Why You Should Use The Kalman Filter Tutorial- #Pokemon Example Kalman filtering, also known as linear quadratic estimation, is an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more precise than those based on a single measurement alone, by using Bayesian inference and estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. Kálmán, one of the primary developers of its theory. This tutorial breaks down the components of the Kalman filter making easy for anyone to understand. It introduces you to the concepts of the Kalman filter using the pokemon analogy. To learn more on PCB Design, Kalman Filter Tutorial and FPGA's then Check out http://www.arduinostartups.com/ Please like and Subscribe for more videos :)

1. Why Use the Kalman Filter?
Pokémon Example

5. Initial Position = 10m
Estimate
@ Time = 0 seconds

6. Position = ?
Estimate
@ Time = 1 second

7. Position = ?
Estimate
@ Time = 1 second

8. Position = ?
Estimate
@ Time = 1 second

9. Radar Position Estimate = 15m
@ Time = 1 second

10. Radar Position Estimate = 15m
@ Time = 1 second
v

11. Radar Position Estimate = 15m
@ Time = 1 second
v
Xf = xi + vi + 1/2at
Vf = vi + at
2

12. Radar Position Estimate = 15m
State Estimate = 16.5m
@ Time = 1 second
Xf = xi + vi + 1/2at
Vf = vi + at
2

13. Radar Position Estimate = 15m
State Estimate = 16.5m
@ Time = 1 second

14. Radar Position Estimate = 15m
State Estimate = 16.5m
@ Time = 1 second

15. Radar Position Estimate = 15m
State Estimate = 16.5m
@ Time = 1 second
?

16. Radar Position Estimate = 15m
State Estimate = 16.5m
@ Time = 1 second
15.75 m?

17. Radar Position Estimate = 15m
State Estimate = 16.5m
@ Time = 1 second
x

18. Radar Position Estimate = 15m
State Estimate = 16.5m
@ Time = 1 second

19. Radar Position Estimate = 15m
State Estimate = 16.5m
@ Time = 1 second

20. Radar Position Estimate = 15m
State Estimate = 16.5m
@ Time = 1 second

21. Radar Position Estimate = 15m
State Estimate = 16.5m
Optimal Estimate = ? m
@ Time = 1 second
Get this using the
Kalman Filter

22. Probability Density Function of (PDF)
15m 16.5m

24. Probability Density Function of (PDF)
15m 16.5m
Probability
1

25. Step 1. Calculate the Kalman Gain
15m 16.5m
Probability
1
Measurement
Error
State Estimate
Error

26. Step 1. Calculate the Kalman Gain
15m 16.5m
Probability
1
Measurement
Error (EMEA)
State Estimate
Error(EEST)
KG = EEST

27. Step 1. Calculate the Kalman Gain
15m 16.5m
Probability
1
Measurement
Error
State Estimate
Error
KG = EEST
0 1
Kalman Gain (KG)

28. Step 1. Calculate the Kalman Gain
15m 16.5m
Probability
1
Measurement
Error
State Estimate
Error
KG = EEST
0 1
Kalman Gain (KG)
Measurements
Are Accurate
&
Estimate Unstable
Estimate Stable
&
Measurements
Are Inaccurate

29. Step 2. Calculate the Current Estimate
15m 16.5m
Probability
1
Measurement
Error
State Estimate
Error
KG = EEST
0 1
Kalman Gain
ESTt = ESTt-1 + KG(MEAS – ESTt-1)

30. Step 3. Calculate New State Estimate Error
15m 16.5m
Probability
1
Measurement
Error
State Estimate
Error
0 1
Kalman Gain
EESTt = [1 – KG](EESTt-1)

31. 15m 16.5m
Probability
1 1 0
Kalman Gain

32. Radar Position Estimate = 15m
State Estimate = 16.5m
@ Time = 1 second
Optimal Estimate = ? m

33. Radar Position Estimate = 15m
State 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

34. Radar Position Estimate = 15m
State Estimate = 16.5m
@ Time = 1 second
1 0
Kalman Gain
Optimal
Estimate = 15 m
Optimal
Estimate = 16.5 m

35. Radar Position Estimate = 20.4m
State Estimate = 22.3m
@ Time = 2 seconds
1 0
Kalman Gain
Optimal
Estimate = 15 m
Optimal
Estimate = 16.5 m

36. Radar Position Estimate = 20.4m
State Estimate = 22.3m
@ Time = 2 seconds

37. Radar Position Estimate = 20.4m
State Estimate = 22.3m
@ Time = 2 seconds
0 1
Kalman Gain (KG)
Measurements
Are Accurate
&
Estimate Unstable
Estimate Stable
&
Measurements
Are Inaccurate

38. 2D Kalman
Filter
3D Kalman
Filter

39. Thank you for Watching
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