Note: Descriptions are shown in the official language in which they were submitted.
$~?~
BARLOW INERTIAL GUIDANCE SYSTEM
technical Field
This invention relates to the field of burgle
survey instruments and in particular relates to
Barlow survey instruments utilizing acceleration
and angular displacement sensors.
background of the Invention
In many prior art Barlow survey systems, a
probe is used that includes acceleration or inkwell
no meter measuring instruments in c~nbination with
azimuth or direction determining instruments such as
magnetometers Examples of such systems are provided
in US. patents 3,8~2,499 and 4~362,054 which disclose
Barlow surveying instruments using an inclinometer
that includes three accelerometers to measure de-
aviation of the Barlow from vertical along with a
three axis magnetometer for azimuth determination
Such systems are subject to errors due to a n~nber of
factors including variations in the err magnetic
--2--
field caused by the nature of the material through
which the Barlow passes. There haze also been a
number of systems that haze used jumbled or strap
down mechanical gyros in place of the magnetometers
for direction or rotation sensing. However, due Jo
sensitivity to stock and vibration, mechanical
gyroscopes do not provide the desired accuracy and
reliability for Barlow systems. Further mechanical
gyros are subject lo drift and procession errors and
require substantial settling periods for stabilization.
These instruments also tend to be mechanically complex
as well as expensive.
Gone approach for reducing the errors inherent
in making inertial type measurements of the probe
location in a Barlow has been the use of Coleman
filtering. However, up to the present time, the use
of Coleman filtering has been limited to alignment of
the probe when stopped in the Barlow and has not
been used in a dynamic sense for error reduction in
measurements made while the probe is moving within the
Barlow.
Myra of the Invention
It is therefore an object of the invention to
provide a Barlow survey apparatus that includes a
probe suitable for insertion in a Barlow; a motion-
is for generating a signal representing the movement
of the probe in the Barlow; and acceleration
measurement instruments within the probe for general-
in three acceleration signals representing components
of acceleration of the probe with respect Jo three
probe axe and an angular rotation measuring means for
generating two rotation signals representing the
--3--
angular rotation of the probe with respect to two
probe axes of rotation. Also included is a firs
circuit or generating a firs synthetic angular
notation signal representing the angular rotation of
the probe about a third probe axis when the probe is
moving and a circuit responsive to the angular
rotation signals for generating a second synthetic
angular rotation signal representing the annular
rotation of the probe about the third probe axis when
the probe is not moving. The invention further
includes a circuit responsive to the rotation signals
and synthetic rotation signal for transforming the
signals representing movement of the probe in the
Barlow into coordinates referenced to the earth and
computation circuits connected to the transform
circuit and the acceleration measuring circuits for
converting the acceleration signals into a first set
of velocl~y signals and a first set of position
signals representing the velocity and position of the
probe in the earth coordinate system.
The invention further includes a alumni filter
that uses the dynamic constraints of zero motion
normal to the Barlow Jo compensate for errors in
acceleration, angular rotation and alignment data used
to generate the velocity and position signals
grief Description of the Drawings
Fig. 1 is an illustration of an apparatus
embodying the invention, including a section through a
Barlow showing a probe used with thy Barlow
surveying apparatus,
Fig. lo is a perspective drawing of the probe
components; and
Fig 2 is logic diagram illustrating the
logic for computing the location of thy probe in the
Barlow.
ye ailed De r Sheehan of the In mention
In Fig. 1 is illustrated a represent
environment for the preferred embodiment of the
invention. Extending below the ground 10 it a
Barlow generally indicated at 12 thaw is lined with
a plurality of Barlow casings 14 and 16. Inserted
into the Barlow 12 is a probe 18 connected to a
cable reel 20 by means of a cable 22 that runs over an
above ground pulley 24. The cable 22 serves Jo lower
the probe 18 through the Barlow 12 and additionally
provides a transmission medium for transmitting data
from the probe 18 to a signal processor 26 above
ground. Another signal transmission line 28 can be
used to provide an indication of the amount of cable
22 that is paid out into the Barlow 12 as well as
data from cable 22 to the signal processor 26.
