Note: Descriptions are shown in the official language in which they were submitted.
AIR DATA AIDED INERTIAL MEASUREMENT UNIT
BACKGROUND
[0001] This disclosure relates generally to inertial measurement units,
and more
particularly to inertial measurement units that utilize air data parameters to
produce error-
compensated output values.
[0002] Many complex vehicle guidance systems, such as aircraft inertial
navigation
systems, utilize an inertial measurement unit (IMU) that senses and outputs
current acceleration
forces experienced by the IMU as well as changes in rotational position (e.g.,
roll, pitch, and
yaw). Such IMUs typically sense the current acceleration in three dimensions
via a triad of
accelerometers, each oriented along one of three mutually-orthogonal axes.
Similarly, changes
in rotational position are typically sensed via a triad of gyroscopes, each
oriented along one of
the three mutually-orthogonal axes.
[0003] Outputs of the IMU (e.g., a three-axis acceleration vector as
well as a three-axis
vector representing changes in rotational speed) are often integrated over
time by an inertial
navigation system to arrive at a position and orientation of the vehicle
relative to a known
starting position and orientation via, e.g., dead reckoning techniques.
However, such integration
techniques can compound sensor errors over time. Some sensor errors, such as
those due to
temperature, can be considered deterministic in nature, and therefore
compensated for in the
integration techniques via pre-defined correction factors. Other errors, such
as turn-on to turn-on
biases and scale factor errors can be unpredictable or stochastic in nature,
thereby preventing the
use of such pre-defined correction factors for effective error compensation
operations. The use
of a fiber optic gyroscope (FOG) or ring laser gyroscope (RLG) can provide
greater accuracy
and consistency of measurements than, e.g., micro-electro-mechanical system
sensors, but at
significant added cost. Accordingly, accuracy of measurement is typically
sacrificed for the
benefit of reduced cost when utilizing MEMS sensors for measuring acceleration
forces and
rotational position changes in IMUs.
SUMMARY
[0004] In one example, an inertial measurement unit includes an inertial
sensor assembly,
an inertial sensor compensation and correction module, and a Kalman estimator
module. The
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inertial sensor assembly includes a plurality of accelerometers and a
plurality of rate gyroscopes.
Each of the plurality of accelerometers is configured to sense acceleration of
the IMU along one
of a plurality of axes. Each of the plurality of rate gyroscopes is configured
to sense rotational
rate of the IMU along one of the plurality of axes. The inertial sensor
compensation and
correction module is configured to apply a set of error compensation values to
acceleration
sensed by the plurality of accelerometers and to rotational rate sensed by the
plurality of rate
gyroscopes to produce a compensated acceleration and a compensated rotational
rate of the IMU.
The Kalman estimator module is configured to determine a change in integrated
acceleration of
the IMU over a time interval based on the compensated acceleration and the
compensated
rotational rate of the IMU, determine a set of error correction values based
on a difference
between the change in the integrated acceleration of the IMU and a change in
true airspeed of the
IMU, and provide the set of error correction values to the inertial sensor
compensation and
correction module. The inertial sensor compensation and correction module is
further
configured to apply the set of error correction values to each of the
compensated acceleration and
the compensated rotational rate to produce an error-corrected acceleration and
an error-corrected
rotation rate, and output the error-corrected acceleration and the error-
corrected rotational rate.
[0005] In
another example, a method includes sensing acceleration of an inertial
measurement unit (IMU) along a plurality of axes via a plurality of
accelerometers of the IMU,
and sensing rotational rate of the IMU along the plurality of axes via a
plurality of rate
gyroscopes of the IMU. The method further includes applying a set of error
compensation
values to each of the sensed acceleration and the sensed rotational rate to
produce a compensated
acceleration and a compensated rotational rate of the IMU, determining a
change in integrated
acceleration of the IMU over a time interval based on the compensated
acceleration and the
compensated rotational rate of the IMU, and determining a set of error
correction values based
on a difference between the change in the integrated acceleration of the IMU
and a change in
true airspeed of the IMU. The method further includes applying the set of
error correction values
to each of the compensated acceleration and the compensated rotational rate to
produce an error-
corrected acceleration and an error-corrected rotational rate, and outputting
the error-corrected
acceleration and the error-corrected rotational rate.
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BRIEF DESCRIPTION OF THE DRAWINGS
[0006] FIG. 1 is a schematic block diagram illustrating an example
inertial measurement
unit (IMU) that utilizes air data inputs to produce error-corrected
acceleration and angular rate
outputs.
[0007] FIG. 2 is a schematic block diagram illustrating further details
of the inertial
sensor compensation and correction module of FIG. 1 to produce error-corrected
acceleration
and angular rate outputs.
[0008] FIG. 3 is a schematic block diagram illustrating further details
of the attitude
determination module of FIG. 1 to determine a vehicle attitude using the error-
corrected and
compensated acceleration and angular rate outputs from the inertial sensor
compensation and
correction module.
[0009] FIG. 4 is a schematic block diagram illustrating further details
of the Kalman
estimator module of FIG. 1 to produce bias and scale factor error correction
values that are
utilized by the IMU to produce error-corrected acceleration and angular rate
outputs.
[0010] FIG. 5 is a schematic block diagram illustrating details of the
Kalman estimator
module of FIG. 1 to produce an initial attitude quaternion representing an
initial attitude of the
IMU.
DETAILED DESCRIPTION
[0011] As described herein, an inertial measurement unit (IMU) utilizes
air data
parameter values, such as true airspeed and angle of attack, to produce error-
corrected angular
rate and acceleration output values. The IMU determines vehicle attitude
parameters based on
sensed acceleration and rotational position information received from
accelerometers and
gyroscopes of the IMU. Air data parameter values received and/or calculated by
the IMU are
utilized to estimate bias and/or scale factor errors of the accelerometer and
gyroscope outputs.
The IMU removes the estimated errors from the sensed angular rate and
acceleration parameters
to produce error-corrected output values, thereby increasing an accuracy of
the IMU outputs.
[0012] FIG. 1 is a schematic block diagram illustrating inertial
measurement unit (IMU)
that utilizes air data inputs to produce error-corrected body-axis
accelerations 12 and body-
axis angular rates 14. As illustrated in FIG. 1, IMU 10 includes inertial
sensor assembly 16,
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inertial sensor compensation and correction module 18, attitude determination
module 20, and
Kalman estimator module 22. Inertial sensor assembly 16 includes
accelerometers 24A, 24B,
and 24C, analog-to-digital converter 26, temperature sensors 28A, 28B, and
28C, analog-to-
digital converter 30, rate gyroscopes 32A, 32B, and 32C, and analog-to-digital
converter 34. As
further illustrated, IMU 10 receives true airspeed 36 and angle of attack 38
as inputs, and
produces body-axis angular rates 12 and body-axis accelerations 14 as outputs.
In other
examples, rather than receive true airspeed 36 and angle of attack 38 as
inputs, IMU 10 can
receive sensor measurements, such as static pressure measurements, total
pressure
measurements, total air temperature measurements, or other sensor measurements
that are usable
by IMU 10 to derive true airspeed 36 and angle of attack 38. Body-axis angular
rates 12 and
body-axis accelerations 14 output from IMU 10 can be utilized by, e.g., an
inertial navigation
system of an aircraft or other moving body to which IMU 10 is mounted.
[0013]
Accelerometers 24A, 24B, and 24C of inertial sensor assembly 16 form a 3-axis
triad of accelerometers, each mounted (e.g., on a circuit board) and aligned
to sense acceleration
forces along one of three mutually-orthogonal axes. Rate gyroscopes 32A, 32B,
and 32C are
similarly mounted (e.g., on the same circuit board) and aligned to sense a
rotational rate along
one of three mutually-orthogonal axes (e.g., roll rate, pitch rate, and yaw
rate). Temperature
sensors 28A, 28B, and 28C are mounted (e.g., on the same circuit board)
proximate
accelerometers 24A-24C and rate gyroscopes 32A-32C to sense a temperature of
an operational
environment within inertial sensor assembly 16. For instance, temperature
sensor 28A can be
mounted proximate accelerometer 24A and rate gyroscope 32A to sense a
temperature of an
operational environment within inertial sensor assembly 16 proximate
accelerometer 24A and
rate gyroscope 32A. Temperature sensor 28B can be mounted proximate
accelerometer 24B and
rate gyroscope 32B to sense a temperature of an operational environment within
inertial sensor
assembly 16 proximate accelerometer 24B and rate gyroscope 32B. Temperature
sensor 28C can
be mounted proximate accelerometer 24C and rate gyroscope 32C to sense a
temperature of an
operational environment within inertial sensor assembly 16 proximate
accelerometer 24C and
rate gyroscope 32C. Any one or more of accelerometers 24A-24B, temperature
sensors 28A-
28C, and rate gyroscopes 32A-32C can be implemented as micro-electro-
mechanical systems
(MEMS).
