Chapter 5: GPS, DGPS, and Backup Systems
GPS is a powerful tool for locating one's position. GPS
was designed and implemented by the United States
Department of Defense for military use. They allow
civilians to use the system, but at a reduced accuracy.
This reduced accuracy is called S/A (Selective
Availability). This reduces the accuracy from ±5 meters to
±100 meters. There have been lengthy debates about S/A,
and whether it should be turned off. Currently this issue
is being debated in the United States Congress. A method
for getting improved accuracy is called DGPS or
Differentially-Corrected GPS. This not only eliminates the
S/A error but also any static errors introduced by the
satellite signals entering earth's atmosphere.
Differential-correction companies offer a number of
different services, from a basic service offering ± 4-meter
accuracy to the premium service at ±1-meter.
The problem here is that GPS needs a direct
line-of-sight
to all satellites that are used in its position solution.
When satellites are blocked by tall buildings, trees,
bridges, etc. GPS loses its lock on the satellites and its
position is unknown. Another type of GPS failure occurs
when the satellites are positioned in such a way that an
accurate position solution is unobtainable. This is known
as a PDOP (Position Dilution of Precision) error.
When GPS loses its position for whatever reason, a backup
system is needed to keep tracking the person. Without a
secondary guidance system, the user is presumed to be at
the last known position.
Dilution of precision (DOP) is a measure of the quality of
the GPS data being received from the satellites. DOP is a
mathematical representation for the quality of the GPS
position solution. The main factors affecting DOP are the
number of satellites being tracked and where these
satellites are positioned in the sky. The most common DOP
factor is position dilution of precision (PDOP). PDOP is
an error indicator of the physical positioning the
satellites have to triangulate the position being
calculated. Geometric dilution of precision
(
GDOP
) error
is another factor in the error calculation made up of PDOP
and satellite timing. A PDOP value of 1 indicates a good
satellite constellation and high-quality data, PDOP values
above 8 are considered poor. The quality of the data
decreases as the PDOP value increases. This PDOP value is
then multiplied by the total error inherent in the system.
The total error of the system is made up of satellite clock
error,
ephemeris
error, receiver errors, ionospheric errors
and S/A (Selective Availability). Atmospheric error is
shown in
Fig. 14
. The GPS status message in Strider "PDOP
too high" corresponds to those PDOP values which are above
8, and an overall accuracy greater than 100 meters. When
Strider receives PDOP values greater than 8 it can no
longer track the user and the Strider accuracy becomes
"BAD".
![Figure 14: Atmospheric Errors cause the Satellite Signal to be Deflected [8]](fig14.gif)
The path of the satellite signal is assumed to be a
straight line. When atmospheric disturbances cause the
signal to be deflected the path is no longer a straight
line. As well, the Ionosphere causes the signal to be
delayed. This increases the time the signal takes to get
to the GPS receiver, and thus reduces the accuracy in the
position solution calculated by the receiver.
Multipath error occurs when the path the data takes from
the satellites is not direct and is reflected to the GPS
receiver. This can be clearly seen in
Fig. 15
showing the
reflection of the satellite signal off mountains, a car and
a building. Since the GPS receiver makes use of the time
interval between transmission of the signal and its
reception at the GPS receiver, the additional reflection
delay causes an error in the position calculation.
![Figure15: Multipath Error [8]](fig15.gif)
When the GPS antenna does not have a direct line-of-sight
to at least three satellites, a GPS position solution is
unobtainable. Experimentation has shown that on the
streets of downtown Toronto, position fixes are only
obtainable at street intersections because of the tall
buildings on either side of the street. In its present
configuration, Strider has only GPS and DGPS receivers, so
that accurate data is unavailable at locations away from
intersections. Furthermore, direction-of-travel
information is severely restricted, since it is based on
the last x positions received as was discussed in section
4.1.2.5.
By placing a stationary GPS receiver at a known location
that has been surveyed, this receiver can calculate the
error in the GPS position solution and then transmit this
error correction to other DGPS receivers in the area. The
DGPS receivers acquire these error correction messages and
corrects the position solutions as seen in
Fig. 16
. This
concept works because the satellites are so far above the
earth that errors measured by one receiver will be almost
exactly the same for any other receiver in a given area.
