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Enhanced Mobile positioning technique for
UMTS users in both outdoor and Indoor
environments
Ilham EL MOURABIT, Aicha SAHEL, Abdelmajid BADRI, Abdennaceur BAGHDAD
Department of electrical engineering, EEA&TI laboratory
Faculty Of Science and Technology (FSTM)
Mohammedia, Morocco
elmourabit.ilham@gmail.com
Abstract— Mobile positioning by cellular networks has
received growing attention and several researches are carried
out to enhance positioning algorithms and techniques that will
be able to give better performance at multiple environments
(outdoors/indoors). In this paper, we are interested in UTDOA
(uplink time difference of arrival) approach to determine the
location of a Mobile Station within an acceptable accuracy
and respect of emergency cases in both areas
(Indoor/Outdoor). The enhancement of this method is
performed with adaptive filtering , with MATLAB software,
using two different algorithm to show the advantages of the
chosen one, and its efficiency in emergency calls even with
legacy phones.
Keywords—positioning, UTDOA, adaptive filter, MATLAB,
accuracy, emergency calls, outdoor/Indoor environments.
I. INTRODUCTION
Positioning methods based on cellular networks are now
gaining more interest thanks to their accuracy, availability
and performance in emergency cases. Among these
techniques we can find three categories [1], which are the
following :
Handset-based positioning: The handset measures
the data needed for its approximate location and
calculates its own position on its own out of this
data.
Network-based positioning: The network measures
all data needed for the handset’s approximate
location and calculates the position of the handset.
The handset is passive in the whole progress.
Hybrid positioning: In hybrid positioning, the
network and the handset work together to first
measure and then calculate the device’s position.
To have a full operability of our approach and to take on
consideration legacy phones, in emergency calls, we are
interested in the second type which depend totally on the
network computing power.
In the following sections, we will first present the
concepts behind UTDOA and adaptive filters with two
different algorithms LMS (Least Mean Square) and NLMS
(Normalized Least Mean Square), then giving the chosen
propagation models for both outdoor and indoor
environments so we can present the results of simulation of
both algorithms for both areas.
II. UPLINK TIME DIFFERENCE OF ARRIVAL
Uplink Time Difference Of Arrival (UTDOA) is a time
based method to estimate the mobile station's location [2].
this technique is well known by its accuracy among the
cellular based methods. From [3], The following table
resume the existent positioning methods along with their
accuracies and precisions in urban areas.
TABLE I. Accuracy and precision in urban areas
Positioning techniques
Accuracy
Precision
Cell ID
526m
95%
Cell ID+TA
80m-800m
-
Angle of Arrival
100m-200m
-
Time Difference of Arrival
624m
95%
Uplink TDOA
<50m
-
Pilot Correlation Method
80m
67%
Observed TDOA
97m
67%
Enhanced Observed TD
80m-110m
-
GPS
5m-30m
-
Assisted GPS
15m-100m
-
The time of arrival of an MS (Mobile Station) signal
can be defined according to one or multiple base stations,
simple measurement coming from one BS (Base Station)
cannot be accurate and need a high synchronization between
the BS and MS clocks which require expensive changes on
the handset (not suitable for emergency cases with legacy
phones); so instead of time of arrival we are interested in
time difference of arrival between two base stations with
known coordinates (xi , yi). For hyperbolic lateration, the
mobile terminal’s position is determined by the distance
differences (di -dj) instead of the absolute distance d . A
hyperbola is defined to be the set of all points for which the
difference from two fixed points is constant [4]. Then two
BSs with known locations determine a hyperbolic curve.
The intersection of two hyperbolic curves can determine a
unique point. Therefore, three BSs are required to locate a
mobile terminal in 2D coordinates. The mobile terminal’s
position (x, y ) can be derived from equation (1) :
(1)
knowing that the speed of propagation is estimated to be
c=3.108 , we can replace the distances in (1) with their
corresponding times according to the following formula
c=di/ti. After some simplification we can write the previous
equations in the form:
(2)
which describes an hyperbolic form of our curves. The
fig. 1 shows the results of a hyperbolic lateration with three
base stations to determine the location of an MS.
Figure 1. TDOA hyperbolic solution
This method has been chosen, firstly, because the
cellular signals can arrive at almost everywhere which make
it more available than satellite signals, then among those
techniques based on these signals we prefer to work with
the network based positioning approach so the legacy
phones can be taken into consideration when treating
emergency cases. Finally, UTDOA is the best network
based method in term of accuracy compared to other
solutions.
III. ADAPTIVE FILTERS
Usually when we use the UTDOA, the time difference is
obtained by performing a cross correlation of signals
received by two different base stations, the idea here is to
pre-filter the signals with adaptive filters before doing the
cross correlation so we can minimize the noise effect to
have more accurate position.
Adaptive filters are dynamic filters which iteratively
alter their characteristics in order to achieve an optimal
desired output [5]. Figure 1 shows a block diagram of the
adaptive noise cancellation system.
Figure 2. Adaptive filter's block diagram
The coefficients of the filter are algorithmically adjusted
after each iteration by the adaptive algorithm. Next we will
introduce two types of these algorithms that are included in
our simulation to determine the best one serving our needs.
