Real Time Localization Using Receiver Signal Strength Indicator

Real Time Localization Systems Using
Receiver Signal Strength Indicator

Mohammed Rana Basheer
Advisor: Dr. Jag Sarangapani

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

2

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.

3

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

4

Real Time Location Systems (RTLS)
 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)

RSSI A n log(r ) Boeing factory floor*
*http://www.ce.washington.edu/sm03/boeingtour.htm

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

 Classified into
 Range Based
 Range Free

Friis Transmission Equation RSSI vs. Distance
5

RSSI Profile of ERL 114

6

Localization Hardware

 IEEE 802.15.4 transceiver from
XBee

 Operating frequency 2.45 GHz RTLS Tag MST Mote
with 100 MHz Bandwidth

 8051 variant microcontroller

 8KB RAM and 128 KB code space

 Spatial diversity with 2 antennas

RTLS Receiver

7

Motivation for RTLS using RSSI
 Time 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

8

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

9

Cohesion of completed work
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

Range-Based
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

Localization
Using RSSI
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
Cross-Correlation 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,

10

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

Weighted least square to the rescue

Transmitter location estimation
Friis Transmission base station from Signal
happens in
Transmitter Euclidean distance
Equation equation
Strength
Weights are the radial distancestation
Base variance

affected by outliers R-Factor
and are called the

Receivers

11

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]

12

Assumptions
 Received signal amplitude random variable X is
Ricean distributed with PDF given by
2 x A2 x 2 Ax
f X x | A, X 2
exp 2
I0 2
X 2 X X

 Radial distance random variable R is related to
RSSI X as 1
n l0
R g( X )
X2
where n is the path loss exponent and l0 accounts
for antenna geometry, wavelength etc.

13

Mean & Variance of Radial Distance Estimate
 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
1 1
1
n n
2
2 2l 0 2 n 2 2l 0 1
E(R | K , X ) X
1 K M2 ,1, K
2 1 n 2l 0 1 4 2
X M2 ,1, K 2
X M2 ,1, K
2 2
2
1
n
2
2 8 X 2l 0 1
Var( R | K , X ) 1 K M2 ,1, K
n 2l0 2 1 4 2
X M2 ,1, K
2

where M , , is the Confluent Hyper-geometric Function (CHF) and K A2 2 2
X
is the ratio of the power in the deterministic LoS component to the NLoS
energy or the signal to noise ratio for localization.

14

Localization Receiver and R - Factor
 A receiver for RSSI based RTLS, is called a localization receiver if the signal to
noise ratio K A2 2 X for the received signals is greater than 9
2

 Mean and Variance of radial distance estimate is given by
2n 2
E R | r0 , K r0 r0 Bias
n2 K
2 4
2l A n
0
n
2r02
Var ( R | r0 , K ) 2
n K n2 K

 R-Factor (Receiver Error Factor) measures the variance in radial distance
estimate by a localization receiver
r02 1 2r0n 2 2
Var( R | r0 , K ) X cr0b 2
X
n2 K 2 n 2l0
 MSE is proportional to R-Factor
r02
MSE 2
2n 2 8n 10 2n 2 8n 10
n K

15

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

16

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

17

Simulation of R-Factor vs. Diversity Count
Variation of R-Factor with increasing diversity channel count

LoS Conditions NLoS Conditions

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

18

Localization Experiment
Receiver layout in ERL 114

22% 28% 22%
CDF of Localization Error decrease
26% decreasedecrease
30% 24%
Summary of Localization Error Levels decrease
decreasedecrease
Localization Error (cm)
Localization Method
Mean Median 90th percentile Std. dev
TIX + PSS 342 298 432 62.81
TIX with R-factor 267 214 335 40.32
TIX with R-factor and Spatial Diversity 254 210 329 40.15

*Gwon et al. 2004
19

Conclusions and Contributions
Conclusions Contributions
 Existing localization schemes can  A novel parameter called R-
use R-Factor to identify subset of Factor to identify receivers with
receivers that will result in better low range estimation errors was
location estimation
presented

 R-Factor combined with RMS
channel diversity was shown  R-factor for selection
theoretically and experimentally combination, averaging and root
to improve localization accuracy mean square diversity
combination were derived
 RMS diversity combination was
shown to have better localization
performance than averaging and
selection diversity combination

20

Paper 2: Receiver Placement Using Delaunay Refinement
based Triangulation in an RSSI Based Localization
Delaunay refinement
Where do I
placement is place solution
the these
receivers?
Possible Applications
• Locate cellphones to track foot
traffic
• Coupons for visiting shops
• Theft prevention

Transmitter being localized
with guaranteed accuracy

Shopping Mall Layout
21

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

xt2 yt2 xi2 yi2 ri 2
xi xt y i yt
2 2
 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]
22

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

23

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
2 – Parameter Non-Linear Estimation Problem
xt2 yt2 xi2 yi2 ri 2
xi xt yi yt ;i 1,2,  N
2 2

3 – Parameter Linear Estimation Problem
Rs xi2 yi2 ri 2
xi xt yi yt ;i 1,2,  N
2 2
Constraint Rs xt2 yt2
24

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 Rs xt2 yt2
25

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
26

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 !!!!

