3630-08-lec13-kalman

# 3630-08-lec13-kalman - Introduction Process Model Example...

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Introduction Process Model Example Fusion Kalman Filter EKF Summary The Kalman Filter Henrik I Christensen Robotics & Intelligent Machines @ GT Georgia Institute of Technology, Atlanta, GA 30332-0760 [email protected] Henrik I Christensen The Kalman Filter 1 / 31

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Introduction Process Model Example Fusion Kalman Filter EKF Summary Outline 1 Introduction 2 Process Model 3 A simple example 4 Fusion of variables 5 The Discrete Kalman Filter 6 Extended Kalman Filter 7 Summary Henrik I Christensen The Kalman Filter 2 / 31
Introduction Process Model Example Fusion Kalman Filter EKF Summary Introduction Recapitulation of system models Integration of stochastic variables How to perform fusion in a more general sense Doing this in a non-linear system Henrik I Christensen The Kalman Filter 3 / 31

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Introduction Process Model Example Fusion Kalman Filter EKF Summary Outline 1 Introduction 2 Process Model 3 A simple example 4 Fusion of variables 5 The Discrete Kalman Filter 6 Extended Kalman Filter 7 Summary Henrik I Christensen The Kalman Filter 4 / 31
Introduction Process Model Example Fusion Kalman Filter EKF Summary State space model s t = Fs t - 1 + Gu t + w t z t = Hs t + v t where F is the system model, G is the deterministic input, H is a prediction of where features are in the world, w is the system noise, and v is the measurement noise p ( w ) N (0 , Q ) p ( v ) N (0 , R ) Henrik I Christensen The Kalman Filter 5 / 31

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Introduction Process Model Example Fusion Kalman Filter EKF Summary State state model example x t = x t - 1 + v t - 1 T + 1 2 a t - 1 T 2 v t = v t - 1 + a t - 1 T a t = a t - 1 s t = x t v t a t F = 1 T 1 2 T 2 0 1 T 0 0 1 G = [001] T Henrik I Christensen The Kalman Filter 6 / 31
Introduction Process Model Example Fusion Kalman Filter EKF Summary Outline 1 Introduction 2 Process Model 3 A simple example 4 Fusion of variables 5 The Discrete Kalman Filter 6 Extended Kalman Filter 7 Summary Henrik I Christensen The Kalman Filter 7 / 31

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Introduction Process Model Example Fusion Kalman Filter EKF Summary A small example - I -3 -2 -1 0 1 2 3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 N ( - 1 , 1) Henrik I Christensen The Kalman Filter 8 / 31
Introduction Process Model Example Fusion Kalman Filter EKF Summary A small example - II -3 -2 -1 0 1 2 3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

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