This correction factor not only corrects S/A but will also
reduce other static errors such as ionosphere, timing, and
atmospheric errors.
![Figure 16:DGPSCorrection [1]](fig16.gif)
Figure 16: DGPS Correction
[1]
With the aid of a DGPS receiver and the differential
corrections from the reference receiver, the accuracy of
GPS improves to less than 4 meters. With this improved
accuracy, Strider can inform the visually impaired the
exact address of the house that they are currently standing
in front of. Without the DGPS accuracy, Strider could
place the user a block away from the actual location. Even
with this improved accuracy, the whole system fails when
the GPS receiver cannot obtain a position solution.
Therefore, a backup system for GPS must accompany Strider
for this to be a viable product for the visually impaired.
The accuracy of the location given by the GPS receiver is
based upon a number of factors as was previously discussed.
The GPS receiver could in fact be tracking six or more
satellites but a position fix may not be obtainable because
of the satellite's physical position in the sky, being
blocked by a building, etc. When the GPS receiver is using
three satellites to determine a position solution, GPS-2D
accuracy is obtained. This means that no altitude
information will be available and the overall positional
accuracy is reduced. When the GPS receiver is using four
or more satellites to determine a position solution, GPS-3D
accuracy is obtained. The altitude of the receiver is
available and an increase in the overall accuracy is
achieved. This increased accuracy is achieved because the
GPS receiver can use the satellites that offer the lowest
PDOP values in its position solution. When this position
is then differentially-corrected these 2D and 3D accuracies
become DGPS-2D and DGPS-3D. The differential accuracy is
also dependent upon which service the user has.
Table 2
presents the different GPS accuracies that have been
observed during field-testing, with a differential quality
of ±1-meter offered by the OEM 4000 DGPS receiver
manufactured by
DCI
(Differential Corrections
Incorporated), and using the Lassen GPS receiver
manufactured by
Trimble Navigation Incorporated
. See
Appendices
G
and
H
for the technical specifications of the
DGPS and GPS receivers respectively.
Table 2: GPS Accuracies Observed During Field Tests
|
Name
|
Accuracy (meters)
|
|
GPS-2D
|
100
|
|
GPS-3D
|
80
|
|
DGPS-2D
|
3-5
|
|
DGPS-3D
|
1-2
|
A 1994 fourth-year project
[9]
by Dentremont, at Carleton
University entitled "Inertial Guidance System" was
conducted based on the 1993 project "A Navigational System
for the Visually Impaired". It investigates a backup
system for the 1993 project. A number of different
possible solutions were looked at and rejected mainly based
upon size, weight, and cost. These possible solutions will
be summarized here. The primary findings from this 1994
project was a backup system containing either an
accelerometer
or a threshold switch for measuring distance
travelled, and a compass for measuring direction of travel.
By integrating the acceleration of the user twice, distance
travelled can be obtained using an accelerometer. There
are a number of different ways for measuring an
acceleration, each of which has its own particular
advantages and disadvantages. The following summarizes the
main accelerometers researched in the 1994 project
[9]
. The
following sections 5.4.1.1 through 5.4.1.5 are based on the
1994 fourth-year project
[9]
.
A pendulous accelerometer is based on the principle that
acceleration displaces a mass m and the angle q the mass is
displaced from rest can be used to determine acceleration,
see
Fig. 17
. The problem here is the ability to accurately
measure such a small angle q of displacement. A
person-based accelerometer would be measuring accelerations
well below a
g
, and friction would cause serious
degradation to the accuracy of this accelerometer. The
pendulous accelerometer has not been designed because of
these reasons, but the principles behind it are used in
other designs.
![Figure 17: Pendulous Accelerometer [9]](fig17.gif)
A pendulum is being used to determine the acceleration
being applied to it.
The basic principle behind this accelerometer is its
utilization of torque. The torque of the gyroscope is used
to counter the torque cause by the pendulum and the
acceleration applied to it, which is proportional to the
acceleration of the unit. A diagram of this accelerometer
is shown in
Fig. 18
. The range of accelerations it can
measure is quite high and its cost is also high.
