (c,d) fails!

71. 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

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

73. Backup Slides

74. GPS PHY and MAC Layers

76. 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 × 1012 (repeat about one week)
P code is encrypted called P(Y) code