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significantly within the last decade, it can still fail from its’ principle and due
to inaccessibility of the RF signal from satellites in particular situations. These
situations are consideredfor critical and should be avoided from safety reasons. The
GPS signal is not available in manylocations due to signal shielding e.g. in urban
areas, underground spaces, inside buildings, tunnels, deep and narrowvalleys, etc.
While the GPS is not able to meet the basic requirements in terms of integrity and
availability in ageneral sense, therefore the localization control system can’trely
exclusively onthe GPS. The vehicle canbe equipped not only withasatellite receiver
of navigation data, butalso it can employother on-board sensors e.g. odometry or
inertial navigation sensor.Each of these sensors have their ownspecific features and
disadvantages and compared to the GPS theymainly employthe dead-reckoning
principle to obtain some suitable navigation information.
Application of sensors forinertial navigation (gyros,accelerometers, tilt sensors)
does not depend on operational condition. Their usage has to takeinto account many
fluctuating parameters (e.g. sensor drift, bias, non-linearity). Precise estimation of
the sensor parameters has direct impacts on desirable accuracyand reliability of the
localization system in this case.
Dead reckoning by the means of odometry fails if insufficient adhesion between
the vehicle wheel and ground occurs, due to adhesion or type of the surface (e.g.
rain, ice or leaves, soft-type of surface). Quality of adhesion impairs particularly
when the vehicle accelerates or brakes. Authors in [1] evaluate the vehicle speed
based on afuzzy inference system and neural networks using differences and rapid
changes between odometry sensors joined with multiple wheels.
There are manyreferences in robotics field on data fusion from gyroscopes, ac-

celerometers and odometry.The most of them solvedata fusion problems employing
the Kalman filter [2], or PDAF techniques [7]. Our approach doesn’tuse classical
state vector to determine current measured values and their errors. Instead of this
we recognize occurrence of error situation directly and repair these situations by
interpolation methods subsequently.
Aiming to achieve better final performance of the navigation system, we intro-
duce an application-oriented approach to fusion of data measured by the odometry
and onboard accelerometer in the following. The presented approach is drivenby
abelief, that the most typical errors of these sensors are uncorrelated. Significant
odometry errors occur during acceleration or braking intervals, which can be suc-
cessfully discovered by accelerometers. On the other hand, long-lasting and more
or less constant motion speeds are very good preconditions for error-free odometry
measurement. Then, accelerometers are typically useless in these cases. Therefore,
combination of both the sensor types has been assumed to improve the quality of the
localization solution.
2Problem Setup
Navigation of the vehicle consists of determination of forward position on its’ path
and in precise detection of motion direction, in particular in curves. If the GPS signal
Vehicle Localization Using Inertial Sensors and GPS 137
is permanently available, accuracyofthe GPS is sufficient even for determination of
changes between twotracks after passing acurveofcrossing. Wheneverthe signal of
the GPS is lost, the correct tracking of the vehicle position has to be maintained. One
of the worst-case situations comes about when the vehicle drivesthrough ashielded
region doing some maneuvers. The GPS needs relatively long time for retrievalof
actual position again.
This problem situation can be partially overcome by application of inertial sen-
sors, principally gyros and accelerometers with active axis oriented perpendicularly
to the motion direction. The gyros can be used for preserving information about
heading. Forprecise solution of heading in along-term period correction mecha-
nisms have to be employed. One of the powerful approaches is amap-matching

algorithm [3], which desires at least an estimate of the traveled distance to deter-
mine the position and heading. The odometry can be used for this purpose, butit
suffers from randomly occurred, unpredictable and almost unbound errors due to
insufficient wheel adhesion.
On the other hand, the main constrains of the inertial system navigation system
performance to estimate the traveled distance are set by the finite (and limited)
resolution of the sensors themselves. Even asmall butpermanent offset error in
acceleration will be integrated and results in aremarkable error in speed. After
double integration it raises inalarge error in distance.Therefore,very precise and low
offset sensors and error correction mechanisms (feedback algorithms) are necessary
to obtain an acceptable inertial navigation platform. Therefore our contribution deals
Accelerometer Odometry GPS
Slippage detection
Slippagecorrection
Switch strategy
by availability
of GPS
(GPS /ODO)
Travelleddistance
Offset
Correction
Calibration
Fig.1. Principal overviewofthe proposed method.
with adesign of arobust feedback algorithm to perform the double integration of
acceleration from accelerometer with acceptable final errors enabling to use the
method output as atemporal-substitute dead-reckoning system. Forsimplification,
in the first steps, the method has been designed for the case of accelerometer in
question with its’ active axis having mounted collinear with the vehicle driving
direction. Global overviewofthe proposed method and mutual interconnections of
particular sensors in the approach to distance measurement are illustrated in the

