Simulation Method to Identify Actual TOA and Angle of Incidence across Large Number of Small Time…
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Simulation Method to Identify Actual TOA and Angle of
Incidence across Large Number of Small Time Interval
Measures in Location Aware Services
Srinivasa Gopal
GAVS Information Services Private Limited
E-mail: gopal.srinivasan@gavsin.com, srinivsa32@hotmail.com
ABSTRACT: A positioning system uses time of travel and angle of incidence as two measures for identifying the
location. These measurements are taken at the destination. However, the signal takes a geodesic path. The speed
of signal in the air will vary with respect to time during the time of travel of the signal from the sensor to the mobile
device and also the angle of incidence would not be the same throughout the journey of the signal, as the geodesic
path and the velocity curve would be influenced by a lot of factors. A lot of measurements are required along the
geodesic path to determine the exact TOA and the angle of incidence at the destination. Since the signal travels
close to the speed of light, any small differences in the time interval measurements will yield a conflict in determining
the exact location. Survey based data to measure a possible continuous distribution of velocity and the direction of
travel along a geodesic path would be difficult to set up. The paper analyses a simulation based method to identify a
possible distribution of velocity and the direction of travel a long the geodesic path.
Keywords—Location Aware Services, Time of Arrival (TOA), Angle of Incidence, Velocity of Travel, Simulation,
Survey Measurements.
INTRODUCTION
A
positioning system uses time of travel and angle of
incidence as two measures for identifying the location.
Since, the speed of signal in the air will vary with respect to
time during the time of travel of the signal from the sensor
to the mobile device and also the angle of incidence would
not be the same throughout the journey of the signal, a lot
of small measurements are required along the time interval
to determine the exact speed of travel and the total distance
traveled by the signal. Since the signal travels close to the
speed of light, any small differences in the time interval
will yield a conflict in determining distance. The GPS
algorithm would hence be rendered in effective in
identifying small changes in locations of say less than
25 kms, if only one sensor used.
require a lot of measurements along the time interval to
determine the exact speed of travel of the signal and the net
angle of incidence of the signal.
Correcting the Time of arrival and the Angle
of Incidence Measurements
The following experiments would be required to determine
the following adjustment measurements
 Adjustment of the actual time of travel from the
measured time of travel based on the possible changes
of the velocity of the signal during the life- time of the
signal.
 Adjustment of the angle of incidence of the signal based
on possible changes of the direction of the signal during
the life-time of the signal.
SURVEY DATA VS SIMULATION
Simulation Runs
Survey data stored in a database super-imposed with real
time measurements can yield satisfactory results. But,
survey data cannot be obtained without performing
experiments which involve extensive infrastructural setup.
Simulation data however can arrive at satisfactory results
with a good amount of accuracy. Also as speed of the
signal would vary, so if based on the time of travel we
calculate the position it may yield unsatisfactory results.
Also the angle of incidence of the signal would be
localized, as the signal would not travel in the same
direction throughout its lifetime. In reality one would
The runs would be performed by measuring possible values
of velocity of the signal over 1000 time intervals. The
simulation run itself would be run 1000 times. This would
generate possible values of the velocity during the time
intervals. Finally a regression equation with starting and
ending values would be obtained. This regression equation
will be used to adjust the values of time of arrival and angle
of incidence, based on the possible changes of the direction
of the originating packet and possible changes to the
velocity of the signal.
Simulation Method to Identify Actual TOA and Angle of Incidence across Large Number of Small Time…
Inference of Variations
Post Simulation Adjustments to
Measurements
Adjustments can either be made using Regression and
Random number generation techniques. Adjustments to the
measurements can also be made using logical derivations
based on possible states of the signal with respect to the
direction of travel and the angle of incidence. In the case of
logical derivations, multiple measurements of the TOA and
the angle of incidence can be taken measurement of the
TOA and Angle of Incidence at just the destination. This
combined with the simulation data shown above can yield
conclusive data for adjustments to the measurements
obtained at the destination.
Variations of Velocity and Angle of Travel
during the Time of Travel
Simulation of Velocity Variations
Veolocity
Distribution
Velocity
Distribution
Simulation of Velocity Variations
Angle
Angle
Localised
Angle of
of Incidece
Localised
Angle
Incidence
The variation in the direction of travel of the signal shown
implies that when taking into account the angle of
incidence of the signal, it cannot be assumed to be a
straight line. For example an angle of incidence of
5 degrees at the destination, it can be seen by simulation
studies that there are many possible finite states of the
direction vector, before it becomes 5 degrees at the
destination. The simulation study above shows that the
direction vector can change from 60 degrees to 5 degrees at
the destination during smaller intervals of measurement
during the time of travel. So the angle of 5 degrees is
localized from a prior discrete step in the time interval. The
angle of incidence is localized from the previous discrete
time interval and is not continuous over a time interval
range starting from source to destination. Similarly changes
in the velocity vector shows that the time measurement is
not discrete over the entire time interval and the signal
would take a path which is influenced by several
atmospheric conditions.
3.5
3
2.5
2
1.5
1
0.5
0
Time
Time
Intervals
Intervals
during
during
the
life
life
ofthetravel
of travel
147
100
90
80
70
60
50
40
30
20
10
0
LocalisedAngle
Angleof
Localised
of Incidence
Incidece
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
Time
of Travel
Time
of travel
CONCLUSIONS
It is shown that the TOA measurement and the angle of
incidence measurements which are taken into consideration
for computing positions in location aware services at the
point of arrival of the signal, would not be accurate due to
the following reasons
1. The signal would take a geodesic path in space which is
not a straight line.
2. In the course of the geodesic path the signal would
continuously change its velocity and so the
measurement of the velocity of the signal at its
destination path would not be accurate.
3. In the course of its path in the air, the signal would also
continuously change its direction. So, the measurement
of the angle of incidence at the destination is also
ineffective.
4. A measurement technique where the AOI and the TOA
is monitored continuously over a large number of time
intervals was initiated.
5. Survey based measurements would take sufficient
amount of infrastructural set up, so a simulation based
experiment was designed.
6. A method of applying adjustments was also discussed.
REFERENCES
Simulation Run 3
Simulation Run 3
Simulation Run 2
Simulation Run 2
Simulation Run 1
Simulation Run 1
[1] Solheim, F.S., Vivekanandan, J., Ware, R.H. and Rocken, C.
- Journal of Geophysical Research, 1999, cosmic.ucar.edu
Propagation delays induced in GPS signals by dry air, water
vapor.
[2] Brown, A., Gerein, N. and Taylor, K., Proceedings of the
ION National Technical Meeting, 2000,
navsys.com
Modeling and Simulation of GPS Using Software Signal
Generation and Digital Signal Reconstruction.
Time Interval