When a radio transmitter is mobile, obstacles in the radio path can cause temporal variation in Received Signal Strength Indicator (RSSI) measured by receivers due to multipath and shadow fading. While fading, in general, is detrimental to accurately localizing a target, fading correlation between adjacent receivers may be exploited to improve localization accuracy. However, multipath fading correlation is a short range phenomenon that rapidly falls to zero within a wavelength whereas, shadow fading correlation is independent of signal wavelength and has longer range thereby making it suitable for localization with wireless transceivers that operate at shorter wavelength. Therefore, this paper presents a novel wireless localization scheme that employs a combination of cross-correlation between shadow fading noise and copula technique to recursively estimate the location of a transmitter. A stochastic filter that models multipath fading as an Ornstein-Uhlenbeck process followed by a Generalized Auto Regressive Conditional Heteroskedasticity (GARCH) filtering is proposed to extract shadow fading residuals from measured RSSI values. Subsequently, Student-T Copula function is used to create the log likelihood function, which acts as the cost function for localization, by combining spatial shadow fading correlation arising among adjacent receivers due to pedestrian traffic in the area. Maximum Likelihood Estimate (MLE) is used for position estimation as it inherits the statistical consistency and asymptotic normality. The performance of our proposed localization method is validated over simulations and hardware experiments.

1. Localization of Objects Using Cross-
Correlation of Shadow Fading Noise
and Copulas
Mohammed Rana Basheer, S. Jagannathan
Dept. of Electrical and Computer Engineering
Rolla, MO, USA
{mrbxcf, sarangap}@mst.edu

2. Introduction
 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)
Boeing factory floor*
 RSSI based localization is cheaper as it involves mostly a software
updated on an existing wireless infrastructure
 However, accuracy and periodic radio profiling issues have limited
their adoption in factory environment
*http://www.ce.washington.edu/sm03/boeingtour.htm
2

3. Localization Errors
 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
3

4. RSSI Profile of ERL 114
 Spans 12m x 13m
 Typical lab floor with tables,
partitions, heavy equipments such
as pumps etc.
 0.6m x 0.6m grid
RSSI (dB)
Layout of ERL 114
4

5. Similarity in Fading Noise Statistics
 Fading noise depends on the radio signal propagation environment
 Adjacent wireless receivers
will experience similar
fading noise statistics
 Cross-correlation in fading
noise between adjacent
receivers may be used to Rx2
determine their relative Rx1
position to a common
transmitter
Tx
Shadow Fading
5

6. Previous Work
 Cross-correlation of multipath
noise signals from adjacent
receivers were used by Basheer
et. al.1 for localizing transmitters
 However, multipath cross-
correlation tapers of to zero within
a wavelength of radial separation
 Cross-correlation in shadow
fading noise between adjacent
receivers arising due to pedestrian
or machinery traffic in their vicinity
was found to span larger distance
Multipath noise correlation with distance
1Basheer,M.R.; Jagannathan, S.; , "Localization of objects using stochastic tunneling," Wireless Communications
and Networking Conference (WCNC), 2011 IEEE , pp.587-592, 28-31 March 2011 6

7. Previous Work (contd.)
 Non-Parametric Methods treat the localization as a
dimensionality reduction problem
Pi [ri1 , ri 2 ,..., riK ]T RK Xi [ xi , yi , zi ]T R3
 Multi Dimensional Scaling (MDS)2
 Local Linear Embedding (LLE)3
 Isomap4
 However, linear relationship requirement between cross-correlation
and radial distance breaks rapidly at distances more than a
wavelength of radial separation in wireless devices
2X. Ji, and H. Zha, "Sensor positioning in wireless ad-hoc sensor networks using multidimensional scaling," 23rd Annual Joint Conf. of the
IEEE Computer and Communication Society, vol.4, pp. 2652- 2661, Mar. 2004.
3N. Patwari and A. O. Hero, “Manifold learning algorithms for localization in wireless sensor networks,” in Proceedings of the IEEE
International Conference on Acoustics, Speech and Signal Processing (ICASSP), vol. 3, pp. 857-880, May 2004.
4Wang C, Chen J, Sun Y, Shen X. “Wireless sensor networks localization with Isomap,” IEEE International Conference on Communications,
2009.
7

