Note: Descriptions are shown in the official language in which they were submitted.
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Description
Positioning System for Racecars
The present invention relates to a positioning system for racecars, in
particular for use
at Formula 1 races.
Sports racing with various types of racecars has been known and popular for
centuries. Its popularity has led to the ongoing development and application
of special
vehicles for different types of races, track preparation measures, driving
techniques, etc.
New developments aimed at enhancing safety, providing more information to the
public,
increasing car speed, etc, are constantly being made.
US 5,731,788 discloses a system and a method for checking position and
managing
racing sailboat positions and speeds, which involve the strategic placement of
GPS
receivers and transmitters in a buoy and a committee boat that mark the
starting line of
the boat race, as well as radio and GPS receivers on the sailboat. GPS and
radio units are
placed in a start buoy and a start vessel, and another GPS and radio receiver
unit receives
GPS signals from positioning satellites and radio signals from the start buoy
and the
committee boat. The information received from the race boat is processed to
find the
relative and absolute positions and speeds, and the estimated arrival time
using the
intersection of the current sailboat course with the starting line for display
in a user-
friendly race management device.
US 3,714,649 describes an example of a vehicle monitoring system using a fully
automatic system to monitor car racing or the like. Each vehicle carries a
transponder,
which registers its own passing of a position event, for example crossing the
starting-
finish line, entering or leaving the grandstand area, etc., and transmits a
characteristic
signal to a receiver on the track shoulder next to the position event in a
time-division
multiplex method with the transponders of all other vehicles. A main
transmitter
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transmits a time-division synchronization signal to all vehicle transponders
and every
transponder is embodied to send a position event signal only for a
predetermined time
period of the synchronization signal. The receivers on the track shoulder feed
a central
control unit, which is also synchronized with the main transmitter, and enters
the
appearance of each vehicle's position event in real time. A clock and a
computer are
provided for determining the order, lap speeds, etc. from the entered data.
The system for
recognizing a position event is based on the principle that the vehicle's
inductance
crosses a variable magnetic field whose polarity defines the position of the
respective
event.
US 4,949,067 also describes a car racing status warning system which comprises
a
transmitter operated by a section monitor or another racing official, and a
sufficient
number of receiver units to allow each racecar to have a receiver unit. The
transmitter
sends an encoded signal that can be received along the entire track, and
corresponds to a
red, yellow or green flag. The receiver units, which are self contained and
include a
built-in power supply, receive and decode the signal and switch on green,
yellow or red
lights. The system offers the race participants an essentially instant
notification of
danger on the track.
The object of the invention is to provide a positioning system for racecars
offering
expanded functions, simplified use and enhanced safety over the previous prior
art.
Additional advantages of the invention will be described in greater detail
below.
This object is accomplished by the features of Claim 1. Preferred embodiments
of
the invention are defined in the dependent claims.
Basically, according to a first embodiment, the invention consists of a
vehicle-
information device that is housed in the racecar and comprises a positioning
device for
collecting and outputting positioning data, which can be used to identify the
racecar's
position, and a transmitter, which transmits the positioning data to a central
unit. This
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guarantees a cost-effective and reliable identification of vehicle position.
In particular,
the above precludes any confusion between racecars, because each racecar
ascertains and
transmits its own positioning data. The transmitter can also be used to
transmit additional
data to the central unit.
An advantageous embodiment of the invention as a positioning system entails a
plurality of such vehicle-information devices in conjunction with a
calculation device,
which uses stored racetrack data to calculate the position of the respective
racecars on a
racetrack from transmitted positioning data. By using a virtual image of the
racetrack in
the form of racetrack data, the respective positions of the racecars can be
identified using
the transmitted positioning data, without requiring that position-identifying
devices be set
up at all major points of the racetrack. The location at which a vehicle
leaves the
racetrack or has stopped can also be precisely ascertained without additional
expense.
The track data can be reused if professionally stored; with appropriate
measures, they
can also be updated, wholly or in part, when the track is modified. It is also
possible to
transmit the track data to another positioning system.
