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A Hybrid TOA/RSS Based Location Estimation. Zafer Sahinoglu, [email protected] Digital Communications and Networking Group, MTL September 14 th , 2004. Outline. Hybrid ranging observation scenarios Modeling of RSS and TOA observations Problem formulation and Derivation of CRBs Results - PowerPoint PPT Presentation
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September 2004
Z. Sahinoglu, Mitsubishi Electric research LabsSlide 1
doc.: 15-04-0522-01-004a
Submission
A Hybrid TOA/RSS Based Location Estimation
Zafer Sahinoglu, [email protected]
Digital Communications and Networking Group, MTL
September 14th, 2004
September 2004
Z. Sahinoglu, Mitsubishi Electric research LabsSlide 2
doc.: 15-04-0522-01-004a
Submission
Outline
Hybrid ranging observation scenarios Modeling of RSS and TOA observations Problem formulation and Derivation of CRBs Results Summary and Conclusions
For More Details Proc. IEEE ICC 2004, June 2004, Paris IEEE Communications Letters, to appear in October 2004
September 2004
Z. Sahinoglu, Mitsubishi Electric research LabsSlide 3
doc.: 15-04-0522-01-004a
Submission
Hybrid Ranging Observation Scenarios
September 2004
Z. Sahinoglu, Mitsubishi Electric research LabsSlide 4
doc.: 15-04-0522-01-004a
Submission
Wideband Channel Measurement Experiment [PATWARI]
Office area partitioned by 1.8m high cubicle walls DSSS Tx and Rx (Sigtek model ST-515) 40MHz chip rate, fc = 2.443GHz Omni-directional antennas 1m above the floor The Rx
Down converts and correlates I and Q samples with the known PN signal and outputs a power-delay profile (PDP)
Samples of the leading edge of the PDP is compared to an over-sampled (120MHz) template of the auto-correlation of the PN
SNR>25dB
September 2004
Z. Sahinoglu, Mitsubishi Electric research LabsSlide 5
doc.: 15-04-0522-01-004a
Submission
Modeling of TOA and RSS Observations
RSS obscured by log-normal shadowing Frequency-selective fading reduced by wideband average Time-averaging reduce fading due to motion of objects in channel, reciprocal
channel averaging helps to reduce device calibration errors Log-normal shadowing remains
TOA is affected predominantly by multipath Positive bias due to multipath assumed known and subtracted
Resulting statistic:
0
,100,
,,,
log10)dBm()dBm(
)dB()dBm()dBm(
d
dnPP
XPP
jiji
jijiji
2, ,0~)dB( shji NX
2,, ,~ Tjiji cdNT
September 2004
Z. Sahinoglu, Mitsubishi Electric research LabsSlide 6
doc.: 15-04-0522-01-004a
Submission
Relative Location Estimation Problem
1 sensor device (SN) m TOA devices with indexes 1,…,m n RSS devices with indexes m+1,…m+n
Estimate the actual coordinate
TOA observation: [ Ti,j ], time delay between devices i and j
RSS observation: [ Pi,j ], received power at device j from i The estimation is based on (m-1) TOA and n RSS observations in the
TDOA/RSS case Observation vector:
X = [XT ; XR]= [ T1,2, T2,3…,Tm-1,m ; P0,m+1,…, P0,m+n ], TDOA/RSS hybrid scheme X = [XT ; XR]= [ T1, T2…,Tm ; P0,m+1,…, P0,m+n ], TOA/RSS hybrid scheme
000 , yx
September 2004
Z. Sahinoglu, Mitsubishi Electric research LabsSlide 7
doc.: 15-04-0522-01-004a
Submission
Motivation for the Cramer-Rao Study The CRB provides the lower bound on the covariance matrix of any unbiased
estimator Theoretical confirmation of whether a given scheme can satisfy applications
precision ranging requirements Quantification of how random system/environment variables affect the precision
ranging Useful for selection and optimization of design parameters
The CRB of any unbiased estimator is
is the Fisher Information Matrix
The log-likelihood function is
10 0ˆcov( ) ( )I
0̂
)( 0I ))(()( 00 00 XlEI
RSS
R
RSSTOA TOA
TNi
iXNNi Ni
iiXi PfTflXl )|(log)|(log)|( 0,0|01,|,00 00
September 2004
Z. Sahinoglu, Mitsubishi Electric research LabsSlide 8
doc.: 15-04-0522-01-004a
Submission
2
0,0,
,22
0,
2,
222,222
20,22
2
)(1
)(
RSS RSSTDOA RSSTDOA TDOA
RSS
NijiNj ji
ji
Ni Nj j
ji
Ni TjiNj
jiT
Nii
T
TDOA
CRB
dd
Ab
d
A
cb
Ac
dbc
Ncard
Derivation of the CRB in TOA/RSS
210
log10p
sh
nb
where and 0 , ,,
,0 ,0
i j i ji j
i j
d dA
d d
The CRB
TOA/RSS contribution RSS contributionTOA contribution
September 2004
Z. Sahinoglu, Mitsubishi Electric research LabsSlide 9
doc.: 15-04-0522-01-004a
Submission
Definition: Geometric Conditioning
Illustration of the geometric conditioning (A1,2) of devices “1” and “2” with respect to device “0”.