8. Localization Block Diagram
IEEE 802.15.4
Receiver 1 Z s1 Base Station
IEEE 802.15.4 Z s2 Copula
Receiver 2
Optimization XT,YT
Function
Z sM
IEEE 802.15.4
Receiver M
XT,YT =Transmitter Coordinates
Zsi = Shadow Fading Residual from ith receiver 8

9. Shadow Fading Extraction Block
Diagram
RSSI From AR(1)
X (t ) Ornstein- X s (t )
IEEE 802.15.4 + Z si
Uhlenbeck Filter
Receiver GARCH(1,1)
X(t) = RSSI at time instance t
Xs(t) = Shadow Fading Residual + Path Loss
Zsi = Shadow Fading Residual
9

10. Copula Optimization Function
Z s1 Build Semi- ~ Stochastic Optimization
Parametric CDF
F1
Student-t Copula
~ XT,YT
Function Cv, P
Z s2 Build Semi-
F2
Parametric CDF
~ P( x, y)
FM
Z sM Build Semi- Compute pair-wise
Parametric CDF Cross-Correlation
Zsi = Shadow Fading Residual
= Semi-Parameter Shadow Fading CDF Possible Transmitter
i
P(x,y) = MxM shadow fading cross-correlation Coordinates (x,y)
Cv,p = Student-t copula function
10

11. Extracting Shadow Fading Residuals
 Valenzuela et. al. has
shown that multipath effects
can be removed without
degrading shadow fading
effects in RSSI by spatial
averaging the received
signal power over 10λ
distance5
 Therefore, multipath noise
can be treated as a mean Shadow fading from received signal power5
reverting process
 In this paper multipath noise is modeled as a stochastic process called
Ornstein Uhlenbeck (OU) to isolate shadow fading residuals from RSSI
5R.A.Valenzuela, O. Landron, and D.L. Jacobs, "Estimating local mean signal strength of indoor multipath
propagation," IEEE Trans. on Veh. Technol., vol.46, no.1, pp. 203-212, Feb 1997. 11

12. OU Model for Multipath Noise
X(t) is the received signal strength at time instance t
dX(t) is a small change in RSSI for a delta increment in time dt,
Xs(t) is the local mean of RSSI which is a combination of deterministic path
loss and shadow fading due to pedestrian traffic,
v(t) is the rate at which the multipath noise revert to the short range mean
set by shadow fading noise and deterministic path loss
2
f is the variance of multipath noise
dW(t) is the delta increment of a standard Brownian motion.
 Estimate v(t) and σf for OU model using maximum likelihood estimators6
6L.Valdivieso, W. Schoutens and F. Tuerlinckx, “Maximum likelihood estimation in processes of Ornstein-
Uhlenbeck type,” Statistical Inference for Stochastic Processes, vol. 12, No. 1, pp. 1-19, 2009. 12

13. AR+GARCH to Isolate Shadow Fading
Residuals
 Autoregressive Model (AR) for Xs(t) is used to separate path loss
from shadow fading residuals
AR(1)
where μr(t) accounts for all the deterministic power loses, β is the
auto-correlation between successive samples of Xs(t) and
ϵs(t)=σs(t)Zs is the deviation of the shadow fading process from the
AR(1) process assumption, s2 t is the shadow fading variance and Zs
is the stationary zero mean unit variance shadow fading residual.
 Generalized Auto Regressive Conditional Heteroskedasticity
(GARCH) for s2 t to account for changes in pedestrian traffic
GARCH(1,1)
13

14. CDF of Shadow Fading Residuals
 Semi-parametric CDF is used since the derivation of a parametric
distribution for Zs obtained after OU and GARCH filtering of RSSI
values is very difficult
FiU ( x), x U i Upper Tail (Parametric)
~ ˆ
Fi N ( x) Fi N ( x), Li x Ui Mode (Empirical)
Fi L ( x), x Li Lower Tail (Parametric)
 Regions around the mode of the residuals will be modeled using non-
parametric empirical CDF
ˆ N 1 N
Fi ( x) I Z s k ) x ; i 1,2, , M
(
N k 1 i
where I(·) is the indicator function, Zsi Zs(i1) , Zs(i2) , Zs(iN ) are N
shadow fading residuals from ith receiver in the localization area
14