Individuals of skill in the art are familiar with the fact that positioning
data can be
gathered in the vehicle in a wide variety of ways. For example, the vehicle
can be
equipped with a GPS (global positioning system, a global, satellite-supported
navigation
system) receiver or another satellite receiver, a direction finder or a gyro
sensor. A
redundant combination of such receivers or sensors can also be used. If
desired,
individual racecars can also be equipped with various positioning devices to
obtain
positioning data. In the use of direction finders, it is necessary to expand
the positioning
system with at least three direction-finding transmitters whose exact position
on the
racetrack is known. The position of the direction finder can be found by
appropriately
measuring the distance between the direction-finding transmitters and the
respective
direction finder.
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As mentioned above, the transmitter provided in the vehicle-information device
can
be used to transmit vehicle-operating information, such as vehicle speed,
engine RPM, or
similar data. Such data are obtained using suitable sensors, or from the
vehicle electronic
system and can, for example, enable fast identification of stoppage or other
danger
situations for the racecar. In order to avoid misuse of the positioning and/or
operating
data, the data can be sent wholly or partially encrypted using known methods.
Also
relating to these preferred features of the invention, it is not necessary
that the respective
vehicle-information devices or racecars be equipped in the same way.
Preferably, the positioning system according to the invention comprises a
central unit
equipped with the aforementioned calculation device, a memory for storing
racetrack data
and one or more receivers for receiving the positioning and vehicle operating
information
transmitted by the respective vehicle-information devices. In these devices,
the system
components that do not have to be physically separate can be embodied as
individual
components, partial groups or as an integrated unit.
It is also advantageous if the central unit comprises a transmitter that can
be used to
transmit safety data, and one or more racecars participating in the
positioning system have
appropriate receivers and display devices to, if desired, receive and
appropriately display
the safety data. Thus, for example, if the positioning system according to the
invention
determined that a racecar had stopped, it could transmit a corresponding
warning,
analogous to the green, yellow and red flags used in Formula 1 racing, to
signal the event
to the other racecars participating in the positioning system.
In particular, the receivers installed in the racecars could also contain an
identifying
device, which would permit the control center to respond selectively to each
receiver. In
this way, it is possible to differentiate between the racecars participating
in the
positioning system based on danger status. For example, the vehicles that
reach the
danger zone after a long period of time could be signaled "green light," while
the racecars
that will soon pass the danger zone will be signaled "red light." All other
racecars will be
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signaled "yellow light." Other differentiation methods known to the industry,
such as
time-division multiplexing or frequency-division multiplexing, can also be
used to permit
selective response to the various racecars.
To circumvent the need for all racecars to participate in the positioning
system and to
insure greater track safety, the customary section monitors can also take part
in the
positioning system in that one or more of them is or are equipped with
receivers and
display devices that receive and appropriately display the transmitted safety
data. Here as
well, the use of an identifying device or the like can make it possible to
selectively
address each section monitor. For reasons of security, the safety information
can be sent
wholly or partially encrypted using known methods.
Preferably, the positioning system according to the invention includes a
display
device that permits a visual display of the current positions of selected
racecars on the
racecourse using the track data and the calculated vehicle positions. This
task can, if
desired, be performed by the calculation device so that no additional hardware
is
necessary for the display device. For example, the calculation device could
convert the
obtained position information with the track data into a video signal, which
could be sent
to the TV stations broadcasting the race. The display device can also comprise
one or
more large screens or video screens that present such visual displays of
selected vehicle
positions to the spectators at the racetrack. The result is a system which, in
addition to its
safety advantages, also has the special advantage of informing the spectators -
regardless
of where they are sitting -- about the latest race information pertaining the
entire course in
real time, thus substantially enhancing the appeal of attending a race.
Likewise, the display device can include a data-processing device which, among
other
things, can enable a visual display of the current positions of selected
racecars on the
track on visual data-processing devices, connected, for example, via a fixed
network or
radio link to the data-processing device for transmitting data. The above
could, for
example, be used to create a virtual broadcast of the race via the Internet.
Other race
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information collected by the positioning system according to the invention,
for example,
the current placement or the current speed of selected racecars, could be
called up and
viewed on such a data-processing device integrated into the positioning system
with
suitable linkage to the visual data-processing devices. In this way, the data-
processing
device is integrated into the positioning system in such a manner that the
relevant race
data contained in the positioning system can be converted and processed by an
operator
feeding them into a data network, and that a desired audio and/or video
representation of
the racing events and/or the desired race data is possible on the respective
visual data-
processing device. The respective displays of a plurality of visual data-
processing
devices can be different. For example, a mobile telephone acting as a visual
data-
processing device could be used to show the respective placement and lead of
selected
racecars, while a computer linked to the data-processing device via Internet
could present
a virtual depiction of the racing events, e.g., the current positions of any
selected racecars
on the track, on the screen. Preferably, the desired display type and/or the
information to
be displayed will be selected by interactive entry between the user of the
visual data-
processing device and the data-processing device.
