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A Hybrid TOA/RSS Based Location Estimation

A Hybrid TOA/RSS Based Location Estimation. Zafer Sahinoglu, zafer@merl.com Digital Communications and Networking Group, MTL September 11 th , 2004. Outline. Hybrid ranging observation scenarios Modeling of RSS and TOA observations Problem formulation and Derivation of CRBs Results

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A Hybrid TOA/RSS Based Location Estimation

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  1. A Hybrid TOA/RSS Based Location Estimation Zafer Sahinoglu, zafer@merl.com Digital Communications and Networking Group, MTL September 11th, 2004

  2. 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

  3. Hybrid Ranging Observation Scenarios

  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

  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:

  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 iand j • RSS observation: [ Pi,j ], received power at devicejfromi • 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

  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

  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 0 C B

  9. Derivation of the CRB in TOA/RSS • The CRB TOA contribution TOA/RSS contribution RSS contribution where and

  10. Four reference devices at four corners, separation 18m RSS suppresses singularities of TOA at corners Figures below gives in meters The CRB for TOA vs TOA/RSS

  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

  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)

  13. The Spatial Average of the CRBs Spatial mean of the lower bound in meters APR separation around the square in meters

  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

  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. 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.

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