Kalman Filter from the Ground Up 1

I Introduction to Kalman Filter 1 The Necessity of Prediction 2 Essential background I 3 The – filter 4 Kalman Filter in one dimension 5 Adding process noise II Multivariate Kalman Filter 6 Foreword 7 Essential background II 8 Kalman Filter Equations Derivation 9 Multivariate KF Examples III Non-linear Kalman Filters 10 Foreword 11 Essential background III 12 Non-linearity problem 13 Extended Kalman Filter (EKF) 14 Unscented Kalman Filter (UKF) 15 Non-linear filters comparison 16 Conclusion IV Kalman Filter in practice 17 Sensors Fusion 18 Variable measurement error 19 Treating missing measurements 20 Treating outliers 21 Kalman Filter Initialization 22 KF Development Process Appendices V Appendices A The expectation of variance B Confidence Interval C Modeling linear dynamic systems D Derivative of matrix product trace E Pendulum motion simulation F Statistical Linear Regression G The product of univariate Gaussian PDFs H Product of multivariate Gaussian PDFs Bibliography Index