According to the invention, all or selected components of the positioning
system are
preferably provided in redundant fashion to ensure the function of the
positioning system
even in the event of the failure of one or more components. This is especially
true for
safety components, for example the positioning system's calculation device.
Alternately, the positioning system according to the invention can be realized
in the
sense of a second embodiment, in which instead of the positioning device and
the
transmitter, the respective vehicle-information devices have only one
transmitter for
transmitting directional signals. Using at least three spatially separate
direction finders
included in the system, positioning data can be obtained outside the vehicle,
where they
can be processed by the calculation device as described above. Because, for
example, the
direction finder can be connected to the central unit by cable, if desired,
there is no need
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for a receiver in the central unit. All other features of the invention are
the same as in the
first embodiment.
It is also possible that this second embodiment will only be used on selected
racecars,
and/or the two embodiments of the inventions will coexist among race drivers.
The invention is described in greater detail below by way of an exemplary
embodiment illustrated in the following drawings. Shown are in:
Fig. 1 a racetrack mapped out by track data according to a preferred
embodiment of
the invention;
Fig. 2A a racetrack with a positioning system according to a preferred
embodiment of
the invention, in the first embodiment;
Fig. 2B a racetrack with a positioning system according to a preferred
embodiment of
the invention, in the second embodiment;
Fig. 3A a racetrack with a vehicle-information device according to a preferred
embodiment of the invention, in the first embodiment;
Fig. 3B a racetrack with a vehicle-information device according to a preferred
embodiment of the invention in the second embodiment; and
Fig. 3C a racecar with a vehicle-information device according to a second
embodiment.
In Figure 1, track data map out a racetrack 2 according to an advantageous
embodiment of a positioning system 1 according to the invention. The figure
shows a
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plurality of racecars 3A, 3B, 3C and 3X on racetrack 2, participating in the
positioning
system.
To be able to calculate the position of one or more of racecars 3 on racetrack
2,
racetrack 2 is stored by positioning system 1 in the form of visual track data
in such a way
that it is possible to compare the track data with the positioning data
received from the
respective racecars 3. This comparison is made in a calculation device 9, for
example a
digital EDP system of positioning system 1. Accordingly, the track data can be
preferably
stored in a professional way in a storage device of calculation device 1. It
is also possible
to store the track data in a storage device (10) linked to calculation device
9, or to store
the track data on a memory storage unit which is accordingly read by a reading
device in
place of the storage device (10).
According to the embodiment shown in Figure 1, the racetrack 2 is represented
by
ordered sequences of corner points 11, which are measured in a fixed
coordinate system
12 and function as track data. Connecting the corner points 11 one after the
other by
straight-line pieces thus defines an interior or exterior boundary of track 2.
Using this
method, it is possible to represent any two-dimensional track topology. Also,
individual
track sections and the preset travel direction can be defined using corner
points 11 and/or
the corner-point sequences. Of course, it is possible to use other methods for
mapping
tracks known to individuals of skill in the art.
In the embodiment shown in Figure 1, the positions of the racecars 3 are
ascertained
using the coordinate system 12. Because, however, comparing coordinate data
from
different coordinate systems requires only an arithmetical conversion, the
positioning data
of each racecar 3 can also be identified using other coordinate systems. This
could be the
case, for example, if some racecars were tracked by GPS receiver, while the
positioning
information of other racecars 3D was generated via direction-finding receivers
participating in a locally installed direction-finding system 23.
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The figure assumes and indicates that the racecars 3 move counterclockwise on
racetrack 2. If it is also assumed that racecar 3X is stopped, racecar 3A is
located near the
danger site. Racecar 3B is still at a safe distance from the immediate danger
zone, while
according to the drawing, vehicle 3C is not in immediate danger. The fact that
the
position of racecar 3 essentially has not changed indicates that it has
stopped. The
individual degree of danger for the remaining cars 3A, 3B, 3C can be
determined by
ascertaining the affected track section and the respective positions of the
remaining
racecars 3A, 3B, 3C participating in positioning system 1.
