1. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami
Wireless Sensor Network Positioning
Techniques
Mohammad Reza Gholami
Communication Systems Group
Department of Signals and Systems
Chalmers University of Technology
PhD Defense
Nov 12, 2013
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2. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami
Global positioning system (GPS)
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Real sample
http://en.wikipedia.org/wiki/Global_Positioning_System

3. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami
GPS drawbacks for positioning
• Limited access
• Latency
• Power constraint
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Position from the network
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4. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami
Outline
• Introduction
• Positioning problem
• Measurement models
• Performance measures
• Contributions (statistical and geometric
approaches)
• Conclusions
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5. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami
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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6. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami
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7. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami7

8. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami
Problem statement
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9. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami9
Problem statement
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- MLE
- Least squares
- Geometric estimators
…
- centralized
- distributed
- noncooperative
- cooperative

10. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami
Measurement models
• Time-of-arrival (TOA):
• Time-difference-of-arrival (TDOA):
• Two-way TOA (TW-TOA):
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TW-TOA

11. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami
Performance metrics
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• Estimation error
• Cumulative density function (CDF)
• Cramér-Rao lower bound (CRLB)

12. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami
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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13. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami13
Simulation results
 Measurement noise: i.i.d. Gaussian
 CRLB, MLE, and the linear estimators
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14. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami14
CRLB analysis (for target 14)
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Conv.: only primary nodes Coop. 1: both primary and secondary ref. nodes
Coop. 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.

15. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami15
Performance of estimators (for target 9)
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- The proposed
linear estimator
asymptotically
attains the CRLB
5 10 15 20 25 30 35 40 45 50
5
10
15
20
25
30
σ [m]
RMSE[m]
Linear estimator
MLE
CRLB
CRLB
Linear estimator
MLE

16. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami
 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

17. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami
Examined estimators
• MLE (complex), Two suboptimal efficient estimators (based on LS and
SDP) followed by a refining step
• Network deployment
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0 2 4 6 8 10
0
2
4
6
8
10
12
σ [m]
RMSE[m]
LS & LS+Fine
CRLB & MLE
SDP & SDP+Fine

18. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami18
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Geometric interpretation
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19. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami
 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.

20. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami20
Numerical results
Tightness:
Relative tightness:
Estimate from Projection onto convex sets
(POCS) approach
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21. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami21
Bound 3
Bound 2
Bound 1
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22. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami
An application
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23. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami
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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24. Chalmers University of Technology
Wireless Sensor Network Positioning Techniques Mohammad Reza Gholami24