Localization of Objects using Stochastic

Tunneling

Mohammed Rana Basheer and S. Jagannathan

Department of Electrical and Computer Engineering,

Missouri University of Science & Technology

300 W 16th Street, Rolla, MO 65401

mrbxcf@mst.edu, sarangap@mst.edu

Real Time Location System (RTLS)

• Used for locating or tracking assets in places where GPS signals are not readily available

• Uses Time of Arrival (ToA), Time Difference of Arrival (TDoA), Angle of Arrival (AoA) or Received Signal Strength Indicator (RSSI)

• Cost, accuracy and calibration issues have limited their adoption in factory environment.

Figure 1. Boeing factory floor*

*http://www.ce.washington.edu/sm03/boeingtour.htm

RTLS using RSSI• Uses signal strength of received

radio signals to locate objects

• In free space, Friis transmission equation gives the relation between signal strength and distance between a transmitter and receiver at far field

Figure 3. Ideal Variation of RSSI with DistanceAsset

Shop Floor

area

RF

Receivers

Figure 2. Asset Tracking using RTLS

RSSIdB = A – nlog(r)

Limitations of RTLS using RSSI• Multipath fading noise results in

fast variation of received signal

strength

• Bounded localization error only

under Line of Sight (LoS)

condition

• Shadow fading under LoS

• Costly periodic radio profiling

required for Non-LoS condition

Figure 4. Localizing wireless tags in

a room/container

Problem Statement

Previous Work

1. Yi Shang, Wheeler Ruml, Ying Zhang, and Markus P. J. Fromherz, “Localization from mere connectivity,” in Mobihoc „03, June

2003, pp. 201–212.

2. N. Patwari and A. O. Hero, “Manifold learning algorithms forlocalization in wireless sensor networks,” in Proceedings of theIEEE

International Conference on Acoustics, Speech and SignalProcessing (ICASSP), May 2004, volume 3, pp. 857–860.

3. Wang C, Chen J, Sun Y, Shen X. Wireless sensor networks localization with Isomap. IEEE International Conference on

Communications, 2009.

Limitations

Figure 5. Multipath noise correlation with distance

Limitations (Contd.)• Highly non-linear surface at high frequency violates

linearity assumptions used by MDS, LLE and Isomap

Figure 6. Multi-tag correlation variance at Frequency =27MHz

Proposed Idea• Localization problem is expressed as estimating the radial distance

parameter between wireless tags using maximum-a-posteriori estimator

• Non-linear relationship between RSSI fading correlation coefficients and

radial distance is used instead of linear approximations used in MDS, LLE

and Isomap

• Parameter estimation space is reduced by imposing triangular inequality

constraints

• Finally, the high convergence time arising due to uneven non-convex

terrain of the localization cost function is improved by stochastic tunneling

operator

Steps• The joint distribution of RSSI between a pair of co-located tags that are

under NLoS condition with a common transmitter is derived to find the

estimator for correlation coefficient

• Large sample PDF of correlation coefficient estimator under NLoS

conditions is derived to generate the localization cost function

• For a network with greater than 3 wireless tags, triangle inequality

constraints are added to reduce the estimation space

• Monte Carlo Markov Chain optimization method called Constrained

Simulated Annealing is used to solved this highly uneven cost function

• Finally, stochastic tunneling operator is applied to improve convergence

speed

Joint PDF of Received Signal Strength

Under NLoS

Estimating DBED Parameters

PDF of Correlation Coefficient Estimate

Triangle Inequality Constraint

Radial separation Estimation

Stochastic Optimization• Non-linear greedy optimization techniques can get stuck in

local maxima

• Monte Carlo Markov Chain optimization using Constrained

Simulated Annealing (CSA) is used

• Simulated annealing is guaranteed to convergence at the

expense of computation time

Figure 7. Local localization likelihood function at various frequencies

Constrained Simulated Annealing*• CSA is a variant of the popular Simulated Annealing (SA) optimization

• Generation function generates sample parameter values where the

optimization objective function is evaluated

• Acceptance function that depends on a parameter Tacc called the

“Annealing Temperature” determines the probability of moving away from

a local maxima

• CSA looks for saddle points (local maxima) that occur at the local maxima

in radial distance space and local minima in Lagrange multiplier space

• Separate acceptance functions for radial separation and Lagrange

multiplier space to account for their different optimization objectives

*B. W. Wah, Y. Chen, and T. Wang, "Simulated annealing with asymptotic convergence for nonlinear constrained

optimization," J. of Global Optimization, Vol. 39, No. 1, pp. 1-37, Sep. 2007

Stochastic Tunneling*

Figure 8. Tunneling Effect

*W. Wenzel, and K. Hamacher, "Stochastic Tunneling Approach for

Global Minimization of Complex Potential Energy Landscapes,"

American Physical Society, vol. 82, No. 5, pp. 3003-3007, Apr. 1999.

Simulation Results• m=20 wireless tags and n=4 anchor nodes in a 20m x 20m x 20m

cubical workspace

• Anchor nodes positioned at corners of this cubical workspace

• Wireless tags were distributed randomly in the cubical workspace

• correlation coefficient matrix was generated from double truncated

normal random variables with mean and variance computed from

N=100 pair wise RSSI samples and true radial separation between

tags

• 50 Monte Carlo simulation trials were performed to determine the

mean, median, standard deviation and 90th percentile of localization

errors.

CDF of Localization Errors

Figure 9. CDF of localization error at 27MHz

Table 1. Summary of Localization Error

MethodF

(MHz)

Localization Error (m)

Mean Median90th

percentileStandard deviation

LOCUST

100

2.562 2.399 4.739 1.487

LLE 24.378 23.967 30.628 6.121

MDS 23.232 22.841 29.597 5.096

LOCUST

70

1.865 1.942 2.568 0.665

LLE 17.42 17.832 23.223 4.324

MDS 13.44 13.243 17.806 3.426

LOCUST

27

0.545 0.503 0.864 0.256

LLE 3.245 3.286 5.229 1.485

MDS 2.888 2.929 3.984 0.893

LOCUST

10

0.231 0.246 0.483 0.124

LLE 0.173 0.154 0.304 0.112

MDS 0.181 0.165 0.298 0.092

Summary

Questions