Figures 2A and 2B show various features of a positioning system 1 according to
an
advantageous exemplary embodiment of the invention according to the first and
second
/embodiment of the invention. They show a racetrack 2 containing a number of
racecars
3 participating in positioning system 1, as well as two GPS satellites 24.
Positioned along
the racetrack 2 are a number of section monitors 22, grandstands 20 and a
video screen
21, with the first and last being components of the exemplary positioning
system 1. In the
figures, positioning system 1 also includes a central unit 7, a
transmitter/receiver system 8
and a calculation device 9. In Figure 2B, positioning system 1 also includes
three
direction finders 23.
In Figure 2A, according to the first embodiment of the invention, racecar 3D
utilizes a
GPS receiver as a positioning device 5, the receiver receiving radio signals
from GPS
satellites 24. From these signals, the GPS receiver or another suitable
positioning device
in the racecar 3 obtains positioning data, which can be used to determine the
current
position of racecar 3. A transmitter 6 in racecar 3 transmits the obtained
positioning data
to a central unit 7, which is equipped with a reception device 8 associated
with transmitter
6. Accordingly, the respective transmitters 6 of racecars 3 and central unit 7
of the
preferred embodiment shown in Figure 2A form a star network. Together,
positioning
device 5 and transmitter 6 in racecar 3 form a vehicle-information device 4.
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In Figure 2B, according to the second embodiment of the invention, the
position of
vehicle 3D is determined by a direction-finding transmitter 6B that is
installed in vehicle
3D and has at least three direction-finding receivers 23 near racetrack 2, and
by the
calculation device 9 comprising central unit 7. The direction-finding
transmitter 6B
transmits direction-finding signals, which are received by the direction-
finding
transmitters, processed and routed as positioning data to central unit 7,
where they are
used in calculation device 9 to determine the position of vehicle 3D. The
positioning data
can be transmitted in a known manner, for example via cable, from the
direction-fording
receivers 23 to central unit 7. The foregoing could eliminate the need for a
receiver 8 in
central unit 7. In the illustrated embodiment, receiver 8 is used to receive
vehicle
operating information and/or redundant positioning data from a data
transmitter 6A
located in the vehicle, which is preferably used to check the position or the
operating
condition of racecar 3D.
According to the invention, each racecar 3 participating in positioning system
1 has a
vehicle-information device 4. These devices can, however, be designed
according to
different operating principles. The steps described above to obtain
positioning data and
to calculate the position of a racecar 3 are likewise performed, mutatis
mutandis, for the
respective vehicles.
In a calculation device 9 assigned to central unit 7, which comprises a memory
10, the
track data stored in 10 are used to calculate the position of racecar 3 on
racetrack 2. The
position calculated in this manner provides information regarding the
placement of
racecar 3 among the racecars 3 participating in positioning system 1, and also
about
whether racecar 3 is stopped, has slowed down dangerously or has left
racetrack 2.
Figures 2A and 2B show examples of a stopped vehicle 3X participating in the
positioning system. Calculation device 9 uses the position information
obtained therein
to determine such a stopped state, or a corresponding device connected to
calculation
device 9, preferably located in the central unit 7, ascertains this fact.
Subsequently, the
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transmitter/receiver system 8 transmits an appropriate message to racecars 3
and/or to
section monitors 22. For security reasons, transmitter/receiver system 8
preferably
transmits the data according to the invention in encrypted form. Because the
position of
the stopped racecar 3X is known, it is possible, using an identifying device
or another
differentiator known to persons of skill in the art, to transmit a targeted
message to the
section monitor 22X closest to racecar 3X. It is accordingly possible to send
a different
message to racecar 3C than to racecars 3B or 3A. As mentioned above, in this
way
vehicle 3A could be signaled "red light" depending on the degree of danger,
while racecar
3B could be signaled "yellow light," and the vehicles 3C "green light," which
could be
displayed in the respective vehicles 3. By the same token, the danger could be
displayed
on the track shoulder using appropriate display devices, for example by waving
a flag or
using a traffic light.
Figures 2A and 2B show a big screen video display 21, which makes possible a
visual
display of the current positions of selected racecars 3 on racetrack 2. The
big screen
video display 21 is supplied with signals generated in the calculation device
9 or in
another display device using the positions calculated in calculation device 9
and the
stored track data as described above. Such or similar signals can also be
supplied to TV
stations or to other communications services, for example to an Internet
provider, to be
broadcast. The display does not have to be limited to displaying vehicle
positions; it can
also include information regarding the respective vehicles 3 or other racing
or advertising
information.