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[0014] As illustrated, inertial sensor assembly 16 further includes
analog-to-digital (A-to-
D) converters 26, 30, and 34. Each of A-to-D converters 26, 30, and 34
includes discrete and/or
integrated logic circuitry to convert an analog signal input, such as a
voltage, to a digital
numerical representation proportional to a magnitude of the analog signal
input. In operation, A-
to-D converter 26 converts a voltage output from each of accelerometers 24A-
24C to a digital
numerical representation proportional to a magnitude of the voltage output
from the respective
one of accelerometers 24A-24C. A-to-D converter 30 converts a voltage output
from each of
temperature sensors 28A-28C to a digital numerical representation proportional
to a magnitude
of the voltage output from the respective one of temperature sensors 28A-28C.
A-to-D
converter 34 converts a voltage output from each of rate gyroscopes 32A-32C to
a digital
numerical representation proportional to a magnitude of the voltage output
from the respective
one or rate gyroscopes 32A-32C.
[0015] Each of inertial sensor compensation and correction module 18,
attitude
determination module 20, and Kalman estimator module 22 can be implemented in
hardware,
software, or combinations of hardware and software. For example, IMU 10 can
include one or
more processors and computer-readable memory encoded with instructions that,
when executed
by the one or more processors, cause IMU 10 to operate in accordance with
techniques described
herein. Examples of the one or more processors include any one or more of a
microprocessor, a
controller, a digital signal processor (DSP), an application specific
integrated circuit (ASIC), a
field-programmable gate array (FPGA), or other equivalent discrete or
integrated logic circuitry.
Computer-readable memory of IMU 10 can be configured to store information
within IMU 10
during operation. The computer-readable memory can be described, in some
examples, as
computer-readable storage media. In some examples, a computer-readable storage
medium can
include a non-transitory medium. The term "non-transitory" can indicate that
the storage
medium is not embodied in a carrier wave or a propagated signal. In certain
examples, a non-
transitory storage medium can store data that can, over time, change (e.g., in
RAM or cache).
Computer-readable memory of IMU 10 can include volatile and non-volatile
memories.
Examples of volatile memories can include random access memories (RAM),
dynamic random
access memories (DRAM), static random access memories (SRAM), and other forms
of volatile
memories Examples of non-volatile memories can include magnetic hard discs,
optical discs,
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floppy discs, flash memories, or forms of electrically programmable memories
(EPROM) or
electrically erasable and programmable (EEPROM) memories.
[0016] As illustrated in FIG. 1, the outputs of A-to-D converter 26, A-
to-D converter 30,
and A-to-D converter 34 are provided as inputs to inertial sensor compensation
and correction
module 18, which also receives Kalman scale factor and bias error corrections
from Kalman
estimator module 22. Inertial sensor compensation and correction module 18
outputs body-axis
angular rates 12 and body-axis accelerations 14 (i.e., error-corrected output
values) via, e.g., a
data bus or other communicative connection for use by an inertial navigation
system or other
consuming system. Body-axis angular rates 12 and body-axis accelerations 14
are also provided
to attitude determination module 20 and Kalman estimator module 22 as inputs.
Attitude
determination module 20 further receives tilt error correction values 6q and
initial attitude
quaternion emit from Kalman estimator module 22 and provides attitude
information outputs to
Kalman estimator module 22 in the form of attitude quatemion qc. Kalman
estimator module 22
further receives true airspeed 36 and angle of attack 38 from, e.g., an
aircraft air data system, and
provides Kalman scale factor and bias error corrections to inertial sensor
compensation and
correction module 18 for use in modifying inputs received from accelerometers
24A-24C and
rate gyroscopes 32A-32C to produce error-corrected output:, body-axis angular
rates 12 and
body-axis accelerations 14, as is further described below.
[0017] In operation, accelerometers 24A-24C and rate gyroscopes 32A-32C
sense
acceleration forces and rotational rates along the three mutually-orthogonal
axes. Temperature
sensors 28A-28C sense a temperature of an operational environment of
accelerometers 24A-
24C and rate gyroscopes 32A-32C, for example on one or more circuit boards
within a housing
of IMU 10 that encloses components of 1MU 10. The outputs of each of
accelerometers 24A-
24C, temperature sensors 28A-28C, and rate gyroscopes 32A-32C are provided to
inertial
sensor compensation and correction module 18 via A-to-D converters 26, 30, and
34, illustrated
in FIG. 1 as VA, VT, and V. That is, VA represents a three-dimensional vector,
each element of
the vector corresponding to the output from one of accelerometers 24A, 24B,
and 24C.
Similarly, VT represents a three-dimensional vector, each element
corresponding to the output
from one of temperature sensors 28A, 28B, and 28C. Vu, also represents a three-
dimensional
vector, each element of the vector corresponding to the output from one of
rate gyroscopes 32A,
32B, and 32C.
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[0018] Inertial sensor compensation and correction module 18 applies
compensation and
correction factors to adjust each of the inputs VA, VT, and V. to produce body-
axis angular rates
12 and body-axis accelerations 14. Body-axis angular rates 12 and body-axis
accelerations 12
each represent three-axis outputs of error-compensated and error-corrected
output values
corresponding to the adjusted inputs VA, VT, and V. As is further described
below, inertial
sensor compensation and correction module 18 applies compensation and
correction factors to
inputs VA, VT, and V. to adjust inputs VA, VT, and V. to compensate for sensor
scale factor
errors corresponding to an error in the slope of the sensor output over a
temperature range, bias
errors corresponding to a non-zero offset in the sensor output over the
temperature range, non-
linearity errors corresponding to non-linearity of the sensor output over the
temperature range,
and non-orthogonality errors corresponding to offsets in the mutual-
orthogonality of the sensor
installations along the three axes within inertial sensor assembly 16. Such
temperature-
dependent scale factor errors, temperature-dependent bias errors, non-
linearity errors, and non-
orthogonality errors can be considered deterministic in nature. As such,
compensation and
correction factors applied by inertial sensor compensation and correction
module 18 to
compensate sensor inputs VA, VT, and Võ for the deterministic errors can be
pre-determined
during, e.g., a testing phase in a laboratory or manufacturing facility and
stored in computer-
readable memory of IMU 10 for use by inertial sensor compensation and
correction module 18
during operation.
[0019] Accordingly, inertial sensor compensation and correction module 18
applies
compensation and correction factors to adjust sensor inputs VA, VT and V. to
compensate for
deterministic errors, such as temperature dependent errors and sensor
installation position and
alignment errors. In addition, as illustrated in FIG. 1, inertial sensor
compensation and
correction module 18 receives Kalman scale factor and bias error correction
values from Kalman
estimator module 22 and also applies the Kalman scale factor and bias error
correction values to
sensor inputs VA, VT and V. to correct for non-deterministic sensor errors, as
is further described
below.
[0020] Inertial sensor compensation and correction module 18 outputs the
error-
compensated and error-corrected sensor inputs VA, VT and V. (i.e., compensated
and corrected
via application of the temperature-dependent scale factor error compensation
values, the Kalman
scale factor error correction values, the temperature-dependent bias error
compensation values,
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the Kalman bias error correction values, the non-linearity error compensation
values, and the
non-orthogonality error compensation values) as body-axis angular rates 12 and
body-axis
accelerations 14. As such, body-axis angular rates 12 and body-axis
accelerations 14 represent
error-compensated and error-corrected output values of rate gyroscopes 32A-32C
and
accelerometers 24A-24C, respectively, after compensation for deterministic
errors (e.g.,
temperature-dependent scale factor errors, temperature-dependent bias errors,
sensor non-
linearity errors, and non-orthogonality errors) and correction for non-
deterministic scale factor
and bias errors that may arise during operation of IMU 10 (e.g., turn-on to
turn-on bias and scale
factor errors, vibration-related bias and scale factor errors, or other non-
deterministic errors).
[0021] As illustrated in FIG. 1, Kalman estimator module 22 receives as
inputs body-axis
angular rates 12 and body-axis accelerations 14 from inertial sensor
compensation and correction
module 18, as well as true airspeed 36 and angle of attack 38 from, e.g., an
aircraft air data
system. In addition, Kalman estimator module 22 receives attitude information
corresponding to
aircraft roll and pitch in the form of attitude quaternion qc from attitude
determination module
20.
[0022] As is further described below, attitude determination module 20
utilizes body-axis
angular rates 12 and body-axis accelerations 14 to determine an attitude
quaternion qc
corresponding to a coordinate transform between local level and body-axis roll
and pitch of, e.g.,
an aircraft within which IMU 10 is installed. The determined attitude
quaternion qc is provided
to Kalman estimator module 22.
[0023] Kalman estimator module 22 utilizes attitude quaternion qc
determined by attitude
determination module 20 as well as body-axis angular rates 12 and body-axis
accelerations 14 to
determine a change in an integrated body-axis acceleration over a relative
short time duration
(e.g., 0.5 seconds, 1.0 second, or other time durations), as is further
described below. Kalman
estimator module 22 compares the determined change in the integrated body-axis
acceleration
over the time duration to a difference in the received true airspeed 36 over
the same time
duration to determine an airspeed difference value. Kalman estimator module 22
provides the
airspeed difference value as input to an extended Kalman filter implemented by
Kalman
estimator module 22 to determine estimated scale factor errors and bias errors
for each of
accelerometers 24A-24C and rate gyroscopes 32A-32C. The estimated scale factor
errors and
bias errors for each of accelerometers 24A-24C and rate gyroscopes 32A-32C are
provided to
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inertial sensor compensation and correction module 18 as Kalman scale factor
error correction
values and Kalman bias error correction values associated with each of
accelerometers 24A-24C
and rate gyroscopes 32A-32C.