15. CDF of Upper and Lower Tails of
Shadow Fading Residuals
 Upper and lower tails, were sample points are sparse by
definition, a parametric Generalized Pareto Distribution7
(GPD) was applied
1 x Ui
FiU ( x) 1 i
i i
1 x Li
Fi L ( x) 1 i
i i
where Ui and Li are the upper and lower location parameters for a
Generalized Pareto Distribution (GPD) while ζi is the shape parameter
that controls the rate at which the tail of a distribution goes to zero and
ϑi is the scale parameter that accounts for variance in tail data
7J.
R. M. Hosking and J. R. Wallis, “Parameter and quantile estimation for the Generalized Pareto
Distribution,” Technometrics, Vol. 29, No. 3, pp. 339-349j, Aug 1987 15

16. Shadow Fading Wireless Propagation
Model
 Geometrically Based Single Bounce
Elliptical Model (GBSBEM) Wireless
Channel Model8 is assumed under
shadow fading
 Any radio signal that reaches the
receiver after bouncing off of a
scatterer in the localization region can
GBSBEM Wireless Channel Model8
affect signal fading if and only if its
ToA satisfies
r
t m
c
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
8J.C.Liberti, and T.S. Rappaport, "A geometrically based model for line-of-sight multipath radio channels,"
Vehicular Tech. Conf., 1996. 'Mobile Tech. for the Human Race'., IEEE 46th , vol.2, pp.844-848, May 1996. 16

17. Shadow Fading Correlation Coefficient
 IEEE 802.15.4 receivers computes RSSI as the squared sum of incoming signal
amplitude arriving within an RSSI integration time9
 Radio signal attenuation for scatterers are assumed to be Normally distributed
while Poisson distribution is assumed for pedestrian traffic in the localization area
 Theorem 1: Shadow fading noise correlation
coefficient (ρ) between two IEEE 802.15.4 receivers
R1 and R2 separated by radial distances r1 and r2
respectively from a common transmitter is given by
S12
S1 S 2 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 .
9Hyeon-Jin Jeon, T. Demeechai, Woo-Geun Lee, Dong-Hwan Kim and Tae-Gyu Chang, "IEEE 802.15.4
BPSK Receiver Architecture Based on a New Efficient Detection Scheme," IEEE Trans. on Signal Processing, 17
vol.58, no.9, pp.4711-4719, Sept. 2010.

18. Likelihood Function from Student-t Copula
 Copula10 function helps to create joint distributions from marginal
CDFs and their inter-dependency
 Gaussian and Student-t Copula models linear dependency
 Gumbel, Frank and Clayton Copulas model tail dependency
 Theorem 2: The likelihood function (LP) for estimating the position
of a transmitter from N shadow fading residuals measured by M
IEEE 802.15.4 receivers is given by
1 ~N 1 ~N 1 ~N
LP cv, P tv F1 Z s1 , tv F2 Z s2 ,, tv FM Z sM
1
where tn is the inverse CDF or quantile function vector of a
student-t distribution with degree of freedom v, cv,P {•} 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.
10R. B. Nelsen, “An Introduction to Copulas, Lectures Notes in Statistics,” Springer Verlag, New York, 1998.
18

19. Shadow Fading Correlation Simulations
r2 vs. ρ
r12=10m
r1=10m
τm=0.1μs
ω=1 interferer/sq. m
Simulation Scenario
τm vs. ρ
r1=10m r1=10m
r2=10m r2=10m
r12=10m τm=0.1μs
ω=1 interferer/sq. m r12 vs. ρ
ω=1 interferer/sq. m
19

20. Wireless Hardware
 MSP430 16-bit Microcontroller
 CC2420 Radio is an IEEE 802.15.4
receiver operating at 2.45 GHz Z1 Mote
 Patch Antenna
 8 bit RSSI values
 Tiny OS
Mote internals
20

21. 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 5.234 2.377 Food Court Layout
T4 2.739 2.912 4.138 1.839  Degree of freedom v=4, U and L for
Summary of Localization Errors GPD set at 90th and 10th percentile
Localization Error (m) were heuristically chosen to give the
Method best localization results
Mean Median 90th Perc. Std. Dev
Proposed
Method
2.778 2.751 4.2405 1.791
MDS 12.343 15.925 25.358 6.464
21

22. Summary
 Extended the operating frequency range of cross-
correlation based localization from 10MHz to 2.45GHz
 Copula likelihood function was found to be a better cost
function for cross-correlation based localization than
MDS as it adapts to LoS conditions between receiver and
transmitter
 Cross-correlation based localization method is
particularly suited for fading rich environment such as
factory floor, malls etc. where there is a high pedestrian
or machinery traffic
22

23. Questions?
Thank you!