Fig. 1.
138 L. P
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2.1 Data Analysis and Preprocessing
The approach to estimation of the traveled distance is based on processing of signal
from odometer and accelerometers. As the odometer measurements may be pro-
cessed directly,the acceleration data are corrupted by remarkable noise (caused by
vehicle vibrations while driving and/or noise of the sensing system itself).
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
-2
-1
0
1
2
x10
4
Frequence(Hz)
Fig.2. Frequencyspectrum of the accelerometer signal.
Even thought data from accelerometer do not need to be filtered before further
processing (integration itself provides astrong low-pass filtration effect), we have
been interested in filtration of the signal for experiment evaluation purposes.
The intention wastofind suitable structure and parameters of afilter providing
relatively smooth shape of the signal without damaging the integral (mean) value of
the origin.The parameter has to be determined asatrade-offbetween the smoothness
(but also the levelofdegradation) of the signal and the levelofnoise in the output

signal. To optimize the achievedresults, twofiltering techniques have been applied;
the former uses sliding- windowaveraging as the latter employs standard 4th-order
Butterworth low-pass filter.
The Fig. 3introduces not only the influence of particular parameters in the
process of filtration, butitalso illustrates some other issues related to the used
sensor offset. As the vehicle speed can be obtained by simple integration of the
acceleration along time:
v ( t )=

t
0
( a ( t ) − offset( t )) dt (1)
where a stands for measured acceleration and offset for actual offset of acceler-
ation sensor,being basically an unknown butconstrained function of time.
The Fig. 3compares direct (reference) speed measurements obtained from the
GPS and integration of the acceleration after filtration. The precision of the pre-
ceeding process result strongly depends on the exact estimation of the sensor offset.
Unfortunately,the sensor offset is highly variable with time and it is not possible to
estimate its’ exact model. Moreover, the sensor offset depends on the past behaviour
of the vehicle, where its’ evolution is drivenbyunknown transfer characteristic with
substantial hysteresis as can be seen in the Fig. 4.
The integration of data plotted in the Fig. 3assumes that an accelerated body
performs abounded motion with final return to the original position (a forth-and-
back motion). This additional information allows us to determine an average offset
Vehicle Localization Using Inertial Sensors and GPS 139
along themeasured data sequence. However, some deviations ofintegrated datafrom
the reference GPS shape are clearly visible (e.g. the amplitude of the integrated data
is lower than the reference).
0 50 100 150 200 250 300 350 400 450 500
-15

-10
-5
0
5
10
15
Time [s]
Speed[m/s]
GPS
Signal from
accelerometers afterintegration
→
raw /Butterworthfilter, seedetails
0.1Hz
0.3Hz
More then 1Hz
140 145 150 155 160 165 170
8
8.2
8.4
8.6
8.8
9
GPS
Detail view -filtration
Fig.3. An example of signal degradation after afiltering.
-10 -8 -6 -4 -2 0 2 4 6 8 10
-10
-8
-6

