Real Time Localization Systems Using Receiver Signal Strength Indicator

Mohammed Rana Basheer Advisor: Dr. Jag Sarangapani

2

Publications Refereed Journal Papers

M.R. Basheer, and S. Jagannathan, "Enhancing Localization Accuracy in an RSSI Based RTLS Using R-Factor and Diversity Combination", in review, International Journal of Wireless Information Networks

M.R. Basheer, and S. Jagannathan, "Receiver Placement Using Delaunay Refinement-based Triangulation in an RSSI Based Localization“, revised and resubmitted, IEEE/ACM Transactions on Networking

M.R. Basheer, and S. Jagannathan, "Localization of RFID Tags using Stochastic Tunneling", accepted, IEEE Transactions on Mobile Computing

M.R. Basheer, and S. Jagannathan, "Localization and Tracking of Objects Using Cross-Correlation of Shadow Fading Noise", minor revision, revised and resubmitted, IEEE Transactions on Mobile Computing

M.R. Basheer, and S. Jagannathan, "Placement of Receivers for Shadow Fading Cross-Correlation Based Localization", to be submitted

3

Publications (contd.) Refereed conference papers

M.R. Basheer, and S. Jagannathan, "R-Factor: A New Parameter to Enhance Location Accuracy in RSSI Based Real-time Location Systems," Sensor, Mesh and Ad Hoc Communications and Networks, SECON '09. 6th Annual IEEE Communications Society Conference on , pp. 1-9, 22-26 June 2009.

M.R. Basheer, and S. Jagannathan, "A New Receiver Placement Scheme Using Delaunay Refinement-Based Triangulation," Wireless Communications and Networking Conference (WCNC), 2010 IEEE, pp.1-6, 18-21 April 2010.

M.R. Basheer, and S. Jagannathan, "Localization of objects using stochastic tunneling," Wireless Communications and Networking Conference (WCNC), 2011 IEEE, pp.587-592, 28-31 March 2011.

M.R. Basheer, and S. Jagannathan, " Localization of Objects Using Cross-Correlation of Shadow Fading Noise and Copulas," Global Communication Conference (GLOBECOM), 2011 IEEE, 6-8 Dec 2011.

M.R. Basheer, and S. Jagannathan, " Placement of Receivers for Shadow Fading Cross-Correlation Based Localization," Submitted to IEEE Local Computer Networks (LCN) 2012.

4

Presentation Outline Introduction and Background

Paper 1: Enhancing Localization Accuracy in an RSSI Based RTLS Using R-Factor and Diversity Combination

Paper 2: Receiver Placement Using Delaunay Refinement-based Triangulation in an RSSI Based Localization

Paper 3: Localization of RFID Tags using Stochastic Tunneling

Paper 4: Localization and Tracking of Objects Using Cross-Correlation of Shadow Fading Noise

Paper 5: Placement of Receivers for Shadow Fading Cross-Correlation Based Localization

Conclusions

Future Work

5

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

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

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

Real Time Location Systems (RTLS)

Friis Transmission Equation RSSI vs. Distance

)log(rnARSSI

RTLS using RSSI Uses signal strength of radio signals to locate objects

Classified into Range Based Range Free

RSSI Profile of ERL 114

6

7

RTLS Receiver

RTLS Tag MST Mote

Localization Hardware

IEEE 802.15.4 transceiver from XBee

Operating frequency 2.45 GHz with 100 MHz Bandwidth

8051 variant microcontroller

8KB RAM and 128 KB code space

Spatial diversity with 2 antennas

8

Motivation for RTLS using RSSITime and Angle based methods are costly and require dedicated

hardware

RSSI information easily accessible through API

Localization can be easily deployed on existing wireless infrastructure as a software upgrade

Time and Angle based localization achieves better accuracy under LoS condition

Coarse grained localization

Periodic radio profiling of target area under range free methods or calibration of parameters under range based method is essential

9

Goal and Objectives of the Dissertation Goal—Given a location error threshold, determine the location of a

transmitter and track it in a workspace by placing the appropriate number of receivers at the right position in a workspace.

