![[Help]](brevet2_fichiers/help.gif)
![[Bottom]](brevet2_fichiers/bottom.gif)
![[Add to Shopping Cart]](brevet2_fichiers/order.gif)
| United States Patent |
6,498,969 |
| Alacoque , et al. |
December 24, 2002 |
Method and a system for locating a vehicle on a track
Abstract
A method of locating a rail vehicle on a rail track includes the following
steps: measuring the speed of the vehicle at different times using means
providing an approximate value of the actual speed of the vehicle; measuring an
inertial magnitude at different times using a single inertial sensor disposed on
board the vehicle, the inertial magnitude being chosen to depend only on the
speed of the vehicle and a geometrical characteristic specific to the track;
calculating the abscissa of the vehicle on the track by means of a convergent
algorithm based on a non-linear observer, from the known values of the measured
approximate speed of the vehicle at different times preceding the time at which
the vehicle is to be located, the measurements of the inertial magnitude and a
database in which the geometrical characteristics specific to the track and its
spatial derivative are stored for different curvilinear abscissae, the database
being obtained by a learning process conducted beforehand.
| Inventors: |
Alacoque; Jean-Claude (Communay, FR);
Alamir; Mazen (St Martin d'Heres, FR) |
| Assignee: |
Alstom (Paris, FR) |
| Appl. No.: |
983675 |
| Filed: |
October 25, 2001 |
Foreign Application Priority Data
|
Dec 04, 2000[FR] |
00 15696 |
| Current U.S. Class: |
701/19; 246/122R |
| Intern'l Class: |
B61L 023/00 |
| Field of Search: |
701/19,20,214 246/122 R
|
References Cited [Referenced
By]
U.S. Patent Documents
| 3954064 |
May., 1976 |
Minovitch |
104/130. |
| 4148260 |
Apr., 1979 |
Minovitch |
104/138. |
| 4573131 |
Feb., 1986 |
Corbin |
33/1. |
| 5893043 |
Apr., 1999 |
Moehlenbrink et al. |
246/182. |
| 5986547 |
Nov., 1999 |
Korver et al. |
246/121. |
| 6278914 |
Aug., 2001 |
Gaudreau et al. |
105/199. |
| Foreign Patent Documents |
| 0 605 848 |
Jul., 1994 |
EP. |
|
| 0 795 454 |
Sep., 1997 |
EP. |
|
| 2 632 411 |
Dec., 1989 |
FR. |
|
Primary
Examiner: Cuchlinski, Jr.; William A.
Assistant Examiner:
Hernandez; Olga
Attorney, Agent or Firm: Sughrue Mion, PLLC
Claims
There is claimed:
1. A method of locating a rail vehicle on a
rail track which includes the following steps:
measuring the speed of
said vehicle at different times using means providing an approximate value of
the actual speed of said vehicle;
measuring an inertial magnitude at
different times using a single inertial sensor disposed on board said vehicle,
said inertial magnitude being chosen to depend only on said speed of said
vehicle and a geometrical characteristic specific to said track;
calculating an abscissa of said vehicle on said track by means of a
convergent algorithm based on a non-linear observer, from known values of the
measured approximate speed of said vehicle at different times preceding the time
at which said vehicle is to be located, said measurements of said inertial
magnitude and a database in which said geometrical characteristics specific to
said track and the spatial derivative of each said geometrical characteristic
are stored for different curvilinear abscissae, said database being obtained by
a learning process conducted beforehand.
2. The method claimed in claim
1 of locating a rail vehicle on a rail track, wherein Si represents a
curvilinear abscissa of said vehicle at time t.sub.i and:
said speed Vm
of said vehicle is measured at constant time intervals DT.sub.o, said
measurements of said speed Vm(t.sub.i) being effected at times t.sub.i,
i.epsilon.[1,N] of an observation time window T.sub.o preceding the measurement
time t.sub.N at which said vehicle is to be located and being stored in a
memory;
said measurements of said inertial magnitude y(t.sub.i) effected
on board said vehicle for said different times t.sub.i are stored in a memory;
and an estimated curvilinear abscissa SN of said vehicle at the time t.sub.N is
calculated by successive iteration, each new measurement time t.sub.N generating
a new calculation iteration for which said observation window T.sub.o is shifted
by an amount DT.sub.o so that the starting point i=0 of the new observation
window T.sub.o coincides with the abscissa of the measurement point i=1 of said
observation window T.sub.o of the preceding iteration, said estimated
curvilinear abscissa SN being calculated using the equation: ##EQU15##
in which Vi is the corrected speed of said vehicle at each time t.sub.i
of said observation window T.sub.o, e(S0) is the relative speed error and S0 is
the corrected curvilinear abscissa of the starting point of said observation
window T.sub.o, e(S0) and S0 being obtained in the preceding iteration by a
convergent algorithm based on a non-linear observer from measurements of said
speed Vm(t.sub.i), said single inertial magnitude y(t.sub.i) at each time
t.sub.i and said geometrical characteristic RO(Si) and its spatial derivative
DRO(Si) at the level of the curvilinear abscissa Si estimated using the equation
##EQU16##
3. The method claimed in claim 1 of locating a vehicle on a
track, wherein said database contains triplets obtained by measuring said
inertial magnitude y(t.sub.j) at different abscissae S.sub.j during a previous
journey of a vehicle along said track under operating conditions guaranteeing a
precise knowledge of the data of said triplets.