[0024] Inertial sensor compensation module 18 applies the received
Kalman scale factor
error correction values and bias error correction values, the temperature-
dependent scale factor
and bias error compensation values, the non-linearity error compensation
values, and the non-
orthogonality error compensation values to each of the received inputs from
accelerometers
24A-24C and rate gyroscopes 32A-32C to produce error-corrected output values
body-axis
angular rates 12 and body-axis accelerations 14. Accordingly, IMU 10,
implementing
techniques of this disclosure, iteratively determines Kalman scale factor and
bias error correction
values that are applied to (e.g., subtracted from, added to, or otherwise
applied to) sensed values
from accelerometers 24A-24C and rate gyroscopes 32A-32C to correct for non-
deterministic
scale factor errors and bias errors that are unpredictable in nature. The
compensation for
deterministic errors (e.g., via the temperature-dependent scale factor and
bias error compensation
values, the non-linearity error compensation values, and the non-orthogonality
error
compensation values) as well as the non-deterministic errors (e.g., via the
Kalman scale factor
and bias error correction values) increases the accuracy of body-axis angular
rates 12 and body-
axis accelerations 14 representing outputs of IMU 10 to consuming systems. As
such, the
techniques described herein can enable more accurate and precise operation of
consuming
systems, such as inertial navigation or other consuming systems.
[0025] FIG. 2 is a schematic block diagram illustrating further details
of inertial sensor
compensation and correction module 18 of FIG. 1 to produce error-compensated
body-axis
angular rates 12 and body-axis accelerations 14. As illustrated in FIG. 2,
inertial sensor
compensation and correction module 18 includes temperature low-pass filter 40,
accelerometer
low-pass filter 42, rate gyroscope low-pass filter 44, temperature module 46,
temperature
averaging module 48, accelerometer thermal scale factor and bias module 50,
rate gyroscope
thermal scale factor and bias module 52, acceleration cluster module 54, body
accelerations
module 56, output body accelerations module 58, angular rate cluster module
60, body angular
rates module 62, and output body angular rates module 64. As further
illustrated, inertial sensor
compensation and correction module 18 receives VT, VA, and V. as inputs from
inertial sensor
assembly 16 (FIG. 1). In addition, inertial sensor compensation and correction
module 18
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receives Kalman accelerometer scale factor and bias error correction values
EK_A and Kalman
rate gyroscope scale factor and bias error correction values EKG from Kalman
estimator module
22. Inertial sensor compensation and correction module 18 outputs body-axis
accelerations 14
and body-axis angular rates 12 via, e.g., one or more communication data buses
for use by a
consuming system, such as an aircraft inertial navigation system, stability
augmentation system,
or other consuming system. In addition, inertial sensor compensation and
correction module 18
provides compensated and corrected body-axis accelerations Acomp-B as input to
Kalman
estimator module 22 as well as compensated and corrected body-axis angular
rates wcon,p_s as
input to both Kalman estimator module 22 and attitude determination module 20.
Kalman
estimator module 22 provides tilt error correction values 8q as input to
attitude determination
module 20.
[0026] Each of temperature low-pass filter 40, accelerometer low-pass
filter 42, and rate
gyroscope low-pass filter 44 are low-pass filters (e.g., Butterworth low-pass
filters or other types
of low-pass filters) implemented in hardware and/or software and configured to
pass signals with
frequencies lower than a cutoff frequency and attenuate signals with
frequencies higher than the
cutoff frequency. Each of temperature low-pass filter 40, accelerometer low-
pass filter 42, and
rate gyroscope low-pass filter 44 can be configured with a same or different
cutoff frequency.
[0027] The output of temperature low-pass filter 40 is provided to
temperature module
46, which in turn provides temperatures T(n) as outputs to each of
accelerometer thermal scale
factor and bias module 50 and rate gyroscope thermal scale factor and bias
module 52.
Accelerometer thermal scale factor and bias module 50 outputs temperature-
dependent
accelerometer scale factor and bias error compensation values Asp_g to
acceleration cluster
module 54. Rate gyroscope thermal scale factor and bias module 52 outputs
temperature-
dependent rate gyroscope scale factor and bias error compensation values Gsp_B
to angular rate
cluster module 60. The combined operations of temperature module 46,
temperature averaging
module 48, accelerometer thermal scale factor and bias module 50, and rate
gyroscope thermal
scale factor and bias module 52 form temperature compensation operations that
provide
temperature compensation scale factor and bias error compensation values for
application to
(e.g., subtraction from) input values sensed by accelerometers 24A-24C and
rate gyroscopes
32A-32C (FIG. 1).
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[0028] Acceleration cluster module 54 receives the temperature
compensation scale
factor and bias error compensation values ASF-B from accelerometer thermal
scale factor and bias
module 50 and applies the temperature-dependent accelerometer scale factor
error compensation
values and the temperature-dependent accelerometer bias error compensation
values, as well as
the accelerometer non-linearity error compensation values and the
accelerometer non-
orthogonality error compensation values (e.g., stored in computer-readable
memory of IMU 10)
to produce compensated accelerometer values Acomp-s in the sensor axis that
are provided to body
accelerations module 56. Body accelerations module 56 receives the compensated
sensor-axis
accelerations Acomp_s from acceleration cluster module 54 and Kalman
accelerometer scale factor
and bias error correction values EK_A from Kalman estimator module 22. Body
accelerations
module 56 converts the compensated sensor-axis accelerations Acomp_s to the
aircraft (or other
vehicle) body-axis and applies the Kalman accelerometer scale factor and bias
error correction
values EK_A to produce compensated and corrected accelerometer values Acomp_B
in the body-axis
that are provided as input to both output body accelerations module 58 and
Kalman estimator
module 22. Output body accelerations module 58 bandwidth-limits the received
compensated
and corrected body-axis accelerations Acomp-B to produce body-axis
accelerations 14. The
combined operations of acceleration cluster module 54, body accelerations
module 56 and output
body accelerations module 58 form accelerometer compensation operations that
apply both
deterministic error compensation values (e.g., temperature-dependent
accelerometer scale factor
error compensation values, temperature-dependent accelerometer bias error
compensation
values, accelerometer non-linearity error compensation values, and
accelerometer non-
orthogonality error compensation values) and non-deterministic correction
values (e.g., Kalman
accelerometer scale factor error correction values and Kalman accelerometer
bias error
correction values) to produce body-axis accelerations 14 (i.e., accelerations
along each of the
three axes of accelerometers 24A-24C) that are error-compensation and error-
corrected for both
the deterministic and non-deterministic errors.
[0029] As further illustrated in FIG. 2, angular rate cluster module 60
receives the
temperature compensation scale factor and bias error compensation values GSF-B
from rate
gyroscope thermal scale factor and bias module 52 and applies the temperature-
dependent rate
gyroscope scale factor error compensation values and the temperature-dependent
rate-gyroscope
bias error compensation values, as well as the rate gyroscope non-linearity
error compensation
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values and the rate gyroscope non-orthogonality error compensation values
(e.g., stored in
computer-readable memory of IMU 10) to produce compensated angular rate values
cocomp_s fl
the sensor axis that are provided to body angular rates module 62. Body
angular rates module 62
receives the compensated sensor-axis angular rate values cocomp_s from angular
rate cluster
module 60 and Kalman rate gyroscope scale factor and bias error correction
values EKG from
Kalman estimator module 22. Body angular rates module 62 converts the
compensated sensor-
axis angular rates wcomp-s to the aircraft (or other vehicle) body-axis and
applies the Kalman rate
gyroscope scale factor and bias error correction values EKG to produce
compensated and
corrected angular rate values wcomp_B in the body-axis that are provided as
input to output body
angular rates module 64, Kalman estimator module 22, and qttitude
determination module 20.
Output body angular rates module 64 bandwidth-limits the received compensated
and corrected
body-axis angular rates (Ocomp-B to produce body-axis angular rates 12. The
combined operations
of angular rate cluster module 60, body angular rates module 62 and output
body angular rates
module 64 form rate gyroscope compensation operations that apply deterministic
error
compensation values (e.g., temperature-dependent rate gyroscope scale factor
error
compensation values, temperature-dependent rate gyroscope bias error
compensation values, rate
gyroscope non-linearity error compensation values, and rate gyroscope non-
orthogonality error
compensation values) and non-deterministic error-correction values (e.g.,
Kalman rate gyroscope
scale factor error correction values and Kalman rate gyroscope bias error
correction values) to
produce body-axis angular rates 12 (i.e., angular rates in each of the three
axes of rate
gyroscopes 32A-32C) that are error-compensation and error-corrected to
compensate and correct
for both the deterministic and non-deterministic errors.