Objectives Develop algorithms for localization and tracking of wireless devices from

radio signal strength signals

Develop algorithms for placing wireless receivers around the workspace so that the error in locating a transmitter at any point in this workspace is less than a predefined threshold

Demonstrate the efficacy of the placement and localization algorithms analytically, in simulation environment and experimentally through hardware

Both range-based and range free methods are developed

10

Cohesion of completed work

Localization Using RSSI

Range-Based

Cross-Correlation

Paper 1. M.R. Basheer, and S. Jagannathan, "Enhancing Localization Accuracy in an RSSI Based RTLS Using R-Factor and Diversity Combination", under review at International Journal of Wireless Information Networks

Paper 2. M.R. Basheer, and S. Jagannathan, "Receiver Placement Using Delaunay Refinement-based Triangulation in an RSSI Based Localization", Revised and resubmitted to IEEE/ACM Transactions on Networking

Paper 3. M.R. Basheer, and S. Jagannathan, "Localization of RFID Tags using Stochastic Tunneling", Accepted at IEEE Transactions on Mobile Computing

Paper 4. M.R. Basheer, and S. Jagannathan, " Localization and Tracking of Objects Using Cross-Correlation of Shadow Fading Noise", Minor revision, revised and resubmitted, IEEE Transactions on Mobile Computing,

Paper 5. M.R. Basheer, and S. Jagannathan, "Placement of Receivers for Shadow Fading Cross-Correlation Based Localization", to be submitted,

11

Paper 1: Enhancing Localization Accuracy in an RSSI Based RTLS Using R-Factor and Diversity Combination

Friis Transmission Equation

Euclidean distance equation

affected by outliers

Weighted least square to the rescue

Weights are the radial distance variance and are called the R-Factor

Transmitter

Receivers

Base station

Transmitter location estimation happens in base station from Signal

Strength

12

Paper 1: Enhancing Localization Accuracy in an RSSI Based RTLS Using R-Factor and Diversity Combination Objectives

Derive a statistical parameter called the R-factor to grade radial distance estimates to a transmitter from RSSI values

Non-coherent diversity combination techniques that can improve radial distance estimation

Previous efforts involved Proximity in Signal Space (PSS), a heuristic algorithm that uses signal strength to

classify receivers for localization accuracy [Gwon 04]

Chi-square test to classify Line of Sight (LoS) condition at the receiver into Ricean or Rayleigh [Lakhzouri 03]

Binary classification of receivers into good or bad based on a test for Gaussian distribution [Venkatraman 02]

13

Assumptions

Received signal amplitude random variable X is Ricean distributed with PDF given by

Radial distance random variable R is related to RSSI X as

where n is the path loss exponent and l0 accounts for antenna geometry, wavelength etc.

202

22

22

2exp,|

XXXXX

AxI

xAxAxf

n

X

lXgR

1

20)(

14

where is the Confluent Hyper-geometric Function (CHF) and is the ratio of the power in the deterministic LoS component to the NLoS energy or the signal to noise ratio for localization.

The mean and variance of the radial distance estimate by a receiver to a transmitter using Friis transmission equation based estimator under Ricean environment is given by

KMKKM

l

ln

n

KM

lKRE

n

X

X

n

X

X ,1,2

1

41

,1,21

222

,1,21

2),|( 2

11

22

0

02

2

1

22

02

KMKKM

l

lnKRVar

n

X

XX ,1,

2

1

41

,1,21

28),|( 2

12

22

0

02

22

Mean & Variance of Radial Distance Estimate

22 2 XAK ,,M

15

Localization Receiver and R - Factor A receiver for RSSI based RTLS, is called a localization receiver if the signal to noise ratio for the received signals is greater than 9

Mean and Variance of radial distance estimate is given by

22 2 XAK

0200

22,| r

Kn

nrKrRE

Kn

r

Kn

AlKrRVar

nn

2

20

2

42

00

22),|(

R-Factor (Receiver Error Factor) measures the variance in radial distance estimate by a localization receiver

20

2

02

20

02

20 2

),|(2

1X

bX

n

crln

rKrRVar

Kn

r

MSE is proportional to R-Factor

10821082 222

20 nnnnKn

rMSE

Bias

16

Localization Error and R-Factor

Theorem 1: (Comparison of localization accuracy under LoS and NLoS) For the same amount of NLoS energy at a localization receiver and a receiver under NLoS conditions, the MSE of the radial distance estimate for the localization receiver is lower than that of the receiver under the NLoS condition

Theorem 2: (R-factor and localization accuracy) The upper bound of the localization error decreases with R-factor in a Ricean environment for a RSSI based RTLS

