EE 570: Location and Navigation: Theory & Practice
EE 570: Location and Navigation: Theory & Practice
EE 570: Location and Navigation: Theory & Practice
Practice
Navigation Sensors and INS Mechanization
Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 1 of 19
Navigation Sensors and INS Mechanization
Inertial Sensors
Accelerometers Gyroscopes
Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 3 of 19
Navigation Sensors and INS Mechanization
Inertial Sensors - Gyroscope
Inertial Sensors
Accelerometers Gyroscopes
Microelectromechanical
Mech Suspension
Magnetic Suspension
Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 4 of 19
Navigation Sensors and INS Mechanization
Inertial Sensors – Accelerometer: Pendulous Mass
spring
force resolved along the
Reaction force
k
displacement (x)
sensitive axis
Modeled as a basic 2nd Mass
order system
f = m& x&+ bx&+ kx
damper
b
In steady state
hence
Sense axis
Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 5 of 19
Navigation Sensors and INS Mechanization
Inertial Sensors – Accelerometer: Pendulous Mass
Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 6 of 19
Navigation Sensors and INS Mechanization
Inertial Sensors – Accelerometer: Pendulous Mass
• Pendulous Accelerometer
Closed loop configuration
o Improved linearity
Sensitive axis
Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 7 of 19
Navigation Sensors and INS Mechanization
Inertial Sensors – Accelerometer: Vibratory
• Vibratory accelerometers
Vibrating Beam Accelerometers (VBA)
Acceleration causes a change in resonance frequency
Sensitive axis
f 0 = k Tension
Mass
Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 8 of 19
Navigation Sensors and INS Mechanization
Inertial Sensors - Accelerometer: Vibratory
• MEMS Accelerometers
www.ett.bme.hu/memsedu
Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 9 of 19
Navigation Sensors and INS Mechanization
Inertial Sensors - Accelerometer: Vibratory
• MEMS Accelerometers
Spring and mass from silicon and add fingers make a
variable differential capacitor
Change in displacement => change in capacitance
MASS APPLIED
ACCELERATION
Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 10 of 19
Navigation Sensors and INS Mechanization
Inertial Sensors – Gyroscopes: Rotating Mass
Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 11 of 19
Navigation Sensors and INS Mechanization
Inertial Sensors – Gyroscopes: Rotating Mass
H(t)
) t
H(t+d
o Results in precession about the y-axis
– =wH wdt
z z
y
Precession y
rate (w)
x
Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 12 of 19
Navigation Sensors and INS Mechanization
Inertial Sensors – Gyroscopes: Sagnac Effect Gyros
Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 13 of 19
Navigation Sensors and INS Mechanization
Inertial Sensors - Gyroscopes: Sagnac Effect Gyros
r
t
cto
n De
c2 Tra
te
Phase
De
8 NAw
fc �2Dtf c = 2Dtc / l0 =
cl0
Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 14 of 19
Navigation Sensors and INS Mechanization
Inertial Sensors - Gyroscopes: Sagnac Effect Gyros
n
io
ot
m
ar
ne
aCorolis = 2w �v Li aCorolis = 2w �v
n
io
ot
m
ar
ne
Li
Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 16 of 19
Navigation Sensors and INS Mechanization
Inertial Sensors - Gyroscopes: Coriolis Effect
Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 17 of 19
Navigation Sensors and INS Mechanization
Inertial Sensors - Gyroscopes: Coriolis Effect
www.ett.bme.hu/memsedu
Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 18 of 19
Navigation Sensors and INS Mechanization
Inertial Sensors - Summary
• Accelerometers
Measure specific force of the body frame wrt the inertial
frame in the body frame coordinates
rb
o Need to subtract the acceleration due to f ib
gravity to obtain the motion induced quantity
In general, all points on a rigid body do NOT experience the
same linear velocity
• Gyroscopes
Measure the inertial angular velocity
o Essentially, the rate of change of orientation rb
All points on a rigid body experience the wib
same angular velocity
Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 19 of 19