A Hybrid TOA/RSS Based Location Estimation Zafer Sahinoglu, zafer@merl.com Digital Communications and Networking Group, MTL September 11th, 2004 12/5/2018

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 12/5/2018

Hybrid Ranging Observation Scenarios 12/5/2018

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 12/5/2018

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: 12/5/2018

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 12/5/2018

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 12/5/2018

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 12/5/2018

Derivation of the CRB in TOA/RSS TOA contribution TOA/RSS contribution RSS contribution where and 12/5/2018

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 12/5/2018

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 12/5/2018

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) 12/5/2018

The Spatial Average of the CRBs Spatial mean of the lower bound in meters APR separation around the square in meters 12/5/2018

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 12/5/2018

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. 12/5/2018