4. The method claimed in
claim 3 of locating a vehicle on a track, wherein for any estimated abscissa Si
of said track said values of said geometrical characteristic RO(Si) and said
spatial derivative DRO(Si) are calculated by interpolation between two triplets
stored in said database.
5. The method claimed in claim 1 of locating a
vehicle on a track, wherein said inertial sensor is a yaw rate gyro.
6.
The method claimed in claim 1 of locating a vehicle on a track, wherein said
inertial sensor is a roll rate gyro.
7. The method claimed in claim 2 of
locating a vehicle, wherein said relative measured speed error e(S1) and said
corrected abscissa S1 are calculated in each observation window T.sub.o from the
following sliding horizon state observer equations: ##EQU17##
in which
e,f,g . . . represent the successive derivatives of said relative speed error e,
k and .alpha. are parameters, and G is the gradient of the criterion J as a
function of the state of said system which is given by the solution A of the
following differential matrix equation: ##EQU18##
where ##EQU19##
8. The method claimed in claim 7 of locating a vehicle on a track,
wherein said derivative e(S0) of said relative measured speed error is
considered to be zero in said observation window T.sub.o and said relative speed
error e(S1) and said corrected abscissa S1 of said observation window T.sub.o
respectively corresponding to e(S0) and S0 of said observation window T.sub.o in
the next calculation iteration are calculated from the following equations:
##EQU20##
in which k and .alpha. are variable parameters,
G=.vertline.G.sub.1 G.sub.2.vertline. where ##EQU21##
and ##EQU22##
9. The method claimed in claim 1 of locating a vehicle on a track, used
to control one or more controlled systems of the rail vehicle.
10. A
system for locating a vehicle on a track employing the method claimed in claim
1, which system includes:
measuring means providing the approximate
speed of said vehicle;
a single inertial sensor;
a database in
which a geometrical characteristic specific to said track and its spatial
derivative for different curvilinear abscissae of said track are stored; and
a computer receiving the information from said measuring means and from
said sensor, said computer being connected to said database to calculate the
abscissa of said vehicle on said track.
11. The system claimed in claim
10 wherein Si represents a curvilinear abscissa of said vehicle at time t.sub.i
and:
said speed Vm of said vehicle is measured at constant time
intervals DT.sub.o, said measurements of said speed Vm(t.sub.i) being effected
at times t.sub.i, i.epsilon.[1,N] d of an observation time window T.sub.o
preceding the measurement time t.sub.N at which said vehicle is to be located
and being stored in a memory;
said measurements of said inertial
magnitude y(t.sub.i) effected on board said vehicle for said different times
t.sub.i are stored in a memory; and an estimated curvilinear abscissa SN of said
vehicle at the time t.sub.N is calculated by successive iteration, each new
measurement time t.sub.N generating a new calculation iteration for which said
observation window T.sub.o is shifted by an amount DT.sub.o so that the starting
point i=0 of the new observation window T.sub.o coincides with the abscissa of
the measurement point i=1 of said observation window T.sub.o of the preceding
iteration, said estimated curvilinear abscissa SN being calculated using the
equation: ##EQU23##
in which Vi is the corrected speed of said vehicle
at each time t.sub.i of said observation window T.sub.o, e(S0) is the relative
speed error and S0 is the corrected curvilinear abscissa of the starting point
of said observation window T.sub.o, e(S0) and S0 being obtained in the preceding
iteration by a convergent algorithm based on a non-linear observer from
measurements of said speed Vm(t.sub.i), said single inertial magnitude
y(t.sub.i) at each time t.sub.i and said geometrical characteristic RO(Si) and
its spatial derivative DRO(Si) at the level of the curvilinear abscissa Si
estimated using the equation ##EQU24##
12. The system claimed in claim
10, wherein said database contains triplets obtained by measuring said inertial
magnitude y(t.sub.j) at different abscissae s.sub.j during a previous journey of
a vehicle along said track under operating conditions guaranteeing a precise
knowledge of the data of said triplets.