Theorem 3: (Localization accuracy and receiver count) Localization accuracy using w+1 receivers is better in comparison with deploying w receivers in an RSSI based RTLS system when the maximum R-factor is kept the same in both cases

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Channel Diversity and R-Factor Diversity is a method to improve certain aspects of the received

signal by using two or more communication channels

Two commonly used diversity schemes are Spatial Diversity using multiple antennas Frequency Diversity

For RTLS using RSSI only non-coherent combination is possible

Diversity channels were combined using one of the following methods Selection Combination: Best signal out from all channels Averaging: Mean of signals from all channels Root Mean Square: Compute RMS of signal from all channels

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Simulation of R-Factor vs. Diversity Count

LoS Conditions NLoS Conditions

Variation of R-Factor with increasing diversity channel count

From simulations, combining RSSI from diversity channels using RMS produced the lowest R-Factor and consequently the best localization accuracy

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Receiver layout in ERL 114

CDF of Localization Error

*Gwon et al. 2004

Localization Experiment

Localization MethodLocalization Error (cm)

Mean Median 90th percentile Std. dev

TIX + PSS 342 298 432 62.81TIX with R-factor 267 214 335 40.32

TIX with R-factor and Spatial Diversity 254 210 329 40.15

Summary of Localization Error Levels

22% decrease26%

decrease

28% decrease30%

decrease

22% decrease24%

decrease

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Conclusions and Contributions

Conclusions Existing localization schemes can

use R-Factor to identify subset of receivers that will result in better location estimation

R-Factor combined with RMS channel diversity was shown theoretically and experimentally to improve localization accuracy

RMS diversity combination was shown to have better localization performance than averaging and selection diversity combination

Contributions A novel parameter called R-

Factor to identify receivers with low range estimation errors was presented

R-factor for selection combination, averaging and root mean square diversity combination were derived

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Paper 2: Receiver Placement Using Delaunay Refinement based Triangulation in an RSSI Based Localization

Where do I place these receivers?

Shopping Mall Layout

Delaunay refinement placement is the solution

Transmitter being localized with guaranteed accuracy

Possible Applications• Locate cellphones to track foot traffic• Coupons for visiting shops• Theft prevention

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Objective is to find a receiver layout that will locate a transmitter with error less than a preset threshold with least number of receivers

Euclidean equation that relates the transmitter location to radial distance

between transmitter and receiver is non-linear in xt and yt

Previous effort involved Delaunay Triangulation based placement that combines heuristics and wireless

coverage requirements [Wu 07] Receiver position based on minimizing the condition number of a linear

equation [Isler 06] Radial errors are assumed to be Gaussian distributed and then receiver

positions are selected based on minimization of Fisher information determinant [Martinez 05]

Paper 2: Receiver Placement Using Delaunay Refinement based Triangulation in an RSSI Based Localization

22

22222iiitt

titi

ryxyxyyxx

23

Wireless Propagation Model

Under far-field conditions between transmitter and receiver

However measured signal strength involves noise Pi = Pi*+ei

Estimate of di from Pi , represented as ri is

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Multi-Lateration Using CWLS Constrained Weighted Least Squares provides a

method to linearize a non-linear equation and solve for parameters in a linear least square sense

Niryxyx

yyxx iiitttiti ,2,1;

22

22222

2 – Parameter Non-Linear Estimation Problem

NiryxR

yyxx iiistiti ,2,1;

22

222

Constraint22tts yxR

3 – Parameter Linear Estimation Problem

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Localization Error Under CWLS Theorem 1: For an RTLS setup with N receivers the

localization error in estimating the position of the transmitter at location η using CWLS is given by

where λ1, λ2 and λ3 are the eigenvalues of the matrix ,

are the R-factors and ξ≥0 is the

Lagrange multiplier and as the cost of violating 22tts yxR

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Receiver Placement Quality Metric Maximum localization error at location η occurs when ξ=0

Receiver placement quality metric is the maximum localization error throughout the workspace G

Objective is to attain with least number of receivers

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Optimal Unconstrained Receiver Placement

Theorem 2: A receiver placement strategy whose objective is to span the largest area under localization coverage with least number of receiver while ensuring no coverage holes exists within the placement grid, will have all its receivers placed in an equilateral triangular grid with grid spacing equal to the communication range of the wireless device

Bounding walls around a workspace prevents equilateral grid placement of receivers !!!!