The position information obtained by the positioning system 1 according to the
invention relating to the participating racecars 3 can also be used to
automatically direct
or control television and surveillance cameras to one or more vehicles 3 along
track 2.
Also, the image captured by the camera that has the best view of a selected
racecar 3 can
be displayed automatically. A person of skill in the art can easily recognize
several other,
equally applicable variations of this principle.
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The vehicles taking part in the race require minimal outfitting or refitting.
Figures
3A, 3B and 3C show different embodiments of the two versions of a racecar 3
equipped
according to the invention. According to the invention, the vehicles 3 are
equipped with
an antenna 30 and a vehicle-information device 4, which are installed
professionally in or
on the vehicle. The latter are indicated by dotted lines in Figure 3B.
Figure 3A shows a racecar with a minimally equipped vehicle-information device
4
according to the first embodiment of the invention, whereby vehicle-
information device 4
comprises only the essential components. Accordingly, vehicle-information
device 4
comprises only a positioning device S and a transmitter 6.
In the illustrated embodiment, a GPS receiver functions as a positioning
device 5 and
a data transmitter 6A fulfils the role of the transmitter 6. Using the antenna
30, GPS
radio signals are transmitted from a GPS satellite 24 to the GPS receiver,
where they are
processed into positioning data. The positioning data are converted
accordingly in data
transmitter 6A and supplied to antenna 30, from which they are sent to a
receiver 8 in
central unit 7. It is known to a person of skill in the art that it is
possible, if desired, to
distribute the tasks among the components S, 6 comprising vehicle-information
device 4
in a different way. As mentioned above, other positioning devices 5 and
transmitters 6
can also be used according to the invention.
Figure 3B shows a racecar with a minimally equipped vehicle-information device
4
according to the second embodiment of the invention, whereby the vehicle-
information
device 4 comprises only the essential components. Accordingly, the vehicle-
information
device 4 consists of only one direction-finding transmitter 6B, which
transmits direction-
fmding signals via antenna 30 to corresponding direction-finding receivers 23,
from
where they are processed as described above.
According to the invention, the respective vehicle-information devices 4 of
the
vehicles 3 participating in the positioning system can be additionally
connected to one or
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more devices 33 - 39, or even include them; these devices transmit vehicle
operating data
or redundant positioning data directly, or via vehicle-information device 4,
to transmitter
6 for transmitting these vehicle operating data and/or positioning data to
central unit 7. A
vehicle 3 equipped with many different accessory devices is shown in Figure
3C.
According to the invention, these additional devices 33 - 39 can vary among
the
respective vehicles 3. The type of additional equipment of each vehicle 3
depends,
among other things, on the weight of the devices 33 - 39 and their cost and
space
requirements.
The racecar 3 of the embodiment shown in Figure 3C corresponds to both the
first
and the second embodiments of the invention, because the illustrated vehicle-
information
device 4 is equipped with both a direction-finding transmitter 6 and a
positioning device 5
and a transmitter 6. As a result, it is possible to redundantly track the
vehicle using the
positioning system according to the invention.
The shown vehicle-information device 4 optionally uses a GPS receiver as
positioning
device 5. Using antenna 30 or a separate antenna, GPS receiver 5 receives GPS
signals
40 from GPS satellites 23, from which it obtains GPS positioning data that are
then
routed to data transmitter 6 to be transmitted to central unit 7. Although the
thus obtained
GPS data are known to be faulty, according to the invention no correction is
absolutely
required, because the error equally affects all vehicles 3 participating in
the positioning
system. If desired, a GPS receiver can be installed in central unit 7, whose
GPS data will
be compared with the fixed, known position of central unit 7 to generate a
correction
vector for the GPS information from the vehicles 3.
For redundant positioning of racecar 3, the illustrated vehicle-information
device 4
also contains a direction-finding transmitter 6, which transmits direction
signals to the
direction-finding receivers 23 set up near racetrack 2 via antenna 30 or a
separate
antenna. As described above, that is where positioning data are obtained from
the
direction signals to be used in central unit 7. If desired, data transmitter 6
assumes the
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function of direction-finding transmitter 6, or the two transmitters 6 are
produced as an
integral unit.
