a portable and cost-effective configuration of strap-down ins/gps for general-purpose use

1

A Portable and Cost-effective Configuration

of Strap-down INS/GPSfor General-purpose Use

＊Masaru Naruoka (Univ. of Tokyo)

Takeshi Tsuchiya (Univ. of Tokyo)

23/04/22 2006 KSAS/JSASS Joint Symposium 2

A Portable and Cost-effective Configuration of Strap-down INS/GPS for General-purpose Use

Outline

1. Background: we need precise, small, light and inexpensive navigation system.

2. Method: my system

3. Evaluation: how precise?

4. Conclusion



Background (1/5)Many Needs for Precise Navigation data

Many applications for requiring precise navigation data (position, velocity, attitude) Of course, navigate aircrafts, spacecrafts Observe cars, trains, etc. Control robots, UAVs

Can we apply accumulated navigation technologies of aircrafts to these applications?



Background (2/5)One of technologies: INS/GPS

INS/GPS Navigation System

High update ratiobut

Accumulate Error

Cancel Errorbut

Low update ratio

Cancel Errorand

High update ratio

Time

Error

INS

Time

Error

GPS

Time

Error

INS/GPS

Inertial Navigation System(INS)

Global Positioning System(GPS)+



Background (3/5)Mechanism of INS/GPS

Position, Velocity, Attitude

Inertial Sensors

Position

Velocity

Position

Velocity

Attitude

INS GPS

Integration

Acceleration

AngularSpeed

INS/GPS

Radiowave

Satellites

the laws of motion triangle surveying

Receiver



Background (4/5)Traditional vs. Developing INS/GPS

Traditional Now developed

Big (> 1000

cm3)

Heavy (> 1 kg)

Small (< 1000

cm3)

Light (< 1 kg)

Expensive

(> $100K)

Cost-Effective

(< $100K)

Only Aircrafts and

Spacecrafts!

Ultra Precise(Error: <1m, <1deg)

Precise?

motivationTrade-Off



Background (5/5)Goal of my study

Meaningful to discuss about the trade-off between precision and other specifications.

The goal of my study1. Develop as small, light, cost-effective

INS/GPS system as possible.

2. Investigate its precision correctly



Method (1/7)Components

Big, heavy, expensive dedicated components Ring laser gyro Military-use GPS

Small, light, inexpensive components MEMS inertial sensors Civil-use GPS

Do not use Use



Method (2/7)MEMS Sensors and Civil-use GPS

MEMS inertial sensors Electronic circuit and sensing element integrated Small(~1 cm2), Light(<1 g), Inexpensive(<$100) BUT, an INS device using MEMS inertial sensors

accumulates error very quickly.

Civil-use GPS receiver Mainly for car navigation system Small(~10 cm2), Light(<10g), Inexpensive(~$100) AND good precision (Error: 10~20m)



Method (3/7)INS/GPS Algorithm

Strap-down configuration No need for any mechanical gimbals

Integration by extended Kalman filtering (EKF) Loose-coupling: require small calculation power

Use quaternions actively Mathematically simple model to compensate for lar

ge MEMS sensor error Eliminate singular points derived from Euler angles



Method (4/7)Equations: equations of motion for INS

ne

eeie

eie

enn

enen

nie

nbnb

nbn

e

qr

qrg

qa

qrdt

d ~0~2

00~0~0

////

znen

en

en

ne rh

dt

dqq

dt

d

,0~

2

1~

/

bnn

ennie

bib

bn

bn qqq

dt

d ~000~2

1~

///

• Velocity (3[North, East, Down Speed] States)

• Position (4[Latitude, Longitude, Azimuth] + 1[Height] = 5 States)

• Attitude (4[Roll, Pitch, Heading] States) quaternion

Acceleration

Angular Speed

Gravity



Method (5/7)Equations: Linearization for EKF

ne

ne

ne rrr

hhhqu

q nen

e

ne

,~1~

bnb

n

bn q

uq ~1~

gggaaa bib

bib

bib

bbb ,, ///

• Jacobian i.e. Additive (4 States) • Multiplicative (3 States)

Obtain linearized form for EKF by following substitution to the equations of motion