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Constrained Receiver Placement Requirements Equilateral triangular grid wherever possible

Near bounding walls triangular grids that are as close to equilateral triangle as possible

Placement should satisfy localization error constraint

Should complete in linear time

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Delaunay Refinement Triangulation

Originally developed to generate mesh for Finite Element Modeling and Computer Games

Delaunay Refinement satisfies all our receiver placement requirements

However, boundary walls results in sub-optimal receiver count

Delaunay meshing of a 3D object*

* G E O M E T R I C A (http://www-sop.inria.fr/geometrica/ ) 

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Receiver Count Under Delaunay Refinement Placing

Theorem 3 (Upper Bound for Receiver Count): For a given workspace G, and a localization error threshold (ϵu), the receiver count generated using Delaunay refinement triangulation on G is suboptimal and is upper bounded by the receiver count for an optimal triangulation of the above receiver placement problem as,

where

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Local Feature Size and Receiver Count

Local feature size can be described approximately as a measure of the feature (segments and vertices) density of a graph

Removing shorter segments in an input layout resulting in the bound getting tighter

Shorter segments in a layout are those segments that are less than twice wavelength

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Bounded Receiver Count

Shopping mall layout Airport layout

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Experimental Result

Layout using (DR) (11 receivers) Layout using DT* (16 receivers)

*Wu 07

Localization area is ERL 114 that measures approx. 12m x 12m

Upper threshold for localization error set at 1m

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Localization Error (m)Layout Method

Mean Median 75th

percentile Std. dev

DT 1.137 1.038 1.589 0.786DR 0.808 0.678 1.189 0.657

CDF plot of Localization Error

Summary of Localization Error

Localization Accuracy Results

Test Points

28% decrease

34% decrease

25% decrease

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Conclusions and ContributionsConclusions CWLS Multi-lateration on

receivers placed using Delaunay Refinement achieved better localization accuracy

Better performance of DR due to more triangular regions that are close to equilateral triangle than comparable method

Receiver count though sub-optimal was lower than comparable placement algorithm

Contributions CWLS Localization error was

derived

Relationship between R-factor and localization error under RSSI based RTLS using CWLS

A sub-optimal receiver placement algorithm with guarantees on localization accuracy presented

Paper 3: Localization of RFID Tags using Stochastic Tunneling Multipath fading and shadow fading noise are

the primary cause for large localization error in an indoor environment

Tx

Rx

Tx

Rx

Multipath Fading Shadow Fading

36

Spatial Correlation in Fading Noise

37

38

RFID Basics Typically passive device that are energized by radio waves from a tag

reader

RFID Tag varies the Radar Cross Section (RCS) to communicate its unique identification to the tag reader

Passive RFID system overview1

1Nikitin et al. 2006.

13.56MHz Passive RFID Tag

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Application Scenario

Tag Reader

Anchor nodes placed around the

reader

Container with RFID tags

Displays tag ID and location

Movement causes multipath noise

Similarity in fading noise experienced by neighboring

RFID tags is exploited to localize them

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Objective

Localizing RFID tags in a container

Objective to derive a RSSI localization method that works under fading noise

Localize multiple RFID tags simultaneously from a common transmitter

Anchor nodes provide localization correction and reorient the generated location to a global coordinate

Past Work Multi-Dimensional Scaling (MDS) [Ji 04] Local Linear Embedding (LLE) [Costa 06]

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RFID Tag Localization Flow Chart

42

Assumptions In-phase and Quadrature-phase of backscattered signal

amplitudes are normally distributed

Distribution of backscattered energy around the tag reader is given by a circular normal distribution called von-Mises Distribution

Backscattered signal concentration

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Theorem 1: Joint PDF of backscattered RSSI values measured by a tag reader from any two RFID tags separated by radial distance r12 is given by

Backscattered Signal PDF

where P1 and P2 are the backscattered RSSI random variables from tag 1 and 2 respectively with p1 and p2 being their realizations, µ1 and µ2 are their average values, 0≤ρ12≤1 and are the backscattered RSSI correlation parameters and I0(◦) is the zeroth order modified Bessel function of the first kind

where Θ12 is the azimuth orientation of the tag reader, δθ12 is the concentration of

multipath signals around the tag reader orientation Θ12 , , λ is operating wavelength and In(◦) and Jn(◦) are the modified and ordinary Bessel functions respectively of the first kind and order n

