ee 495 modern navigation systems inertial sensor errors wed, feb 11 ee 495 modern navigation systems...

EE 495 Modern Navigation SystemsInertial Sensor Errors

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

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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!!!!

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



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...

Documents

sensor output

modern navigation systemsslide

steadystate sensor response

modern navigation systemsakin

powerpoint presentation

ideal sense axis alignment

sense axismisalignment

major ins error source