PhD_Defense

Chalmers University of Technology

Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami

Wireless Sensor Network PositioningTechniques

Mohammad Reza Gholami

Communication Systems GroupDepartment of Signals and SystemsChalmers University of Technology

PhD DefenseNov 12, 2013

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Global positioning system (GPS)

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Real sample

http://en.wikipedia.org/wiki/Global_Positioning_System



GPS drawbacks for positioning

• Limited access

• Latency • Power constraint

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Position from the network

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Outline

• Introduction• Positioning problem• Measurement models• Performance measures• Contributions (statistical and geometric

approaches)• Conclusions

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Wireless sensor networks (WSNs) positioning

WSN: position information for processing the data GPS not applicable in some scenarios Extracting the position information from the network

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Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami 6



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Problem statement

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Problem statement

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- MLE- Least squares- Geometric estimators…

- centralized- distributed

- noncooperative- cooperative



Measurement models• Time-of-arrival (TOA):

• Time-difference-of-arrival (TDOA):

• Two-way TOA (TW-TOA):

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TW-TOA



Performance metrics

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• Estimation error • Cumulative density function (CDF)

• Cramér-Rao lower bound (CRLB)



Contributions

(TW)TOA- based positioning - increasing the number of reference nodes - increasing signal-to-noise ratios

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• Limitations (delay, cost) Cooperative idea

• Primary reference nodes (PRNs) measure TW-TOA • Secondary reference nodes (SRNs) & other targets can listen to signals exchanged

between PRNs and a target, thereby measure TDOA (eavesdropping)

[Paper A] M. R. Gholami, S. Gezici, and E. G. Ström, “Improved position estimation using hybrid TW-TOA and TDOA in cooperative networks,” IEEE Trans. Signal Process., vol. 60, no. 7, pp. 3770–3785, Jul. 2012.

MLE, a linear estimator, CRLB

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Simulation results Measurement noise: i.i.d. Gaussian CRLB, MLE, and the linear estimators

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CRLB analysis (for target 14)

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Conv.: only primary nodes Coop. 1: both primary and secondary ref. nodesCoop. 2: primary, secondary, and pseudo secondary

• For an efficient estimator

- Cooperation improves the estimation accuracy, especially for low SNR

- Joint estimation with unknown turn-around time implies a performance loss

Coop. 2

Coop. 1Conv.



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Performance of estimators (for target 9)

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- The proposed linear estimator asymptotically attains the CRLB

CRLB

Linear estimatorMLE



TDOA- based positioning - Affine function to model the local clock -TOA estimation for unsynchonized clock

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[Paper B] M. R. Gholami, S. Gezici, and E. G. Ström, ``TDOA-based positioning in the presence of unknown clock skew,” IEEE Trans. Commun., vol. 61, no. 6, pp. 2522--2534, Jun. 2013.

Unknown



Examined estimators• MLE (complex), Two suboptimal efficient estimators (based on LS and

SDP) followed by a refining step• Network deployment

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Geometric interpretation

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Upper-bound on position estimates

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Other bounds: 1-maximum length based on 2-norm 2-maximum length based on bounding box covering the intersection

[Paper D] M. R. Gholami, E. G. Ström, H. Wymeersch, and M. Rydström, ``Upper bounds on position error of a single location estimate in wireless sensor networks,” submitted to Signal Processing, Sep. 2013.



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Numerical results

Tightness:

Relative tightness:

Estimate from Projection onto convex sets(POCS) approach

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Bound 3

Bound 2

Bound 1

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An application

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Conclusions• [A]: Eavesdropping of TW-TOA transmission to reduce positioning delay - derives MLE, CRLB, suboptimal linear algorithm - performance is increased especially at low SNR

• [B]: Positioning with TDOA measurements with imperfect clocks - derives MLE, CRLB, suboptimal algorithms - suboptimal algorithms asymptotically achieve the CRLB

• [C]: Positioning using RSS measurement for unknown channel parameters - formulates the problem as a QCQP and solves it by a low complex algorithm - good trade-off between accuracy and complexity compared to existing approaches

• [D] Upper-bounds on the position errors - reasonably tight in many situations

• [E] Quantifying the feasible sets in cooperative scenarios - the method converges fast - outperforms the existing approach

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