44

Localization from Correlation Coefficient Theorem 2: The large sample approximate PDF of ρ12 is given by

where is the indicator function that restricts the support of this PDF between [0, 1], and and are the PDF and CDF respectively of a standard normal distribution

Pseudo-likelihood method is used to create an approximate likelihood function for M RFID tags from their pair wise PDF

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Algorithm called LOCUST (Localization Using Stochastic Tunneling)

8 RFID tags and 8 anchor nodes in a 20m x 20m x 20m workspace

Wireless tags were positioned randomly i.e. xi, yi and zi of the wireless tags are random variables with continuous uniform distribution in the domain [-10, 10] for i є {1,2,…,m}

Total of 50 simulation trials were done to determine the mean, median, standard deviation and 90th percentile of localization errors.

Simulation Results

46

Summary of Localization Error LevelsMethod F

(MHz)

Localization Error (m)

Mean Median90th

percentile

Std. dev.

LOCUST

20.0

0.454 0.429 0.676 0.172

LLE 2.764 2.67 4.095 0.949

MDS 2.272 2.136 3.378 0.778

LOCUST

15.0

0.343 0.331 0.518 0.127

LLE 1.009 0.969 1.507 0.351

MDS 0.935 0.889 1.429 0.375

LOCUST

10.0

0.233 0.230 0.307 0.056

LLE 0.248 0.245 0.326 0.06

MDS 0.194 0.192 0.263 0.05

LOCUST

5.00

0.201 0.189 0.322 0.09

LLE 0.270 0.260 0.396 0.10

MDS 0.194 0.186 0.308 0.086LOCUST

2.50

0.195 0.191 0.283 0.066

LLE 0.187 0.180 0.272 0.063

MDS 0.202 0.195 0.286 0.062

LOCUST

1.00

0.111 0.103 0.177 0.048

LLE 0.198 0.191 0.291 0.07

MDS 0.127 0.117 0.197 0.062

LOCUST

0.06

0.105 0.099 0.164 0.048

LLE 0.202 0.197 0.289 0.066

MDS 0.177 0.165 0.281 0.072

Method F(MHz)

Localization Error (m)

Mean Median90th

percentile

Std. dev.

LOCUST20.0

1.359 1.259 1.943 0.485LLE 7.90 7.318 11.382 2.652MDS 6.019 5.609 8.486 2.238

LOCUST15.0

0.850 0.804 1.179 0.268LLE 2.866 2.831 3.818 0.874MDS 2.92 2.566 4.923 1.490

LOCUST10.0

0.696 0.702 1.067 0.286LLE 1.684 1.657 2.509 0.599MDS 1.722 1.652 2.383 0.513

LOCUST5.00

0.274 0.243 0.469 0.135LLE 0.542 0.500 0.791 0.201MDS 0.477 0.434 0.786 0.207

LOCUST

2.50

0.236 0.227 0.323 0.066LLE 0.198 0.179 0.287 0.061MDS 0.192 0.192 0.256 0.059

LOCUST

1.00

0.131 0.114 0.278 0.060LLE 0.189 0.185 0.177 0.059MDS 0.118 0.112 0.159 0.041

LOCUST

0.06

0.154 0.170 0.216 0.057LLE 0.213 0.189 0.327 0.081MDS 0.178 0.173 0.261 0.062

Accuracy degrades with increasing frequency

Accuracy degrades with LoS

f = 20MHz f = 10MHz

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Localization Error and Anchor Node CountAnchor Node Count

Localization Error (m)

Mean Median 90th percentile Std. dev.

6 0.486 0.432 0.713 0.253

7 0.354 0.378 0.693 0.173

8 0.293 0.278 0.492 0.142

9 0.223 0.244 0.454 0.119

10 0.215 0.210 0.431 0.113

11 0.220 0.216 0.441 0.121

12 0.236 0.225 0.469 0.136

Localization accuracy degraded after 10 anchor nodes due to the large dimension of the estimated variables

CDF Of localization error at f=20MHz

48

Conclusions and ContributionsConclusions A novel RFID tag localization algorithm

called LOCUST that estimates the position of RFID tags by measuring the correlation between RSSI values between co-located tags was presented

Above 10MHz the non-linear relationship between the correlation coefficient and radial separation results in LOCUST performing better than MDS and LLE

Localization error under LoS condition was larger in comparison to NLoS conditions primarily due to faster drop in correlation coefficient with distance under LoS conditions

