Slides from my dissertation defense. Talks about the error in localizing a transmitter by measuring the signal strength. In addition, it presents new techniques for localization using cross-correlation of fading.
Real Time Localization Using Receiver Signal Strength Indicator
1. 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
2
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.
3
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
4
5. 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
7. 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
8. 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
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
9
10. 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
11. 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
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]
12
13. 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
14. 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
15. 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
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
16
17. 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
18. 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
19. 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
20. 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
21. 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
22. 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
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
23
24. 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
25. 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
26. 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
27. 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
28. 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
29. 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
30. 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
31. 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
33. 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
34. 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
35. Conclusions and Contributions
Conclusions Contributions
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
36. 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
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
13.56MHz Passive RFID Tag
Passive RFID system overview1
1Nikitin et al. 2006.
38
39. 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
40. 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
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 42
43. 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
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
44
45. 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
46. 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
47. 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
48. Conclusions and Contributions
Conclusions Contributions
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
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]
49
50. Localization from Shadow Fading
Correlation
Neighboring receivers
experience similar shadow
fading noise
50
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
52
53. 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
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
where ϵs(t)=σs(t)Zs
Generalized Auto Regressive Conditional Heteroskedasticity
(GARCH) for to account for fast changes in pedestrian traffic
54
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
55
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
56
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 Tracking an IEEE 802.15.4
n-1 and n and rm=cτm and ω is the average scatterer Transmitter
density
57
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
58
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
59
60. 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
Localization Error (m)
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
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
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
62. Conclusions and Contributions
Conclusions Contributions
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
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]
63
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
64
65. 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
67. 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
69. 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
71. Conclusions and Contributions
Conclusions Contributions
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
72. 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
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