1. Cameron Rowe

2.  Introduction  Purpose  Implementation  Simple Example Problem  Extended Kalman Filters  Conclusion  Real World Examples

3.  Optimal Estimator  Recursive Computation  Good when noise follows Gaussian distribution

4.  “Filter” noisy data

5.  Important Variables  x k : current signal value  x_hat k : estimated signal value  z k : linear combination signal value and measurement noise  A : matrix that describes state transition  B : matrix that describes how control signal effects state  H : matrix that describes how measured value is mapped to signal value  Q : process noise  R : measurement noise  K k : Kalman gain  P k : Previous error covariance

7. x k = Ax k-1 + Bu k + w k z k = Hx k + v k For Simple 1D problem

9.  http://bilgin.esme.org/BitsBytes/KalmanFilter forDummies.aspx http://bilgin.esme.org/BitsBytes/KalmanFilter forDummies.aspx

10.  Similar to regular Kalman Filter but works on non-linear system (ex. GPS)  Uses differentiable functions for state transition and observation x k = f(x k-1, u k-1 ) + w k-1 z k = h(x k ) + v k

11.  Good real time processing for events with Gaussian noise distribution  Difficult to set up but efficient and effective with good values  Multi-dimensionality is complicated

12.  https://www.youtube.com/watch?v=095IOfq F4nY https://www.youtube.com/watch?v=095IOfq F4nY  https://www.youtube.com/watch?v=MELYZ5r 5V1c https://www.youtube.com/watch?v=MELYZ5r 5V1c