Although it the invention illustrated in Fig. 1 data
is transmitted to and from the probe 18 by means of
the cable 22, data can be transmitted opposed by
other means such as pressure impulses transmitting
digital data through drilling mud in a measure while
drilling environment for example. The data may also
be stored in a memory in the probe and retrieved at a
later time.
As shown in Fig. lay secured within the probe
18 it a triaxial accelerometer package including three
accelerometers 32, 34 and 36. The accelerometers 32,
34 and 36 are orientated with their sensitize axes
corresponding to the probe body a indicated by the
coordinate system shown at 38~ In the probe body
coordinate system, the x axis as indicated my xb
extends along the Barlow and the y axis a indicated
by ye and the z ax 5 as indicated by zb are
orthogonal with respect Jo the xb axis.
--5--
Also included in the probe 18 ire, a laser gyro
assembly 40 that includes two laser gyros 42 and 44.
The first laser gyro 42 is orientated Lithuania the probe
so as Jo measure the angular rotation of the probe
around the ye axis wherein the angular rotation so
measured is denoted by yo-yo Similarly the second laser
gyro 44 is secured within the probe 18 such that it
will measure probe rotation around the Zb axis a
denoted by I Because the diameter of the probe 18
it relatively small, where is not sufficient room to
provide a laser gyro that will effectively measure
notation around the xb axis.
Also included in the preferred embodiment of
the probe 18 is a microcomputer 46 along with a memory
is 48. Connected to the microprocessor from the
accelerometers 32, 34 and 36 are lines 50, 52 and 54
that serve to transmit acceleration signals ax, a
and a representing acceleration of the probe along
the xb, ye and zb axes respectively In a
similar manner, the microprocessor 46 is connected to
the laser gyro assembly 40 by means of lines 56 and 58
that serve to transmit the angular rotation signal
from the y axis gyro 42 and the angular rotation
signal oh from the z axis gyro 44.
In the embodiment of the invention illustrated
in Fig. lay a velocity signal VP is indicated as
being transmitted by means of a line 60 to the
microprocessor 46. As shown in Fig 1, this signal
would be generated by the rate of rotation of the
pulley 24 thereby giving a measure of the speed or
velocity of the probe in the Barlow 12 with the line
60 included in cable 220 There may be circumstances
however when the VP signal could more profitably be
generated in a different manner such as counting the
pipe section 14 and 16, down hole.
Al
I
In determining the location of the probe and
hence the location of the Barlow, which is of course
the ultimate object of the invention, it is necessary
to transform the various tensor signals which are
generated in the body coordinate system 38 into a
coordinate system that is referenced to the earth
Such a coordinate system is illustrated in Fig. 1 as
shown generally at 62 wherein the axis as indicated
by Al is parallel to the gravity vector go and the
remaining axes y and z are orthogonal to the Al axis
and parallel with the ground. This coordinate system
62 can be termed the level cordite system with the
Al and ye axes representing directions such as
North and East.
The logic by which the microprocessor 4B
converts the acceleration signals on lines 50, 52 and
54, the angular raze signals on lines 56 and 58 and
the velocity signal on line 60 to location signals is
illustrated in Fig. 2. It should be understood,
however, that some of this processing could be
accomplished in the computer 26 located top-side. As
indicated before, one of the primary problems in
generating signals representing the location of the
probe 18 with respect to the earth coordinate system
Al, ye and Al is to accurately convert signals
representing the orientation and movement of the
probe 18 from the body coordinate system xb, ye
and zb into the level or earth coordinate system.
One ox the primary ox jets of the logic shown in Fig.
1 it to perform the coordinate transformation as
accurately as possible utilizing Coleman filtering to
compensate for the errors inherent in the various
signal sources.
Definitions of the various symbols used in jig.
2 are provided in Table I below.