27

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
28

Delaunay Refinement Triangulation
 Originally developed to generate
mesh for Finite Element
Modeling and Computer Games

 Delaunay Refinement satisfies
all our receiver placement
requirements
Delaunay meshing of a 3D object*

 However, boundary walls results
in sub-optimal receiver count

* G E O M E T R I C A (http://www-sop.inria.fr/geometrica/ ) 29

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

30

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

31

Bounded Receiver Count

Shopping mall layout Airport layout

32

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

 Upper threshold for localization error set at 1m

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

*Wu 07
33

Localization Accuracy Results

CDF plot of Localization Error34%
28% 25%
decreasedecreasedecrease
Summary of Localization Error Test Points
Localization Error (m)
Layout 75th
Mean Median Std. dev
Method percentile
DT 1.137 1.038 1.589 0.786
DR 0.808 0.678 1.189 0.657

34

 CWLS Multi-lateration on
 CWLS Localization error was
receivers placed using
Delaunay Refinement achieved derived
better localization accuracy
 Relationship between R-
 Better performance of DR due factor and localization error
to more triangular regions that
under RSSI based RTLS
are close to equilateral triangle
than comparable method using CWLS

 Receiver count though sub-  A sub-optimal receiver
optimal was lower than
placement algorithm with
comparable placement
algorithm guarantees on localization
accuracy presented
35

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

Rx Rx

Tx Tx

Multipath Fading Shadow Fading

36

Spatial Correlation in Fading Noise

37

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

13.56MHz Passive RFID Tag
Passive RFID system overview1

1Nikitin et al. 2006.
38

Application Scenario
Movement causes
multipath noise
Similarity in fading noise
experienced by neighboring
RFID tags is exploited to
localize them
Anchor nodes
Container with placed around the
RFID tags reader

Displays tag ID
and location

39

Objective
 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
Localizing RFID tags in a container
 Past Work
 Multi-Dimensional Scaling (MDS) [Ji 04]
 Local Linear Embedding (LLE) [Costa 06]

40

RFID Tag Localization Flow Chart

41

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 42

Backscattered Signal PDF
 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

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

43

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

44

Simulation Results
 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.
45

Summary of Localization Error Levels
Localization Error (m) Localization Error (m)
F 90th F 90th
Method Method
(MHz) Mean Median percentil Std. dev. (MHz) Mean Median percentil Std. dev.
e e
LOCUST 0.454 0.429 0.676 0.172 LOCUST 1.359 1.259 1.943 0.485
LLE 20.0 2.764 2.67 4.095 0.949 LLE 20.0 7.90 7.318 11.382 2.652
MDS 2.272 2.136 3.378 0.778 MDS 6.019 5.609 8.486 2.238
LOCUST 0.343 0.331 0.518 0.127 LOCUST 0.850 0.804 1.179 0.268
LLE 15.0 1.009 0.969 1.507 0.351 LLE 15.0 2.866 2.831 3.818 0.874
MDS 0.935 0.889 1.429 0.375 MDS 2.92 2.566 4.923 1.490
LOCUST 0.233 0.230 0.307 0.056 LOCUST 0.696 0.702 1.067 0.286
LLE 10.0 0.248 0.245 0.326 0.06 LLE 10.0 1.684 1.657 2.509 0.599
MDS 0.194 0.192 0.263 0.05 MDS 1.722 1.652 2.383 0.513
LOCUST 0.201 0.189 0.322 0.09 LOCUST 0.274 0.243 0.469 0.135
LLE
MDS
5.00 0.270
0.194
Accuracy degrades with LoS
0.260
0.186
0.396
0.308
0.10
0.086
LLE
MDS
5.00 0.542
0.477
0.500
0.434
0.791
0.786
0.201
0.207
LOCUST 0.195 0.191 0.283 0.066 LOCUST 0.236 0.227 0.323 0.066
LLE 2.50 0.187 0.180 0.272 0.063 LLE 2.50 0.198 0.179 0.287 0.061
MDS
LOCUST
0.202
0.111
Accuracy degrades with
0.195
0.103
0.286
0.177
0.062
0.048
MDS
LOCUST
0.192
0.131
0.192
0.114
0.256
0.278
0.059
0.060
LLE
MDS
1.00 0.198
0.127
increasing frequency
0.191
0.117
0.291
f = 10MHz
0.197
0.07
0.062
LLE
MDS
1.00 0.189
0.118
0.185
0.112
0.177
0.159
0.059
0.041
LOCUST
LLE 0.06
0.105
0.202
0.099
0.197
0.164
0.289
0.048
0.066
f =LOCUST 0.06
20MHz
LLE
0.154
0.213
0.170
0.189
0.216
0.327
0.057
0.081
MDS 0.177 0.165 0.281 0.072 MDS 0.178 0.173 0.261 0.062

