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Why Use the Kalman Filter? Pokémon Example

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Page 1: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Why Use the Kalman Filter?Pokémon Example

Page 2: Fun and Easy Kalman filter Tutorial - Using Pokemon Example
Page 3: Fun and Easy Kalman filter Tutorial - Using Pokemon Example
Page 4: Fun and Easy Kalman filter Tutorial - Using Pokemon Example
Page 5: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Initial Position = 10mEstimate@ Time = 0 seconds

Page 6: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Position = ?Estimate@ Time = 1 second

Page 7: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Position = ?Estimate@ Time = 1 second

Page 8: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Position = ?Estimate@ Time = 1 second

Page 9: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Radar Position Estimate = 15m@ Time = 1 second

Page 10: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Radar Position Estimate = 15m@ Time = 1 second

v

Page 11: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Radar Position Estimate = 15m@ Time = 1 second

v

Xf = xi + vi + 1/2atVf = vi + at

2

Page 12: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second

Xf = xi + vi + 1/2atVf = vi + at

2

Page 13: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second

Page 14: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second

Page 15: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second

?

Page 16: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second

15.75 m?

Page 17: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second

x

Page 18: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second

Page 19: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second

Page 20: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second

Page 21: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Radar Position Estimate = 15mState Estimate = 16.5mOptimal Estimate = ? m@ Time = 1 second

Get this using the

Kalman Filter

Page 22: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Probability Density Function of (PDF)

15m 16.5m

Page 23: Fun and Easy Kalman filter Tutorial - Using Pokemon Example
Page 24: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Probability Density Function of (PDF)

15m 16.5m

Prob

ability

1

Page 25: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Step 1. Calculate the Kalman Gain

15m 16.5m

Prob

ability

1Measurement

ErrorState Estimate

Error

Page 26: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Step 1. Calculate the Kalman Gain

15m 16.5m

Prob

ability

1Measurement Error (EMEA)

State Estimate Error(EEST)

KG = EEST

Page 27: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Step 1. Calculate the Kalman Gain

15m 16.5m

Prob

ability

1Measurement

Error

State Estimate Error

KG = EEST

0 1Kalman Gain (KG)

Page 28: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

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

Page 29: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

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)

Page 30: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

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)

Page 31: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

15m 16.5m

Prob

ability

1 1 0Kalman Gain

Page 32: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second

Optimal Estimate = ? m

Page 33: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

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

Page 34: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Radar Position Estimate = 15mState Estimate = 16.5m@ Time = 1 second

1 0Kalman Gain

Optimal Estimate = 15 m

Optimal Estimate = 16.5 m

Page 35: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Radar Position Estimate = 20.4mState Estimate = 22.3m@ Time = 2 seconds

1 0Kalman Gain

Optimal Estimate = 15 m

Optimal Estimate = 16.5 m

Page 36: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Radar Position Estimate = 20.4mState Estimate = 22.3m@ Time = 2 seconds

Page 37: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

Radar Position Estimate = 20.4mState Estimate = 22.3m@ Time = 2 seconds

0 1Kalman Gain (KG)

MeasurementsAre Accurate

&Estimate Unstable

Estimate Stable&

MeasurementsAre Inaccurate

Page 38: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

2D Kalman Filter

3D Kalman Filter

Page 39: Fun and Easy Kalman filter Tutorial - Using Pokemon Example

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