TABLE I
I - Probe body to level coordinate transformation
matrix
Cup = Pipe to probe body coordinate transform
a = Acceleration along 'x' axis of body
a = Acceleration along Ill axis of body
a = Acceleration along 'z' axis of body
a = Acceleration vectors in probe body coordinates
at a first time
0 a = Acceleration vectors in probe body coordinates
at a second time
by - Angular rotation about 'x' axis of probe body
= Angular rotation about 'y' axis of probe body
by = Angular rotation about Ill axis of probe body
V = Velocity of the probe along the pipe
Al = Velocity of to probe in level coordinates as
measured
Al = Velocity of the probe in level coordinates
derived inertial
Q = angular rotation of the earth
ON = Angular rotation of the earth - North component
ED = Angular rotation of the earth - Down component
p - Angular velocity of the level relative to the
earth
R = Position vector with following three components;
= North position coordinate
= East position coordinate
ROD = Down position coordinate
= Latitude
- Error in body to level transformation Cub
= Probe body misalignment in pipe
K = Subop~ional Ragman gain coefficients
glue e Gravity vector g (ROD) = WS~RE-RD)
I - Identity matrix
I = Radius of -the earth
TV = Velocity errors in level coordinates
Ha = Accelerometer errors
go = Gyro errors
I = Gyro bias errors
v = White measurement noise
Al = 'y' gyro white noise power spectral density in
(degree/root hour)
q2 = 'Z' gyro white noise power spectral density in
(degree/root hooks
q3 = Uncertainty of twisting (roll we) of probe
along the barfly while probe is in motion
I = Gyro random walk variance matrix in level
coordinates
.- 9 -
X = Error states
e
Ye = Error dynamics between discrete measurements
= Time mapping for error equations
F = Dynamic error model matrix
H = Velocity measurement matrix
P = Caverns of error states
R = Caverns of white measurement raise
We = Squealer oscillation rate (aboutl/34 min.)
Us
T = ~ody-path misalignment time constant
{I} - Denotes the skew centric matrix representation
of the enclosed vector
--10-
Logic for updating the coordinate transform
motion matrix CAL is indicated within the box 64 of
Fig. 2. Inputs to this logic include the angular
rotation signals yo-yo and by on lines 56 and 58. Slice
5 it is necessary to have a signal representing the
rotation of the probe around the x axis by to update
the transformation logic in box 64, it: is necessary to
generate a synthetic by signal. This is accomplished
when the probe lo is stopped in the Barlow 12 by
means of the logic enclosed within box 66. Two of
the inputs to the logic in box 66 are the angular
rotation signals ox and by on lines 56 and 58 and the
third input it a signal that represents the rotation
of the earth Q. The origin of the Q signal is
indicated in box 68 wherein as shown the signal Q is
composed of three vectors including ON and ED
which represents the rotation of the earth about North
and in a down direction respectively. Also as shown
within box 68 the value of is dependent upon the
latitude of the probe 180 To facilitate operation
of the logic of Fig. 2 in the probe microprocessor
46, the latitude of the Barlow can be stored in
the memory 48 and transmitted to box 68 by means of
line 69. The signal is then transmitted over line
70 to logic 66 which venerates a first synthetic ox
signal on line 72. When the probe it stopped in the
Barlow a logic signal indicating that VP it equal
to zero is transmitted by means of a dashed line 74
thereby being effective to connect the signal on line
72 to the logic 64 over line 73.
The accelerometer errors are calibrated while
the probe is stopped and the acceleration due to
gravity is reset to be equal and opposite to tensed
acceleration.
~11--
Alternatively when the probe is in motion
through the Barlow 12, a second synthetic signal
is generated on line 78 by jeans of the logic shown in
box 80. When the probe is in motion in the Barlow
5 12, the logic signal on line 74 will serve Jo close
the switch 76 thereby connecting line 80 with the line
73. As shown in Fig. 2, the acceleration signals on
line 50, 52 and 54 representing acceleration of the
body a are transmitted over a bus 82 to the logic 78
and a delay circuit 84. The first input into the
logic 78 over a bus I may be termed a which
represents the body acceleration of the probe 18 at a
first time The delay circuit 84 provides a second
body acceleration signal a over bus 86 to the logic
78. An acceptable lime delay for the delay circuit 84
is l/600th of a second. In this manner, synthetic
angular rotation signals about the probe x axis are
produced both for the case when the probe 18 is in
motion and when it is stopped.