[0030] In
operation, temperature module 46 receives low-pass filtered inputs VT from
low-pass filter 40 which represents a three-dimensional vector, each element
corresponding to a
filtered digital representation of a voltage output of one of temperature
sensors 28A, 28B, and
28C. Temperature module 46 converts the voltage representation associated with
each of
temperature sensors 28A-28C to a separate temperature value using a polynomial
curve-fit
having coefficients selected during, e.g., a testing phase to fit an output of
the respective
temperature sensors 28A-28C to a reference temperature input. Temperature
module 46
provides temperatures T(n) (i.e., three temperature values, each corresponding
to one of
temperature sensors 28A-28C) to temperature averaging module 48. Temperature
averaging
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module produces an average temperature output for each of the received input
temperatures T(n),
such as by using a moving average (e.g., over 8 samples, 10 samples, or other
number of
samples) or other central tendency technique. Temperature averaging module 48
provides the
average temperature associated with each of temperature sensors 28A-28C to
each of
accelerometer thermal scale factor and bias module 50 and rate gyroscope
thermal scale factor
and bias module 52.
[0031] Accelerometer thermal scale factor and bias module 50 determines
a temperature-
dependent accelerometer scale factor error compensation value and a
temperature-dependent
accelerometer bias error compensation value corresponding to each of
accelerometers 24A-24C.
For example, accelerometer thermal scale factor and bias module 50 can apply
the average input
temperature value for the one of temperature sensors 28A-28C that is
associated with (e.g.
mounted proximate) accelerometer 24A as input to a polynomial curve fit of
temperature-
dependent accelerometer scale factor errors corresponding to accelerometer 24A
having
coefficients determined during, e.g., a testing phase (e.g., in a laboratory
or manufacturing
phase). Accelerometer thermal scale factor and bias module 50 can similarly
apply average
input temperature values for each of temperature sensors 28B and 28C that are
associated with
accelerometers 24B and 24C as input to separate polynomial curve fits of
temperature-dependent
accelerometer scale factor errors corresponding to each of accelerometer 24B
and 24C having
coefficients determined during the testing and/or manufacturing phase.
Accelerometer thermal
scale factor and bias module 50 applies the average temperature input value
for each of
temperature sensors 28A-28C as input to polynomial curve fits of temperature-
dependent bias
errors corresponding to each of accelerometers 24A-24C (each of the polynomial
curve fits
having coefficients determined during the testing and/or manufacturing phase)
to determine
temperature-dependent bias error compensation values corresponding to each of
accelerometers
24A-24C.
[0032] Rate gyroscope thermal scale factor and bias module 52 determines
a
temperature-dependent rate gyroscope scale factor error compensation value and
a temperature-
dependent rate gyroscope bias error compensation value corresponding to each
of rate
gyroscopes 32A-32C. For example, rate gyroscope thermal scale factor and bias
module 52 can
apply the average input temperature value for the one of temperature sensors
28A-28C that is
associated with (e.g. mounted proximate) rate gyroscope 32A as input to a
polynomial curve fit
13
CA 2995893 2018-02-21
of temperature-dependent rate gyroscope scale factor errors corresponding to
rate gyroscope 32A
having coefficients determined during, e.g., a testing phase (e.g., in a
laboratory or
manufacturing phase). Rate gyroscope thermal scale factor and bias module 52
can similarly
apply average input temperature values for each of temperature sensors 28B and
28C that are
associated with rate gyroscopes 32B and 32C as input to separate polynomial
curve fits of
temperature-dependent rate gyroscope scale factor errors corresponding to each
of rate
gyroscopes 32B and 32C having coefficients determined during the testing
and/or manufacturing
phase. Rate gyroscope thermal scale factor and bias module 52 applies the
average temperature
input value for each of temperature sensors 28A-28C as input to polynomial
curve fits of
temperature-dependent bias errors corresponding to each of rate gyroscopes 32A-
32C (each of
the polynomial curve fits having coefficients determined during the testing
and/or manufacturing
phase) to determine temperature-dependent bias error compensation values
corresponding to
each of rate gyroscopes 32A-32C.
[0033]
Acceleration cluster module 54 receives the temperature-dependent
accelerometer
scale factor error compensation values and the temperature-dependent
accelerometer bias error
compensation values from accelerometer thermal scale factor and bias module
50. In addition,
acceleration cluster module 54 receives low-pass filtered inputs VA from low-
pass filter 42 which
represents a three-dimensional vector, each element corresponding to a
filtered digital
representation of a voltage output of one of accelerometers 24A, 24B, and 24C.
Acceleration
cluster module 54 converts the voltage representation of each filtered input
VA to an acceleration
value (e.g., in meters/second/second). In addition, acceleration cluster
module 54 applies the
received temperature-dependent accelerometer scale factor error compensation
values
corresponding to each of accelerometers 24A-24C to the inputs VA, such as by
multiplying each
of inputs VA by the corresponding temperature-dependent accelerometer scale
factor error
compensation value. Acceleration cluster module 54 applies the received
temperature-dependent
accelerometer bias error compensation values corresponding to each of
accelerometers 24A-24C
to the inputs VA via aggregation techniques (e.g., summing, subtracting, or
other aggregation
techniques). In addition, acceleration cluster module 54 applies (e.g.,
multiplies) the non-
linearity error compensation values and the non-orthogonality error
compensation values
corresponding to each of accelerometers 24A-24C (e.g., determined during a
testing and/or
manufacturing phase and stored in computer-readable memory of IMU 10) to the
respective
14
CA 2995893 2018-02-21
inputs VA to produce compensated sensor-axis accelerations Acomp-S. Sensor-
axis accelerations
AcOITIp-S therefore represent acceleration values associated with each of
accelerometers 24A-24C
in the sensor axis that have been compensated for deterministic errors
corresponding to
temperature-dependent scale factor and bias errors, sensor non-linearity
errors, and non-
orthogonality errors associated with a misalignment (i.e., non-mutually-
orthogonal) of
installation of accelerometers 24A-24C.
[0034]
Body accelerations module 56 receives the compensated sensor-axis
accelerations
Acomp-s and converts the accelerations from the sensor coordinate frame to an
aircraft (or other
vehicle to which IMU 10 is mounted) coordinate frame using a rotational matrix
such as a
direction cosine matrix having direction angles configured to transform the
sensor coordinate
frame to the aircraft body axis frame. In addition, body accelerations module
56 receives
Kalman accelerometer scale factor and bias error correction values EK_A from
Kalman estimator
module 22. As is further described below, Kalman accelerometer scale factor
and bias error
correction values EK_A include scale factor error correction values and bias
error correction
values produced by an extended Kalman filter implemented by Kalman estimator
module 22,
each of the scale factor error correction values and bias error correction
values corresponding to
one of accelerometers 24A-24C.
Body accelerations module 56 applies the Kalman
accelerometer scale factor and bias error correction values EK_A to the
compensated acceleration
values Acomp_s to produce compensated and corrected acceleration values
Acomp_B in the body axis
corresponding to each of accelerometers 24A-24C. The body axis can be defined
by three
mutually-orthogonal axes, a first of the three axes directed through the nose
of the aircraft, a
second of the three axes directed through a bottom of the aircraft toward the
Earth when the
aircraft is on-ground, and a third of the three axes directed orthogonally to
the first axis and to
the second axis and generally through a wing of the aircraft. Compensated and
corrected
acceleration values Acomp-B therefore represent body axis (e.g., aircraft body
axis) accelerations
corresponding to each of accelerometers 24A-24C that are compensated for
deterministic errors
(e.g., temperature-dependent scale factor and bias errors, sensor non-
linearity errors, and non-
orthogonality errors) and corrected for non-deterministic errors via Kalman
scale factor and bias
error correction values EK-A.
[0035]
Body accelerations module 56 provides compensated and corrected acceleration
values Acomp_B to output body accelerations module 58 and Kalman estimator
module 22. Output
CA 2995893 2018-02-21
body accelerations module 58 bandwidth-limits the output of compensated and
corrected
acceleration values Acomp-B via, e.g., an infinite impulse response (IIR) or
other bandwidth-
limiting filter to a defined bandwidth of a consuming system, such as an
aircraft inertial
navigation system. The bandwidth-limited acceleration values are provided by
output body
accelerations module 58 as body-axis accelerations 14.
[0036] As further illustrated in FIG. 2, temperature-dependent rate
gyroscope scale factor
and error compensation values and temperature-dependent rate gyroscope bias
error
compensation values determined by rate gyroscope thermal scale factor and bias
module 52 are
provided to angular rate cluster module 60 as input. In addition, angular rate
cluster module 60
receives low-pass filtered inputs V. from low-pass filter 44 which represents
a three-dimensional
vector, each element corresponding to a filtered digital representation of a
voltage output of one
of rate gyroscopes 32A, 32B, and 32C. Angular rate cluster module 60 converts
the voltage
representation of each filtered input V. to an angular rate value (e.g., in
meters/second). In
addition, angular rate cluster module 60 applies the received temperature-
dependent rate
gyroscope scale factor error compensation values corresponding to each of rate
gyroscopes 32A-
32C to the inputs V., such as by multiplying each of inputs V. by the
corresponding
temperature-dependent rate gyroscope scale factor error compensation value.