Contributions A novel RFID tag localization

algorithm called LOCUST that estimates the position of RFID tags by measuring the correlation between RSSI values between co-located tags was presented

Joint distribution of backscattered power from adjacent RFID tags was derived

Functional relationship between backscatterd signal power correlation, radial separation and line of sight condition was derived

49

Paper 4: Localization and Tracking of Objects Using Cross-Correlation of Shadow Fading Noise Objectives

Increase the frequency of operation of cross-correlation based RSSI localization

Resilient to pedestrian or machinery traffic Improve the convergence speed of cross-correlation

based localization Past work

Network Shadowing [Agarwal 09] Large scale correlation model [Gudmundson 91] Multi-Dimensional Scaling (MDS) [Ji 04] Local Linear Embedding (LLE) [Costa 06]

50

Localization from Shadow Fading Correlation

Neighboring receivers experience similar shadow

fading noise

51

Flowchart of Shadow Fading Cross-Correlation Based Localization

52

Shadow Fading Wireless Channel Model Geometrically Based Single Bounce Elliptical Model (GBSBEM) Wireless Channel Model is assumed under shadow fading

Any radio signal that reaches the receiver after bouncing off of a scatterer in the localization region can affect signal fading if and only if its ToA satisfies

GBSBEM Wireless Channel Model

where r is the radial separation between the transmitter and receiver, c is the speed of radio and τm is the signal integration time at the reciever

IEEE 802.15.4 receivers integrate the signal for 128us before computing the signal strength resulting in τm = 128us

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Shadow Fading Correlation Coefficient

Pedestrian traffic is modelled as Poisson process

Shadow fading attenuation is normally distributed

Theorem 1: Correlation coefficient under GBSBEM given by

Overlapping of scattering regions causing cross-correlation in shadow fading

where |·| is the area operator, S1 and S2 are the elliptical scatterer regions surrounding receivers R1 and R2 respectively, S12 is overlapping region between scattering regions S1 and S2.

54

Extraction of Shadow Fading Residuals Ornstein Uhlenbeck stochastic model usually applied for high volatility stock trading is used to extract shadow fading residuals from RSSI

Autoregressive Model (AR) for Xs(t) to separate path loss from shadow fading residuals

Generalized Auto Regressive Conditional Heteroskedasticity (GARCH) for to account for fast changes in pedestrian traffic

where ϵs(t)=σs(t)Zs

55

Localization Using Student-t Copula Copula function helps to create joint distributions from marginal CDFs

and their inter-dependency Gaussian & Student-t Copula models linear dependency Gumbel, Frank and Clayton Copulas model tail dependency

Theorem 2: For an M receiver localization system, Student-t copula was used since shadow fading correlation coefficient is a linear dependency

where is the inverse CDF or quantile function vector of a student-t distribution with degree of freedom v, is an M-variate student-t copula density with v degree of freedom, P is an MxM correlation coefficient matrix given by Ρ={ρkl}; k,l ϵ {1,2,…,M} and ρkl is the correlation coefficient between receiver k and l and

56

Tracking Using Divergence Divergence arise in classification problem when a measurement x has to be

categorized into two possible groups C1 or C2

Miss-classification occurs when x is assigned to C1 while it should have been in C2 or vice versa

α-Divergence is a measure of the upper bound in Bayes error in classification problems

where C1||C2 implies divergence operation between groups C1 and C2, f(x|Ci) is the

PDF of random variable X given that it belongs to group Ci;iϵ{1,2}, x is a single realization of random variable X and the integration is over the entire range of random variable

For velocity estimation the hypothesis being tested is that the RSSI values that a receivers measures is from a stationary transmitter

57

α-Divergence for a Mobile Transmitter Theorem 3: For a mobile transmitter operating under GBSBEM wireless

channel model, α-divergence of RSSI measured between two time instances n and n-1 is given by

θn-1 is the azimuth angle of arrival of LoS radio signal at the receiver with respect to the direction of motion of the transmitter while rn-1 is the radial separation between the transmitter and receiver at time instance n-1, Δrn is the distance the transmitter travelled between time instances n-1 and n and rm=cτm and ω is the average scatterer density

Tracking an IEEE 802.15.4 Transmitter

58

Speed Estimation Using α-divergence For slow moving (≤1m/s) IEEE 802.15.4 transmitter, α-