Along with the Q signal on line 70, the change
in transformation logic in box 64 receives a signal
on line 90 which represents the angular velocity of
the probe relative to the earth as indicated by box
92. The output of logic 64 Cub on bus 94 represents
the time rate of change of the probe body to level
coordinate transform resulting from the acceleration
signals a and the angular rotation signals by
This signal is then integrated as indicated at 96
thereby producing on bus 98 a signal Cub that
represents the tran~fonmation matrix requited to
convert signals generated in the body coordinate
system 38 into the level coordinate system 62.
The signals on line US r presenting the coordinate
-12-
transform matrix C are transmitted through a summing
junction 100 to a bus 102.
'Foe accelerations a are converted from body
coordinates to level coordinates by means of logic 104
which has received the updated coordinate transform-
anion matrix over bus 102. The resulting output on
bus 106 represents the acceleration of the probe 18 in
level coordinates and is transmitted to a summing
junction 108. Subtracted in the summing junction 108
is a signal go on line 110 what represents acceder-
anion due to gravity resulting in z signal on a bus
112 representing the accelerationvL of the probe 18 in
level coordinates. As indicated by box 113, go it a
function of the depth Rod of the probe 18. This
signal is then integrated as indicated at 114 to
produce a signal on line 116 representing the velocity
Al on bus 116.
The resulting velocity signal AL is then fed
back by means of a line 118 to logic 120 that in turn
generates signals on bus 122 representing the eon-
tripodal acceleration resulting from the Charles
force generated by the earth's rotation. The no-
suiting signal on bus 122 is in urn subtracted from
the acceleration signals Al in summing junction 108.
As a result, it may be appreciated that the resulting
signal on bus 112 represents the acceleration of the
probe 18 in the Barlow taking into account gravity
and acceleration generated by the earth's rotation.
In addition to the velocity signals generated
by the inertial means as described above, velocity
signals are alto produced by actually measuring the
movement of the probe 18 in the Barlow. As
-13-
previously described, ye signal VP on line 60 can
represent the wire line greed o the probe in the
Barlow. This signal is transformed by meals of
logic shown in box 124 Pinto a velocity signal on a
bus 126 representing the velocity of the probe in body
coordinate Vb As indicated in box 24, the
transform matrix Cup includes an identity matrix I
plus a matrix that represents in matrix form the
misalignment of the probe 18 in the pipes 14 and 16.
The resulting velocity signal Vb on bus 126 is when
transformed by means of the coordinate transform
matrix Cub shown at 128 into velocity signals Van in
the level coordinate system on bus 130. These
velocity signals are then transmitted through a
summing junction 132 to a bus 134 and integrated as
shown at 136 to generate on bus 138 signals represent-
in the position cordons R of the probe with
respect to North, East and down as expressed in the
level coordinates 62.
As may be expected, the velocity signals on bus
134 resulting from actual wire line measurements and
the velocity signals on line 118 resulting from in-
ertial signal sources are subject to sundry sources of
errors. In order to provide a signal AL representing
the relative error between velocity signal on busses
118 and 134, the sigrlals on busses 118 and 134 are
applied to a summing junction 140 resulting in the
velocity error signal~VL in level coordinates on bus
141. To compensate for the various sources of errors
that axe present in the generation of the velocity
signals and hence position sunnily, Coleman filtering
is used to estimate the error correction signals.
One of the principal objects of using a reduced
order alumni idler ill to compensate for the missing
-1`4~
or degraded inertial data. This technique makes use
of the fact what over significant distance in the
Barlow, the probe 18 is constrained to follow the
Barlow axis which can be translated into equivalent
velocity information thereby enhancing the Barlow
survey accuracy. The use of dynamic constraints of
this nature provide a significant advantage over the
systems disclosed in the prior art. Computational
burden in the Coleman filtering operation is reduced by
modeling only the most significant error states. For
example, the attitude of the probe 18 is used to
resolve the external velocity VP into level
coordinates fur producing position coordinates.