Angular rate
cluster module 60 applies the received temperature-dependent rate gyroscope
bias error
compensation values corresponding to each of rate gyroscopes 32A-32C to the
inputs V. via
aggregation techniques (e.g., summing, subtracting, or other aggregation
techniques). In
addition, angular rate cluster module 50 applies (e.g., multiplies) the non-
linearity error
compensation values and the non-orthogonality error compensation values
corresponding to each
of rate gyroscopes 32A-32C (e.g., determined during a testing and/or
manufacturing phase and
stored in computer-readable memory of IMU 10) to the respective inputs V. to
produce
compensated sensor-axis angular rates wcomp-s= Sensor-axis angular rates
wcomp_s therefore
represent angular rate values associated with each of rate gyroscopes 32A-32C
in the sensor axis
that have been compensated for deterministic errors corresponding to
temperature-dependent
scale factor and bias errors, sensor non-linearity errors, and non-
orthogonality errors associated
with a misalignment (i.e., non-mutually-orthogonal) of installation of rate
gyroscopes 32A-32C.
[0037] Body angular rates module 62 receives the compensated sensor-axis
angular rate
values wcomp_s and converts the accelerations from the sensor coordinate frame
to an aircraft (or
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CA 2995893 2018-02-21
other vehicle to which IMU 10 is mounted) coordinate frame using a rotational
matrix such as a
direction cosine matrix having direction angles configured to transform the
sensor coordinate
frame to the aircraft body axis frame. In addition, body angular rates module
60 receives
Kalman rate gyroscope scale factor and bias error correction values EKG from
Kalman estimator
module 22. As is further described below, Kalman rate gyroscope scale factor
and bias error
correction values EKG include scale factor error correction values and bias
error correction
values produced by the extended Kalman filter implemented by Kalman estimator
module 22,
each of the scale factor error correction values and bias error correction
values corresponding to
one of rate gyroscopes 32A-32C. Body angular rates module 62 applies the
Kalman rate
gyroscope scale factor and bias error correction values EKG to the compensated
angular rate
values wcomp_s to produce compensated and corrected angular rate values
cocõ,,p_B in the body axis
corresponding to each of rate gyroscopes 32A-32C. As described above, the body
axis can be
defined by three mutually-orthogonal axes, a first of the three axes directed
through the nose of
the aircraft, a second of the three axes directed through a bottom of the
aircraft toward the Earth
when the aircraft is on-ground, and a third of the three axes directed
orthogonally to the first axis
and to the second axis and generally through a wing of the aircraft.
Compensated and corrected
angular rate values cocomp-B therefore represent body axis (e.g., aircraft
body axis) angular rates
corresponding to each of rate gyroscopes 32A-32C that are compensated for
deterministic errors
(e.g., temperature-dependent scale factor and bias errors, sensor non-
linearity errors, and non-
orthogonality errors) as well as corrected for non-deterministic errors via
Kalman scale factor
and bias error correction values EKG.
[0038] Body angular rates module 62 provides compensated and corrected
angular rate
values cocomp-E3 to each of output body angular rates module 64, attitude
determination module 20,
and Kalman estimator module 22. Output body angular rates module 64 bandwidth-
limits the
output of compensated and corrected angular rate values cocomp_s via, e.g., an
infinite impulse
response (IIR) or other bandwidth-limiting filter to a defined bandwidth of a
consuming system,
such as an aircraft inertial navigation system. The bandwidth-limited angular
rate values are
provided by output body angular rates module 64 as body-axis angular rates 12.
[0039] Accordingly, IMU 10 implementing techniques described herein
outputs body-
axis angular rates 12 and body-axis accelerations 14 that are compensated to
correct for
deterministic errors and corrected for non-deterministic errors. The
techniques of this disclosure
=
17
CA 2995893 2018-02-21
therefore increase an accuracy of outputs of IMU 10 and enable IMU 10 to
adaptively modify
such outputs (i.e., body-axis angular rates 12 and body-axis accelerations 14)
to account for
unpredictable errors that can arise during operation of IMU 10 manifesting as
sensor bias and
scale factor errors.
[0040] FIG. 3 is a schematic block diagram illustrating further details
of attitude
determination module 20 of FIG. 1. As illustrated in FIG. 3, attitude
determination module 20
includes body rate delta angles module 66 and propagate attitude quaternion
module 68.
Attitude determination module 20 receives compensated and corrected angular
rate values Wcomp_
B as inputs from inertial sensor compensation and correction module 18.
Attitude determination
module 20 outputs attitude quaternion qc to Kalman estimator module 22.
[0041] As illustrated in FIG. 3, body rate delta angles module 66
receives compensated
and corrected angular rate values rn
¨comp-B (i.e., compensated and corrected angular rates
corresponding to the outputs from each of rate gyroscopes 32A-32C of FIG. 1)
from inertial
sensor compensation and correction module 18 (FIGS. 1 and 2) and provides
angular
displacement changes wo, corresponding to each of rate gyroscopes 32A-32C as
input to
propagate attitude quaternion module 68. Propagate attitude quaternion module
68 receives
angular displacement changes wo, as input from body rate delta angles module
66 as well as
initial attitude quaternion emit and tilt error correction values 6q from
Kalman estimator module
22. Propagate attitude quaternion module 68 provides attitude quaternion qc as
input to Kalman
estimator module 22.
[0042] In operation, body rate delta angles module 66 receives
compensated and
corrected angular rate values cocomp_B corresponding to the compensated and
corrected outputs of
each of rate gyroscopes 32A-32C. Body rate delta angles module 66 integrates
each of the
compensated and corrected angular rate values cbcomp-E3 over a relatively
short time interval, such
as 0.001 seconds (i.e., corresponding to a 1 kHz sampling rate) to produce
angular displacement
changes v corresponding to a change in angular displacement sensed by each of
rate gyroscopes
32A-32C over the time interval.
[0043] Propagate attitude quaternion module 68 receives angular
displacement changes
k, from body rate delta angles module 66 and propagates the angular
displacement changes over
the time interval (e.g., 0.001 seconds) in quaternion form to produce attitude
quaternion qc.
Propagate attitude quaternion module 68 receives initial attitude quaternion
qc,na from Kalman
18
CA 2995893 2018-02-21
estimator module 22 representing an initial attitude of IMU 10, as is further
described below.
Propagate attitude quaternion module 68 propagates the received angular
displacement changes
y. over the time interval relative to the initial attitude quaternion qc,n,t
received from Kalman
estimator module 22 (e.g., during a first execution of the attitude
propagation operations).
Propagate attitude quaternion module 68 applies tilt error correction values
6q to the propagated
attitude quaternion (e.g., via quaternion multiplication) to produce the error-
corrected attitude
quaternion qc.
[0044] As such, IMU 10 implementing techniques of this disclosure
determines vehicle
attitude information represented by attitude quaternion qc that is utilized by
Kalman estimator
module 22 to estimate sensor scale factor and bias errors that are provided as
feedback to adjust
and correct the sensed output values of accelerometers 24A-24C and gyroscopes
32A-32C.
[0045] FIG. 4 is a schematic block diagram illustrating further details
of Kalman
estimator module 22 to produce Kalman accelerometer scale factor and bias
error correction
values EK-A, Kalman rate gyroscope scale factor and bias error correction
values EKG, and tilt
error correction values 6q. As illustrated in FIG. 4, Kalman estimator module
22 includes check
angle of attack (AOA) module 70, check true airspeed (TAS) module 72,
reference velocity
module 74, low-pass filter 76, low-pass filter 78, quaternion to direction-
cosine module 80, low-
pass filter 82, accelerometer root mean square (RMS) module 84, rate gyroscope
RMS module
86, integrate reference velocity module 88, integrate Coriolis acceleration
module 90, integrate
direction-cosine module 92, integrate body accelerations module 94, velocity
boost factor
module 96, accelerometer boost factor module 98, rate gyroscope boost factor
module 100,
measurement matrix module 102, measurement vector module 104, state transition
matrix
module 106, process covariance noise matrix module 108, measurement covariance
noise matrix
module 110, Kalman filter module 112, tilt correction module 114,
accelerometer bias and scale
factor module 116, and rate gyroscope bias and scale factor module 118. As
further illustrated,
Kalman estimator module 22 receives true airspeed 36 and angle of attack 38 as
input from, e.g.,
an aircraft air data system, attitude quaternion qc as input from attitude
determination module 20,
and compensated and corrected body-axis accelerations Acomp_B and compensated
and corrected
body-axis angular rates cocomp_B as input from inertial sensor compensation
and correction module
18. Kalman estimator module 22 outputs tilt error correction values 6q, which
are received as
input by attitude determination module 20. In addition, Kalman estimator
module 22 outputs
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CA 2995893 2018-02-21
accelerometer scale factor and bias error correction values EK_A, as well as
rate gyroscope scale
factor and bias error correction values EKG. Accelerometer scale factor and
bias error correction
values EK-A and rate gyroscope scale factor and bias error correction values
EKG are received as
input by inertial sensor compensation and correction module 18.
[0046] Check AOA module 70 receives angle of attack 38 as input, and
outputs angle of
attack a to reference velocity module 74. Check TAS module 72 receives true
airspeed 36 as
input and provides airspeed Va as output to reference velocity module 74 and
low-pass filter 78,
which passes the filtered reference velocity as input to velocity boost factor
module 96.
Compensated and corrected body-axis accelerations Acomp-n are received as
input by both
accelerometer RMS module 84 and integrate body accelerations module 94.