Divergence is related to transmitter’s velocity as

Bhattacharyya coefficient where α=0.5 is used for velocity estimation

Fully functional dead-reckoning based tracking system can be realized from velocity and transmitter heading measured using either a gyroscope or an antenna array

59

Copula Smoothing Using Bayesian Particle Filter

Dead reckoning based tracking method results in incremental position error over time

Bayes particle filter is a stochastic filter that generates multiple random points or particles around the position estimated from dead reckoning method

Student-t Copula likelihood function computes the likelihood of each generated particle which forms the weight of that particle

The copula smoothed position is the weighted average of all the generated particles

Copula smoothing will generate an accurate solution as long as the dead-reckoning generated position is close to the global maxima of the Likelihood function

60

Static Localization Experimental Results

Transmitter Location

Localization Error (m)

Mean Median 90th Perc. Std. Dev

T1 2.458 2.329 3.962 1.727

T2 2.378 2.267 3.628 1.221

T3 3.537 3.496 5.234 2.377

T4 2.739 2.912 4.138 1.839

MethodLocalization Error (m)

Mean Median 90th Perc. Std. DevMDS 12.343 15.925 25.358 6.464

Proposed Method 2.778 2.751 4.2405 1.791

Localization Errors At Various Locations

Summary of Localization Errors

Layout of food court area with dark lines showing physical boundary

Localization area approx. 1250 sq. m with an average of 1000 people moving in this area during peak lunch hour traffic on a weekend between of 10AM and 1PM

8 Receivers R1 through R8 localizing a transmitter

77% decrease

82% decrease

83% decrease

61

Tracking Experimental Results Tracking experiment performed at ERL 114

8 wireless receivers R1 through R8 tracking a transmitter

3DM-GX2 Attitude Heading Reference System (AHRS) from Microstrain attached to the transmitter

Top view of ERL 114 with tracked points

Comparison of Tracking Errors

MethodTracking RMSE (m)

Mean Min Max Std. Devα-divergence 0.3859 0.0464 0.8652 0.2944

INS 0.2466 0.0025 0.6719 0.1972Copula

Smoothing 0.1777 0.0105 0.4379 0.1505

Summary of Tracking Errors

62

Conclusions and ContributionsConclusions Extended the operating frequency

range of cross-correlation based localization from 20MHz to 2.15GHz

At small velocities α-Divergence based velocity estimation performed better than accelerometer based velocity estimation

Contributions Derived the correlation in shadow fading

noise between adjacent receivers

Developed a stochastic filtering method to isolate shadow fading residuals from RSSI

Developed a transmitter velocity estimation technique that measures α-divergence of RSSI values

Copula smoothing algorithm using Bayesian particle filter was implemented to prevent the accumulation of tracking error over time

63

Paper 5: Placement of Receivers for Shadow Fading Cross-Correlation Based Localization Objectives

Provide a receiver placement algorithm for cross-correlation based localization

Resilient to pedestrian and machinery traffic

Past Work Sub-optimal receiver placement using Delaunay

Refinement [Basheer 10] Optimal receiver placement algorithm [Isler 06] Placement based on maximizing the condition number

[Martinez 05]

64

Shadow Fading Wireless Channel Model Geometrically Based Single Bounce

Elliptical Model (GBSBEM) Wireless Channel Model is assumed under shadow fading

Any radio signal that reaches the receiver after bouncing off of a scatterer in the localization region can affect signal fading if and only if its ToA satisfies

GBSBEM Wireless Channel Model

where r is the radial separation between the transmitter and receiver, c is the speed of radio waves, r/c is the ToA of LoS signal and τm is the signal integration time at the reciever

IEEE 802.15.4 receivers integrate the signal for 128us before computing the signal strength resulting in τm = 128us

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Optimal Unconstrained Receiver Placement Theorem 1: (Equilateral Triangular Grid for Receiver

Placement) A receiver placement strategy whose objective is to span the largest area under localization coverage with least number of receiver while ensuring no coverage holes exists within the grid will have all its receivers placed in an equilateral triangular grid.