![Figure 18: Pendulous Integrating Gyroscope Accelerometer [9a]](fig18.gif)
Liquid placed in a U-tube can be used to measure the
displacement difference when the liquid in the tube is
subjected to an acceleration. Under an acceleration in the
x direction as shown in
Fig. 19
, the liquid in the U-tube
will move and the difference in height from rest can be
used to calculate the applied acceleration. The
difficulties with this type of accelerometer include (a)
the cost of adding accurate detectors, (b) an integrator to
determine the acceleration and (c) a way of canceling out
the effect of the up and down motion, which is inherent
while walking.
![Figure 19: Liquid Level Accelerometer [9]](fig19.gif)
A force-rebalanced accelerometer uses a mass that is
connected to a damper and a spring as shown in
Fig. 20
.
When an acceleration is applied the mass is displaced.
Using the distance the mass moved and knowing the damper
and spring constants, the acceleration can be calculated.
The cost of such an accelerometer increases as the
acceleration to be measured decreases, and for a person
walking the accelerations in question are in the milli-g
range. These accelerometers are mainly used to measure
rocket launches, and other high g acceleration applications.
![Figure20: Force-Rebalanced Accelerometer [9]](fig20.gif)
Three silicon elements are bonded together to construct a
capacitive device. The three elements form a pair of
air-dielectric parallel-plate capacitors. Two electrodes
form the top and bottom elements, and the middle element is
a base common to the two capacitors. The base is
chemically etched to form a rigid central mass that is
suspended by a thin flexible membrane. As an acceleration
is applied, the base plate is deflected resulting in an
uneven change in capacitance between the two capacitors.
The supporting electronics convert this differential
current to an output voltage that is proportional to the
applied acceleration
[9b]
.
Analog Devices has designed this accelerometer the ADXL05
on a single monolithic IC
[10]
that is capable of measuring
accelerations in the milli-g range. "It contains a
polysilicon surface micro-machined sensor and
signal-conditioning circuitry which implements a
force-balance control loop."
[10]
"The
differential-capacitor sensor consists of independent fixed
plates and central plates attached to the main plate that
moves in response to an applied acceleration."
[10]
A
capacitive divider with a common central plate is formed by
the two capacitors connected in series. At rest the
values of the two capacitors are equal, and therefore, the
voltage output at their center plate is zero. When an
acceleration is applied the common central plate moves
closer to one of the fixed plates resulting in a difference
in separation between the two capacitors. This creates a
mismatch in the two capacitances, resulting in a signal at
the central plate. Refer to
Fig. 21
and
Fig. 22
for this
accelerometer at rest and under an applied acceleration
respectively. The output amplitude of the signal varies
directly with the amount of acceleration experienced by the
sensor
[10]
.
![Figure 21: A Simplified Diagram of the ADXL05 Sensor at Rest [10]](fig21.gif)
![Figure 22: ADXL05 Sensor Responding to an Externally Applied Acceleration [10]](fig22.gif)
Four things would normally prevent the use of
accelerometers for a person-based inertial navigational
backup system. The ADXL05 addresses three of these
concerns but fails to solve all concerns. The
accelerometers discussed previously were either too large,
too expensive, or were not accurate enough to measure the
small accelerations which a person would experience while
walking. The ADXL05 accelerometer does solve all of these
concerns. Being silicon based it is light weight,
relatively inexpensive and can accurately measure down to 5
milli-g accelerations. The problem with this and all
accelerometers is that it will not only measure the
acceleration that is applied by the user when beginning to
move forward but may also contain acceleration due to the
earth's gravity. If the accelerometer is not exactly
horizontal, it will contain a component of the earth's
gravity in its acceleration calculation.
Table 3
shows the
off-axis applied accelerations which will affect the sensor.
Table 3: Off Axis Applied Accelerations[10]
|
Angle
|
% of Signal at Output
|
|
0
|
100
|
|
1
|
99.98
|
|
2
|
99.94
|
|
3
|
99.86
|
|
5
|
99.62
|
|
10
|
98.48
|
|
30
|
86.60
|
|
45
|
70.71
|
|
60
|
50.00
|
|
80
|
17.36
|
|
85
|
8.72
|
|
87
|
5.25
|
|
88
|
3.49
|
|
89
|
1.7
|
|
90
|
0
|
A 1-degree variation off the horizontal will result in a
0.02% reduction in the applied acceleration, but more
importantly also results in a 1.7% increase in acceleration
from another axis, namely the acceleration due to gravity.