The shown racecar 3 comprises as additional equipment a tachometer 33, a gear-
train
sensor 34, a ground-motion sensor 35, a gyro sensor 38, an induction-loop
sensor 37, a
wheel-rotation sensor 38, and a position receiver 39. The gyro sensor 36
measures the
acceleration of vehicle 3 using a piezoelectric component installed in the
gyro sensor 36,
and supplies positioning data based on acceleration measurements. The
tachometer 33
and the wheel-rotation sensor 38 measure, using conventional methods, the
rotation speed
of the engine and the wheels and supply corresponding data, preferably in the
form of
pulse information or other digital data. The ground-motion sensor 35 uses
infrared,
ultrasound, or radar signals to determine the speed of vehicle 3 and to
transmit this
information in an appropriate data format. Gear-train sensor 34 determines the
speed of
the driving motor at the gears and transmits this information in data format.
When the
vehicle drives past induction loops embedded in the track in a conventional
way, this can
be read by the induction loop sensor 37 to obtain positioning information.
Small-aperture
position transmitters can also be placed along the track, which emit
positioning signals 49
over a specific area. The positioning signals 49 are received by the position
receiver 39
via antenna 30 or a separate antenna, which converts the positioning signals
49 into
positioning data and to data transmitter 6, which routes them on to central
unit 7.
According to the illustrated embodiment, the data from the respective sensors
or
devices 33 - 38 are routed as data signals 43 - 48 to data transmitter 6 to be
routed to
central unit 7. As indicated in Figure 3C, selected portions of the data
signals 43 - 48
are, if desired, not routed to data transmitter 6 until they have been
converted in vehicle
information device 4. For security reasons, transmitter 6 preferably transmits
the data
according to the invention in encrypted form.
The illustrated vehicle-information device 4 also comprises a data receiver
31, which
receives safety and/or data signals 42 via antenna 30 or a separate antenna,
preferably
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from central unit 7. The signals 42 are accordingly converted in data receiver
31 or in
vehicle-information device 4 to generate, as discussed above, warning or other
messages
via a display device, for example, in the form of a cockpit display light 32
on the
dashboard 32.
According to the invention, the various components of vehicle-information
device 4,
and sensors 33 - 38 are mounted to a suitable place on board vehicle 3, and
appropriately
connected or networked with each other via transmitter 6 to obtain the desired
functioning capability. A person of skill in the art is aware that the
described distribution
of functions can, if desired, be structured differently among the components
encompassed
by the positioning system according to the invention.
In addition to determining RPM, acceleration values, direction of revolution,
and
speed of movement, the data obtained by the physical sensors 33 - 38 can also
be
compared to verify whether the obtained values interact correctly for proper
locomotion
of vehicle 3. For example, if the drive train rotates at an unusually higher
rate than the
wheel RPM, this can be diagnosed immediately as a differential defect, or, if
the wheels
revolve unusually faster than the recorded locomotion speed over the ground,
this can be
immediately diagnosed as wheel slippage. Together with the results of
acceleration
sensor 36 and, optionally, GPS receiver 5, the above can be used to verify a
deviation
from the allowable motion parameters, not only with absolute values, but also
using
redundant supplemental information.
The data obtained by the GPS positioning device 5 and the physical sensors can
be
used to test the correct or faulty motion of vehicle 3 on racetrack 2 in the
direction of
travel with a high degree of certainty. The data obtained by the described
sensors and
devices or similar ones can be used in central unit 7 to ascertain possible
motor failure,
the position, speed, or similar characteristic data of a racecar participating
in the
positioning system.
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CA 02427718 2003-04-29
WO 01/33530 PCT/EP00/10518
-16-
A person of skill in the art can use a limitless number of devices to obtain,
process,
transmit and/or evaluate the positioning and operating data participating in
the present
invention. For example, the data of the different racecars 3 can be
distinguished by using
a frequency-division or time-division multiplex signal or a suitable
identifying device for
the transmitted data.
Therefore, the embodiments and applications of the invention explained in the
description serve merely as examples of what an individual of skill in the art
understands
or could understand in each context as being equivalent, and which, if
desired, could be
used instead of one of the listed examples. Such equivalents are therefore as
much a part
of the invention as the explicitly described, incomplete examples.
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