1. A Hybrid TOA/RSS Based Location Estimation
Zafer Sahinoglu,
Digital Communications and Networking Group, MTL
September 11th, 2004
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2. Hybrid ranging observation scenarios
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
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3. Hybrid Ranging Observation Scenarios
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4. 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
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5. 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:
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6. 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
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7. 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
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8. Definition: Geometric Conditioning
Illustration of the geometric conditioning (A1,2) of devices “1” and “2” with respect to device “0”. 2 A D
d0x1,2 1 B C
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9. Derivation of the CRB in TOA/RSS
TOA contribution
TOA/RSS contribution
RSS contribution
where and
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10. The CRB for TOA vs TOA/RSS
Four reference devices at four corners, separation 18m
RSS suppresses singularities of TOA at corners
Figures below gives in meters
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11. 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
1: index of the reference APR
TDOA contribution
TDOA/RSS contribution
RSS contribution
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12. 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)
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13. The Spatial Average of the CRBs
Spatial mean of the lower bound in meters
APR separation around the square in meters
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14. Summary and Discussion
The RSS measurements can be used to refine wideband TOA based estimations in short ranges
The hybrid schemes TDOA/RSS and TOA/RSS outperform TOA or RSS based schemes alone
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15. 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 , 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.
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