The Coleman filter process is indicated by a
logic block 142 which receives as input the velocity
error signal~VL over bus 141. As indicated in the
logic block, the Coleman gain coefficients are
multiplied by the velocity error signal~VL and added
to the quantities indicated in the matrix 1440 The
revised values indicated in matrix 146 are then
applied to various portions of the logic shown in Fig.
2 in order Jo provide for error compensation. For
example, error compensation terms for the position
coordinates R are applied by means of a bus 148 to a
summing junction 150 Jo provide updated position
coordinates as shown at 152. Similarly, velocity
error terms are applied over bus 154 to a summing
junction 156 and the summing junction 132 in order to
provide error compensation for the velocity signals Al and
30 Al. Error terms for the body to level transform
matrix CAL are provided on bus 15S to the summing
junction 100 and error terms are applied over line 160
to correct for misalignmerlt in toe transformation
logic 124.
--1
In order to enhance the efficiency of the
process, the Coleman coefficients K may be stored in
memory 48 within the probe rather than computed
Donnelly, as indicated by box 162. By placing the
Coleman coefficients K in memory 48, the transformation
processes Jan be dynamically corrected within the
probe 118 Chile it is in the Barlow 12.
In a linear discrete Coleman filter, calculi
anions at the caverns level ultimately provide the
10 Coleman gait coefficients K, which are then used in the
calculation of expected values of the error swept
Ye- These error states include:
IRE] En
In the system model, the error states are a
15 function of I, that is the time mapping for error
equations. The term is equal to:
I + Fit En
where F matrix represents the error dynamics between
discrete measurements:
1 or
noise Eke)
Equation (3) is detailed as follows:
Pi = AL - do + Cub }I CbV En
WOW 0 0
TV = 0 -We 0 ~R-~2Q}~V-{A}~+CbEa En
O O -We
= I + Cue En
T En
-1
The measurement model can be expressed as.
by = Hue v En
where H represents the velocity measurement matrix:
by _ Cb{VL}~ ~V}~CbdV v En
The Coleman gain coefficients K can be represented by:
K = P(-)HT~HP( HUT Al Eke)
where the error caverns update is:
Pi lo Equal)
to gyro process noise caverns matrix is defined
a:
Al
AL = I q2 CAL Eke)
q3
The variance q3 and gyro bias I bayed on the
nonlinear reconstruction of the missing ox gyro are
given below as:
q3 = 3 . 6 Eke)
3 = -4.5
where q = Al = q20
During motion q3 becomes the variance associated
with the logic ox block 78.
"I
I
As may be seen from the above discussion the
constraints inherent in a Barlow survey system where
the probe 18 has substainally zero motion perpendi-
cuter to the pipe casing 14 and 16 of Fig. 1 are used
to facilitate error estimation and correction. For
example, an error signal is generated to correct probe
roll attitude by differencing the expected acceder-
anion signals on the body y and z axes with the sensed
accelerations a and a on lines 52 and 54.
Additionally as the error 5' gnats are processed
over time the estimate of body Jo path misalignment
improves.
The stored gravity Model 113 can be reset in
order to cancel the end acceleration ax, my and a
using the following relation:
glowered = We ore - ROD) En (14)
where We represents the Squealer oscillations.
The techniques described above can be used in a
number of different Barlow applications. For
example in a measure while drilling environment the
described survey method can be used for drill guidance
without the necessity of transmitting data to the
surface. In this case the attitude of the probe 18 it
determined using the logic illustrated at 66 to
provide leveling, azimuth and tool face information.
WIPE surveying on the other hand can make use of
the attitude data developed while the probe 18 is
moving as provided by the logic in block 78 along with
the attitude data generated when the probe is stopped
as provided by the logic in block 66.