For example suppose a person starts walking and the
accelerometer is off 1-degree from horizontal towards the
earth. The acceleration of the person starting to walk is
200 milli-g's. Then:
Error = [(person's acceleration) x (1-degree off axis
factor) +
(earth's gravity) x (89 degree off axis factor)] -
(person's acceleration)
= [0.200 m/s2 x 0.9998 + 9.814 m/s2 x 0.017] - 0.200 m/s2
= [0.199996 + 0.16677] - 0.200
= 0.167 m/s2 (or an error of 83%).
It can also be concluded that over time this error
compounds as the accelerometer continues to be off by even
a degree. The user can be stopped with no acceleration and
the accelerometer will still be influenced by the earth's
acceleration. The only way to compensate for this error is
to place the accelerometer exactly horizontal using
gyroscopes. This not only would be too costly but would
also increase the weight of the unit dramatically. For
this reason, the use of accelerometers for inertial
navigation was abandoned, and other means for measuring
distance travelled were investigated.
An alternative to an accelerometer would be an acceleration
switch. This threshold switch would complete an electrical
circuit when the switch is subjected to an acceleration.
There are a number of different designs from a mass
pressing against a spring which make contact with two pins
at a given acceleration, to a mercury switch making contact
with a sensor at a given acceleration. These switches are
inaccurate and would only be a "guesstimate" of the actual
acceleration of the user. A variation of the acceleration
threshold switch will be looked at in section 5.4.3.3.
Since we are only concerned with distance travelled, we can
ignore acceleration and concentrate on measuring the
physical distance the user travels.
If the user had a wheel they dragged while they walked down
the street, the wheel revolutions could be counted and the
distance travelled by the user could be calculated by
knowing the revolutions and the circumference of the wheel.
This is in fact how a car determines its distance
travelled. Unfortunately, this principle cannot be used
since it would be inconvenient for the visually impaired to
have to drag this rolling wheel while walking around. Even
if the wheel was attached to the white cane, the visually
impaired do not push the cane along the street. Instead
they continuously tap the cane from side to side as they
walk.
It is conceivable that if a pair of sensors were attached
to the user's shoes, that these sensors could determine the
number of steps the user has taken and then transmit this
information to the personal navigation unit. This method
for determining number of steps taken theoretically could
be very accurate. Having a wire up the leg of the person
would be unacceptable, and the amount of engineering time
and cost to create a wireless system would be too
expensive, not to mention making the person wear these
sensors on their footwear.
A variation of the acceleration threshold switch in section
5.4.2 is the pedometer. This very simple device counts the
steps a user makes as they walk. A spring-balanced weight
makes contact with a pin as the user takes a step. This
connection completes an electrical circuit that signals the
navigational unit indicating a step has taken place. A
pedometer not only is accurate in counting steps a person
takes while walking but also is quite inexpensive in the
range of $10 to $20. Since pedometers are inexpensive,
lightweight, accurate and readably available, this is what
has been chosen to measure the distance travelled in the
ANS as part of this thesis.
Calibration of the user's stride length can be done without
"physically" measuring it. Since we have DGPS to track the
user, the system can calibrate itself while the user walks.
For example if the user walks 10 meters as recorded by the
Strider system, and the pedometer records 20 steps taken,
the stride length would be 0.5 meters/step-taken. Then
when GPS fails, for each step the user takes, 0.5 meters
will be associated with it. In addition, whenever DGPS
accuracy is obtained re-calibration of the stride length
may occur.
As the pedestrian takes a step, a heading must be
associated with that step. The two data components (i.e.
step and direction the step was taken) are essential for
pedestrian tracking. Different methods for determining
direction of travel will be discussed here, and one will be
chosen as part of the ANS. The following sections 5.4.4.1
through 5.4.4.3 are based on the 1994 fourth-year
project
[9]
.
