A Hybrid TOA/RSS Based Location Estimation

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A Hybrid TOA/RSS Based Location Estimation

• Zafer Sahinoglu, zafer_at_merl.com
• Digital Communications and Networking Group, MTL
• September 11th, 2004

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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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Hybrid Ranging Observation Scenarios
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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
• SNRgt25dB

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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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Relative Location Estimation Problem

• 1 sensor device (SN)
• m TOA devices with indexes 1,,m
• n RSS devices with indexes m1,mn
• 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,m1,,
  P0,mn , TDOA/RSS hybrid scheme
• X XT XR T1, T2,Tm P0,m1,, P0,mn ,
  TOA/RSS hybrid scheme

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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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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
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Derivation of the CRB in TOA/RSS

• The CRB

TOA/RSS contribution
RSS contribution
TOA contribution
where and
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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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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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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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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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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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References

• PATWARI N. Patwari, A. O. Hero, M. Perkins, N.
  S. Correal, R. J. ODea 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. 3541, Nov 2001.