13. The system claimed in claim
12, wherein for any estimated abscissa Si of said track said values of said
geometrical characteristic RO(Si) and said spatial derivative DRO(Si) are
calculated by interpolation between two triplets stored in said database.
14. The system claimed in claim 10, wherein said inertial sensor is a
yaw rate gyro.
15. The system claimed in claim 10, wherein said inertial
sensor is a roll rate gyro.
16. The method claimed in claim 11, wherein
said relative measured speed error e(S1) and said corrected abscissa S1 are
calculated in each observation window T.sub.o from the following sliding horizon
state observer equations: ##EQU25##
in which e,f,g . . . represent the
successive derivatives of said relative speed error e, k and .alpha. are
parameters, and G is the gradient of the criterion J as a function of the state
of said system which is given by the solution A of the following differential
matrix equation: ##EQU26##
where ##EQU27##
17. The system
claimed in claim 16, wherein said derivative e(S0) of said relative measured
speed error is considered to be zero in said observation window T.sub.o and said
relative speed error e(S1) and said corrected abscissa S1 of said observation
window T.sub.o respectively corresponding to e(S0) and S0of said observation
window T.sub.o in the next calculation iteration are calculated from the
following equations: ##EQU28##
in which k and .alpha. are variable
parameters, G=.vertline.G.sub.1 G.sub.2.vertline. where ##EQU29##
and
##EQU30##
18. The system claimed in claim 10, used to control one or
more controlled systems of the rail vehicle.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method of locating a vehicle on a
track, and especially a rail vehicle on a rail track, enabling great accuracy to
be obtained as to the position of the vehicle from an approximate measurement of
the speed of the vehicle and a single inertial magnitude measured on board the
vehicle.
The invention also relates to a location system implementing
the method and which can be used in particular to control controlled systems
intended to improve the comfort of passengers.
2. Description of the
Prior Art
The simplest technique routinely employed for locating a rail
vehicle on a rail track is to measure the distance traveled on the track from a
starting point by integrating the speed of the vehicle. However, the speed of
the vehicle is usually measured by measuring the rotation speed of the axles.
The diameter of the wheels decreases as they wear down and the wheels skid when
there is a high drive torque and low adhesion. Thus integrating the speed can
lead to high errors between the measured position and the actual position of the
vehicle after a few tens of kilometers.
Another prior art technique for
locating a vehicle consists of equipping the rail tracks with beacons for
precisely locating the rail vehicle on the track on which it is traveling.
However, this technique has the disadvantage of making it necessary to install
beacons along all the rail tracks of a rail network and its cost is therefore
prohibitive. The technique consisting of locating a vehicle by means of the GPS
system has the disadvantage of not enabling the vehicle to be located in shadow
areas such as tunnels.
French patent application FR-99 07 435 filed by
the applicant remedies the above disadvantages by locating a rail vehicle on a
rail track by correlating a track profile calculated from the output of a
plurality of inertial sensors disposed on board the vehicle with a map of the
rail track stored during a previous journey. However, this kind of location
technique requires the presence of a plurality of inertial sensors, which has
the disadvantage that the sensors increase the cost of the rail vehicle. What is
more, this kind of location method does not necessarily guarantee continuous
location because it is based on searching a database for a correlation between
measured values and a stored track profile.
The object of the invention
is to alleviate the above disadvantages by proposing a method that allows
accurate location of a vehicle on a track, by continuous convergence, without
requiring additional trackside equipment, and using only one inertial sensor, so
that it is simple and economical to implement.
SUMMARY OF THE INVENTION
The invention therefore provides a method of locating a rail vehicle on
a rail track which includes the following steps:
measuring the speed of
the vehicle at different times using means providing an approximate value of the
actual speed of the vehicle;
measuring an inertial magnitude at
different times using a single inertial sensor disposed on board the vehicle,
the inertial magnitude being chosen to depend only on the speed of the vehicle
and a geometrical characteristic specific to the track, such as the cant or the
radius of curvature;
calculating the abscissa of the vehicle on the
track by means of a convergent algorithm based on a non-linear observer, from
known values of the measured approximate speed of the vehicle at different times
preceding the time at which the vehicle is to be located, the measurements of
the inertial magnitude and a database in which the geometrical characteristics
specific to the track and its spatial derivative are stored for different
curvilinear abscissae, the database being obtained by a learning process
conducted beforehand.