quaternion

12)(~~ 22

qqqqqqqq

qqqq

1)(

1~1 22

qqq

q

uq

u

Quaternion linearization with keeping the norm unity



Method (6/7)Equations: EKF

EKF Time Update EKF Correct

BuAxxdt

d

g

a

u

u

h

u

r

x bib

b

bn

ne

ne

/,

TbT

kk tBQtBtAIPtAIP 1

TkkkTkkk uuEQxxEP ,

GPS

ne

ne

INS

ne

ne

r

h

q

r

h

q

z

~~

vHxz

kkkk PHKIP )(

kneINS

neINS

ne rrr

kINSINSINSne

kne

INSne hhhq

uq

,~1~

INSbn

kbn

INSbn q

uq ~1~

1 k

Tkkk

Tkkk RHPHHPK

kk

k

bn

ne

ne

k zK

u

h

u

r

x

Tkkk vvER

quaternion

When INS update When GPS data is obtained



Method (7/7)Overall View

AttitudeEq. of Motion

Velocity,Position

Eq. of Motion

Gravity

CoordinateTransformation

Velocity,Position

Attitude

MEMSGyro

MEMSAccelerometer

civil-use

GPSExtended

Kalman Filterupdate correct

correct

INS

: When sensor data is obtained

Leverage quaternion for

system modeling

Strap-down configurati

on

MEMS sensor

s



Evaluation (1/11)Outline

Prototyping Based on my proposed system Calibration is performed

Test for Precision Compare the prototype with an existent

precise navigation device



Evaluation (2/11)Developed Prototype

Size: ~ 100 cm3

Weight: ~ 30 g

Cost: ~ $ 300(w/o structural element)

The prototype shows my system is small, light and low-cost



Evaluation (3/11)Detail of Prototype

USB

AN2131,Cypress24bit100Hz

A/DConverter

AD7739,AnalogDevices

4Hz

GPS

TI M-LA,u-blox

Position, Velocity,etc.ADXRS150,

AnalogDevices

1-Axis

Gyrox3

Angular Speed,Temperature

LI S3L02AS4,STMicroelectronics

3-Axes

Accelerometer

Acceleration

PC

INS/GPSAlgorithm(Kalman Filtering)

(w/o structural element)

Size:Weight:Cost:

under 100 [cm3]under 30 [g]about 30K [JP Yen



Evaluation (4/11)Calibration for MEMS INS

Temperature Drift MisalignmentTemperature-controlled Bath

MEMS Sensor

Temperature

Sen

sed

Val

ue Drifted

Not Driefted

Rate Table

MEMS GyroSensed Axis

Table Angular Speed

Sen

sed

Val

ue

CompletelyOrthgonal

Misaligned

main error source of

MEMS INS that can be

easily removed

settling

rotating



Evaluation (5/11)Calibration of Prototype

Temperature drift Misalignment

The result of calibrations

Temperature

slope not 0 !slope not 0 !

Sensed Angular Speed

(X, Y, Z-axis Gyro)

X

Sensed Acceleration(X-axis Accelerometer)

True Angular Speed (X-axis)vs. vs.

Y,Z



Evaluation (6/11)Test for Precision

Comparison of the prototype with GAIA (2006/06) GAIA: an ultra high-precision INS/GPS

device developed by Japan Aerospace Exploration Agency (JAXA)

Error: < 1m in absolute position In flight of an experimental aircraft, MuPAL-of JAXA



Evaluation (7/11)Scene of Test

PrototypeMuPAL-

GAIA



Evaluation (8/11)Results of Test

Results (The Prototype: Red, GAIA: Green)

Position (3D) Velocity Attitude

Nearly equal to GAIA



Evaluation (9/11)Detail of Results

Mean(Offset)

StandardDeviation

Worst

Horizontal distance [m] 6.44 2.97 17

Altitude [m] 0.85 2.1 6.9

North speed [m/s] 0 0.12 1.25

East speed [m/s] 0 0.12 -1.13

Down speed [m/s] -0.08 0.1 -0.67

Roll [deg] 0 0.26 -1.19

Pitch [deg] -0.67 1.21 -3.9

Heading [deg] 4.17 9.68 23.9

Statistical Summary of the error of the prototype by reference to GAIA

Position

Velocity

Attitude

< 10m

< 2 deg

> 10 deg



Evaluation (10/11)Summary and Discussion of Test

Error: <10m(Position), <2deg(Roll, Pitch) Precise enough for general-purpose use

Heading is the worst (Error: >10 deg) Effect of frequency mode of dynamics

Roll and Pitch is comparatively high mode (> 1Hz) Heading is low mode (< 1 Hz) Overlap with low mode noise that cannot remove

easily (for example, zero-point change)



Evaluation (11/11)Effectiveness of Calibration

With calibration Without calibration

Example : Roll History

Calibration works well.



Conclusion My Navigation System

small, light and cost-effective INS/GPS system for general-purpose use

Strap-down configuration using MEMS sensors and a civil-use GPS receiver

Temperature drift and misalignment calibrated Use EKF and Quaternion The test shows it is precise enough for general-purpose

use; Error is under 10 m in position, and 2 deg in roll and pitch.



Future Work Fight against low frequency noise

Time-Frequency Analysis Wavelet multi resolution analysis Wavelet de-nosing

Other compensation system Earth magnetism sensor for attitude etc.

a portable and cost-effective configuration of strap-down ins/gps for general-purpose use

Documents

generalpurpose usebackground

tokyoa portable

conclusiona portable

inexpensive navigation

konly aircrafts

attitudeof course

tokyotakeshi tsuchiya

mechanism of insgpsposition