Compensated and
corrected body-axis angular rates wcomp-n are received as input by both low-
pass filter 82 and
integrate Coriolis accelerations module 90. Attitude quaternion qc is received
as input by
quaternion to direction-cosine module 80.
[0047] Reference velocity module 74 outputs body-axis reference velocity
vector \Tref,
which is received as input by each of integrate reference velocity module 88,
low-pass filter 76,
and integrate Coriolis acceleration module 90. Low-pass filter 76 provides a
filtered output of
body-axis reference velocity vector Vref to measurement vector module 104.
Integrate reference
velocity module 88 outputs integrated body-axis reference velocity vector Vref
to measurement
matrix module 102. Integrate Coriolis accelerations module 90 outputs
integrated Coriolis
acceleration EAc to measurement vector module 104. Quaternion to direction-
cosine module
outputs direction-cosine matrix C to integrate direction-cosine module 92,
which provides
integrated direction-cosine matrix EC as output to each of measurement matrix
module 102,
measurement vector module 104, and state transition matrix module 106.
Integrate body
accelerations module 94 outputs integrated compensated and corrected body-axis
accelerations
EAcomp-u to measurement vector module 104. Accelerometer RMS module 84
receives
compensated and corrected body-axis accelerations Acomp-B from inertial sensor
compensation
and correction module 18, and outputs accelerations root mean square ARMS to
accelerometer
boost factor module 98. Rate gyroscope RMS module 86 receives filtered
compensated and
corrected body-axis angular rates Wcomp-B from low-pass filter 82 and outputs
angular rates root
mean square WRMS to rate gyroscope boost factor module 100. Velocity boost
factor module
outputs velocity boost factor Kv to measurement covariance noise matrix module
110.
CA 2995893 2018-02-21
Accelerometer boost factor module 98 outputs acceleration boost factor KA,
which is received as
input by each of process covariance noise matrix module 108 and measurement
covariance noise
matrix module 110. Rate gyroscope boost factor module 100 outputs angular rate
boost factor
1(0, to each of process covariance noise matrix module 108 and measurement
covariance noise
matrix module 110.
[0048] Measurement matrix module 102 outputs measurement matrix H to
Kalman filter
module 112. Measurement vector module 104 provides measurement vector y as
input to
Kalman filter module 112. State transition matrix module 106 outputs state
transition matrix (I),
which is received as input by Kalman filter module 112. Process covariance
noise matrix
module 108 outputs process covariance noise matrix Q, and measurement
covariance noise
matrix module 110 outputs measurement covariance noise matrix R. Each of
process covariance
noise matrix Q and measurement covariance noise matrix R is received as input
by Kalman filter
module 112.
[0049] Kalman filter module 112 outputs Kalman state vector X, which is
received as
input by each of tilt correction module 114, accelerometer bias and scale
factor module 116, and
rate gyroscope bias and scale factor module 118. Tilt correction module 114
outputs tilt error
correction values 8q to attitude determination module 20. Accelerometer bias
and scale factor
module 116 provides Kalman accelerometer scale factor and bias error
correction values EK_A as
input to inertial sensor compensation and correction module 118. Rate
gyroscope bias and scale
factor module 118 outputs Kalman rate gyroscope scale factor and bias error
correction values
EKG, which is received as input by inertial sensor compensation and correction
module 18.
[0050] In operation, check AOA module 70 receives angle of attack 38
from, e.g., an
aircraft air data system or other source. Check AOA module 70 determines
whether the received
angle of attack 38 is valid, such as by determining whether angle of attack 38
is within a
predefined range of valid angles of attack and/or by accessing validity
information included with
angle of attack 38 (e.g., status field(s), bit(s), or other information
indicating a validity status of
angle of attack 38). Check AOA module 70 outputs angle of attack a as equal to
the value (e.g.,
scalar value) of angle of attack 38 in response to determining that angle of
attack 38 is valid.
Check AOA module 70 outputs a as equal to a value of zero in response to
determining that
angle of attack 38 is invalid. Similarly, check TAS module 72 receives true
airspeed 36 and
determines a validity status of true airspeed 36 by determining whether true
airspeed 36 is within
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CA 2995893 2018-02-21
a predefined range of valid true airspeeds and/or by accessing validity
information included with
true airspeed 36. Check TAS module 72 outputs airspeed Va as equal to the
value (e.g., scalar
value) of true airspeed 36 in response to determining that true airspeed 36 is
valid. Check TAS
module 72 outputs airspeed Va as equal to a value of zero in response to
determining that true
airspeed 36 is invalid.
[0051] Each of low-pass filters 76, 78, and 82 can be Butterworth
filters, infinite impulse
response filters, or other types of low-pass filters implemented in hardware
and/or software and
configured to pass signals with frequencies lower than a cutoff frequency and
attenuate signals
with frequencies higher than the cutoff frequency. Each of low-pass filters
76, 78, and 82 can be
configured with a same or different cutoff frequency, and can be implemented
using the same or
different types of low-pass filters. Low-pass filter 78 receives airspeed Va
and provides a
filtered output of airspeed Va to velocity boost factor module 96.
[0052] Reference velocity module 74 utilizes angle of attack a and
airspeed Va to
produce body-axis reference velocity vector Vref. That is, reference velocity
module 74 uses
angle of attack a to convert the received scalar airspeed Va into a vector
representation of the
body frame velocity by attributing the airspeed Va to the forward and vertical
body-axis velocity
components using angle of attack a. Low-pass filter 76 receives body-axis
reference velocity
vector Vref and provides a low-pass filtered output of body-axis reference
velocity vector Vref as
input to measurement vector module 104. Quaternion to direction-cosine module
80 applies a
transformation matrix to attitude quatemion qc representing attitude
information of IMU 10 (e.g.,
pitch, roll, and yaw) to produce direction cosine matrix C representing the
attitude information in
direction-cosine form.
[0053] Each of integrate reference velocity module 88, integrate
Coriolis acceleration
module 90, integrate direction-cosine module 92, and integrate body
accelerations module 94
integrate their respective inputs over a same time duration, such as 0.5
seconds, 1.0 seconds, or
other time durations. That is, integrate reference velocity module 88
integrates body-axis
reference velocity vector Vref over the time duration using, e.g., trapezoidal
integration or other
numerical integration operations to produce integrated body-axis reference
velocity vector EVref
that is provided to measurement matrix module 102. Integrate Coriolis
acceleration module 90
determines an instantaneous Coriolis acceleration force experienced by
accelerometers 24A-24C
(FIG. 1) as a cross product of compensated and corrected body-axis angular
rates wcomp_s and
22
CA 2995893 2018-02-21
body-axis reference velocity vector Võf. Integrate Coriolis acceleration
module 90 integrates the
instantaneous Coriolis acceleration over the time duration (i.e., the same
time duration utilized
by integrate reference velocity module 88) to produce integrated Coriolis
acceleration EAc.
Integrate direction-cosine module 92 integrates direction-cosine matrix C over
the same time
duration to produce integrated direction-cosine matrix C. Integrate body
accelerations module
94 integrates compensated and corrected body-axis accelerations Acomp-B over
the same time
duration to produce integrated compensated and corrected body-axis
accelerations E Acomp-B.
[0054] Accelerometer RMS module 84 receives compensated and corrected
body-axis
accelerations Acomp_B and produces accelerations root mean square ARMS by
computing a root
mean square of the received acceleration compensated and corrected body-axis
accelerations
Acomp-B or using other central tendency techniques. Rate gyroscopes RMS module
86 receives
low-pass filtered compensated and corrected body-axis angular rates wcomp_B
from low pass filter
82 and produces angular rates root mean square 0.)Rms by computing a root mean
square of the
received filtered compensated and corrected body-axis angular rates cocomp-B
or using other
central tendency techniques.
[0055] Velocity boost factor module 96 receives low-pass filtered
airspeed Va from low-
pass filter 78 and produces velocity boost factor Kv that is proportional to a
rate of change of
low-pass filtered airspeed Va with respect to time. That is, as the time rate
of change of low-pass
filtered airspeed Va increases, velocity boost factor Kv increases. As the
time rate of change of
low-pass filtered airspeed Va decreases, velocity boost factor Kv decreases.
Similarly,
accelerometer boost factor module 98 produces acceleration boost factor KA
that is proportional
to a time rate of change of accelerations root mean square ARMS. Rate
gyroscope boost factor
module 100 produces angular rate boost factor K. that is proportional to a
time rate of change of
angular rates root mean square cors.
[0056] Measurement matrix module 102, measurement vector module 104,
state
transition matrix module 106, process covariance noise matrix module 108, and
measurement
covariance noise matrix module 110 produce measurement matrix H, measurement
vector y,
state transition matrix (I), process covariance noise matrix Q, and
measurement covariance noise
matrix R, respectively, which are utilized during execution of an extended
Kalman filter
implemented by Kalman filter module 112 to produce Kalman state vector X that
includes tilt
error correction values 6q, Kalman accelerometer scale factor and bias error
correction values
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CA 2995893 2018-02-21
EK-A, and Kalman rate gyroscope scale factor and bias error correction values
EKG.