-4
-2
0
2
4
6
8
10
SpeedfromGPS [m/s]
Speedfromaccelerometer after1.integration [m/s]
Fig.4. Comparison of the vehicle speed from GPS vs. speed via acceleration The shown
behavior givesgood reasons for the exact determination of asensor offset to be the central
topic in the following sections.
3Data Fusion
To obtain the travelled distance value, data fusion based on GPS, odometry and
accelerometer has to be introduced. The fusion method has to respect the possibility
of temporal dropouts in performance of each sensor.Suppose, the GPS signal is
mostly available and therefore our effort is mainly targeted to bridge the GPS-dark
areas.
The recent research has shown that one of the good ways for fusion of the
odometry and accelerometer sensor data is arule-based mechanism. The desired
140 L. P
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behavior is to prefer odometry data to accelerometers as soon as GPS measurement
is not available. As the GPS is lost the navigation system has to ensure immediate

and smooth switching to inertial sensors and odometry.The basic strategy for fusion
and data processing is sketched in the previous Fig. 1.
The odometry data are generally reliable as we suppose precise vehicle wheel
calibration and no slippage between the wheel and the ground. Calibration of the
odometry seems to be astraightforward task to be performed wheneverthe GPS is
in operation and even together with an existing map of the environment.
As long as the odometer has been properly calibrated (or continuously recali-
brated during movements), it is possible to switch the navigation system from GPS
to odometer.Unfortunately,the odometer itself can still cause large and cumulative
errors due to wheel slippage. Our method for data fusion solves in particular some
issues associated with wheel slippage. The core idea of the approach is based on
different essence of errors, which both the odometry and the accelerometer give.The
odometer typically fails in relatively short time intervals mainly during acceleration
or braking periods. These situations can be successfully handled by accelerometer
as long as current sensor parameters for integration are known at atime (in par-
ticular its’ last value of the offset). The odometer and accelerometer can serveas
supplementary sensing pair substituting each other,ifdesired.
During ashort time period, wheneverneither GPS, nor reliable odometry data
are accessible, the measurement of the traveled distance relies only on integration
of acceleration. Precondition to achieve reliable results of such integration stands
in estimation of the current offset, as mentioned above.Besides that, the estimated
offset can also be used for recognition of the odometry slippage.
The final algorithm works in separated time frames (the time length of one
basic frame is typically in order of seconds), while in scope of which offsets of
the accelerometer are estimated. This is done by the means of LSQ method, which
evaluates offset of accelerometer in order to reach aminimal difference between
speeds obtained from odometer and integrated acceleration with subtracted offset.
offs
acc
=arg min

offs
acc
t
2

t
k
= t
1

v
odo
( t
k
) −


t
k
t
1
( a
acc
( t ) − offs
acc
) dt + v
t
1

2

(2)
where t
1
and t
2
stands for time-boundary of processed time frame, v
odo
denotes
the odometric speed, a
acc
meansthe current sensor value from accelerometer, offs
acc
stands for estimated current sensor offset for the time frame and v
t
1
is the initial
velocity (at the beginning of atime frame) computed from acceleration.
The minimization process returns estimation of the apparent accelerometer off-
set. Provided that estimated offset has asharp slope, itisanindication of the odometry
slippage (e.g the estimated accelerometer offset is significantly greater or lesser than
astandard value which varies slowly). This situation is illustrated in Fig. 5
In case, that progress of the apparent accelerometer offset is smooth, the offset
is treated as areal accelerometer offset overthe whole time frame and the final
traveled distance is computed directly by double integration of accelerometer data
Vehicle Localization Using Inertial Sensors and GPS 141
0 10 20 30 40 50 60 70 80 90 100
0.2
0.3
0.4
0.5

Time(s)
Averageacceleration
correction(m/s2)
Intervalswithout slippage
Rejected intervals -interpolated
Fig.5. Selection of rejected intervals and interpolation.
with subtracted estimated offset. This can also be seen as direct locking of evaluation
of accelerometer-based distance onto odometry (via aminimization process).
If anextreme offset (a slippage has occured)is detected, the whole corresponding
interval is marked as odometry-unreliable one and pure accelerometer is used for the
calculation of traveled distance (with no estimation of the offset from odometry).
The evaluation of accelerometer offset has to be treated in another wayinorder to
guarantee proper conditions for the following double integration process in this case.
To solutionof this probleman extrapolation (orinterpolation for slightlytime-shifted
processing) of preceding offset values before slippage (odometry-reliable interval)
can be applied. The 3rd order splines provide reasonable results for interpolation,
see Fig. 5.
In fact, the traveled distance estimation always uses accelerometer data and the
major differences are only in the wayofdetermination of current accelerometer
offset. Then, the final traveled distance is easily computed by double integration
with respect to the average offset of the accelerometer.
4Experiments
The fusion algorithms for odometry and acceleration data were designed for use with
train vehicles to serveascomplementary substitute to GPS-based vehicle position-
ing. Experimental data were gathered with asetup carrying an incremental optical
odometer offering aresolution of 400 pulses/rev. and industrial accelerometer type
CrossbowCXL01LF.The exact reference forward position of the vehicle has been
obtained from differential GPS receivers operating in RTK(Real Time Kinematics)
mode with the order of about –0.01m accuracy. As the RTKmode of the GPS is not
generally suitable for wide practical application due to its’ slowness and additional

