Localization of Mobile Users Using Trajectory Matching

Report
Localization of Mobile Users
Using Trajectory Matching
ACM MELT’08
HyungJune Lee, Martin Wicke,
Branislav Kusy, and Leonidas Guibas
Stanford University
Motivation
• Location is an important and useful resource
– Push local information to nearby mobile users
• Restaurant, Café, Shopping center on sale, …
– Building automation, etc.
• GPS not available
– Indoor, mobile environment
• ~1m-accuracy
– Usable for location-based service
2
Motivation
• RSSI-based localization
• Indoor setting
RSSI graph
– Due to reflection, refraction,
and multi-path fading,
specific model does not work
– More severe link variation
caused by mobility
• Range-free methods
– Connectivity & Triangulation:
DVhop[Niculescu03] , APIT[He05]
– RSSI pattern matching:
RADAR[Bhal00], MoteTrack[Lorincz07]
– Bayesian inference & Hidden Markov Model:
[Haeberlen04], [Ladd04], LOCADIO[Krumm04]
• Idea: Use historical RSSI measurements
3
Outline
• Trace Space
• Localization algorithm
– Training Phase with RBF construction
– Localization Phase
• Evaluation
• Conclusion and Future work
4
Trace Space
• Traces of RSSI readings form a
trace space  k, N .
• Each trace T corresponds to a
location
T=
:
 k, N
→ L=
x
y
3
(x1, y1)
2
1
 R2
(x2, y2)
4
• Learn to match a trace to a
position
i.e., L(∙):  k, N → R2
5
5
Training Phase with RBF Fitting
• Training input r
r  RSSI vectors T
in trace space  k, N
• Training output p
L(r)  p  [ px py ]T
in R2 space
• Solve linear systems of
training data by least-squares
• Obtain L(∙) function
NC
Lx (r )   w j ( r  c j )  ar  b
j 1
where c j is a RBF cent er
w j , a, b ( j  1,, NC )
are solvedby least - squares
6
Localization Phase
• Localization phase
– Calculate the L (∙) given current trace T in test sets
• Sparse interpolation in trace space
– Handles noisy input data gracefully
– Extrapolates to uncharted regions
Location X
LX (T)
LY (T)
Location Y
Illustration from “Scattered Data Interpolation
with Multilevel B-Splines” [Lee97]
7
Evaluation
• MicaZ motes
8
– CC2420 radio chip
• 10 stationary nodes 1
• 1 mobile node
• 14 waypoints location
9
7
6
10
5
4
2
1
3
• Ground-truth: (r(t), p(t))
– Training RSSI vector r(t)
– Training position p(t)
• linear interpolation
between waypoints
RSSI graph
8
Evaluation
• Training phase
: (a), (b), (c), (d), (e)
• Testing phase
: (f), (g), (h), (i)
• 5 runs for each path
• Error measures
– Position error
– Path error
9
Influence of Historical data
2.4 m
1.28 m
History size k
10
Other Link Quality Measures
2.02 m
1.74 m
1.28 m
11
Conclusion
• Historical RSSI values
significantly increase the
fidelity of localization
(mean position error < 1.3 m)
• Our algorithm also works well
with any link quality
measurements, e.g., LQI or PRR,
which allows flexibility of the
algorithm
12
Future work
• Prediction of future location
• Scalability
• Dynamic time warping for different speed
13
Questions?
HyungJune Lee
[email protected]
14
Radial Basis Function Fitting
(Backup)
• Multi-quadratic function
 (d )  1 
d2

2
NC
with   1
L(r )   w j ( r  c j )  ar  b
j 1
where c j is a RBF center
• By least-squares
 1,1

 
 N ,1
 S
 1
 c
 1


1, N

N


C
S
, NC
1
cNC
r (t1 )T

r (t N S )T
0
0
1

   w
 
1   a  
  
0
b
 
0
 p(t1 ) 
  


 p(t N S )


0


where i , j   ( ri  c j ) ,

w  w1 ,  , wN C

T
,
N S  NC
15
Influence of # of RBF centers Nc
(Backup)
# of RBF centers Nc
16
Influence of Average Window Size b
(Backup)
Burst window size b
17

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