Measurement matrix module 102 utilizes integrated reference velocity EVref and
integrated
direction-cosine matrix EC to produce measurement matrix H. Measurement vector
module 104
utilizes low-pass filtered body-axis reference velocity vector Vref,
integrated Coriolis acceleration
EAc, integrated direction-cosine matrix EC, and integrated compensated and
corrected body-axis
accelerations EAcon,p_B to generate measurement vector y. Measurement vector y
represents a
difference between a change in body-axis reference velocity vector Vref over a
time duration and
a change in integrated compensated and corrected body-axis accelerations
EAcomp-B over the
same time duration with effects of integrated Coriolis acceleration EAc and
gravity removed
(e.g., added, subtracted, or otherwise removed). For example, measurement
vector module 104
can add the integrated Coriolis acceleration EAc to the difference between the
change in body-
axis reference velocity vector Vref and integrated compensated and corrected
body-axis
accelerations EAcomp_B, and can subtract a value corresponding to the
acceleration due to gravity
(e.g., 9.8 meters/second/second) from the resulting sum.
[0057]
State transition matrix module 106 utilizes integrated direction-cosine matrix
EC
to populate state transition matrix (I) utilized by Kalman filter module 112
to propagate the
Kalman state forward in time. Process covariance noise matrix module 108
utilizes acceleration
boost factor KA and angular rate boost factor Kõ to produce process noise
covariance matrix Q
that represents an estimate of uncertainty corresponding to process noise
introduced by
computational uncertainties or other process noise. Measurement covariance
noise matrix
module utilizes velocity boost factor Kv, acceleration boost factor KA and
angular rate boost
factor Kõ to produce measurement covariance noise matrix R that represents an
estimate of
uncertainty corresponding to sensor noise from accelerometers 24A-24C and rate
gyroscopes
32A-32C (FIG. 1). Because each of velocity boost factor Kv, acceleration boost
factor KA and
angular rate boost factor Ko, are proportional to a rate of change of their
respective inputs (i.e.,
low-pass filtered airspeed Va, accelerations root mean square ARMS, and
angular rates root mean
square coRms), process covariance noise matrix module 108 and measurement
covariance noise
matrix module 110 effectively increase the effect of process covariance noise
matrix Q and
measurement covariance noise matrix R during execution of the extended Kalman
filter
implemented by Kalman filter module 112 during operational states
corresponding to dynamic
motion of IMU 10.
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[0058] Kalman filter module 112 implements an extended Kalman filter
that utilizes
measurement matrix H, measurement vector y, state transition matrix 4:1),
process covariance
matrix Q, and measurement covariance matrix R to produce Kalman state vector
X. Kalman
state vector X can be, e.g., a 16-element vector including (in any order): two
tilt error correction
values, one corresponding to pitch and the other corresponding to roll; three
accelerometer bias
error correction values, each corresponding to one of accelerometers 24A-24C;
three
accelerometer scale factor error correction values, each corresponding to one
of accelerometers
24A-24C; three rate gyroscope bias error correction values, each corresponding
to one of rate
gyroscopes 32A-32C; three rate gyroscope scale factor error correction values,
each
corresponding to one of rate gyroscopes 32A-32C; and two trinsport rate error
correction values
corresponding to forward pitch rates experienced to maintain level flight
while moving across
the surface of the Earth.
[0059] Tilt correction module 114 utilizes the two tilt error correction
values and the two
transport rate error correction values to produce tilt error correction values
8q, which are utilized
by attitude determination module 20 during propagation of attitude quaternion
qc, as is further
described above. Accelerometer bias and scale factor module 116 applies (e.g.,
adds, subtracts,
or otherwise applies) the three accelerometer bias error correction values to
accelerometer bias
error correction values determined during a previous execution (e.g., a
previous iteration) of
Kalman estimator module 22 to produce three updated accelerometer bias error
correction
values, each corresponding to one of accelerometers 24A-24C. Similarly,
accelerometer bias
and scale factor module 116 applies (e.g., adds, subtracts, or otherwise
applies) the three
accelerometer scale factor error correction values to accelerometer scale
factor error correction
values determined during a previous execution (e.g., a previous iteration) of
Kalman estimator
module 22 to produce three updated accelerometer scale ftor error correction
values, each
corresponding to one of accelerometers 24A-24C. Accelerometer bias and scale
factor module
116 outputs the three updated accelerometer bias error correction values and
the three updated
accelerometer scale factor error correction values as Kalman accelerometer
scale factor and bias
error correction values EK_A, which are received as input by inertial sensor
compensation and
correction module 18 and utilized during accelerometer error correction
operations.
[0060] Rate gyroscope bias and scale factor module 118 applies (e.g.,
adds, subtracts, or
otherwise applies) the three rate gyroscope bias error correction values of
Kalman state vector X
CA 2995893 2018-02-21
to rate gyroscope bias error correction values determined during a previous
execution (e.g., a
previous iteration) of Kalman estimator module 22 to produce three updated
rate gyroscope bias
error correction values, each corresponding to one of rate gyroscopes 32A-32C.
Similarly, rate
gyroscope bias and scale factor module 118 applies (e.g., adds, subtracts, or
otherwise applies)
the three rate gyroscope scale factor error correction values to rate
gyroscope scale factor error
correction values determined during a previous execution (e.g., a previous
iteration) of Kalman
estimator module 22 to produce three updated rate gyroscope scale factor error
correction values,
each corresponding to one of rate gyroscopes 32A-32C. Rate gyroscope bias and
scale factor
module 118 outputs the three updated rate gyroscope bias et-or correction
values and the three
updated rate gyroscope scale factor error correction values as Kalman rate
gyroscope scale factor
and bias error correction values EKG, which are received as input by inertial
sensor
compensation and correction module 18 and utilized during rate gyroscope error
correction
operations.
[0061] Accordingly, IMU 10 implementing Kalman estimator module 22,
iteratively and
adaptively determines scale factor and bias error correction values that are
applied by inertial
sensor compensation and correction module 18 to outputs of accelerometers 24A-
24C and rate
gyroscopes 32A-32C to produce error-compensated outputs body-axis angular
rates 12 and
body-axis accelerations 14. As such, Kalman estimator module 22 can help to
correct body-axis
angular rates 12 and body-axis accelerations 14 for non-deterministic errors
that can be
unpredictable in nature.
[0062] FIG. 5 is a schematic block diagram illustrating details of
Kalman estimator
module 22 of FIG. 1 to produce initial attitude quaternion qeimt representing
an initial attitude of
IMU 10. That is, FIG. 5 illustrates details of Kalman estiroator module 22
that are executed
during an initialization phase of IMU 10, such as after initial power-up,
reset, or other
initialization phases. In general, many modules and operations of Kalman
estimator module 22
described with respect to the example of FIG. 5 are substantially similar to
the modules and
operations of Kalman estimator module 22 that were described above with
respect to FIG. 4. For
purposes of clarity and ease of discussion, the same reference numbers are
used for like modules,
and only differences in modules and operations are described below with
respect to the example
of FIG. 5.
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[0063] As illustrated in FIG. 5, Kalman estimator module 22 includes
update initial
attitude estimate module 120 and update attitude module 122, which are
implemented by Kalman
estimator module 22 during initialization operations. In the example of FIG.
5, measurement
matrix module 102 receives integrated direction-cosine matrix EC from
integrate direction-
cosine module 92 and produces measurement matrix H, which is passed to Kalman
filter module
112. Kalman filter module 112 receives measurement vector y, and measurement
covariance
matrix R as input and executes an extended Kalman filter to produce Kalman
state vector Xc.
Kalman state vector Xc is a three-element vector, the three elements
corresponding to error
correction values of the third row (i.e., pitch and roll components) of
integrated direction-cosine
matrix C. Kalman filter module 112 outputs state vector Xc to update initial
attitude estimate
module 120, which applies (e.g., subtracts, adds, or otherwise applies) the
error correction values
from a previous execution (e.g., a previous iteration) of Kalman estimator
module 22 to
determine an updated initial attitude vector C3x. Update initial attitude
estimate module 120
outputs updated initial attitude vector C3x to measurement vector module 104,
which applies
(e.g., multiplies) updated initial attitude vector C3x to measurement vector y
to produce an
updated measurement vector y. Kalman estimator module 22 iteratively executes
measurement
vector module 104, Kalman filter module 112, and update initial attitude
estimate module 120
for a threshold time duration, such as 10 seconds or other threshold time
durations, to iteratively
determine and modify updated initial attitude vector C3x. Update initial
attitude estimate module
120 provides updated initial attitude vector C3x to update attitude module
122, which converts
the attitude information of initial attitude vector C3x to quaternion form and
outputs initial
attitude quaternion qc,nit to attitude determination module 20 for use during
initialization
operations of IMU 10.
[0064] Accordingly, IMU 10 implementing techniques of this disclosure,
utilizes air data
parameter values, such as true airspeed and angle of attack, to produce error-
corrected angular
rate and acceleration output values. IMU 10 determines vehicle attitude in the
form of attitude
quaternion qc based on sensed acceleration and rotational position information
received from
accelerometers 24A-24C and gyroscopes 32A-32C. The air data parameter values
are utilized
by Kalman estimator module 22 to estimate sensor scale factor and bias errors
that are provided
as feedback to further adjust and correct the sensed output values of
accelerometers 24A-24C
and gyroscopes 32A-32C. Accordingly, the techniques described herein can
increase an
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accuracy of outputs of IMU 10 (i.e., body-axis angular rates 12 and body-axis
accelerations 14)
by modifying the outputs to compensate for deterministic errors (e.g.,
temperature-dependent
scale factor and bias errors, sensor non-linearity errors, and non-
orthogonality errors) and correct
for non-deterministic errors that can manifest as sensor scale factor and bias
errors that arise
during operation of (or between operations of) IMU 10.