According to another feature of the invention:
the speed Vm of the vehicle is measured at constant time intervals
DT.sub.o, the measurements of the speed Vm(t.sub.i) being effected at times
t.sub.i, i.epsilon.[1,N] of an observation time window T.sub.o preceding the
measurement time t.sub.N at which the vehicle is to be located and being stored
in a memory;
the measurements of the inertial magnitude y(t.sub.i)
effected on board the vehicle for the different times t.sub.i are stored in a
memory;
an estimated curvilinear abscissa SN of the vehicle at the time
t.sub.N is calculated by successive iteration, each new measurement time t.sub.N
generating a new calculation iteration for which the observation window T.sub.o
is shifted by an amount DT.sub.o so that the starting point i=0 of the new
observation window T.sub.o coincides with the abscissa of the measurement point
i=1 of the observation window T.sub.o of the preceding iteration, the estimated
curvilinear abscissa SN being calculated using the equation: ##EQU1##
in
which Vi is the corrected speed of the vehicle at each time t.sub.i of the
observation window T.sub.o, e(so) is the relative speed error and so is the
corrected curvilinear abscissa of the starting point of the observation window
T.sub.o, e(so) and so being obtained in the preceding iteration by a convergent
algorithm based on a non-linear observer from measurements of the speed
Vm(t.sub.i), the single inertial magnitude y(t.sub.i) at each time t.sub.i and
the geometrical characteristic RO(Si) and its spatial derivative DRO(Si) at the
level of the curvilinear abscissa Si estimated using the equation ##EQU2##
The method according to the invention can further include one or more of
the following features, individually or in any technically feasible combination
the database contains triplets (S.sub.j, RO.sub.j, DRO.sub.j) obtained
by measuring the inertial magnitude y(.sub.S j) at different abscissae s.sub.j
during a previous journey of a vehicle along the track under operating
conditions guaranteeing a precise knowledge of the data of the triplets;
for any estimated abscissa Si of the track the values of the geometrical
characteristic RO(Si) and the spatial derivative DRO(Si) are calculated by
interpolation between two triplets (S.sub.j, RO.sub.j, DRO.sub.j) stored in the
database;
the inertial sensor is a yaw rate gyro;
the inertial
sensor is a roll rate gyro;
the vehicle is a rail vehicle travelling
along a rail track;
the method of locating a vehicle on a track is used
to control controlled systems of a rail vehicle which have to be controlled in
phase with the geometry of the track, such as a tilt system or an active
transverse suspension system, recorded passenger announcements or a speed
profile imposed on the vehicle.
The invention also provides a system for
locating a vehicle on a track employing the above method and which includes:
measuring means providing the approximate speed of the vehicle;
a single inertial sensor;
a database in which a geometrical
characteristic specific to the track and its spatial derivative for different
curvilinear abscissae of the track are stored; and
a computer receiving
the information from the speed measuring means and from the sensor, the computer
being connected to the database to calculate the abscissa of the vehicle on the
track.
Other features and advantages will emerge from the following
description of one embodiment of a location method according to the invention,
which description is given by way of example only and with reference to the
accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1
is a diagram showing the principle of an observation time window used in one
particular embodiment of a location method according to the invention.
FIG. 2 is a block diagram showing the structure of a location system
according to the invention.
FIG. 3 is a flowchart showing the main steps
of a location method according to the invention.
DETAILED DESCRIPTION OF
THE PREFERRED EMBODIMENTS
FIG. 1 shows a rail vehicle traveling on a
rail track, the rail vehicle incorporating an inertial sensor 12 which is
advantageously a yaw rate gyro, and means 13 for measuring the approximate
actual speed of the vehicle, of the kind usually provided on board a rail
vehicle and using a method based on the rotation speed of the axles. In a
variant of the location method, the inertial sensor 12 is a roll rate gyro or a
transverse acceleration sensor.
