Kalman Filter 1

Early Planar IMU

14x28 mm

Kalman Filter 2

3DOF IMU - Measures Two States

Kalman Filter 3

Tractor Overturn

hr

s

qOP

qOP

qP

rP

rP qOP+ qP

m, JP

2O

Kalman Filter 4

Prevent Rear Overturn

Kalman Filter 5

s = measured signal b = zero drift or bias (function of

temp) f = scale factor (function of temp) w = Gaussian white noise s2 = variance

Sensor Uncertainty

wsfb GYRO

Kalman Filter 6

f = 300 degps/V, 0.05 %/C° b = 1.23 V, 0.05 degps/C° Nonlinearity ±1% s = 0.035 degps/sqrt(Hz) pink noise

LSY530 gyro ±300 degps

wbfVOUT

Kalman Filter 7

Uses state space model Position Velocity

Adaptive time domain filter Combines states Tracks variance-covariance Helps reject zero drift

Kalman Filter

Kalman Filter 8

Kalman Filter - 2D IMU

Kalman Filter 9

Kalman Filter - Simplified

t*

ttt*

t*

ttt*

tt

measuredtoCompare

tCompute

measuredtoCompare

t/Compute

ttimeatandMeasure

Kalman Filter 10

Kalman Filter – Prediction

qlatitude

probability Novice navigator

Kalman Filter 11

Kalman Filter - Measurement

qlatitude

probability Novice navigator

Experienced navigator

Kalman Filter 12

Kalman Filter - Correction

qlatitude

probability Novice navigator

Experienced navigator

Combination

Kalman Filter 13

Kalman Filter - Prediction

qlatitude

probability

constant speed

fixed time

Kalman Filter 14

Kalman Filter – 2D IMU

q angle

probability

elmoddynamic

ttCORRPRED

Kalman Filter 15

Kalman Filter

kk

kkk

1k1kk

xofcovvarPtrack

vxHztsmeasuremenonbased

wxAxstateestimate

noisesensorv

matrixdynamicsensorH

noiseprocessw

matrixdynamicstateA

estimatepriorx

k

1k

1k

matrixgainadaptiveK

vofcovvarR

wofcovvarQ

k

Kalman Filter 16

Kalman Filter

k

kk

k

PHKIP

xHzKxx

RHPHHPK

correction

APAP

xAx

prediction

kk

kkkkk

1TTk

Tk

1kk