accessories needed, it is very useful for evaluation of the thereunder achievedresults.
The real experiment wasperformed on areal railwaytrack with intentionally
created slippage fields (by application of high accelerations and brakings) in specific
parts of the path. This situation can be noted in the following Fig. 6approximately
by the 60th sec of the experiment runtime (circled).
The measured odometry and acceleration data were provided to the described
fusion algorithm, the quality evaluation of which has been done by comparison
with the GPS measurements and which were gathered synchronously.Therefore, the
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0 100 200 300 400 500 600
-15
-10
-5
0
5
10
15
20
Time [s]
Accelerometer(1.int)
Odometry(1.der)
Direct GPS(lin.interpolation)
Speed[m2/s]
Fig.6. Input data before processing.

comparison of the real travelled distance provided by the GPS with the result of our
approach has been straightforward.
The most important step of the described approach stands in the precise estima-
tion of accelerometer offset; mainly in time frames wheneverodometry fails.
The final result of integration with respect to the estimated offset can be seen in
the Fig. 7. The long-term accuracydepends on proper calibration of odometry.This
means that the results of data fusion can’tprovide better accuracythan the odometry.
However, the major odometry error has been successfully corrected. The remaining
distance error after application of suited two-stage integration of acceleration with
respect to current sensor offset is less than 1m after 9minutes drive (see Fig. 7).
5
10
15
20
30 40 50 60 70 80 90 100
0
Time (s)
Speed(m/s)
Odometry Speed odometru
Speed aftercorrection
Real speedfromGPS
0 100 200 300 400 500 600
-1
-0.5
0
0.5
1
Distanceerrors [m]
Time [s]
Fig.7. Result of the correction algorithm and remaining distance error.

Vehicle Localization Using Inertial Sensors and GPS 143
We suppose, remaining distance error arises from inaccuracyofodometer if the
vehicle drivesthrough curves. Turns induce achange of wheel effective diameter
due the centripetal and centrifugal forces.
In order to test robustness of designed approach the designed approach has also
been tested with partially artificial test data sets. These data sets are based on original
real data, butadditional wheel slippages are added by simulation in odometry data.
The Fig. 8illustrates three simulated slippages besides of first real slippage from
acceleration. The first simulated slippage is quite similar to the real one, the second
one is very short butheavy and the last slippage simulates ahard-breaking state of
the vehicle.
The following Fig. 9shows result errors after performingthefusion of accelerom-
eter and odometry data with elimination of slippages. The presented approach proofs
to be very efficient for higher odometry errors in time frame from 1to15seconds.
0 50 100 150 200 250 300
0
2
4
6
8
10
12
14
16
18
20
Time(s)
Speed(m/s)
Odometry Speed
Speed aftercorrection

Real speed from GPS
Fig.8. Results with additional artificial slippage in odometry.
The only bottleneck of the introduced algorithm determined in the experiments
can be seen in imperfect detection of extremely small and narrowodometry errors.
The primary cause for this is likely to be the impossibility to identify small changes
in accelerometer offset to determine these micro-slippages.
5Conclusion
The presented contribution shows one of the possible and robust ways for utilization
of inertial sensors as short and medium time substitute of the satellite navigation
system. Long-term precision depends on calibration of the odometer,nevertheless
local odometer error induced by wheelslippageispossibletobesuccessfullydetected
and treated using an accelerometer.The described method is under development
towards extension for full 2D localization and it is expected to be targeted on
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0 50 100 150 200 250 300
-1
0
1
2
Time (s)
Distance errors(m)
0 50 100 150 200 250 300
-0.2
-0.1