IV. LEAST MEAN SQUARE ALGORITHM
The LMS algorithm [6], is a type of adaptive filter
algorithm that is also known as stochastic gradient-based
algorithm as it utilizes the gradient vector of the filter tap
weights to converge on the optimal wiener solution. With
each iteration of the LMS algorithm, the filter tap weights of
the adaptive filter are updated according to the following
formula:
(3)
The vector wn=[w1 w2 ....... wN] represents the
coefficients of the adaptive FIR filter tap weight vector at
time n. The parameter μ is known as the step size parameter
and is a small positive constant. This step size parameter
controls the influence of the updating factor. Selection of a
y[n]
e[n]
r [n]
-
+
noise n [n]
signal s [n]
+
+
z-∆
Linear
predictor
Adaptive
algorithm
suitable value for μ is imperative to the performance of the
LMS algorithm, if the value is too small the time the
adaptive filter takes to converge on the optimal solution will
be too long; if μ is too large the adaptive filter becomes
unstable and its output diverges.
V. NORMALIZED LEAST MEAN SQUARE
In the standard LMS algorithm, when the convergence
factor μ is large, the algorithm experiences a gradient noise
amplification problem. In order to solve this difficulty, we
can use the NLMS (Normalized Least Mean Square)
algorithm. The correction applied to the weight vector w(n)
at iteration n+1 is ―normalized‖ with respect to the squared
Euclidian norm of the input vector r(n) at iteration n. We
may view the NLMS algorithm as a time-varying step size
algorithm, calculating the convergence factor μ as [7]:
(4)
Where: α is the NLMS adaption constant, which optimize
the convergence rate of the algorithm and should satisfy the
condition 0< α<2, and c is the constant term for
normalization and is always less than 1. In NLMS
algorithm, the filter weights are updated by the Eq. (5).
(5)
VI. SIMULATION AND RESULTS
To show the robustness of the proposed solution, we did
computer simulation in MATLAB, using the DSP and
signal processing toolboxes, of the conventional UTDOA
and those based on LMS and NLMS filters, by comparing
the two techniques we can show the advantages imported by
NLMS algorithm.
In order to perform this simulation we consider the sent
signal to be a sin wave described by the form
(6)
where we set A=1 is the amplitude, is the signal
frequency and is the phase as simulation parameters
of the signal. While the receiver is a set of three base
stations with known coordinates.
The simulation of LMS and NLMS algorithms was
performed using the following criteria:
filter order N = 25
step size µ = 0.19
iterations = 200
Constant c = 0.001
The channel between the MS and each BS is assumed to
follows the COST-207 model i.e. multipath Rayleigh fading
with PN paths and inductive amplitude , the noise
component is an additive white Gaussian noise (AWGN) so
the received signal at the ith base station can be modeled by
the equation
(7)
The root mean square error (RMSE) can be defined as
an accuracy evaluation of multiple location measurements
[8]. It represents the difference between the real position
and the estimated one by each algorithm, its formula is
given as:
(8)
The path loss in outdoors is modeled using the
COST321-Hata model [9] which calculates the path loss in
absence of environmental information (geometry of the
streets and buildings). the path loss is estimated to be:
PL= 46.3 + 33.9 log10(fc) - 13.82 log10(hBS) - a(hMS) + (44.9 -
6.55log10(hBS))log10(d) + CM (9)
where fc is the carrier frequency; hBS is the height of the
BS antenna; hMS is the height of the MS antenna; d is the
distance between MS and BS. In addition, a(hMS) is a
correction factor for the MS antenna height based on the
size of coverage area and CM is 0 dB for medium sized
cities and suburbs and 3 dB for metropolitan areas.
The Log-Distance model is used in indoors
environments [10].
We first investigated the effect of applying both filters
on the RMSE error which represents the accuracy of the
proposed positioning approaches. As shown in figure 2 the
cumulative probability, for outdoor propagation, has
increased significantly with the LMS filter and more
improvement is shown by the NLMS algorithm which allow
us to achieve an accuracy of 100m, as recommended for
emergency cases, in 68% of calls, when the LMS method
gives the same value in just 53% of cases.
We can see the same pattern for the indoor propagation,
figure 3, that show how NLMS method converges quickly
(with 73%) compared to LMS filter (52%).
Figure 3. RMSE cumulative Probability (outdoors)
Figure 4. RMSE cumulative Probability (Indoors)
On the other hand figure 4 demonstrate the power of
LMS and NLMS based filters to minimize the effect of
multipath on the accuracy of user's position.
Finally, to have a better vision of how important this
technique can be, figure 5 shows the cellular structure used
to simulate the network with the actual position of the
mobile station and the estimated positions by the two
algorithms at the same iteration so the convergence and
robustness of NLMS can be highlighted.
Figure 5. Multipath effect
Figure 6. real and estimated position projection on cellular
network structure
VII. CONCLUSION
As shown in this paper, adaptive filtering can increase
enormously the accuracy of UTDOA technique, in addition
the NLMS filter has shown better performance and quicker
convergence than those shown by LMS algorithm. This
work do not treat only the enhancement of the standard
UTDOA using adaptive filters but also includes a
comparative study between two sort of controlling
algorithms and an application in both indoor and outdoor
environments. for future work, this method can be
associated with GPS to develop a hybrid positioning
solution.
ACKNOWLEDGEMENT
This work falls within the scope of telecommunication
projects. We would like to thank the Department of
technology of the MESFCRST for financing our projects.
RELATED WORK
The concept of using adaptive filters to enhance the
Uplink time difference of arrival technique was the subject
of previous papers [11][12], but this work don't limit the
study on one algorithm and extend the approach to include
indoor environment which were just treated by sensing
network subject.
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