Global Positioning System Integrated with an Inertial Navigation System

Michael BekkalaMichael Blair

Michael CarpenterMatthew Guibord

Abhinav ParvataneniDr. Shanker Balasubramaniam

Inertial Navigation System The use of inertial measurements in

navigation Measurements come from inertial

sensors such as:• Accelerometers• Gyroscopes

Very accurate over short term Errors integrate with time

Physics of Accelerometers/Gyroscopes

Accelerometers• Measure acceleration in x, y, z

directions• Types:

MechanicalMicro Electromechanical (MEMS)

• Capacitive• Piezoelectric

Mechanical Accelerometers

Mass suspended in a case by a pair of springs

Acceleration along the axis of the springs displaces the mass.

This displacement is proportional to the applied acceleration

Picture from “Basic Inertial Navigation” by Sherryl Stoval

Capacitive Accelerometers Sense a change in capacitance with respect

to acceleration Diaphragm acts as a mass that undergoes

flexure Two fixed plates sandwich diaphragm,

creating two capacitors Change in capacitance by altering distance between

two plates http://www.sensorland.com/HowPage011.html

Piezoelectric Accelerometers Commonly uses 1 crystal

made of quartz Force exerted by acceleration changes electrostatic force Low output signal and high

output impedance requiresthe use of amplifiers

Picture from Wikipedia.org

Physics of Accelerometers/Gyroscopes

Gyroscopes• Measure Angular velocity in yaw,

pitch, and roll directionsMicro Electromechanical (MEMS)Optical

Micro Electromechanical Gyroscopes

• Coriolis effect• Vibrating elements measure

Coriolis effect (vibrations on sense axis)

• When rotated, 2nd vibration on the drive axis• Angular Velocity

Picture from http://www.howyourelectronicswork.com/2008/09/fiber-optic-gyroscopes.html

Optical Gyroscopes

Sends out two beams of light Sensor can detect interference in the light

beam Very accurate No inherent drift Expensive

Navigation Equations Accelerations and angular velocities

are measured in the body coordinate frame

Need a constant reference for navigation

Rotation from bodyframe to North, East,Down frame gives areference.

Picture from “Accuracy and Improvement of Low Cost INS/GPS for Land Applications” by Shin

Inertial Navigation System

Diagram from Basic Inertial Navigation by Sherryl Stovall

System View of INS Equations

Navigation Equations The navigation equations can be

represented as (Shin, 2001):

100

0cos)(

10

00)(

1

)()2(

1

1

hR

hR

D

CgvfC

vD

Cvr

e

e

bin

bib

nb

nnnen

nie

bnb

n

nb

n

n

Navigation Equations BodyNED

RollPitchθYawψ

cossin0sincos0001

cosθ0sinθ010sinθ0cosθ

1000cosψsinψ0sinψcosψ

CNB

Navigation Equations GPS and INS need to be in the same

reference frame for proper measurements.

GPS data is in Earth Centered Earth Fixed (ECEF)

INS data is in Body frameand has to be translated to the North-East-Down frame

BodyNED, ECEFNEDPicture from “Accuracy and Improvement of Low Cost INS/GPS for Land Applications” by Shin

Integration of GPS and INS Different integration levels:

• Loosely Coupled Corrects errors in the IMU and INS Does not correct GPS

• Tightly Coupled Corrects both INS and GPS errors

Kalman filtering integrates both systems to achieve a more accurate overall system

GPS/INS Integration

Diagram from http://inderscience.metapress.com/media/59dam5dyxldjpg54uc5v/contributions/8/3/w/2/83w217t06m878447.pdf

System View of Integration