46

Localization Error and Anchor Node Count
Anchor Localization Error (m)
Node 90th
Count Mean Median Std. dev.
percentile
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

47
CDF Of localization error at f=20MHz

 A novel RFID tag localization algorithm  A novel RFID tag localization
called LOCUST that estimates the algorithm called LOCUST that
position of RFID tags by measuring the estimates the position of RFID
correlation between RSSI values
tags by measuring the correlation
between co-located tags was presented
between RSSI values between
co-located tags was presented
 Above 10MHz the non-linear
relationship between the correlation
coefficient and radial separation results  Joint distribution of backscattered
in LOCUST performing better than MDS power from adjacent RFID tags
and LLE
was derived
 Localization error under LoS condition
was larger in comparison to NLoS  Functional relationship between
conditions primarily due to faster drop in backscatterd signal power
correlation coefficient with distance correlation, radial separation and
under LoS conditions line of sight condition was derived

48

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]

49

Localization from Shadow Fading
Correlation

Neighboring receivers
experience similar shadow
fading noise

50

Flowchart of Shadow Fading Cross-Correlation
Based Localization

51

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

52

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.

53

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

where ϵs(t)=σs(t)Zs
 Generalized Auto Regressive Conditional Heteroskedasticity
(GARCH) for to account for fast changes in pedestrian traffic

54

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

55

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

56

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 Tracking an IEEE 802.15.4
n-1 and n and rm=cτm and ω is the average scatterer Transmitter
density

57

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

58

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

59

Static Localization Experimental Results
 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

Localization Errors At Various Locations
Transmitter Localization Error (m)
Location 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 77%
5.234 82%
2.377 83%
T4 2.739 2.912 decrease decrease decrease of food court area with dark lines
4.138 1.839 Layout
showing physical boundary
Summary of Localization Errors
Method
Mean Median 90th Perc. Std. Dev
MDS 12.343 15.925 25.358 6.464
Proposed
Method
2.778 2.751 4.2405 1.791

60

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

Summary of Tracking Errors
Tracking RMSE (m)
Method
Mean Min Max Std. Dev
α-divergence 0.3859 0.0464 0.8652 0.2944
INS 0.2466 0.0025 0.6719 0.1972
Copula
0.1777 0.0105 0.4379 0.1505
Smoothing
Comparison of Tracking Errors

61

 Extended the operating frequency  Derived the correlation in shadow fading
range of cross-correlation based noise between adjacent receivers
localization from 20MHz to 2.15GHz
 Developed a stochastic filtering method
 At small velocities α-Divergence to isolate shadow fading residuals from
based velocity estimation performed RSSI
better than accelerometer based
velocity estimation  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

62

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]
63

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

64

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

65

Receiver placement near bounding walls

Localization coverage hole near bounding walls

66

Receiver Placement Quality Metric
 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
67

Flowchart of Receiver Placement Algorithm

Localization Coverage
Localization Error
Coverage Grid
Equilateralholes

68

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
Receiver count vs. communication
range
 Improvement in receiver count
was at the expense of search time

69

Simulation Results
No. of
Tx.
rx. in Media 90th Std.
Location Mean
range n Perc. 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

70

 Developed a receiver placement  Derived the optimal unconstrained
algorithm for cross-correlation – placement for cross-correlation based
based localization localization

 Derived the Cramer-Rao lower bound
 Average localization error was
for transmitter location estimation
well under the designed 1m error variance under cross-correlation based
localization method
 This method generated lower
receiver count for a given  A receiver placement algorithm was
communication range when developed for the cross-correlation
compared with a Delaunay method that ensures the localization
refinement based placement accuracy within the workspace is less
than a pre-specified threshold.

71

Conclusions and Future Work--Dissertation
Conclusions Future work
 Localization from cross-  Explore techniques that can
correlation of RSSI is suited for measure transmitter heading from
multipath rich environment such RSSI values so that the
as factory floor, food court etc. requirement for compass or
 Our technique takes advantage gyroscope can be removed
of the temporal correlation in
RSSI that arise in co-located  Improve the execution time for
receivers due to the movement receiver placement algorithm for
of people or machinery in its cross-correlation based localization
vicinity
 Performance of our proposed
 Improve the accuracy of shadow
algorithms were validated using fading correlation by better
hardware experiments on IEEE modeling of the shadow fading
802.15.4 receivers cross-correlation likelihood

72

Questions

Thank you!

73

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.

74

Real Time Localization Using Receiver Signal Strength Indicator

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