1 0
2
d0x1,2
A
B C
D
0,20,1
2,12,102,1 dd
ddA x
September 2004
Z. Sahinoglu, Mitsubishi Electric research LabsSlide 10
doc.: 15-04-0522-01-004a
Submission
The CRB for TOA vs TOA/RSS
/ 2dB Pn 8.1Tc / 2dB Pn 8.1Tc
Four reference devices at four corners, separation 18m RSS suppresses singularities of TOA at corners Figures below gives in metersCRB
September 2004
Z. Sahinoglu, Mitsubishi Electric research LabsSlide 11
doc.: 15-04-0522-01-004a
Submission
2
0,0,
,22
0,
,,1
20,
20,1,1
222
,,1,1222
20,,12222
2
)(
)()2(
1
cos2
1)(
RSS RSSTDOA
RSS
TDOA TDOA
TDOA RSS
NijiNj ji
ji
Ni
Nj i
jij
ii
Ni TjiNj
jijiT
Ni Niij
TT
TDOA
CRB
dd
Ab
d
AA
ddA
cb
AAAc
dbcc
Ncard
Derivation of the CRB in TDOA/RSS The variance of the TDOA observations are twice higher than the TOA 1 TOA measurement is sacrificed for offset removal The CRB must therefore be higher than the TOA/RSS Geometric conditioning of APRs with respect to RNs directly affect the bound
TDOA/RSS contribution RSS contributionTDOA contribution
1: index of the reference APR
September 2004
Z. Sahinoglu, Mitsubishi Electric research LabsSlide 12
doc.: 15-04-0522-01-004a
Submission
The CRB for TOA/RSS vs TDOA/RSS
In TDOA/RSS, one reference device placed in the center, the other three around a circle to maintain a symmetric plot
The radius of the circle is selected such that the area would be equal to 18x18m square
TDOA/RSS inferior due to sacrificing 1 independent TOA measurement and increased standard deviation
The plots show the bounds in meters (np = 2.3)
/ 2dB Pn 8.1Tc / 2dB Pn 8.1Tc
September 2004
Z. Sahinoglu, Mitsubishi Electric research LabsSlide 13
doc.: 15-04-0522-01-004a
Submission
The Spatial Average of the CRBs
/ 2dB Pn 8.1Tc
Spa
tial
mea
n of
the
low
er b
ound
in m
eter
s
CRB
Device separation around the square (in meters)
September 2004
Z. Sahinoglu, Mitsubishi Electric research LabsSlide 14
doc.: 15-04-0522-01-004a
Submission
Summary and Discussion The Cramer Rao Bounds of the hybrid schemes are given The RSS measurements can be used to refine wideband TOA based
estimations in short ranges The hybrid schemes TDOA/RSS and TOA/RSS have lower CRBs than TOA or RSS
based schemes alone
The following areas can be explored to be factored into the analysis of the CRBs to derive more accurate bounds
September 2004
Z. Sahinoglu, Mitsubishi Electric research LabsSlide 15
doc.: 15-04-0522-01-004a
Submission
References[PATWARI] N. Patwari, A. O. Hero, M. Perkins, N. S. Correal, R. J. O’Dea “Relative Location Estimation in Wireless Sensor
Networks,” IEEE Trans. Signal Processing, vol. 51, pp. 2137-2148, August 2003
[CAPKUN] S. Capkun, M. Hamdi, and J.-P. Hubaux. GPS-free positioning in mobile ad-hoc network. In 34th IEEE Hawaii International Conference on System Sciences (HICSS-34), Jan. 2001
[DOHERTY] L. Doherty, K. S. pister, and L. E. Ghaoui. Convex position estimation in wireless sensor networks. In IEEE INFOCOM, vol. 3, pages 1655 –1663, 2001.
[ALBOVITCZ] J. Albowicz, A. Chen, and L. Zhang. Recursive position estimation in sensor networks. In IEEE International Conference on Network Protocols, pp. 35–41, Nov 2001.