0
Time(s)
Speed (m/s)
0 50 100 150 200 250 300
-1
0
1
2
Time (s)
Distance errors(m)
0 50 100 150 200 250 300
-0.2
-0.1
0
Time(s)
Speed (m/s)
Fig.9. Speed and distance differences between corrected and GPS data.
improvement of the estimation mechanism for acceleration sensor offset with the
objective to achieve higher precision in path-integration. It is assumed, that possible
solution to this might lead via dynamic optimisation of processing frames size
and combination of their different sizes and/or combining with the sliding-window
approach.
Acknowledgement
The presented research has been supported within the IST-2001-FET framework
under project no. 38873 "PeLoTe". The work is also supported by the Ministry of
Education of the Czech Republic within the frame of the projects "Decision making
and Control for Manufacturing" number MSM 212300013.
References
1. B.Allotta, P.Toni, M.Malvezzi, P. Presciani, G.Cocci, V.Colla, “Distance”, Proc. of World
Congress on Railway Research 2001,Koeln, Germany, 2001

2. B.Barsahn, Hugh F. Durrant-Whyte, “Inertial Navigation System for mobile robots”,
IEEE Transaction on robotics and automation,vol.11 no. 3, pages 328–342, June 1995
3. A. Filip, H.Mocek, L.Bazant, “GPS/GNSS Based Train Positioning for safety Critical
Applications”, Signal +Draht [93],vol.5, pp.16–21 (in German) pp.51-55 (in English)
4. A. Filip, L. Bazant, H. Mocek ,J.Taufer,and V. Maixner,“Dynamic properties of
GNSS/ INS based trainposition locator for signalling applications”, The proceedings of
the Comprail 2002 conference,Greece, 2002
5. A.Lawrence, Modern Inertial Technology -Navigation Guidance,and Control,ISBN
0-387-98507-7, Springer 1998.
6. R. M
´
azl, “Preliminary study for the train locator project -accelerometer and odometer
data fusion”, Research report no. GLR 66/02, CTU,FEE, Dep. of Cybernetics,The
Gerstner Lab for Intelligent Decision Making and Control, Prague, 2002. (Czech lang.)
7. Y.Bar-Shalom, Thomas E. Fortmann, “Tracking and Data Association”, Volume 179 in
Mathematics in science and engineering,ISBN 0-12-079760-7, Academic press, 1988
An Experimental Study of Localization Using
Wireless Ethernet
    
  
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   
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Abstract.            
             
              
            
            
  

1Introduction
           
         
              
           
          
         
          
              
        
          
            
          
              
             
           
          
          
            
          
           
         
      


 
Fig.1.         
              
              
   

          
              
           
             
          
              
      
            
 
2OnMonte-Carlo Localization
           
            
             
  p ( x
t
)     x   t 
          belief     
x   t    Bel ( x
t
)       
            
         
Bel ( x
t
)
a
t

←−


p ( x
t
| x
t

,a
t

) Bel ( x
t

)dx
t


Bel ( x
t
)
s
t
←− p ( s
t
| x
t
) Bel ( x
t
) 
 a
t


      t

<t s
t
   
         p ( s
t
| x
t
)

p ( x
t
| x
t − 1
, a
t − 1
) 

       


           
Bel ( x
t
)        
particle filters 




Re-sampling 


3 Experimental Setup










  






 


4 Properties of Wi-Fi Signal Strength






148 A. Howard, S. Siddiqi, and G.S. Sukhatme
-100
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0 6 12 18 24 30 36 42 48
Level (dB)
Time (hours)
(a)
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0 5 10 15 20 25 30
Level (dB)
Range (m)
(b)
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-180 -120 -60 0 60 120 180
Level (dB)
Orientation (degrees)
(c)
Fig.2. Signal strength measurements for wireless beacon B. (a) Signal strength plotted as a
function of time overa48hour period. (b) Signal strength as afunction of beacon range. (c)
Signal strength as afunction of robot orientation.
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0
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Level (dB)
(a)
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0
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Level (dB)
(b)
Fig.3. (a) Signal strength recorded by robot Fly overtwo complete circuits of the environment.
(b) Signal strength recorded by robot Bug overasimilar circuit.
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Level (dB)
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0
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Level (dB)
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0