Equilateral grid is not possible near bounding walls

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Receiver placement near bounding walls

Localization coverage hole near bounding walls

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Theorem 2: Cramer-Rao Lower Bound for the variance in estimating the transmitter at Cartesian coordinate from receivers that are under localization coverage with a transmitter using cross-correlation of shadow fading residuals between receiver pairs is given by

Receiver placement quality metric is for workspace G

Objective is to attain with least number of receivers

Receiver Placement Quality MetricReceiver Placement Quality Metric

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Flowchart of Receiver Placement Algorithm

Equilateral GridCoverage holesLocalization CoverageLocalization Error

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Simulation Results Delaunay Refinement was used to

search for receiver positions in linear time

Receiver count for cross-correlation coverage placement was lower than using Delaunay Refinement search

Delaunay refinement generates more receivers near sharp edges

Improvement in receiver count was at the expense of search time

Receiver count vs. communication range

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Simulation ResultsTx.

Location

No. of rx. in range

Localization Error (m)

Mean Median

90th Perc.

Std. Dev

T1 4 0.894 0.792 1.579 0.466

T2 3 0.926 0.883 1.526 0.472

T3 4 0.792 0.828 1.377 0.418

T4 4 0.779 0.698 1.534 0.481

T5 4 0.879 0.927 1.445 0.407

T6 3 0.955 1.100 1.693 0.562

T7 5 0.652 0.690 1.076 0.325

T8 6 0.677 0.550 1.401 0.484

T9 3 0.907 0.943 1.484 0.475

T10 4 0.712 0.762 1.167 0.360

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Conclusions and Contributions

Contributions Derived the optimal unconstrained

placement for cross-correlation based localization

Derived the Cramer-Rao lower bound for transmitter location estimation variance under cross-correlation based localization method

A receiver placement algorithm was developed for the cross-correlation method that ensures the localization accuracy within the workspace is less than a pre-specified threshold.

Conclusions Developed a receiver placement

algorithm for cross-correlation –based localization

Average localization error was well under the designed 1m error

This method generated lower receiver count for a given communication range when compared with a Delaunay refinement based placement

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Conclusions and Future Work--Dissertation

Conclusions Localization from cross-

correlation of RSSI is suited for multipath rich environment such as factory floor, food court etc.

Our technique takes advantage of the temporal correlation in RSSI that arise in co-located receivers due to the movement of people or machinery in its vicinity

Performance of our proposed algorithms were validated using hardware experiments on IEEE 802.15.4 receivers

Future work Explore techniques that can

measure transmitter heading from RSSI values so that the requirement for compass or gyroscope can be removed

Improve the execution time for receiver placement algorithm for cross-correlation based localization

Improve the accuracy of shadow fading correlation by better modeling of the shadow fading cross-correlation likelihood

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Questions

Thank you!

References [Costa 06] J. A. Costa , N. Patwari, and A. O. Hero, “Distributed weighted-multidimensional scaling for node

localization in sensor networks,” ACM Trans. on Sensor Networks, vol.2, No.1, pp.39-64, Feb. 2006.

[Gwon 04] Y. Gwon and R. Jain, “Error characteristics and calibration-free techniques for wireless LAN-based location estimation,” Proc. of ACM MobiWac, pp. 2-9, October 2004.

[Isler 06] V. Isler, “Placement and distributed deployment of sensor teams for triangulation based localization,” In Proc. IEEE ICRA, pp. 3095-3100, May, 2006.

[Ji 04] X. Ji, and H. Zha, “Sensor positioning in wireless ad-hoc sensor networks using multidimensional scaling,” 23rd Annual Joint Conf. of the IEEE Computer and Commun. Soc. , vol.4, pp. 2652- 2661, Mar. 2004.

[Lakhzouri 03] A. Lakhzouri, E. S. Lohan, R. Hamila, and M. Renfors, “Extended kalman filter channel estimation for line-of-sight detection in WCDMA mobile positioning,” EURASIP Journal on Applied Signal Processing, vol. 2003, no. 13, pp. 1268-1278, 2003.

[Martinez 05] S. Martínez, and F. Bullo, “Optimal sensor placement and motion coordination for target tracking,” Proc. of the inter. Conf. on Robotics and Automation, Barcelona, Spain, pp. 4544-4549, April 2005.

[Venkatraman 02] S. Venkatraman and J. Caffery Jr., “Statistical approach to nonline-of-sight BS identification,” Proc. of the 5th International Symp. on Wireless Personal Multimedia Comm., vol. 1, pp. 296–300, Hawaii, USA, October 2002.

[Wu 07] C. Wu, K. Lee, and Y. Chung, “A Delaunay Triangulation based method for wireless sensor network deployment,” Computer Communications, Volume 30, Issue 14-15, pp. 2744-2752, Oct 2007.

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