A fluxgate compass is a coil of wire wrapped around a
metallic bar as would be found in a transformer. This
wrapping is excited by an alternating current, which
induces a voltage in a second coil. This induced voltage
can be picked off amplified and converted to an electrical
signal. The level of the voltage will be influenced by the
magnetic field passing through the device. In the north –
south plane the magnetic field will have the greatest
effect on the voltage, and therefore in the east – west
plane the least effect on voltage. Current consumption of
the device and cost are the two main problems with this
solution.[9c, 9d]
Polarized light was investigated since bees use it to
navigate, and an experiment with simple Polaroid's was
inconclusive.
[9]
It appeared that considerable development
and expensive photo sensors would be needed, and it was
unlikely that the resolution that could be obtained would
be accurate enough for this application. Using polarized
light would also only work during the day, and outside.
This is considered unacceptable and was not investigated
any further.
This compass uses a freely pivoting magnet and
"Hall-effect" sensors to determine the position of the
magnetic bar. Four such sensors are used, positioned
equally around the magnet, and they can determine the four
main directions (north, south, east and west) in which the
magnetic bar is pointing.
[9]
When the magnet is positioned
between sensors, this too can be determined thus giving
additional four positions (northeast, southeast, southwest,
and northwest). Therefore, only eight directions can be
accurately determined, i.e. a 45-degree resolution. An
analog version of this compass is available producing a
sin/cosine output that offers a higher degree of accuracy
but its cost is comparable with the digital Vector 2X
Compass covered next.
The Vector 2X compass made by Precision Navigation
Incorporated uses an inductive magnetometer to determine
the direction the compass is pointing. This technology
uses two inductive coils aligned perpendicular to each
other to measure the X and Y components of the earth's
magnetic field. These two components can then be used to
determine the earth's magnetic north compared with that of
the compass's reading. The Vector 2X compass determines
magnetic north to be the direction for which the X-axis
field is at its maximum and the Y-axis field is at zero.
Simple trigonometry can then be used to determine with a
high degree of accuracy the direction of the compass. The
Vector 2X compass is lightweight, small, consumes very
little power, and has a 1-degree resolution with 2-degree
accuracy. The unit cost for this compass is $50 U.S., and
can be digitally connected to a microprocessor very easily.
This compass was incorporated in the personal guidance
system for determining direction of travel. Specifications
for the Vector 2X Compass can be found in
Appendix I
.
Point Research Corporation
of Santa Ana, California has
developed a lightweight miniature Dead Reckoning Module
(DRM) for drift-free navigation by personnel on foot. The
DRM has been built for military use. It uses a solid-state
3-dimensional compass and an electronic pedometer. The
pager-sized module also includes a barometric altimeter and
a temperature sensor. GPS can be connected to this module,
and when GPS is available, the module will blend the data
with the "Dead Reckoning" data using a Kalman filter.
[13]
It provides continuous navigation solution through many
buildings, in canyons, or other areas where the GPS signal
is compromised. The electronic pedometer is implemented
using tri-axial accelerometers. The 3-dimensional compass
uses a tri-axial arrangement of magnetometers providing a
three dimensional vector of the earth's magnetic field
relative to the platform.
[13]
Since this was built for military use, the system is very
expensive but is extremely rugged and quite accurate with
an error of approximately 2% of the distance travelled when
GPS is unavailable. Ideally, this would be perfect for
this ANS except it costs $2 500 US per unit, this is an
unacceptable expense for a alternative to GPS. Point
Research Corp. is planning to make a civilian model of the
DRM, which will reduce the price but may still be too
expensive for this particular application.
The ANS (Alternative Navigation System) chosen consists of
a mechanical pedometer for determining distance travelled
and the Vector 2X compass for determining the direction of
travel. A Motorola microcontroller coordinates and
collects the data from the pedometer and compass, and
transmits this information to the laptop computer.
The alternate guidance system must be accurate,
lightweight, small, and affordable since this will be used
by the visually impaired. The cost of the components
chosen will total less than $100, the size and weight of
these devices are also acceptable. Weighing less than a
couple hundred grams and all components could fit of a
circuit board approximately 5cm x 5cm. The accuracy of the
system is acceptable, as will be shown in Chapter 7.
It is important to point out here that essentially the same
idea of using a pedometer and compass as an alternative to
GPS, has been developed for military use, as was shown in
section 5.5. The system proposed here might be less
accurate but costs under $100 where as the personal dead
reckoning system for military use costs $2 500.
