1. Kalman Filter 1 Early Planar IMU 14x28 mm

2. Kalman Filter 2 3DOF IMU - Measures Two States

3. Kalman Filter 3 Tractor Overturn h r s  OP PP PP PP  OP +   P m, J P

4. Kalman Filter 4 Prevent Rear Overturn

5. Kalman Filter 5 s = measured signal b = zero drift or bias (function of temp) f = scale factor (function of temp) w = Gaussian white noise  2 = variance Sensor Uncertainty

6. Kalman Filter 6 f = 300 degps/V, 0.05 %/C° b = 1.23 V, 0.05 degps/C° Nonlinearity ±1%  = 0.035 degps/sqrt(Hz) pink noise LSY530 gyro ±300 degps

7. Kalman Filter 7 Uses state space model Position Velocity Adaptive time domain filter Combines states Tracks variance-covariance Helps reject zero drift Kalman Filter

8. 8 Kalman Filter - 2D IMU

9. Kalman Filter 9 Kalman Filter - Simplified

10. Kalman Filter 10 Kalman Filter – Prediction  latitude probability Novice navigator

11. Kalman Filter 11 Kalman Filter - Measurement  latitude probability Novice navigator Experienced navigator

12. Kalman Filter 12 Kalman Filter - Correction  latitude probability Novice navigator Experienced navigator Combination

13. Kalman Filter 13 Kalman Filter - Prediction  latitude probability constant speed fixed time

14. Kalman Filter 14 Kalman Filter – 2D IMU  angle probability

15. Kalman Filter 15 Kalman Filter

16. 16 Kalman Filter