Date post: | 12-Jan-2017 |
Category: |
Engineering |
Upload: | ritesh-kanjee |
View: | 148 times |
Download: | 7 times |
Why Use the Kalman Filter?Pokémon Example
Initial Position = 10mEstimate@ Time = 0 seconds
Position = ?Estimate@ Time = 1 second
Position = ?Estimate@ Time = 1 second
Position = ?Estimate@ Time = 1 second
Radar Position Estimate = 15m@ Time = 1 second
Radar Position Estimate = 15m@ Time = 1 second
v
Radar Position Estimate = 15m@ Time = 1 second
v
Xf = xi + vi + 1/2atVf = vi + at
2
Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second
Xf = xi + vi + 1/2atVf = vi + at
2
Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second
Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second
Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second
?
Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second
15.75 m?
Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second
x
Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second
Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second
Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second
Radar Position Estimate = 15mState Estimate = 16.5mOptimal Estimate = ? m@ Time = 1 second
Get this using the
Kalman Filter
Probability Density Function of (PDF)
15m 16.5m
Probability Density Function of (PDF)
15m 16.5m
Prob
ability
1
Step 1. Calculate the Kalman Gain
15m 16.5m
Prob
ability
1Measurement
ErrorState Estimate
Error
Step 1. Calculate the Kalman Gain
15m 16.5m
Prob
ability
1Measurement Error (EMEA)
State Estimate Error(EEST)
KG = EEST
Step 1. Calculate the Kalman Gain
15m 16.5m
Prob
ability
1Measurement
Error
State Estimate Error
KG = EEST
0 1Kalman Gain (KG)
Step 1. Calculate the Kalman Gain
15m 16.5m
Prob
ability
1Measurement
Error
State Estimate Error
KG = EEST
0 1Kalman Gain (KG)
MeasurementsAre Accurate
&Estimate Unstable
Estimate Stable&
MeasurementsAre Inaccurate
Step 2. Calculate the Current Estimate
15m 16.5m
Prob
ability
1Measurement
Error
State Estimate Error
KG = EEST
0 1Kalman Gain
ESTt = ESTt-1 + KG(MEAS – ESTt-1)
Step 3. Calculate New State Estimate Error
15m 16.5m
Prob
ability
1Measurement
Error
State Estimate Error
0 1Kalman Gain
EESTt = [1 – KG](EESTt-1)
15m 16.5m
Prob
ability
1 1 0Kalman Gain
Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second
Optimal Estimate = ? m
Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second
IF KG = 0.75
ESTt = 16.5 + 0.75(15m – 16.5m)= 16.5 + (-1.125 m)= 15.375 m
Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second
1 0Kalman Gain
Optimal Estimate = 15 m
Optimal Estimate = 16.5 m
Radar Position Estimate = 20.4mState Estimate = 22.3m@ Time = 2 seconds
1 0Kalman Gain
Optimal Estimate = 15 m
Optimal Estimate = 16.5 m
Radar Position Estimate = 20.4mState Estimate = 22.3m@ Time = 2 seconds
Radar Position Estimate = 20.4mState Estimate = 22.3m@ Time = 2 seconds
0 1Kalman Gain (KG)
MeasurementsAre Accurate
&Estimate Unstable
Estimate Stable&
MeasurementsAre Inaccurate
2D Kalman Filter
3D Kalman Filter
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