[0065] Discussion of Possible Embodiments
[0066] The following are non-exclusive descriptions of possible
embodiments of the
present invention.
[0067] An inertial measurement unit includes an inertial sensor
assembly, an inertial
sensor compensation and correction module, and a Kalman estimator module. The
inertial
sensor assembly includes a plurality of accelerometers and a plurality of rate
gyroscopes. Each
of the plurality of accelerometers is configured to sense acceleration of the
IMU along one of a
plurality of axes. Each of the plurality of rate gyroscopes is configured to
sense rotational rate of
the IMU along one of the plurality of axes. The inertial sensor compensation
and correction
module is configured to apply a set of error compensation values to
acceleration sensed by the
plurality of accelerometers and to rotational rate sensed by the plurality of
rate gyroscopes to
produce a compensated acceleration and a compensated rotational rate of the
IMU. The Kalman
estimator module is configured to determine a change in integrated
acceleration of the IMU over
a time interval based on the compensated acceleration and the compensated
rotational rate of the
IMU, determine a set of error correction values based on a difference between
the change in the
integrated acceleration of the IMU and a change in true airspeed of the IMU,
and provide the set
of error correction values to the inertial sensor compensation and correction
module. The inertial
sensor compensation and correction module is further configured to apply the
set of error
correction values to each of the compensated acceleration and the compensated
rotational rate to
produce an error-corrected acceleration and an error-corrected rotation rate,
and output the error-
corrected acceleration and the error-corrected rotational rate.
[0068] The inertial measurement unit of the preceding paragraph can
optionally include,
additionally and/or alternatively, any one or more of the following features,
configurations,
operations and/or additional components:
[0069] The Kalman estimator module can be configured to determine the
set of error
correction values via an extended Kalman filter that utilizes the difference
between the change in
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CA 2995893 2018-02-21
the integrated acceleration of the IMU and the change in the true airspeed of
the IMU as input
and produces the set of error correction values as output.
[0070] The
inertial sensor assembly can further include a plurality of temperature
sensors
configured to sense temperature of an operating environment of the plurality
of accelerometers
and the plurality of rate gyroscopes. The set of error compensation values can
include
temperature-dependent error compensation values. The inertial sensor
compensation and
correction module can be configured to apply the set of error compensation
values by
determining the temperature-dependent error compensation values based on
sensed temperature
from each of the plurality of temperature sensors.
[0071] The
temperature-dependent error compensation values can include temperature-
dependent scale factor error compensation values, temperature-dependent bias
error
compensation values, and temperature-dependent non-linearity error
compensation values for
each of the plurality of accelerometers and each of the plurality of rate
gyroscopes.
[0072]
Each of the temperature-dependent scale factor error compensation values can
correspond to an error in a slope of sensor output over a temperature range
for a respective one
of the plurality of accelerometers and the plurality of rate gyroscopes. Each
of the temperature-
dependent bias error compensation values can correspond to a non-zero offset
error of sensor
output over the temperature range for a respective one of the plurality of
accelerometers and the
plurality of rate gyroscopes.
Each of the temperature-dependent non-linearity error
compensation values can correspond to a non-linearity of the sensor output
over the temperature
range for a respective one of the plurality of accelerometers and the
plurality of rate gyroscopes.
[0073] The
set of error compensation values can include a non-orthogonality error
compensation value corresponding to a non-orthogonality error of the plurality
of axes.
[0074] The
plurality of axes can include a first plurality of axes defining a sensor axis
reference frame. The Kalman estimator module can be configured to determine
the change in the
integrated acceleration of the IMU by transforming the compensated
acceleration from the sensor
axis reference frame to a body axis reference frame defined by a second
plurality of axes aligned
with respect to a moving body that includes the IMU, and integrating the
compensated
acceleration in the body axis reference frame over the time interval.
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[0075] The Kalman estimator module can be further configured to
determine the set of
error correction values by removing an effect of gravity from the difference
between the change
in the integrated acceleration of the IMU and the change in the true airspeed
of the IMU.
[0076] The Kalman estimator module can be configured to remove the
effect of gravity
from the compensated acceleration by determining the effect of gravity based
on mass attraction
as a function of a radial distance between the IMU and a center of Earth.
[0077] The plurality of accelerometers can include three accelerometers.
The plurality of
rate gyroscopes can include three rate gyroscopes. The plurality of axes can
include three axes.
Each of the three accelerometers can be aligned to sense the acceleration of
the IMU along one
of the three axes. Each of the three rate gyroscopes can be aligned to sense
the rotational rate of
the IMU along one of the three axes.
[0078] A method includes sensing acceleration of an inertial measurement
unit (IMU)
along a plurality of axes via a plurality of accelerometers of the IMU, and
sensing rotational rate
of the IMU along the plurality of axes via a plurality of rate gyroscopes of
the IMU. The method
further includes applying a set of error compensation values to each of the
sensed acceleration
and the sensed rotational rate to produce a compensated acceleration and a
compensated
rotational rate of the IMU, determining a change in integrated acceleration of
the IMU over a
time interval based on the compensated acceleration and the compensated
rotational rate of the
IMU, and determining a set of error correction values based on a difference
between the change
in the integrated acceleration of the IMU and a change in true airspeed of the
IMU. The method
further includes applying the set of error correction values to each of the
compensated
acceleration and the compensated rotational rate to produce an error-corrected
acceleration and
an error-corrected rotational rate, and outputting the error-corrected
acceleration and the error-
corrected rotational rate.
[0079] The method of the preceding paragraph can optionally include,
additionally
and/or alternatively, any one or more of the following features,
configurations, operations and/or
additional components:
[0080] Determining the set of error correction values can include
determining the set of
error correction values via an extended Kalman filter that utilizes the
difference between the
change in the integrated acceleration of the IMU and the change in the true
airspeed of the IMU
as input and produces the set of error correction values as output.
CA 2995893 2018-02-21
[0081] The
method can further include sensing temperature of an operating environment
of the plurality of accelerometers and the plurality of rate gyroscopes via a
plurality of
temperature sensors of the IMU. The set of error compensation values can
include temperature-
dependent error compensation values. Applying the set of error compensation
values can include
determining the temperature-dependent error compensation values based on the
sensed
temperature from each of the plurality of temperature sensors.
[0082] The
temperature-dependent error compensation values can include temperature-
dependent scale factor error compensation values, temperature-dependent bias
error
compensation values, and temperature-dependent non-linearity error
compensation values for
each of the plurality of accelerometers and each of the plurality of rate
gyroscopes.
[0083]
Each of the temperature-dependent scale factor error compensation values can
correspond to an error in a slope of sensor output over a temperature range
for a respective one
of the plurality of accelerometers and the plurality of rate gyroscopes. Each
of the temperature-
dependent bias error compensation values can correspond to a non-zero offset
error of sensor
output over the temperature range for a respective one of the plurality of
accelerometers and the
plurality of rate gyroscopes.
Each of the temperature-dependent non-linearity error
compensation values can correspond to a non-linearity of the sensor output
over the temperature
range for a respective one of the plurality of accelerometers and the
plurality of rate gyroscopes.
[0084] The
set of error compensation values can include a non-orthogonality error
compensation value corresponding to a non-orthogonality error of the plurality
of axes.
[0085] The
plurality of axes can include a first plurality of axes defining a sensor axis
reference frame. Determining the change in the integrated acceleration of the
IMU can include
transforming the compensated acceleration from the sensor axis reference frame
to a body axis
reference frame defined by a second plurality of axes aligned with respect to
a moving body that
includes the IMU, and integrating the compensated acceleration in the body
axis reference frame
over the time interval.
[0086]
Determining the change in the integrated acceleration of the IMU can further
include removing an effect of gravity from the compensated acceleration prior
to integrating the
compensated acceleration in the body axis reference frame.
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[0087] Removing the effect of gravity from the compensated acceleration
can include
determining the effect of gravity based on mass attraction as a function of a
radial distance
between the IMU and a center of Earth.
[0088] The plurality of accelerometers can include three accelerometers.
The plurality of
axes can include three axes. Each of the three accelerometers can be aligned
to sense the
acceleration of the 1MU along one of the three axes. Each of the three rate
gyroscopes can be
aligned to sense the rotational rate of the IMU along one of the three axes.
[0089] While the invention has been described with reference to an
exemplary
embodiment(s), it will be understood by those skilled in the art that various
changes may be
made and equivalents may be substituted for elements thereof without departing
from the scope
of the invention. In addition, many modifications may be made to adapt a
particular situation or
material to the teachings of the invention without departing from the
essential scope thereof.
Therefore, it is intended that the invention not be limited to the particular
embodiment(s)
disclosed, but that the invention will include all embodiments falling within
the scope of the
appended claims.
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