FIG. 2 is a block diagram of a system
for locating a rail vehicle enabling a vehicle to be located accurately on a
rail track. As can be seen in FIG. 2, the location system includes a computer 14
which is connected to the yaw rate gyro 12 and to the means 13 for measuring the
approximate speed of the vehicle. The computer 14 is associated with a database
16 in which a geometrical characteristic RO.sub.j specific to the track and its
spatial derivative DRO.sub.j for different abscissa S.sub.j of the track are
stored in the form of triplets (s.sub.j, RO.sub.j, DRO.sub.j). The geometrical
characteristic stored in the database 16 depends on the inertial sensor 12 used
and must enable a theoretical value of the inertial measurement supplied by the
sensor 12 to be calculated, in conjunction with the speed of the vehicle.
Accordingly, if the inertial sensor 12 is a yaw rate gyro, the
characteristic RO contained in the database 16 is the curvature of the track.
The curvature .rho.(s) of a rail track varies only very slowly as a function of
the abscissa s within a curve and the measured value y(t) supplied by a yaw rate
gyro can therefore be written y(t).apprxeq..rho.(s).V(s) where .rho.(s) is the
curvature of the track at the abscissa s and V(s) is the speed of the vehicle.
If the inertial sensor 12 is a roll rate gyro, the characteristic RO
contained in the database 16 is the cant D(s) of the track. The cant is
generally small compared to the distance L between the rails, and the
measurement y(t) supplied by the roll rate gyro can be written: ##EQU3##
The triplets (RO.sub.j, DRO.sub.j, S.sub.j) in the database 16 are
obtained by a learning process entailing a rail vehicle travelling over the rail
tracks and measuring the inertial value by means of the inertial measurement
means 12 for different abscissae s.sub.j obtained by integrating the speed of
the vehicle. Of course, during this journey of the vehicle for instructing the
database 16, the speed-measuring means 13 are calibrated and the traveling
conditions are chosen so that there is no slip between the wheels and the rails,
so that the measured speed and therefore the abscissae of the track obtained are
accurate. The geometrical characteristic of the track and the cant are
calculated off-line, by inverse application of one of the previous equations,
and then by differentiating with respect to the abscissa.
As described
next with reference to FIG. 3, which is a flowchart showing the general
functioning of the location system, the computer 14 successively iterates a
series of calculation steps based on values measured by the yaw rate gyro 12 and
the speed measuring means 13 in an observation time window of width To shown in
FIG. 1.
As described next with reference to FIG. 3, which is a flowchart
showing the general functioning of the location system, the computer 14 iterates
a series of calculation steps in an observation time window of width T.sub.o in
which the values y(t.sub.i) produced by the yaw rate gyro 12 and the values
Vm(t.sub.i) produced by the speed measuring means 13 are stored at different
times t.sub.i, i.epsilon.[1,N], corresponding to a curvilinear abscissa Si of
the vehicle, the various times t.sub.i being separated by a fixed period
DT.sub.o. As in FIG. 1, in which the preceding iteration observation window
T.sub.o is shown in dashed line, the observation window T.sub.o is shifted by
the time interval DT.sub.o on each new iteration so that the new abscissa S0,
corresponding to the starting point of the new observation window, corresponds
to the abscissa S1 of the observation window used in the preceding iteration.
To simplify the calculations, it is assumed in the particular embodiment
of the location method described hereinafter that the speed varies slowly and
therefore that the derivative e(S0) of the relative error on the measured speed
is zero over the observation time T.sub.o. The series of calculation steps
performed by the computer 14 on each iteration, i.e. each time that the
observation window is shifted in time by DT.sub.o, is described hereinafter. The
last point t.sub.N corresponds to the last measurement point.
In a first
step 18 the computer 14 receives and stores in its memory the Nth value
Y(t.sub.N) from the yaw rate gyro 12 and the Nth value Vm(t.sub.N) from the
speed measuring means 13 and added in the memory to the measurements obtained at
the various times t.sub.i situated in the observation time window of width
T.sub.o preceding the current time t.sub.N at which the vehicle is to be
located.
During the first step 18, the computer 14 also receives the
observed curvilinear abscissa S0 and the relative speed error e(S0) calculated
by the computer 14 during the preceding iteration. The abscissa S0 corresponds
to the starting point of the new observation window. To start the calculation
process it is assumed for the first calculation iteration, for which there is no
preceding iteration, that the starting curvilinear abscissa S0 is known
approximately and that e(S0) is zero, for example.
From the above data,
the computer 14 calculates the corrected speed V(t.sub.i) for each time t.sub.i
in the observation window T.sub.o from the equation:
V(ti)=(1+e(S0)).multidot.V.sub.m (ti)
In the next step 20 the
computer 14 calculates an estimate Si of each curvilinear abscissa by time
integration of the corrected speed V(ti) in the observation window T.sub.o, in
other words: ##EQU4##
At the end of step 20, for i=N, the estimated
position of the vehicle at the current time t.sub.N is known from the equation:
##EQU5##
that abscissa corresponding to the corrected position of the
rail vehicle on the rail track obtained by the location method.
