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EE 495 Modern Navigation SystemsInertial Sensor Errors
Wed, Feb 11 EE 495 Modern Navigation Systems Slide 1 of 14
Inertial Sensor ErrorsInertial Sensor Modeling - Terminology
• Accuracy: Proximity of the measurement to the true value
• Precision: The consistency with which a measurement
can be obtained
• Resolution: The magnitude of the smallest detectable change.
• Sensitivity: The ratio between the change in the output
signal to a small change in input physical signal. Slope of the input-output fit line.
• Linearity: The deviation of the output from a "best” straight line fit for a
given range of the sensor
Wed, Feb 11 EE 495 Modern Navigation Systems
Akin to the mean
Akin to the standard deviation
Slide 2 of 15
Inertial Sensor ErrorsInertial Sensor Modeling – Accuracy vs Precision
Neither accurate nor preciseAccurate but not precise
Precise but not accurate Both accurate and precise
Wed, Feb 11 EE 495 Modern Navigation Systems Slide 3 of 15
Inertial Sensor ErrorsInertial Sensor Modeling – Error Sources
• Bias – Often the most critical error source Fixed Bias
o Deterministic in nature and can be addressed by calibrationo Often modeled as a function of temperature
Bias Stabilityo Varies from run-to-run as a random constant
Bias Instabilityo In-run bias drift – Typically modeled as a random walk
Gyro bias errors are a major INS error source
FBb
BSb
BIb
static FB BSb b b
dynamic BIb b
, , ,a BI a FB a BS af b b b b , , ,g BI g FB g BS gb b b b
Wed, Feb 11 EE 495 Modern Navigation Systems Slide 4 of 15
Inertial Sensor ErrorsInertial Sensor Modeling – Error Sources
• Scale Factor Fixed Scale Factor Error
o Deterministic in nature and can be addressed by calibration
o Often modeled as a function of temperature Scale Factor Stability (accel) or (gyro)
o Varies from run-to-run as a random constanto Typically given in parts-per-million (ppm)
The scale factor represents a linear approximation to the steady-state sensor response over a given input range – True sensor response may have some non-linear characteristics
Input
Ou
tpu
t
True
Measured
Scale Factor Error
Ref: Park, 04
af s f gs
Wed, Feb 11 EE 495 Modern Navigation Systems
as
Slide 5 of 15
Inertial Sensor ErrorsInertial Sensor Modeling – Error Sources
• Misalignment Refers to the angular difference between the ideal sense
axis alignment and true sense axis vectoro A deterministic quantity typically given in milliradians
Combining Misalignment & Scale Factor
zxmbx
by
bz
z-se
nse
axis
zym
Normalized z-sense axis, ,z a zx x a zy yf m f m f , ,z g zx x g zy ym m
, , ,
, , ,
, , ,
a x a xy a xz xb
a yx a y a yz y a ib
a zx a zy a z z
s m m f
f m s m f M f
m m s f
Wed, Feb 11 EE 495 Modern Navigation Systems Slide 6 of 15
Inertial Sensor ErrorsInertial Sensor Modeling – Error Sources
• Cross-Axis Response Refers to the sensor output which occurs when the device
is presented with a stimulus which is vectorially orthogonal to the sense axis
Misalignment and cross-axis response are often difficult to distinguish – Particularly during testing and calibration activities
Wed, Feb 11 EE 495 Modern Navigation Systems Slide 7 of 15
Inertial Sensor ErrorsInertial Sensor Modeling – Error Sources
• Other noise sources Typically characterized as additive in nature
o May have a compound form– White noise
» Gyros: White noise in rate Angle random walk» Accels: White noise in accel Velocity random walk
– Quantization noise» May be due to LSB resolution in ADC’s
– Flicker noise– Colored noise
A more detailed discussion of noise will be given at a later date
Wed, Feb 11 EE 495 Modern Navigation Systems Slide 8 of 15
Inertial Sensor ErrorsInertial Sensor Modeling – Error Sources
• Gyro Specific Errors G-sensitivity
o The gyro may be sensitive to accelerationo Primarily due to device mass assymetryo Mostly in Coriolis-based devices (MEMS)
G2-Sensitivityo Anisoelastic effects o Due to products of orthogonal forces
b bib g ibG f
Wed, Feb 11 EE 495 Modern Navigation Systems
The gyro may be sensitive to linear acceleration!!!!
Slide 9 of 15
Inertial Sensor ErrorsInertial Sensor Modeling – Error Sources
• Accelerometer Specific Errors Axis Offset
o The accel may be mounted at a lever-arm distance from the “center” of the Inertial Measurement Unit (IMU)
– Leads to an “2r” type effect
x
y
z
2 2 2 2x y z y zf x x x
Wed, Feb 11 EE 495 Modern Navigation Systems
The accelerometer may be sensitive to angular rates!!!!
Slide 10 of 15
Inertial Sensor ErrorsInertial Sensor Modeling – Sensor Models
• Accelerometer measurement model
• Gyro measurement Model
• Typically, each measures along a single sense axis requiring three of each to measure the 3-tupple vector
b b b bib ib ib a a ib af f f b I M f w
b b b b bib ib ib g g ib g ib gb I M G f w
Wed, Feb 11 EE 495 Modern Navigation Systems Slide 11 of 15
Inertial Sensor ErrorsInertial Sensor Modeling – Applications
• Accelerometer Application Areas
Ref: “INS/GPS Technology Trends“ byGeorge T. Schmidt RTO-EN-SET-116(2010)
Wed, Feb 11 EE 495 Modern Navigation Systems Slide 12 of 15
Inertial Sensor ErrorsInertial Sensor Modeling – Applications
• Gyro Application Areas
Ref: “INS/GPS Technology Trends“ byGeorge T. Schmidt RTO-EN-SET-116(2010)
Earth Rate
Wed, Feb 11 EE 495 Modern Navigation Systems Slide 13 of 15
Inertial Sensor ErrorsInertial Sensor Modeling – Applications
Ref: INS Tutorial, Norwegian Space Centre, 2008.06.09
Cost as a function of Performance and technologyDifferent “Grades” of Inertial Sensors
Wed, Feb 11 EE 495 Modern Navigation Systems Slide 14 of 15
Inertial Sensor ErrorsInertial Sensor Modeling – SoA in MEMS Inertial
Wed, Feb 11 EE 495 Modern Navigation Systems
Bias
Inst
abili
ty (
/hr)
Angle Random Walk ( )0.0001 0.001 0.01 0.1 1 10
0.00
10.
010.
11
10
Commercial Grade
Tactical Grade
Navigation Grade
Strategic Grade
…
…
Analog Devices MEMS ADIS16137
Sensonor MEMS SAR500
Honeywell MEMS OPG
NorthropHRG SIRU
VectorNav MEMS VN200
Honeywell HRG GG1320
emcore FOG EMP-1.2k
KVH FOG 1750IMU
Boeing MEMS DRG
Slide 15 of 15