EE 495 Modern Navigation Systems Inertial Sensor Errors Wed, Feb 11 EE 495 Modern Navigation Systems Slide 1 of 14.

EE 495 Modern Navigation SystemsInertial Sensor Errors

Wed, Feb 11 EE 495 Modern Navigation Systems Slide 1 of 14

http://www.erau.edu/

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


http://upload.wikimedia.org/wikipedia/commons/3/38/Accuracy_and_precision.svg

Inertial Sensor ErrorsInertial Sensor Modeling – Accuracy vs Precision

Neither accurate nor preciseAccurate but not precise

Precise but not accurate Both accurate and precise



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




• 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


as

Slide 5 of 15



• 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




• 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




• 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




• 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


The gyro may be sensitive to linear acceleration!!!!

Slide 9 of 15



• 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


The accelerometer may be sensitive to angular rates!!!!

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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



Inertial Sensor ErrorsInertial Sensor Modeling – Applications

• Accelerometer Application Areas

Ref: “INS/GPS Technology Trends“ byGeorge T. Schmidt RTO-EN-SET-116(2010)




• Gyro Application Areas

Ref: “INS/GPS Technology Trends“ byGeorge T. Schmidt RTO-EN-SET-116(2010)

Earth Rate




Ref: INS Tutorial, Norwegian Space Centre, 2008.06.09

Cost as a function of Performance and technologyDifferent “Grades” of Inertial Sensors



Inertial Sensor ErrorsInertial Sensor Modeling – SoA in MEMS Inertial


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


EE 495 Modern Navigation Systems Inertial Sensor Errors Wed, Feb 11 EE 495 Modern Navigation Systems Slide 1 of 14.

Documents

sensor output

modern navigation systemsslide

steadystate sensor response

modern navigation systemsakin

powerpoint presentation

ideal sense axis alignment

sense axismisalignment

major ins error source