The
subsequent calculation steps calculate the corrected abscissa S1 of the point 1
of the observation window T.sub.o and the relative speed error e(S1) observed at
the same point 1, the values S1 and e(S1) serving respectively as reference data
S0 and e(S0) for calculating the corrected position of the vehicle on the next
calculation iteration.
In step 22, the computer 14 initially calculates
the values of the radius of curvature RO(Si) and its spatial derivative DRO(Si)
for each estimated curvilinear abscissa Si. The values RO(Si) and DRO(Si) are
calculated by linear interpolation between two adjacent triplets (RO.sub.j,
DRO.sub.j, s.sub.j) extracted from the database 16.
In the same step 22
the inertial measurement y(Si) at each estimated curvilinear abscissa Si is
estimated using the equation y(Si)=RO(Si).multidot.V(t.sub.i)
In the
next step 24 the computer 14 calculates the derivative of the observed abscissa
S(S1) and the derivative of the relative speed error e(S1) for the speed
measured at the point 1 in the observation window T.sub.o using the sliding
horizon state observer method, the theory of which is described in a paper by
Mazen ALAMIR published in 1999 in the journal "International Journal of
Control", volume 72, N.sup.o 13, pages 1204 to 1217.
The values S(S1)
and e(S1) are calculated from the following equations, obtained by applying the
mathematical method defined above to the location of the rail vehicle: ##EQU6##
where G=.vertline.G.sub.1 G.sub.2.vertline. where ##EQU7##
and
##EQU8##
The intermediate variables X1i and X2i are determined from the
following equations:
X.sub.1i
=2.multidot.(RO(si).multidot.V(ti)-y(ti)).multidot.V(ti).multidot.DRO(si),
X.sub.2i
=2.multidot.(RO(si).multidot.V(ti)-y(ti)).multidot.Vm(ti).multidot.RO(si)
In the above equations, k and .alpha. are parameters. For example
##EQU9##
to guarantee that the observer makes an estimate with a minimum
error and .alpha.=1 to guarantee stability in a straight line.
Calculating S(S1) and e(S1) then yields, by time integration, the
corrected value S1 and the value e(S1) respectively corresponding to the
corrected abscissa and the relative speed error for the speed at point 1 in the
observation window T.sub.o.
The values S1 and e(S1) obtained in step 24
are then fed back to the input of the first calculation step 18 so that they can
be used during the next calculation iteration, the values S1 and e(s1) obtained
in this way corresponding to the values of S0 and e(S0) used in the new
calculation iteration, for which the observation window T.sub.o is shifted so
that the starting point i=0 of the new observation window corresponds to the
point i=1 of the preceding observation window.
The above kind of
location method has the advantage of locating the rail vehicle accurately at
each measurement time t.sub.N.
The location method according to the
invention can advantageously be used to control controlled systems of a rail
vehicle which need to be controlled in phase with the geometry of the rail
track, such as a tilt system or an active transverse suspension system, or speed
profiles imposed on the vehicle.
The invention that has just been
described has the advantage of being economical to implement, requiring only one
inertial sensor on board the vehicle, the approximate speed of the vehicle and a
database containing a geometrical characteristic specific to the track.
Of course, the invention is in no way limited to the example previously
described, which assumes that the speed varies slowly and therefore that the
derivative of the relative error on the speed is zero over the time window
T.sub.o in order to simplify the calculations. To the contrary, the location
method can more generally use the sliding horizon state observer theory and take
account of faster variations in the speed by using the following equations:
##EQU10##
in which e,f,g . . . represent the successive derivatives of
the relative speed error e, with f=e,g=f, and so on.
In the above
equations, k and .alpha. are variable parameters and G is the gradient of the
criterion J as a function of the state of the system, which is given by the
solution A of the following differential matrix equation: ##EQU11##
where ##EQU12##
Accordingly, taking the case of a zero order
observer, i.e. taking e=0 in the observation window T.sub.o, the equations
employed in the particular embodiment previously described are obtained, namely:
##EQU13##
In the case of a second order observer, i.e. for g=0 in the
observation window T.sub.o the following equation is then obtained: ##EQU14##
* * * * *
![[Add to Shopping Cart]](brevet2_fichiers/order.gif)
![[Top]](brevet2_fichiers/top.gif)