g. giorgetti, acm mswim 2008 – vancouver - october 28, 2008 300 $ 70 $ 115 $ 185 $ optimal rss...

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008

300 $

70 $

115 $

185 $

Optimal RSS Threshold in Connectivity-Based Localization Schemes

Gianni GiorgettiSandeep K.S. GuptaGianfranco Manes

ACM MSWiM - Vancouver October 28, 2008

IMPACT LABhttp://impact.asu.edu

Arizona State University


What is this about?

• Localization: the problem of locating devices and/or people

• Localization based on proximity• We can reduce the error by optimal selection of

one of the parameters

Optimal RSS Threshold in Connectivity-Based Localization Schemes


Remote Monitoring Applications

Gateway

Server

Mesh sensornetwork

(x, y) = ?

(x, y) = ?

(x, y) = ?(x, y) = ?(x, y) = ?

(x, y) = ?

(x, y) = ?

(x, y) = ?

(x, y) = ?


Why not to use GPS?

GPS Board - 300 $ x N

GPS Receiver - 70 $ x N

Wireless Node - 115 $ x N

Sensor Board - 185 $ x N

Shopping List:

NOT RELIABLE INDOORSNOT RELIABLE INDOORS

Sometimes “good enough” is good enough

Sometimes “good enough” is good enough


Collaborative Localization

Inputs:• A set of anchor nodes • In-network measurementsOutput:• Node Coordinates

RF-Based Approaches:• Scene analysis (Fingerprinting) • Range-Based (RSS, Interferometric)• Connectivity

d1

d2

d3

d4d5


Radio-Based, Range-Free Localization

What we like about connectivity:1.Easy to acquire 2.Easy to communicate (binary value)3.Easy to process4.Reasonable accuracy

1 HOP2 HOPS

3 HOPS


Example – 49 node network

Comm. Range = ~ 33 mConnectivity = 9Avg. Error = 6 – 10 m (0.2 – 0.3 R)

Comm. Range = ~ 33 mConnectivity = 9Avg. Error = 6 – 10 m (0.2 – 0.3 R)


Does it work indoors?


Why it doesn’t work…

• Every node is in the radio range of every node• Nodes at different locations have the same neighbor sets• Impossible to distinguish between nodes at different locations

IDEA: TO REDUCE CONNECTIVITYBY SETTING A TRESHOLD.

WHAT IS THE OPTIMAL VALUE?


1D Localization

1100

01010101RSS1

RSS2

RSS3

RSS4

…

Connectivity-BasedLocalization

00 11

= -72 dBm


Log-Normal Shadowing Model

5 10 15 20 25 30 35 40 45 50-100

-90

-80

-70

-60

-50

Distance [m]

RS

S [d

bm

]RSS vs Dist [np=3.0, sdb=3.0]

Path-Loss Exponent


Measurement Model

Connectivity is a random variable

Probability of detecting the nodes as “connected”

Parameter Estimation Problem:We want to estimate d using observations C={0,1}. Is there a value Pth that will reduce the estimation error?


Fisher Information

00 11

Large value of F Small ErrorSmall value of F Large Error

Fisher Information: measures the amount of information that a random variable carries about an unknown parameter

Cramér-Rao bound: minimum theoretical estimation error


What does F tell us?

The available Fisher information:1.Decreases with the distance2.Decreases with the noise in the RSS data3.Depends on how we set the threshold


A toy problem

00

-95-90-85-80-75-70-65-60-55-50-45

RSS [dBM]

pdf

There are two nodes (Node 1 and Node 2). You have to decide which one is closer using connectivity information. How do you set the threshold?


Optimal Connectivity Threshold

00

-95-90-85-80-75-70-65-60-55-50-45

RSS [dBM]

pdf

11

For a single device the optimal threshold is equal to the expected received power. (p = 0.5)


Network Localization

• Fisher Information Matrix• Cramér-Rao Bound:

Anchors Blind Nodes


CRB for 2D Network


CRB for 3D Network

Using the CRB we can determine the optimal threshold

We cannot compute the CRB at runtime (it requires knowledge of the node positions)


Optimal Connectivity

• Setting the optimal threshold is equivalent to finding an optimal connectivity value.• Easier to deal with (it doesn’t depend on the hardware)• We investigated how this optimal connectivity value changes with different network parameters.


Invariance of the optimal conn.

GOOD NEWS: The optimal connectivity doesn’t change with network scaling and with the propagation model parameters


Approximation and Simulations

• The Optimal Connectivity value increases with the network size. • We find a formula to approximate the optimal connectivity value

2D


Using the approximate formula we find:

Opt. Conn = 9.27

(Pth = -53.3 dBm)

Opt. Conn = 11.1

(Pth = -34.3 dBm)

Case Studies

http://www.eecs.umich.edu/~hero/localize/ http://www.eng.yale.edu/enalab/XYZ/data_set_1.htm

G. Giorgetti, ACM MSWiM 2008 – Vancouver - October 28, 2008http://impact.asu.edu

THANKS!

g. giorgetti, acm mswim 2008 – vancouver - october 28, 2008 300 $ 70 $ 115 $ 185 $ optimal rss...

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