5
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Level (dB)
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0
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0

5
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Level (dB)
(a) (b)
Fig.4. Interpolated signal strength maps generated using the filters K
1
and K
1
· K
2
(described
in the text). The maps were generated using the sample set shown in Figure 2(a).
doors, and so on. Some of the variation in the signal strength plot is likely to be
aresult of such changes in the environment. More importantly,however,all of the
variation is confined to arelative narrowband of around 10 dB.
Figure 2(b) shows aplot of signal strength as afunction of range from one the
beacons. This data wasgathered by one of the robots overtwo complete laps around



log r 










  






map 






5 Mapping Wi-Fi Signal Strength
    
           








Ψ = { ( x
0
, ψ
0
) , ( x
1
, ψ
1
) , } 
i x
i
ψ
i

Φ = { ( x
0
, φ
0
) , ( x
1
, φ
1
) , }         
φ
i
x
i


φ
i
=

j
K ( | x
j
− x
i
| ) ψ
j

j
K ( | x
j
− x
i
| )
. 

 
K ( s ) s = | x
j
− x
i
| 
x
j
x
i


K ( s ) 

K
1
( s ) =

1  s < d
0 

    d   

 d = 1 



K
2
( s ) = s
− m

m 


   

p ( φ | x ) 
p ( φ | x ) = exp
− ( φ − φ
i

)
2
2 σ
2

 φ
i
        i   x  σ
2

             
        σ          
           
   best      
      sufficient        
6Localization
            
        
             
              
            
         
     
          
           
             

-8
-6
-4

-2
0
2
4
6
8
10
-20 -15 -10 -5 0 5 10 15 20
True
Estimated
0.01
0.1
1
10
0 10 20 30 40 50 60 70 80 90
Location error (m)
Distance travelled (m)
-8
-6
-4
-2
0
2
4
6
8
10
-20 -15 -10 -5 0 5 10 15
True
Estimated

0.01
0.1
1
10
0 10 20 30 40 50 60 70 80 90
Location error (m)
Distance travelled (m)
-8
-6
-4
-2
0
2
4
6
8
10
-20 -15 -10 -5 0 5 10 15 20
True
Estimated
0.01
0.1
1
10
0 10 20 30 40 50 60 70 80 90
Location error (m)
Distance travelled (m)
Fig.5.           
              
 +                

           
     
     different robots    
          
 opposite 
           
            
            
             
              
            
0 . 40 ± 0 . 09          
           
           
    0 . 26 ± 03    
           
            

 
0 . 25 ± 0 . 02 




0 . 10 




  

 0 . 87 ± 0 . 34
 0 . 55 ± 0 . 12
  
 0 . 45 ± 0 . 14
 0 . 40 ± 0 . 09
           
            
            
           
        
7Conclusion
            
          
          
             
          
          
              
         
     0 . 50       
          
             
        
          
Resources
          
           
             
 
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Acknowledgments


References
      
   IEEE Transactions on Signal
Processing
   
INFOCOM (2)
 
IEEE International Conference on Robotics and Automation (ICRA99)
         

  
Proceedings of the International Conference on
Advanced Robotics (ICAR 2003)
    
 IEEE
Transactions on Wireless Communication
           

 
 Proceedings of the 2002 IEEE/RSJ International
Conference on Intelligent Robots and Systems
   
Artificial Intelligence Journal





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


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

              
            
          
              
  
           
              
                 
             
             
         

           
           
             
           
           
             

              
            
             
            
            
               
             
            
             
            
            
            
 
           
               
        
           
             
             

          
              
          
               
        
         
          
               
            
          

           
         
 
 


 

 



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• 
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• 

• 




• 



• 





          


   






 
        
     
            
           
            
          
          
             
          
          
           
           
           
              
             
               
   
            

         
    
•          
            
            
            
          
•    
           

            
  
 
• 

• 






   
           
            
    
          
         
•   
•      

•           
•            
    
          
            
            
             
             

          
          
            
              
              
           
           
              
             
             
        
 
           
             
           
              
             
  
               
             
           

             
            
            
    
              
 
           
           
            