A Hybrid TOA/RSS Based Location Estimation

1. A Hybrid TOA/RSS Based Location Estimation Zafer Sahinoglu, zafer@merl.com Digital Communications and Networking Group, MTL September 14th, 2004 Z. Sahinoglu, Mitsubishi Electric research Labs

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 Z. Sahinoglu, Mitsubishi Electric research Labs

3. Hybrid Ranging Observation Scenarios Z. Sahinoglu, Mitsubishi Electric research Labs

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 Z. Sahinoglu, Mitsubishi Electric research Labs

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: Z. Sahinoglu, Mitsubishi Electric research Labs

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 Z. Sahinoglu, Mitsubishi Electric research Labs

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 Z. Sahinoglu, Mitsubishi Electric research Labs

8. Derivation of the CRB in TOA/RSS • The CRB TOA contribution TOA/RSS contribution RSS contribution where and Z. Sahinoglu, Mitsubishi Electric research Labs

9. 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 Z. Sahinoglu, Mitsubishi Electric research Labs

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 Z. Sahinoglu, Mitsubishi Electric research Labs

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 Z. Sahinoglu, Mitsubishi Electric research Labs

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) Z. Sahinoglu, Mitsubishi Electric research Labs

13. The Spatial Average of the CRBs Spatial mean of the lower bound in meters Device separation around the square (in meters) Z. Sahinoglu, Mitsubishi Electric research Labs

14. 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 Z. Sahinoglu, Mitsubishi Electric research Labs

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. Z. Sahinoglu, Mitsubishi Electric research Labs